Datasets:
TAUR-dev
/
D-EVAL__standard_eval_v1__SIE-countdown3arg_ppo_only-rl

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What is the solution to the long multiplication equation below? 42 x 94 Think step by step.
3948
"{\"arg1\": 42, \"arg2\": 94, \"solution\": 3948}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n42 x 94\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(42 \\times 94\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 42\n × 94\n ------\n ```\n\n2. **Multiply 42 by 4 (the units digit of 94):**\n - Multiply 42 by 4:\n ```\n 42\n × 4\n ------\n 16...
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[ "Certainly! Let's solve the long multiplication problem \\(42 \\times 94\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 42\n × 94\n ```\n\n2. **Multiply 42 by 4 (the units digit of 94):**\n - \\(42 \\times 4 = 168\\)\n - Write 8 in the ones place and carry...
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[ "To solve the long multiplication problem \\(42 \\times 94\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down the numbers one above the other.\n ```\n 42\n × 94\n ```\n\n2. **Multiply 42 by 4 (the ones digit of 94)**:\n - Multiply 42 by 4: \n \\[\n 42 \\times 4 = 168...
{"continuation_phrases": ["But I need to verify this.", "But I need to verify this."], "continuations": [" Let me check my work using another method:**\n\n5. **Verification using standard algorithm**:\n - Break it into simpler parts: \n \\[\n 42 \\times 90 = 3780\n \\]\n \\[\n 42 \\times 4 = 168\n...
[ "To solve the long multiplication problem \\(42 \\times 94\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down the numbers one above the other.\n ```\n 42\n × 94\n ```\n\n2. **Multiply 42 by 4 (the ones digit of 94)**:\n - Multiply 42 by 4: \n \\[\n 42 \\times 4 = 168...
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[ "To solve the long multiplication problem \\(42 \\times 94\\), we can break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n```\n 42\n × 94\n ------\n```\n\nWe'll multiply 42 by each digit in 94 separately and then add those products together.\n\n1. Multiply 42 by 4:\n ```\n ...
{"all_responses": ["To solve the long multiplication problem \\(42 \\times 94\\), we can break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n```\n 42\n \u00d7 94\n ------\n```\n\nWe'll multiply 42 by each digit in 94 separately and then add those products together.\n\n1. Multiply...
[ "To solve the long multiplication problem \\(42 \\times 94\\), we can break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n```\n 42\n × 94\n ------\n```\n\nWe'll multiply 42 by each digit in 94 separately and then add those products together.\n\n1. Multiply 42 by 4:\n ```\n ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 42 x 94 is\", \"answer\": \"3948\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
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What is the solution to the long multiplication equation below? 72 x 43 Think step by step.
3096
"{\"arg1\": 72, \"arg2\": 43, \"solution\": 3096}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n72 x 43\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(72 \\times 43\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 72\n × 43\n ----\n ```\n\n2. **Multiply 72 by 3 (the ones digit of 43):**\n - Multiply 72 by 3:\n ```\n 72\n × 3\n ----\n 216\n ```\n...
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[ "To solve the long multiplication problem \\(72 \\times 43\\), we can break it down into simpler steps using the distributive property of multiplication over addition:\n\n1. First, let's express 43 as \\(40 + 3\\).\n So, \\(72 \\times 43 = 72 \\times (40 + 3)\\).\n\n2. Now, use the distributive property:\n \\(7...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\( 72 \\times 43 \\), we will break it down into simpler steps and multiply each digit of one number by each digit of the other number.\n\n1. **Multiply 72 by 3 (the units digit of 43):**\n \\[\n 72 \\times 3 = 216\n \\]\n\n2. **Multiply 72 by 40 (the tens digit of 4...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But to confirm,"], "continuations": [" \n\nLet's redo the addition:\n\\[\n216 + 2880 = 3096\n\\]\nIt seems I made an error in my initial breakdown. Let\u2019s correct that:\n\n1. **First part:** Multiply 72 by 3.\n \\[\n 72 \\times 3 = 216\n \\]\n\...
[ "To solve the long multiplication problem \\( 72 \\times 43 \\), we will break it down into simpler steps and multiply each digit of one number by each digit of the other number.\n\n1. **Multiply 72 by 3 (the units digit of 43):**\n \\[\n 72 \\times 3 = 216\n \\]\n\n2. **Multiply 72 by 40 (the tens digit of 4...
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[ "To solve the long multiplication of 72 and 43, follow these steps:\n\n1. **Multiply the ones digit of 72 by the ones digit of 43:**\n - The ones digit of 72 is 2.\n - The ones digit of 43 is 3.\n - \\(2 \\times 3 = 6\\)\n So, write down 6.\n\n2. **Multiply the ones digit of 72 by the tens digit of 43 (whic...
{"all_responses": ["To solve the long multiplication of 72 and 43, follow these steps:\n\n1. **Multiply the ones digit of 72 by the ones digit of 43:**\n - The ones digit of 72 is 2.\n - The ones digit of 43 is 3.\n - \\(2 \\times 3 = 6\\)\n So, write down 6.\n\n2. **Multiply the ones digit of 72 by the tens di...
[ "To solve the long multiplication of 72 and 43, follow these steps:\n\n1. **Multiply the ones digit of 72 by the ones digit of 43:**\n - The ones digit of 72 is 2.\n - The ones digit of 43 is 3.\n - \\(2 \\times 3 = 6\\)\n So, write down 6.\n\n2. **Multiply the ones digit of 72 by the tens digit of 43 (whic...
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[ true, false, false ]
[ "3096", "3196", "2956" ]
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[ [ true ], [ false ], [ false ] ]
[ [ "3096" ], [ "3196" ], [ "2956" ] ]
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[ true ]
[ "3096" ]
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[ [ false, false, true ] ]
[ [ "indeed \\( 3096 \\)", "\\( 3096 \\)", "3096" ] ]
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[ false, false, false, false ]
[ "3066", "3098", "3098", "3098" ]
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[ [ "3066" ], [ "3098" ], [ "3098" ], [ "3098" ] ]
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[ true, true, true ]
[ "3096", "3096", "3096" ]
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[ [ true ], [ false, true ], [ false, true ] ]
[ [ "3096" ], [ "indeed \\( 3096 \\)", "3096" ], [ "\\( 3096 \\)", "3096" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 72 x 43 is\", \"answer\": \"3196\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{3196}" ]
[ false ]
[ "3196" ]
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[ [ false ] ]
[ [ "3196" ] ]
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What is the solution to the long multiplication equation below? 53 x 42 Think step by step.
2226
"{\"arg1\": 53, \"arg2\": 42, \"solution\": 2226}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n53 x 42\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
null
null
null
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[ "To solve the long multiplication problem \\(53 \\times 42\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 53\n × 42\n ```\n\n2. **Multiply 53 by 2 (the ones digit of 42):**\n - Multiply 53 by 2:\n ```\n 53\n × 2\n _______\n 106\n ```\...
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[ "To solve the long multiplication problem \\(53 \\times 42\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 53\n × 42\n ----\n ```\n\n2. **Multiply 53 by 2 (the ones digit of 42):**\n - Multiply 53 by 2:\n ```\n 53\n × 2\n ------\n 106\n ```\n\...
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[ "To solve the long multiplication problem \\(53 \\times 42\\), we can break it down into simpler steps:\n\n1. **Multiply 53 by 2 (the ones digit of 42):**\n \\[\n 53 \\times 2 = 106\n \\]\n Write down 6 and carry over 1.\n\n2. **Multiply 53 by 4 (the tens digit of 42) and add the carried over 1:**\n \\[\n...
{"continuation_phrases": ["Wait, let me try", "Hold on, let me verify this answer."], "continuations": [" again for clarity:\n \n First, multiply 53 by 2:\n \\[\n 53 \\times 2 = 106\n \\]\n Then, multiply 53 by 4 and add the carried over 1:\n \\[\n 53 \\times 4 = 212 \\\\\n 212 + 1 = 213\n \\]\n F...
[ "To solve the long multiplication problem \\(53 \\times 42\\), we can break it down into simpler steps:\n\n1. **Multiply 53 by 2 (the ones digit of 42):**\n \\[\n 53 \\times 2 = 106\n \\]\n Write down 6 and carry over 1.\n\n2. **Multiply 53 by 4 (the tens digit of 42) and add the carried over 1:**\n \\[\n...
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[ "To solve the long multiplication problem \\(53 \\times 42\\), we will follow these steps:\n\n1. **Multiply 53 by 2 (the ones digit of 42):**\n - \\(53 \\times 2 = 106\\)\n - Write down 6 and carry over 1.\n\n2. **Multiply 53 by 4 (the tens digit of 42) and add the carried over 1:**\n - \\(53 \\times 4 = 212\...
{"all_responses": ["To solve the long multiplication problem \\(53 \\times 42\\), we will follow these steps:\n\n1. **Multiply 53 by 2 (the ones digit of 42):**\n - \\(53 \\times 2 = 106\\)\n - Write down 6 and carry over 1.\n\n2. **Multiply 53 by 4 (the tens digit of 42) and add the carried over 1:**\n - \\(53 \...
[ "To solve the long multiplication problem \\(53 \\times 42\\), we will follow these steps:\n\n1. **Multiply 53 by 2 (the ones digit of 42):**\n - \\(53 \\times 2 = 106\\)\n - Write down 6 and carry over 1.\n\n2. **Multiply 53 by 4 (the tens digit of 42) and add the carried over 1:**\n - \\(53 \\times 4 = 212\...
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[ false ]
[ "53" ]
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[ [ false ] ]
[ [ "53" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}]"}]
[ true, true, true ]
[ "2226", "2226", "2226" ]
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[ [ true ], [ true ], [ true ] ]
[ [ "2226" ], [ "2226" ], [ "2226" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': True}]"}, {"value": "[{'answer_block': None, 'comparison_type': None, 'correct_an...
[ false ]
[ "2196" ]
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[{"answer_block": null, "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": "legacy", "extracted_answer": null, "final_answer": null, "is_correct": null, "is_equivalent": null, "legacy_result": false}]
[ [ false, false ] ]
[ [ "indeed 2196", "2196" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}, {'answer_block': None, 'comparison_type': None, 'correct_answer': None, '...
[ false, false, false, false ]
[ "2166", "2166", "2166", "2166" ]
[{"all_matches": ["('2166', 619)", "('2166', 618)", "('2166', 525)", "('213', 471)", "('6', 428)", "('213', 341)", "('212', 294)", "('53', 202)", "('106', 155)", "('53', 90)"], "all_numbers_in_line": null, "boxed_attempt": null, "choice_labels": null, "confidence": 0.9889415481832544, "extracted_answer": "2166", "extra...
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[ [ false ], [ false, false ], [ false, false ], [ false, false ] ]
[ [ "2166" ], [ "\\(\\boxed{2166}\\)", "2166" ], [ "indeed:", "2166" ], [ "indeed:", "2166" ] ]
[{"value": "[{'all_extracted_answers': ['2166'], 'all_extractions': [\"{'content': '2166', 'start_pos': 618, 'end_pos': 630, 'phrase_pair': ('\\\\\\\\boxed{', '}'), 'full_match': '\\\\\\\\boxed{2166}'}\"], 'all_matches': None, 'all_numbers_in_line': None, 'choice_labels': None, 'confidence': 0.9, 'extracted_answer': '2...
[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}]"}, {"value": "[{'answer_block': None, 'comparison_type': None, 'correct_a...
[ false, false, false ]
[ "213", "2196", "2196" ]
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[ [ false ], [ false ], [ false, false ] ]
[ [ "213" ], [ "2196" ], [ "indeed 2196", "2196" ] ]
[{"value": "[{'all_extracted_answers': None, 'all_extractions': None, 'all_matches': [\"('213', 521)\", \"('106', 492)\", \"('213', 369)\", \"('212', 313)\", \"('53', 219)\", \"('106', 170)\", \"('53', 103)\"], 'all_numbers_in_line': None, 'choice_labels': None, 'confidence': 0.885925925925926, 'extracted_answer': '213...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the product of 53 x 42 is\", \"answer\": \"2226\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{2226}" ]
[ true ]
[ "2226" ]
[ { "all_matches": [ "('2226', 1)", "('2226', 0)" ], "all_numbers_in_line": null, "choice_labels": null, "confidence": 0.5416666666666666, "extracted_answer": "2226", "extracted_choice_letter": null, "extracted_choice_text": null, "extractor": "pattern_based", "full...
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[ [ true ] ]
[ [ "2226" ] ]
[ [ { "all_extracted_answers": [ "2226" ], "all_extractions": [ "{'content': '2226', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '2226'}" ], "confidence": 0.9500000000000001, "extracted_answer": "2226", "extractor": "...
[ [ { "answer_block": null, "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": "legacy", "extracted_answer": null, "final_answer": null, "is_correct": null, "is_equivalent": null, "legacy_result": true } ] ]
What is the solution to the long multiplication equation below? 87 x 98 Think step by step.
8526
"{\"arg1\": 87, \"arg2\": 98, \"solution\": 8526}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n87 x 98\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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null
null
null
null
null
null
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[ "To solve the long multiplication problem \\(87 \\times 98\\), we can break it down into simpler steps:\n\n1. **Multiply 87 by 8 (the units digit of 98):**\n \\[\n 87 \\times 8 = 696\n \\]\n\n2. **Multiply 87 by 90 (the tens digit of 98, which is 9 times 10):**\n \\[\n 87 \\times 90 = 87 \\times 9 \\times...
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[ "Certainly! Let's solve this problem step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n \\[\n 87 \\\\\n \\times 98 \\\\\n ------\n \\]\n\n2. **Multiply 87 by 8 (the units digit of 98):**\n \\[\n 87 \\times 8 = 696\n \\]\n Write 696 under the line.\n\n3. **Multiply 87 b...
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[ "Certainly! Let's solve the long multiplication problem \\(87 \\times 98\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 87\n × 98\n ------\n```\n\n### Step 2: Multiply 87 by 8 (the units digit of 98)\n```\n 87\n × 98\n ------\n 606 ...
{"continuation_phrases": ["However,", "But to confirm,"], "continuations": [" we need to account for the carry-over from the previous step.\n\n### Step 3: Multiply 87 by 9 (the tens digit of 98) and add the carry-over\nFirst, multiply 87 by 9:\n```\n 87\n \u00d7 90\n ------\n 783\n```\nNow, add the carry-ove...
[ "Certainly! Let's solve the long multiplication problem \\(87 \\times 98\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 87\n × 98\n ------\n```\n\n### Step 2: Multiply 87 by 8 (the units digit of 98)\n```\n 87\n × 98\n ------\n 606 ...
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[ "To solve the long multiplication problem \\(87 \\times 98\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\n\\[ 87 \\]\n\\[ 98 \\]\n\nWe will multiply each digit of 87 by each digit of 98 and then add up all those ...
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[ "To solve the long multiplication problem \\(87 \\times 98\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\n\\[ 87 \\]\n\\[ 98 \\]\n\nWe will multiply each digit of 87 by each digit of 98 and then add up all those ...
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[ true ]
[ "8526" ]
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[ [ "8526" ] ]
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[ false, true, true ]
[ "1479", "8526", "8526" ]
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[ [ false, false ] ]
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[ "8526", "8526", "8526", "8526" ]
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[ [ "8526" ], [ "indeed \\(\\boxed{8526}\\)", "8526" ], [ "8526" ], [ "\\(\\boxed{8526}\\)", "8526" ] ]
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[ [ "8054" ], [ ":", "8406" ], [ "8535" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 87 x 98 is:\", \"answer\": \"8526\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
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[ "\\boxed{8526}" ]
[ true ]
[ "8526" ]
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[ [ true ] ]
[ [ "8526" ] ]
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What is the solution to the long multiplication equation below? 54 x 19 Think step by step.
1026
"{\"arg1\": 54, \"arg2\": 19, \"solution\": 1026}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n54 x 19\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(54 \\times 19\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 19 into tens and ones.\n\\[ 19 = 10 + 9 \\]\n\n#### Step 2: Multiply 54 by each part of 19 separately.\n\n**First part:**\n\\[ 54 \\times 10 \\]\nThis is s...
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[ "To solve the long multiplication problem \\(54 \\times 19\\), we can break it down into simpler steps:\n\nStep 1: Break down 19 into 10 + 9.\n\\(54 \\times 19 = 54 \\times (10 + 9)\\)\n\nStep 2: Distribute 54 across the sum of 10 and 9:\n\\(= 54 \\times 10 + 54 \\times 9\\)\n\nStep 3: Multiply each term separately...
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[ "To solve the long multiplication problem \\(54 \\times 19\\), we can break it down into simpler steps:\n\n### Step 1: Break Down the Multiplication\nFirst, let's write out the numbers:\n\\[ 54 \\]\nand\n\\[ 19 \\]\n\nWe will multiply each digit of 54 by each digit of 19.\n\n### Step 2: Multiply 54 by 9 (the units ...
{"continuation_phrases": ["Wait, how?", "Hold on, let me verify this answer."], "continuations": [" Let me explain again carefully.\nSure! Let's go through this step-by-step again:\n\n1. **Break Down the Multiplication**:\n - We need to find \\(54 \\times 19\\).\n \n2. **Multiply 54 by 9 (units place)**:\n \\[ 54...
[ "To solve the long multiplication problem \\(54 \\times 19\\), we can break it down into simpler steps:\n\n### Step 1: Break Down the Multiplication\nFirst, let's write out the numbers:\n\\[ 54 \\]\nand\n\\[ 19 \\]\n\nWe will multiply each digit of 54 by each digit of 19.\n\n### Step 2: Multiply 54 by 9 (the units ...
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[ "To solve the long multiplication problem \\( 54 \\times 19 \\), we will break it down into simpler steps.\n\nStep 1: Break down the numbers.\n\\[ 54 = 50 + 4 \\]\n\\[ 19 = 10 + 9 \\]\n\nStep 2: Multiply each part of the first number (54) by each part of the second number (19).\n- Multiply 50 by 19:\n\\[ 50 \\times...
{"all_responses": ["To solve the long multiplication problem \\( 54 \\times 19 \\), we will break it down into simpler steps.\n\nStep 1: Break down the numbers.\n\\[ 54 = 50 + 4 \\]\n\\[ 19 = 10 + 9 \\]\n\nStep 2: Multiply each part of the first number (54) by each part of the second number (19).\n- Multiply 50 by 19:\...
[ "To solve the long multiplication problem \\( 54 \\times 19 \\), we will break it down into simpler steps.\n\nStep 1: Break down the numbers.\n\\[ 54 = 50 + 4 \\]\n\\[ 19 = 10 + 9 \\]\n\nStep 2: Multiply each part of the first number (54) by each part of the second number (19).\n- Multiply 50 by 19:\n\\[ 50 \\times...
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[ [ "indeed \\(1026\\)", "1026" ] ]
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[ [ "1026" ], [ "1026" ], [ "indeed \\(1026\\)", "1026" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 54 x 19 is:\", \"answer\": \"594\"}]}" ]
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What is the solution to the long multiplication equation below? 33 x 42 Think step by step.
1386
"{\"arg1\": 33, \"arg2\": 42, \"solution\": 1386}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n33 x 42\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(33 \\times 42\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(33\\) can be written as \\(30 + 3\\).\n - \\(42\\) can be written as \\(40 + 2\\).\n\n2. **Multiply each part of the first number by each part of the second number:**\...
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[ "Certainly! Let's solve the long multiplication problem \\(33 \\times 42\\) step by step.\n\n### Step 1: Set up the multiplication\nWe need to multiply 33 by 42. We can break this down into simpler steps using the distributive property of multiplication over addition:\n\n\\[ 33 \\times 42 = (30 + 3) \\times (40 + 2...
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[ "To solve the long multiplication problem \\(33 \\times 42\\), we can break it down into simpler steps:\n\n1. **Multiply 33 by 2:**\n - 33 × 2 = 66\n\n2. **Multiply 33 by 40 (which is 4 times 20):**\n - First, calculate 33 × 40.\n - We know that 33 × 4 = 132, so 33 × 40 = 1320.\n\nNow, add the two results t...
{"continuation_phrases": ["Wait, let me try", "But to confirm,"], "continuations": [" this again.\n - Correctly, 33 \u00d7 4 = 132, then 132 \u00d7 10 = 1320.\n\nSo, 33 \u00d7 40 = 1320\n\n3. **Add the results from steps 1 and 2:**\n - 66 + 1320 = 1386\n\nTherefore, \\(33 \\times 42 = 1386\\).", " we can use anot...
[ "To solve the long multiplication problem \\(33 \\times 42\\), we can break it down into simpler steps:\n\n1. **Multiply 33 by 2:**\n - 33 × 2 = 66\n\n2. **Multiply 33 by 40 (which is 4 times 20):**\n - First, calculate 33 × 40.\n - We know that 33 × 4 = 132, so 33 × 40 = 1320.\n\nNow, add the two results t...
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[ "To solve the long multiplication problem \\(33 \\times 42\\), we will follow these steps:\n\n1. **Multiply the ones digit of the bottom number by the top number:**\n - The ones digit of 33 is 3.\n - Multiply 3 by 2 (the ones digit of 42): \n \\[\n 3 \\times 2 = 6\n \\]\n - Write down this result ...
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[ "To solve the long multiplication problem \\(33 \\times 42\\), we will follow these steps:\n\n1. **Multiply the ones digit of the bottom number by the top number:**\n - The ones digit of 33 is 3.\n - Multiply 3 by 2 (the ones digit of 42): \n \\[\n 3 \\times 2 = 6\n \\]\n - Write down this result ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 33 x 42 is\", \"answer\": \"1486\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
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[ "\\boxed{1486}" ]
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What is the solution to the long multiplication equation below? 63 x 12 Think step by step.
756
"{\"arg1\": 63, \"arg2\": 12, \"solution\": 756}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n63 x 12\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(63 \\times 12\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nFirst, let's rewrite 12 as \\(10 + 2\\). This will make our calculation easier.\n\nSo, \\(63 \\times 12 = 63 \\times (10 + 2)\\)\n\n#### Step ...
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[ "To solve the long multiplication problem \\(63 \\times 12\\), we can break it down into simpler steps:\n\nStep 1: Break down the numbers into tens and ones.\n- 63 can be thought of as 60 + 3\n- 12 can be thought of as 10 + 2\n\nStep 2: Multiply each part separately.\n\nFor 60:\n\\[60 \\times 12 = (60 \\times 10) +...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "Certainly! Let's solve the long multiplication problem \\( 63 \\times 12 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 63\n × 12\n ----\n ```\n\n2. **Multiply 63 by 2 (the units digit of 12):**\n - Multiply 63 by 2:\n ```\n 63\n × 2\n ...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But I need to verify this."], "continuations": [" When I add 126 and 630, it should be 756. However, there seems to have been an error in the addition process. Let's correct it.\n\n### Corrected Addition Process:\n\n1. **First, align the numbers correctl...
[ "Certainly! Let's solve the long multiplication problem \\( 63 \\times 12 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 63\n × 12\n ----\n ```\n\n2. **Multiply 63 by 2 (the units digit of 12):**\n - Multiply 63 by 2:\n ```\n 63\n × 2\n ...
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[ "To solve the long multiplication problem \\( 63 \\times 12 \\), we will follow these steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 63\n × 12\n ----\n ```\n\n2. **Multiply 63 by 2 (the units digit of 12):**\n - Multiply 63 by 2:\n ```\n 63\n × 2\n ...
{"all_responses": ["To solve the long multiplication problem \\( 63 \\times 12 \\), we will follow these steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 63\n \u00d7 12\n ----\n ```\n\n2. **Multiply 63 by 2 (the units digit of 12):**\n - Multiply 63 by 2:\n ```\n ...
[ "To solve the long multiplication problem \\( 63 \\times 12 \\), we will follow these steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 63\n × 12\n ----\n ```\n\n2. **Multiply 63 by 2 (the units digit of 12):**\n - Multiply 63 by 2:\n ```\n 63\n × 2\n ...
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[ "756", "1152", "756" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Therefore, the solution to 63 x 12 is\", \"answer\": \"756\"}]}" ]
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What is the solution to the long multiplication equation below? 92 x 59 Think step by step.
5428
"{\"arg1\": 92, \"arg2\": 59, \"solution\": 5428}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n92 x 59\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(92 \\times 59\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 92\n × 59\n ------\n ```\n\n2. **Multiply 92 by 9 (the units digit of 59):**\n - Multiply 92 by 9:\n ```\n 828\n × 9\n ------\n 74...
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[ "Certainly! Let's solve the multiplication problem \\( 92 \\times 59 \\) step by step.\n\n### Step 1: Break down the numbers into parts\nFirst, let's break down the numbers into more manageable parts:\n- \\( 92 = 90 + 2 \\)\n- \\( 59 = 50 + 9 \\)\n\n### Step 2: Multiply each part of the first number by the second n...
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[ "To solve the long multiplication problem \\( 92 \\times 59 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 92\n × 59\n ------\n ```\n\n2. **Multiply 92 by 9 (the units digit of 59):**\n - Multiply 92 by 9:\n \\[\n 92 \\times 9 = 828\n \\]\n - Write down...
{"continuation_phrases": ["Wait, how?", "Hold on, let me verify this answer."], "continuations": [" Let's double-check our work.\n \n Correcting the mistake:\n - From step 2, we correctly got 828.\n - From step 3, we should have multiplied 92 by 50 first without shifting:\n \\[\n 92 \\times 50 = 4600\n ...
[ "To solve the long multiplication problem \\( 92 \\times 59 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 92\n × 59\n ------\n ```\n\n2. **Multiply 92 by 9 (the units digit of 59):**\n - Multiply 92 by 9:\n \\[\n 92 \\times 9 = 828\n \\]\n - Write down...
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[ "To solve the long multiplication problem \\(92 \\times 59\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 92\n × 59\n ------\n ```\n\n2. **Multiply 92 by 9 (the units digit of 59):**\n - Multiply 92 by 9:\n ```\n 828\n × 9\n ------\n 7462\n ...
{"all_responses": ["To solve the long multiplication problem \\(92 \\times 59\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 92\n \u00d7 59\n ------\n ```\n\n2. **Multiply 92 by 9 (the units digit of 59):**\n - Multiply 92 by 9:\n ```\n 828\n \u00d7 9\n ...
[ "To solve the long multiplication problem \\(92 \\times 59\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 92\n × 59\n ------\n ```\n\n2. **Multiply 92 by 9 (the units digit of 59):**\n - Multiply 92 by 9:\n ```\n 828\n × 9\n ------\n 7462\n ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 92 \\u00d7 9 = 7462.\", \"answer\": \"7462\"}, {\"context\": \"So, 92 \\u00d7 50 = 4600.\", \"answer\": \"4600\"}, {\"context\": \"Therefore, the product of 92 \\u00d7 59 is 12062.\", \"answer\": \"12062\"}]}" ]
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What is the solution to the long multiplication equation below? 57 x 81 Think step by step.
4617
"{\"arg1\": 57, \"arg2\": 81, \"solution\": 4617}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n57 x 81\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(57 \\times 81\\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 57\n × 81\n```\n\n### Step 2: Multiply 57 by 1 (the units digit of 81)\n- Multiply 57 by 1: \n ```\n 57\n × 1\n -----...
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[ "Certainly! Let's solve this step-by-step.\n\n### Step 1: Break down the numbers\nFirst, we can break down the numbers into smaller parts:\n- \\(57 = 50 + 7\\)\n- \\(81 = 80 + 1\\)\n\n### Step 2: Multiply each part of the first number by each part of the second number\nNow, let's multiply these broken-down parts:\n...
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[ "To solve the long multiplication problem \\( 57 \\times 81 \\), we will follow these steps:\n\n### Step 1: Multiply 57 by 1 (the rightmost digit of 81)\n- Multiply 57 by 1:\n \\[\n 57 \\times 1 = 57\n \\]\n\n### Step 2: Multiply 57 by 8 (the next digit of 81)\n- Multiply 57 by 8:\n \\[\n 57 \\times 8 = 456\n ...
{"continuation_phrases": ["But to confirm,", "Wait, this result is"], "continuations": [" let's break it down properly.\n \n### Step 3: Break down 57 into tens and ones for easier calculation\n- 57 can be broken down as \\( 50 + 7 \\).\n\n### Step 4: Multiply 57 by 8 (the next digit of 81) again but separately\n- Mult...
[ "To solve the long multiplication problem \\( 57 \\times 81 \\), we will follow these steps:\n\n### Step 1: Multiply 57 by 1 (the rightmost digit of 81)\n- Multiply 57 by 1:\n \\[\n 57 \\times 1 = 57\n \\]\n\n### Step 2: Multiply 57 by 8 (the next digit of 81)\n- Multiply 57 by 8:\n \\[\n 57 \\times 8 = 456\n ...
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[ "To solve the long multiplication problem \\(57 \\times 81\\), follow these steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 57\n × 81\n ----\n```\n\n### Step 2: Multiply 57 by 1 (the ones digit of 81).\n- \\(57 \\times 1 = 57\\)\n- Write down 7 and carry over 5.\n\n```\n 57\n × 81\n...
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[ "To solve the long multiplication problem \\(57 \\times 81\\), follow these steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 57\n × 81\n ----\n```\n\n### Step 2: Multiply 57 by 1 (the ones digit of 81).\n- \\(57 \\times 1 = 57\\)\n- Write down 7 and carry over 5.\n\n```\n 57\n × 81\n...
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[ [ "indeed \\( 4569 \\)", "4569" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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[ "\\boxed{533}", "\\boxed{57}", "\\boxed{456}" ]
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What is the solution to the long multiplication equation below? 25 x 27 Think step by step.
675
"{\"arg1\": 25, \"arg2\": 27, \"solution\": 675}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n25 x 27\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(25 \\times 27\\), we can break it down into simpler steps:\n\n1. **Multiply 25 by 7 (the units digit of 27):**\n - \\(25 \\times 7 = 175\\)\n - Write down 5 and carry over 1.\n\n2. **Multiply 25 by 20 (the tens digit of 27, which is 20 because 27 has two digits):**\n...
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[ "To solve the long multiplication of 25 and 27, we'll follow these steps:\n\n1. **Multiply the units digits:**\n - Multiply 5 (from 25) by 7 (from 27).\n \\[\n 5 \\times 7 = 35\n \\]\n - Write down 5 and carry over 3.\n\n2. **Multiply the tens digit of one number by the tens digit of the other numbe...
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[ "To solve the long multiplication problem \\(25 \\times 27\\), we can break it down into simpler steps:\n\n1. **Break down the numbers**: \n - \\(25\\) can be thought of as \\(20 + 5\\).\n - \\(27\\) can be thought of as \\(20 + 7\\).\n\n2. **Multiply each part**:\n - Multiply \\(20\\) by \\(27\\):\n \\[\...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But I need to verify this."], "continuations": [" \n\nLet's do it again carefully:\n\n- First, multiply \\(25\\) by \\(27\\):\n \\[\n 25 \\times 27 = 25 \\times (20 + 7) = 25 \\times 20 + 25 \\times 7 = 500 + 175 = 675\n \\]\n\nSo, the correct result ...
[ "To solve the long multiplication problem \\(25 \\times 27\\), we can break it down into simpler steps:\n\n1. **Break down the numbers**: \n - \\(25\\) can be thought of as \\(20 + 5\\).\n - \\(27\\) can be thought of as \\(20 + 7\\).\n\n2. **Multiply each part**:\n - Multiply \\(20\\) by \\(27\\):\n \\[\...
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[ "To solve the long multiplication of 25 and 27, we can break it down into simpler steps:\n\n1) First, let's multiply 25 by 7 (the units digit of 27):\n\n 25 × 7 = 175\n\n2) Now, let's multiply 25 by 20 (which is 27 - 7):\n\n 25 × 20 = 500\n\n3) Finally, add these two results together:\n \n 175 + 500 = 675\n...
{"all_responses": ["To solve the long multiplication of 25 and 27, we can break it down into simpler steps:\n\n1) First, let's multiply 25 by 7 (the units digit of 27):\n\n 25 \u00d7 7 = 175\n\n2) Now, let's multiply 25 by 20 (which is 27 - 7):\n\n 25 \u00d7 20 = 500\n\n3) Finally, add these two results together:\n...
[ "To solve the long multiplication of 25 and 27, we can break it down into simpler steps:\n\n1) First, let's multiply 25 by 7 (the units digit of 27):\n\n 25 × 7 = 175\n\n2) Now, let's multiply 25 by 20 (which is 27 - 7):\n\n 25 × 20 = 500\n\n3) Finally, add these two results together:\n \n 175 + 500 = 675\n...
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[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 25 x 27 is\", \"answer\": \"675\"}]}" ]
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[ [ { "all_extracted_answers": [ "675" ], "all_extractions": [ "{'content': '675', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '675'}" ], "confidence": 0.9500000000000001, "extracted_answer": "675", "extractor": "stri...
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What is the solution to the long multiplication equation below? 33 x 18 Think step by step.
594
"{\"arg1\": 33, \"arg2\": 18, \"solution\": 594}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n33 x 18\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(33 \\times 18\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 33 and 18 into tens and units.\n- \\(33 = 30 + 3\\)\n- \\(18 = 10 + 8\\)\n\n#### Step 2: Multiply each part of 33 by each part of 18.\n\n**First Multiplica...
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[ "To solve the multiplication problem \\(33 \\times 18\\), we can break it down into simpler steps:\n\nStep 1: Break down 33 and 18 into their place values.\n - 33 = 30 + 3\n - 18 = 10 + 8\n\nStep 2: Multiply each part of 33 by each part of 18.\n - \\(30 \\times 10 = 300\\)\n - \\(30 \\times 8 = 240\\)\n -...
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[ "Certainly! Let's solve this step by step:\n\n### Step 1: Break down the numbers into tens and units.\n- \\(33\\) can be broken down into \\(30 + 3\\).\n- \\(18\\) can be broken down into \\(10 + 8\\).\n\n### Step 2: Multiply each part of the first number (30+3) by the second number (10+8).\n#### First part:\n\\[30...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But to confirm,"], "continuations": [" \n\n### Corrected Calculation:\n\\[30 \\times 10 = 300\\]\n\\[30 \\times 8 = 240\\]\n\\[3 \\times 10 = 30\\]\n\\[3 \\times 8 = 24\\]\n\nNow add them together:\n\\[300 + 240 = 540\\]\n\\[540 + 30 = 570\\]\n\\[570 + 2...
[ "Certainly! Let's solve this step by step:\n\n### Step 1: Break down the numbers into tens and units.\n- \\(33\\) can be broken down into \\(30 + 3\\).\n- \\(18\\) can be broken down into \\(10 + 8\\).\n\n### Step 2: Multiply each part of the first number (30+3) by the second number (10+8).\n#### First part:\n\\[30...
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[ "To solve the long multiplication problem \\(33 \\times 18\\), let's break it down into steps:\n\n### Step 1: Break down the numbers\n- First, write out the numbers you're multiplying:\n ```\n 33\n × 18\n ```\n\n### Step 2: Multiply 33 by 8 (the units digit of 18)\n- Multiply 33 by 8:\n - 30 * 8 = 240 (write...
{"all_responses": ["To solve the long multiplication problem \\(33 \\times 18\\), let's break it down into steps:\n\n### Step 1: Break down the numbers\n- First, write out the numbers you're multiplying:\n ```\n 33\n \u00d7 18\n ```\n\n### Step 2: Multiply 33 by 8 (the units digit of 18)\n- Multiply 33 by 8:\n -...
[ "To solve the long multiplication problem \\(33 \\times 18\\), let's break it down into steps:\n\n### Step 1: Break down the numbers\n- First, write out the numbers you're multiplying:\n ```\n 33\n × 18\n ```\n\n### Step 2: Multiply 33 by 8 (the units digit of 18)\n- Multiply 33 by 8:\n - 30 * 8 = 240 (write...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the...
[ true ]
[ "594" ]
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[ [ true ] ]
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[ "694", "694", "33" ]
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[ [ false, false, false, true ] ]
[ [ ":", "indeed **594**", "indeed \\(594\\)", "594" ] ]
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[ false, true, true, true ]
[ "564", "594", "594", "594" ]
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[ [ "\\(33 \\times 18 = 564\\)", "564" ], [ "\\(594\\)", "594" ], [ "594" ], [ "594" ] ]
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[ true, true, true ]
[ "594", "594", "594" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Now add these two sums:\", \"answer\": \"594\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{594}" ]
[ true ]
[ "594" ]
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[ [ true ] ]
[ [ "594" ] ]
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What is the solution to the long multiplication equation below? 65 x 72 Think step by step.
4680
"{\"arg1\": 65, \"arg2\": 72, \"solution\": 4680}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n65 x 72\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
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[ "To solve the long multiplication problem \\(65 \\times 72\\), we can break it down into simpler steps:\n\n1. **Multiply 65 by 2 (the ones digit of 72):**\n - \\(65 \\times 2 = 130\\)\n - Write down 0 and carry over 1.\n\n2. **Multiply 65 by 7 (the tens digit of 72) and add the carried-over 1:**\n - \\(65 \\t...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "To solve the long multiplication problem \\(65 \\times 72\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 65\n x 72\n ----\n ```\n\n2. **Multiply 65 by 2 (the ones digit of 72):**\n - Multiply 65 by 2:\n ```\n 65\n x 2\n -----\n 130\n ```\n - Writ...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(65 \\times 72\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\\[65 = 60 + 5\\]\n\\[72 = 70 + 2\\]\n\nNow, multiply each part separately and then add the results:\n\n1. M...
{"continuation_phrases": ["But I need to verify this.", "Wait, let me try"], "continuations": [" Let me do it again carefully: \n\nFirst, calculate \\(65 \\times 72\\):\n\n\\[65 \\times 72 = 65 \\times (70 + 2) = 65 \\times 70 + 65 \\times 2\\]\n\\[= 4550 + 130\\]\n\\[= 4680\\]\n\nTherefore, the correct answer is \\(46...
[ "To solve the long multiplication problem \\(65 \\times 72\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\\[65 = 60 + 5\\]\n\\[72 = 70 + 2\\]\n\nNow, multiply each part separately and then add the results:\n\n1. M...
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[ "To solve the long multiplication problem \\( 65 \\times 72 \\), we can break it down into simpler steps:\n\n1. **Multiply 65 by 2 (the ones digit of 72):**\n - \\( 65 \\times 2 = 130 \\)\n - Write down 130.\n\n2. **Multiply 65 by 70 (the tens digit of 72, which is 7 multiplied by 10):**\n - \\( 65 \\times 70...
{"all_responses": ["To solve the long multiplication problem \\( 65 \\times 72 \\), we can break it down into simpler steps:\n\n1. **Multiply 65 by 2 (the ones digit of 72):**\n - \\( 65 \\times 2 = 130 \\)\n - Write down 130.\n\n2. **Multiply 65 by 70 (the tens digit of 72, which is 7 multiplied by 10):**\n - \\...
[ "To solve the long multiplication problem \\( 65 \\times 72 \\), we can break it down into simpler steps:\n\n1. **Multiply 65 by 2 (the ones digit of 72):**\n - \\( 65 \\times 2 = 130 \\)\n - Write down 130.\n\n2. **Multiply 65 by 70 (the tens digit of 72, which is 7 multiplied by 10):**\n - \\( 65 \\times 70...
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[ [ false ] ]
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[ "4680", "4680", "4680" ]
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[ [ true ], [ true ], [ true ] ]
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[ [ true, false, false, true ] ]
[ [ "4680", "\\(4680\\)", "indeed \\(4680\\)", "4680" ] ]
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[ "4680", "4680", "4680", "4680" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Therefore, the solution to 65 x 72 is\", \"answer\": \"586\"}, {\"context\": \"First part: 130\", \"answer\": \"130\"}, {\"context\": \"Second part: 456\", \"answer\": \"456\"}]}" ]
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What is the solution to the long multiplication equation below? 60 x 97 Think step by step.
5820
"{\"arg1\": 60, \"arg2\": 97, \"solution\": 5820}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n60 x 97\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(60 \\times 97\\), we can break it down into simpler steps:\n\n1. **Multiply 60 by 7 (the units digit of 97):**\n - \\(60 \\times 7 = 420\\)\n\n2. **Multiply 60 by 90 (the tens digit of 97, which is 9 multiplied by 10):**\n - \\(60 \\times 90 = 5400\\) (because \\(60 ...
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[ "To solve the long multiplication problem \\( 60 \\times 97 \\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 60 and 97 in two rows, aligning them vertically.\n\n\\[\n\\begin{array}{r}\n 60 \\\\\n\\times 97 \\\\\n\\hline\n\\end{array}\n\\]\n\n2. **Multiply 60 by 7**:\n - Multiply ...
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[ "Certainly! Let's solve this step-by-step:\n\n1) First, let's write down the numbers we're multiplying:\n 60\n × 97\n -----\n\n2) Now, let's multiply 60 by 7 (the units digit of 97):\n 60\n × 7\n ----\n 420\n\n3) Next, let's multiply 60 by 9 (the tens digit of 97), but remember to shift one place to...
{"continuation_phrases": ["Wait! I can double check this answer.", "Wait! I can double check this answer."], "continuations": [" If we multiply 60 * 97 directly using standard long multiplication method, we get:\n 60\n \u00d7 97\n ----\n 4200 (this is incorrect, as it should be 540)\n 600\n ----\n 5820 (...
[ "Certainly! Let's solve this step-by-step:\n\n1) First, let's write down the numbers we're multiplying:\n 60\n × 97\n -----\n\n2) Now, let's multiply 60 by 7 (the units digit of 97):\n 60\n × 7\n ----\n 420\n\n3) Next, let's multiply 60 by 9 (the tens digit of 97), but remember to shift one place to...
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[ "To solve \\(60 \\times 97\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, express 97 as the sum of two numbers that are easier to multiply with 60. A good choice would be 100 - 3 because:\n\\[97 = 100 - 3\\]\n\nNow, rewrite the original express...
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[ "To solve \\(60 \\times 97\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, express 97 as the sum of two numbers that are easier to multiply with 60. A good choice would be 100 - 3 because:\n\\[97 = 100 - 3\\]\n\nNow, rewrite the original express...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 60 x 97 is\", \"answer\": \"5820\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{5820}" ]
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What is the solution to the long multiplication equation below? 83 x 96 Think step by step.
7968
"{\"arg1\": 83, \"arg2\": 96, \"solution\": 7968}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n83 x 96\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(83 \\times 96\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 83\n × 96\n ```\n\n2. **Multiply 83 by 6 (the ones digit of 96):**\n - Multiply 83 by 6:\n ```\n 498\n ```\n - Write down 498.\n\n3. **Multiply 83 by 90...
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[ "To solve the long multiplication problem \\(83 \\times 96\\), you can follow these steps:\n\n1. **Multiply 83 by 6 (the ones digit of 96):**\n - \\(83 \\times 6 = 498\\)\n\n2. **Multiply 83 by 90 (the tens digit of 96, which is 9 times 10):**\n - First, multiply 83 by 9: \n \\[\n 83 \\times 9 = 747\n ...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "Certainly! Let's break down the multiplication of 83 and 96 step by step.\n\n### Step-by-Step Solution:\n\n1. **Multiply 83 by 6 (the units digit of 96):**\n \\[\n 83 \\times 6 = 498\n \\]\n\n2. **Multiply 83 by 90 (the tens digit of 96, which is 9 times 10):**\n \\[\n 83 \\times 90 = 7470\n \\]\n No...
{"continuation_phrases": ["But to confirm,", "However,"], "continuations": [" we can also calculate it directly as:\n \\[\n 83 \\times 90 = 7470\n \\]\n And then add the carry-over from the first step:\n \\[\n 7470 + 498 = 7968\n \\]\n\nSo, the final answer is \\( 7968 \\).", " since we are dealing with n...
[ "Certainly! Let's break down the multiplication of 83 and 96 step by step.\n\n### Step-by-Step Solution:\n\n1. **Multiply 83 by 6 (the units digit of 96):**\n \\[\n 83 \\times 6 = 498\n \\]\n\n2. **Multiply 83 by 90 (the tens digit of 96, which is 9 times 10):**\n \\[\n 83 \\times 90 = 7470\n \\]\n No...
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[ "Certainly! Let's solve the long multiplication problem \\( 83 \\times 96 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 83\n × 96\n ```\n\n2. **Multiply 83 by 6 (the ones digit of 96):**\n - Multiply 83 by 6:\n ```\n 498\n + 830\n ------\n ...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\( 83 \\times 96 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 83\n \u00d7 96\n ```\n\n2. **Multiply 83 by 6 (the ones digit of 96):**\n - Multiply 83 by 6:\n ```\n 498\n + 8...
[ "Certainly! Let's solve the long multiplication problem \\( 83 \\times 96 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 83\n × 96\n ```\n\n2. **Multiply 83 by 6 (the ones digit of 96):**\n - Multiply 83 by 6:\n ```\n 498\n + 830\n ------\n ...
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[ [ false ] ]
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[ [ "\\(7968\\)", "7968" ], [ "79680" ], [ "75298" ] ]
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[ [ "\\( 7968 \\)", "\\( 7968 \\)", "7968" ] ]
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[ false, false, false, false ]
[ "8088", "8088", "8088", "8088" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"This gives us 74700.\", \"answer\": \"74700\"}, {\"context\": \"Add 498 and 74700:\", \"answer\": \"498\"}, {\"context\": \"Add 498 and 74700:\", \"answer\": \"74700\"}, {\"context\": \"So, the product of 83 x 96 is 75198.\", \"answer\": \"75198\"}]}" ]
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[ "\\boxed{74700}", "\\boxed{498}", "\\boxed{74700}", "\\boxed{75198}" ]
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[ "74700", "498", "74700", "75198" ]
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[ [ "74700" ], [ "498" ], [ "74700" ], [ "75198" ] ]
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What is the solution to the long multiplication equation below? 89 x 97 Think step by step.
8633
"{\"arg1\": 89, \"arg2\": 97, \"solution\": 8633}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n89 x 97\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(89 \\times 97\\), we can break it down into simpler steps:\n\n1. **Multiply 89 by 7 (the units digit of 97):**\n - \\(89 \\times 7 = 623\\)\n\n2. **Multiply 89 by 90 (which is 9 times 10):**\n - First, calculate \\(89 \\times 9 = 801\\)\n - Then, add a zero at the ...
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[ "To solve the long multiplication problem \\(89 \\times 97\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write 89 and 97 one under the other.\n\n ```\n 89\n × 97\n ----\n ```\n\n2. **Multiply 89 by 7 (the units digit of 97)**:\n \n - Multiply 89 by 7: \n ```\n 89\...
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[ "To solve \\( 89 \\times 97 \\) using long multiplication, follow these steps:\n\n1. **Write down the numbers:**\n ```\n 89\n × 97\n ```\n\n2. **Multiply 89 by 7 (the ones digit of 97):**\n - \\( 89 \\times 7 = 623 \\)\n Write 3 in the ones place and carry over 6.\n\n3. **Multiply 89 by 9 (the tens di...
{"continuation_phrases": ["Wait, how?", "Hold on, let me verify this answer."], "continuations": [" Let's correct this.\n \n Actually, we should have:\n - \\( 89 \\times 9 = 801 \\)\n - Now, add the carried-over 8: \\( 801 + 8 = 809 \\)\n - So, write 9 in the hundreds place.\n\nPutting it all together:\n```\n...
[ "To solve \\( 89 \\times 97 \\) using long multiplication, follow these steps:\n\n1. **Write down the numbers:**\n ```\n 89\n × 97\n ```\n\n2. **Multiply 89 by 7 (the ones digit of 97):**\n - \\( 89 \\times 7 = 623 \\)\n Write 3 in the ones place and carry over 6.\n\n3. **Multiply 89 by 9 (the tens di...
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[ "To solve the long multiplication problem \\( 89 \\times 97 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 89\n × 97\n ```\n\n2. **Multiply 89 by 7 (the ones digit of 97):**\n - Multiply 89 by 7:\n ```\n 623\n × 7\n --------\n 6061\n ```\n\n3...
{"all_responses": ["To solve the long multiplication problem \\( 89 \\times 97 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 89\n \u00d7 97\n ```\n\n2. **Multiply 89 by 7 (the ones digit of 97):**\n - Multiply 89 by 7:\n ```\n 623\n \u00d7 7\n --------\n ...
[ "To solve the long multiplication problem \\( 89 \\times 97 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 89\n × 97\n ```\n\n2. **Multiply 89 by 7 (the ones digit of 97):**\n - Multiply 89 by 7:\n ```\n 623\n × 7\n --------\n 6061\n ```\n\n3...
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[ "85333", "8633", "8633" ]
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[ [ false ], [ true ], [ true ] ]
[ [ "85333" ], [ "8633" ], [ "8633" ] ]
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[ false ]
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[ [ false, false ] ]
[ [ "indeed \\( 8593 \\)", "8593" ] ]
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[ false, true, true, true ]
[ "14071", "8633", "8633", "8633" ]
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[ [ "14071" ], [ ": \\( 89 \\times 97 = 8633 \\)", "8633" ], [ "8633" ], [ "8633" ] ]
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[ "8533", "8593", "8593" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 89 x 97 is\", \"answer\": \"8633\"}, {\"context\": \"89 x 7 =\", \"answer\": \"623\"}, {\"context\": \"89 x 90 (which is 9 times 10):\", \"answer\": \"8010\"}, {\"context\": \"Add the results from steps 1 and 2:\", \"answer\": \"8633\"}]}" ]
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[ "\\boxed{8633}", "\\boxed{623}", "\\boxed{8010}", "\\boxed{8633}" ]
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[ "8633", "623", "8010", "8633" ]
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[ [ true ], [ false ], [ false ], [ true ] ]
[ [ "8633" ], [ "623" ], [ "8010" ], [ "8633" ] ]
[ [ { "all_extracted_answers": [ "8633" ], "all_extractions": [ "{'content': '8633', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '8633'}" ], "confidence": 0.9500000000000001, "extracted_answer": "8633", "extractor": "...
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What is the solution to the long multiplication equation below? 37 x 61 Think step by step.
2257
"{\"arg1\": 37, \"arg2\": 61, \"solution\": 2257}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n37 x 61\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(37 \\times 61\\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 37\n × 61\n```\n\n### Step 2: Multiply 37 by 1 (the units digit of 61)\n- Multiply 37 by 1: \n ```\n 37\n × 1\n ------...
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[ "Certainly! Let's break down the multiplication of 37 and 61 step by step.\n\n### Step-by-Step Solution:\n\n#### Step 1: Break Down the Numbers\nWe can think of 37 as \\( (40 - 3) \\) and 61 as \\( (60 + 1) \\).\n\nSo, we have:\n\\[ 37 = 40 - 3 \\]\n\\[ 61 = 60 + 1 \\]\n\n#### Step 2: Multiply Each Part\nNow let's ...
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[ "To solve the long multiplication problem \\(37 \\times 61\\), we will break it down into simpler steps:\n\n### Step 1: Break down the numbers\n- The number 37 can be broken down into 30 and 7.\n- The number 61 can be broken down into 60 and 1.\n\nSo, \\(37 \\times 61 = (30 + 7) \\times (60 + 1)\\)\n\n### Step 2: U...
{"continuation_phrases": ["Wait, let me try", "But to confirm,"], "continuations": [" that again...\n\n### Step 2: Correct breakdown\nLet's correctly break down both numbers:\n- 37 = 30 + 7\n- 61 = 60 + 1\n\n### Step 3: Multiply each part of one number by each part of the other number\nWe'll multiply these parts separa...
[ "To solve the long multiplication problem \\(37 \\times 61\\), we will break it down into simpler steps:\n\n### Step 1: Break down the numbers\n- The number 37 can be broken down into 30 and 7.\n- The number 61 can be broken down into 60 and 1.\n\nSo, \\(37 \\times 61 = (30 + 7) \\times (60 + 1)\\)\n\n### Step 2: U...
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[ "To solve the long multiplication of 37 and 61, we'll follow these steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 37 by 1 (the units digit of 61)\n\\[ 37 \\times 1 = 37 \\]\nWrite down 37.\n\n#### Step 2: Multiply 37 by 6 (the tens digit of 61)\n\\[ 37 \\times 6 = 222 \\]\n\nNow add this result to th...
{"all_responses": ["To solve the long multiplication of 37 and 61, we'll follow these steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 37 by 1 (the units digit of 61)\n\\[ 37 \\times 1 = 37 \\]\nWrite down 37.\n\n#### Step 2: Multiply 37 by 6 (the tens digit of 61)\n\\[ 37 \\times 6 = 222 \\]\n\nNow add th...
[ "To solve the long multiplication of 37 and 61, we'll follow these steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 37 by 1 (the units digit of 61)\n\\[ 37 \\times 1 = 37 \\]\nWrite down 37.\n\n#### Step 2: Multiply 37 by 6 (the tens digit of 61)\n\\[ 37 \\times 6 = 222 \\]\n\nNow add this result to th...
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[ false ]
[ "259" ]
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[ [ false ] ]
[ [ "259" ] ]
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[ "2523", "2227", "2287" ]
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[ [ "2523" ], [ "2227" ], [ "2287" ] ]
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[ [ false, true ] ]
[ [ "indeed **2257**", "2257" ] ]
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[ "2597", "2257", "2257", "2597" ]
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[ true, true, true ]
[ "2257", "2257", "2257" ]
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[ [ true ], [ true ], [ false, true ] ]
[ [ "2257" ], [ "2257" ], [ "indeed **2257**", "2257" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 37 x 61 = 259.\", \"answer\": \"259\"}, {\"context\": \"The result from multiplying by 1 is 37.\", \"answer\": \"37\"}, {\"context\": \"The result from multiplying by 6 is 222.\", \"answer\": \"222\"}]}" ]
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[ "\\boxed{259}", "\\boxed{37}", "\\boxed{222}" ]
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[ "259", "37", "222" ]
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[ [ false ], [ false ], [ false ] ]
[ [ "259" ], [ "37" ], [ "222" ] ]
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What is the solution to the long multiplication equation below? 55 x 54 Think step by step.
2970
"{\"arg1\": 55, \"arg2\": 54, \"solution\": 2970}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n55 x 54\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(55 \\times 54\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(55\\) can be written as \\(50 + 5\\).\n - \\(54\\) can be written as \\(50 + 4\\).\n\n2. **Multiply each part of the first number by each part of the second number:**\...
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[ "To solve the long multiplication problem \\(55 \\times 54\\), we can break it down into simpler steps:\n\n1. **Write out the numbers:**\n ```\n 55\n × 54\n ```\n\n2. **Multiply each digit of the bottom number (54) by the top number (55):**\n\n - First, multiply 55 by 4:\n ```\n 55\n × ...
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[ "To solve the long multiplication of 55 and 54, we can break it down into simpler steps:\n\nStep 1: Multiply 55 by 4 (the units digit of 54)\n55 * 4 = 220\n\nStep 2: Multiply 55 by 50 (since 54 has a 5 in the tens place)\n55 * 50 = 2750\n\nStep 3: Add the results from Step 1 and Step 2\n220 + 2750 = 2970\n\nSo, 55 ...
{"continuation_phrases": ["Wait! I can double check this answer.", "But I need to verify this."], "continuations": [" Let's do it again carefully.\n\nStep 1: Multiply 55 by 4\n55 * 4 = 220\n\nStep 2: Multiply 55 by 50\n55 * 50 = 2750\n\nStep 3: Add the results from Step 1 and Step 2\n220 + 2750 = 2970\n\nSo, the correc...
[ "To solve the long multiplication of 55 and 54, we can break it down into simpler steps:\n\nStep 1: Multiply 55 by 4 (the units digit of 54)\n55 * 4 = 220\n\nStep 2: Multiply 55 by 50 (since 54 has a 5 in the tens place)\n55 * 50 = 2750\n\nStep 3: Add the results from Step 1 and Step 2\n220 + 2750 = 2970\n\nSo, 55 ...
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[ "To solve the multiplication problem \\(55 \\times 54\\), we can use the standard algorithm for multiplying numbers. Here's how you can do it step by step:\n\n1. **Write down the numbers:**\n ```\n 55\n × 54\n ```\n\n2. **Multiply 55 by 4 (the units digit of 54):**\n - 55 × 4 = 220\n\n3. **Multiply 55 b...
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[ "To solve the multiplication problem \\(55 \\times 54\\), we can use the standard algorithm for multiplying numbers. Here's how you can do it step by step:\n\n1. **Write down the numbers:**\n ```\n 55\n × 54\n ```\n\n2. **Multiply 55 by 4 (the units digit of 54):**\n - 55 × 4 = 220\n\n3. **Multiply 55 b...
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[ "2970", "3020", "55" ]
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[ [ "2970" ], [ "3020" ], [ "55" ] ]
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[ [ "indeed 2970", "indeed 2970", "2970" ] ]
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[ "2970", "2970", "2970", "2970" ]
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[ [ "2970" ], [ "2970" ], [ "\\(2970\\)", "2970" ], [ "indeed \\(2970\\)", "2970" ] ]
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[ [ true ], [ false, true ], [ false, true ] ]
[ [ "2970" ], [ "indeed 2970", "2970" ], [ "indeed 2970", "2970" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 55 x 54 is\", \"answer\": \"3070\"}]}" ]
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[ "\\boxed{3070}" ]
[ false ]
[ "3070" ]
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[ [ false ] ]
[ [ "3070" ] ]
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What is the solution to the long multiplication equation below? 99 x 63 Think step by step.
6237
"{\"arg1\": 99, \"arg2\": 63, \"solution\": 6237}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n99 x 63\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(99 \\times 63\\), we can break it down into simpler steps:\n\n1. **Break down 63**: We know that 63 can be broken down into 60 + 3.\n So, \\(99 \\times 63 = 99 \\times (60 + 3)\\).\n\n2. **Use the distributive property**:\n This means we need to multiply 99 by 60 and...
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[ "To solve \\( 99 \\times 63 \\) using long multiplication, we follow these steps:\n\n1. **Write down the numbers:**\n ```\n 99\n × 63\n ```\n\n2. **Multiply 99 by 3 (the ones digit of 63):**\n - \\( 99 \\times 3 = 297 \\)\n Write 297 under the line.\n\n3. **Multiply 99 by 60 (the tens digit of 63),...
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[ "To solve the long multiplication problem \\(99 \\times 63\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 63 as a sum of two numbers that are easier to multiply with 99:\n\\[63 = 60 + 3\\]\n\nNow, apply the distributive property:\...
{"continuation_phrases": ["But to confirm,", "But to confirm,"], "continuations": [" let\u2019s add these together directly after calculating them individually:\n\n\\[99 \\times 60 = 99 \\times (6 \\times 10) = (99 \\times 6) \\times 10 = 594 \\times 10 = 5940\\]\n\\[99 \\times 3 = 297\\]\n\nAdding these results:\n\\[5...
[ "To solve the long multiplication problem \\(99 \\times 63\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 63 as a sum of two numbers that are easier to multiply with 99:\n\\[63 = 60 + 3\\]\n\nNow, apply the distributive property:\...
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[ "To solve the long multiplication problem \\( 99 \\times 63 \\), let's break it down into steps:\n\n1. **Break down 63**: We can think of 63 as \\( 60 + 3 \\).\n2. **Multiply each part by 99**:\n - First, multiply 99 by 60: \n \\[\n 99 \\times 60 = 5940\n \\]\n - Next, multiply 99 by 3:\n \\[\n ...
{"all_responses": ["To solve the long multiplication problem \\( 99 \\times 63 \\), let's break it down into steps:\n\n1. **Break down 63**: We can think of 63 as \\( 60 + 3 \\).\n2. **Multiply each part by 99**:\n - First, multiply 99 by 60: \n \\[\n 99 \\times 60 = 5940\n \\]\n - Next, multiply 99 by ...
[ "To solve the long multiplication problem \\( 99 \\times 63 \\), let's break it down into steps:\n\n1. **Break down 63**: We can think of 63 as \\( 60 + 3 \\).\n2. **Multiply each part by 99**:\n - First, multiply 99 by 60: \n \\[\n 99 \\times 60 = 5940\n \\]\n - Next, multiply 99 by 3:\n \\[\n ...
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[ "63813", "6237", "6213" ]
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[ [ "\\( 6237 \\)", "6237" ], [ "indeed \\( 6237 \\)", "6237" ], [ "\\( 6237 \\)", "6237" ], [ "\\( 6237 \\)", "6237" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 99 x 63 is\", \"answer\": \"6237\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{6237}" ]
[ true ]
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What is the solution to the long multiplication equation below? 61 x 88 Think step by step.
5368
"{\"arg1\": 61, \"arg2\": 88, \"solution\": 5368}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n61 x 88\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(61 \\times 88\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 61 and 88 into their place values.\n- \\(61 = 60 + 1\\)\n- \\(88 = 80 + 8\\)\n\n#### Step 2: Multiply each part of 61 by each part of 88.\n\n**First Multip...
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[ "To solve the long multiplication problem \\(61 \\times 88\\), we can break it down into simpler steps:\n\n### Step 1: Multiply 61 by 80 (which is 8 tens)\n- First, multiply 61 by 8:\n \\[\n 61 \\times 8 = 488\n \\]\n- Since this is 8 tens, add a zero at the end:\n \\[\n 488 \\rightarrow 4880\n \\]\n\n### Ste...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(61 \\times 88\\), we can break it down into smaller steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\\[ 61 = 60 + 1 \\]\n\\[ 88 = 80 + 8 \\]\n\nNow, we will multiply each part separately and then add the resu...
{"continuation_phrases": ["Wait, this result is", "Wait! I can double check this answer."], "continuations": [" incorrect because I made an error in my previous explanation. Let me correct that now.\n\nThe correct approach should be:\n\nStep 1: Multiply 61 by 80.\n\\[ 61 \\times 80 = 61 \\times (8 \\times 10) \\]\n\\[ ...
[ "To solve the long multiplication problem \\(61 \\times 88\\), we can break it down into smaller steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\\[ 61 = 60 + 1 \\]\n\\[ 88 = 80 + 8 \\]\n\nNow, we will multiply each part separately and then add the resu...
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[ "Certainly! Let's solve this step-by-step:\n\n### Step 1: Break down the numbers into tens and ones.\n- \\(61\\) can be broken down into \\(60 + 1\\).\n- \\(88\\) can be broken down into \\(80 + 8\\).\n\n### Step 2: Multiply each part of the first number by each part of the second number.\n\n#### First Multiplicati...
{"all_responses": ["Certainly! Let's solve this step-by-step:\n\n### Step 1: Break down the numbers into tens and ones.\n- \\(61\\) can be broken down into \\(60 + 1\\).\n- \\(88\\) can be broken down into \\(80 + 8\\).\n\n### Step 2: Multiply each part of the first number by each part of the second number.\n\n#### Fir...
[ "Certainly! Let's solve this step-by-step:\n\n### Step 1: Break down the numbers into tens and ones.\n- \\(61\\) can be broken down into \\(60 + 1\\).\n- \\(88\\) can be broken down into \\(80 + 8\\).\n\n### Step 2: Multiply each part of the first number by each part of the second number.\n\n#### First Multiplicati...
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[ [ false, true ] ]
[ [ "indeed 5368", "5368" ] ]
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[ [ "5368" ], [ "\\(5368\\)", "5368" ], [ "indeed \\(5368\\)", "5368" ], [ "5368" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer is:\", \"answer\": \"6328\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{6328}" ]
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[ [ false ] ]
[ [ "6328" ] ]
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What is the solution to the long multiplication equation below? 20 x 30 Think step by step.
600
"{\"arg1\": 20, \"arg2\": 30, \"solution\": 600}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n20 x 30\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(20 \\times 30\\), let's break it down into steps:\n\n1. **Write the numbers vertically:**\n ```\n 20\n × 30\n ```\n\n2. **Multiply each digit of the bottom number (30) by the top number (20):**\n\n - Multiply 20 by 0:\n ```\n 20\n × 30\n ---...
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[ "To solve the long multiplication problem \\( 20 \\times 30 \\), let's break it down step by step:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\times & 30 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 20 by 0 (the ones digit of 30):**\n \\[\n 20 \\times 0 = 0\n \\...
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[ "To solve the long multiplication problem \\(20 \\times 30\\), let's break it down into steps:\n\n1. **Write down the numbers:**\n ```\n 20\n × 30\n ```\n\n2. **Multiply each digit of the second number (30) by the first digit of the top number (2):**\n - Multiply 2 by 0: \\(2 \\times 0 = 0\\)\n - Mult...
{"continuation_phrases": ["But to confirm,", "Wait, let me try"], "continuations": [" we can think of this as multiplying 20 by 3.\n\n3. **Place these results under each other aligned by their place values:**\n ```\n 20\n \u00d7 30\n ------\n 00\n 60\n ```\n\n4. **Now, multiply each digit of the secon...
[ "To solve the long multiplication problem \\(20 \\times 30\\), let's break it down into steps:\n\n1. **Write down the numbers:**\n ```\n 20\n × 30\n ```\n\n2. **Multiply each digit of the second number (30) by the first digit of the top number (2):**\n - Multiply 2 by 0: \\(2 \\times 0 = 0\\)\n - Mult...
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[ "To solve the long multiplication problem \\( 20 \\times 30 \\), let's break it down into steps:\n\n1. **Write the numbers**: \n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\hline\n & 30 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the ones place of the bottom number by the top number**:\n - The ones...
{"all_responses": ["To solve the long multiplication problem \\( 20 \\times 30 \\), let's break it down into steps:\n\n1. **Write the numbers**: \n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\hline\n & 30 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the ones place of the bottom number by the top number**:...
[ "To solve the long multiplication problem \\( 20 \\times 30 \\), let's break it down into steps:\n\n1. **Write the numbers**: \n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\hline\n & 30 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the ones place of the bottom number by the top number**:\n - The ones...
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[ "600" ]
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[ [ true ] ]
[ [ "600" ] ]
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[ true, false, false ]
[ "600", "6000", "60" ]
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[ [ true ], [ false ], [ false, false ] ]
[ [ "600" ], [ "6000" ], [ "\\(600\\)", "60" ] ]
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[ [ true ] ]
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[ true, true, true, true ]
[ "600", "600", "600", "600" ]
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[ [ true ], [ true ], [ true ], [ true ] ]
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[ false, true, true ]
[ "0", "600", "600" ]
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[ [ false ], [ true ], [ true ] ]
[ [ "0" ], [ "600" ], [ "600" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 20 x 30 = 600.\", \"answer\": \"600\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{600}" ]
[ true ]
[ "600" ]
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[ [ true ] ]
[ [ "600" ] ]
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What is the solution to the long multiplication equation below? 95 x 59 Think step by step.
5605
"{\"arg1\": 95, \"arg2\": 59, \"solution\": 5605}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n95 x 59\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(95 \\times 59\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 95\n × 59\n ------\n ```\n\n2. **Multiply 95 by 9 (the units digit of 59):**\n - Multiply 95 by 9:\n ```\n 95\n × 9\n ------\n 85...
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[ "To solve the long multiplication of 95 and 59, we'll break it down into steps:\n\n### Step 1: Multiply 5 (from 95) by 9 (from 59)\n- \\(5 \\times 9 = 45\\)\n\n### Step 2: Multiply 50 (the tens digit from 95) by 9 (from 59)\n- \\(50 \\times 9 = 450\\)\n\nNow add these two results together:\n- \\(45 + 450 = 495\\)\n...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(95 \\times 59\\), we will break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n\\[95 \\times 59 = (100 - 5) \\times (60 - 1)\\]\n\nNow, expand this using the distributive property:\n\n\\[= 100 \\times 60 + 100 \\times (-1) + 5 \\times 60 + 5...
{"continuation_phrases": ["But according to", "However,"], "continuations": [" my calculation there was an error in simplification, let me correct it:\n\nLet's redo it correctly:\n\n\\[95 \\times 59 = 95 \\times (60 - 1)\\]\n\\[= 95 \\times 60 - 95 \\times 1\\]\n\\[= 5700 - 95\\]\n\\[= 5605\\]\n\nSo, the final answer i...
[ "To solve the long multiplication problem \\(95 \\times 59\\), we will break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n\\[95 \\times 59 = (100 - 5) \\times (60 - 1)\\]\n\nNow, expand this using the distributive property:\n\n\\[= 100 \\times 60 + 100 \\times (-1) + 5 \\times 60 + 5...
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[ "To solve the long multiplication problem \\( 95 \\times 59 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 95 = 90 + 5 \\)\n - \\( 59 = 50 + 9 \\)\n\n2. **Multiply each part of the first number by each part of the second number separately:**\n\n First, multiply \\( 90 ...
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[ "To solve the long multiplication problem \\( 95 \\times 59 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 95 = 90 + 5 \\)\n - \\( 59 = 50 + 9 \\)\n\n2. **Multiply each part of the first number by each part of the second number separately:**\n\n First, multiply \\( 90 ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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What is the solution to the long multiplication equation below? 43 x 93 Think step by step.
3999
"{\"arg1\": 43, \"arg2\": 93, \"solution\": 3999}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n43 x 93\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(43 \\times 93\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 43\n × 93\n ------\n ```\n\n2. **Multiply 43 by 3 (the units digit of 93):**\n - Multiply 43 by 3:\n ```\n 43\n × 3\n ------\n 129\n...
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[ "To solve the long multiplication problem \\(43 \\times 93\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's rewrite 93 as \\(90 + 3\\). This will help us separate the numbers and make the calculation easier:\n\n\\[43 \\times 93 = 43 \\times...
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[ "To solve the long multiplication of \\(43 \\times 93\\), we will break it down into smaller steps and perform each multiplication separately before adding them together.\n\n### Step-by-Step Solution:\n\n1. **Multiply 43 by 3:**\n - \\(43 \\times 3 = 129\\)\n\n2. **Multiply 43 by 90 (which is 9 times 10):**\n -...
{"continuation_phrases": ["Wait, let me try", "Wait, let me try"], "continuations": [" again!\n\n### Correcting My Mistake:\n\nLet's redo the correct breakdown:\n\n1. **Multiply 43 by 3:**\n - \\(43 \\times 3 = 129\\)\n\n2. **Multiply 43 by 90 (which is 9 times 10):**\n - First, calculate \\(43 \\times 9\\):\n ...
[ "To solve the long multiplication of \\(43 \\times 93\\), we will break it down into smaller steps and perform each multiplication separately before adding them together.\n\n### Step-by-Step Solution:\n\n1. **Multiply 43 by 3:**\n - \\(43 \\times 3 = 129\\)\n\n2. **Multiply 43 by 90 (which is 9 times 10):**\n -...
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[ "To solve the long multiplication problem \\(43 \\times 93\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 93 as the sum of two numbers that are easier to multiply with 43:\n\\[93 = 90 + 3\\]\n\nNow, apply the distributive property...
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[ "To solve the long multiplication problem \\(43 \\times 93\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 93 as the sum of two numbers that are easier to multiply with 43:\n\\[93 = 90 + 3\\]\n\nNow, apply the distributive property...
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What is the solution to the long multiplication equation below? 51 x 51 Think step by step.
2601
"{\"arg1\": 51, \"arg2\": 51, \"solution\": 2601}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n51 x 51\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(51 \\times 51\\), we can break it down into simpler steps:\n\nStep 1: Write down the numbers one under the other:\n```\n 51\n × 51\n```\n\nStep 2: Multiply each digit of the bottom number (51) by each digit of the top number (51). We do this for both digits in 51.\...
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[ "To solve \\( 51 \\times 51 \\) using long multiplication, follow these steps:\n\n### Step-by-Step Solution for \\( 51 \\times 51 \\):\n\n1. **Write down the numbers:**\n ```\n 51\n × 51\n ```\n\n2. **Multiply each digit of the bottom number (51) by each digit of the top number (51):**\n\n - Multipl...
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[ "To solve the long multiplication problem \\(51 \\times 51\\), we can break it down into simpler steps:\n\nStep 1: Multiply the units digit of both numbers.\n- The units digit of 51 is 1.\n- Multiplying 1 (units) by 1 (units): \\(1 \\times 1 = 1\\).\n\nStep 2: Multiply the tens digit of one number by the tens digit...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But to confirm,"], "continuations": [" \n\nLet's recheck and add them up properly:\n\nStep 1: Units digit times units digit = 1 \u00d7 1 = 1\nStep 2: Tens digit of 51 multiplied by tens digit of 51 = 5 \u00d7 5 = 25\nStep 3: Units digit of 51 multiplied ...
[ "To solve the long multiplication problem \\(51 \\times 51\\), we can break it down into simpler steps:\n\nStep 1: Multiply the units digit of both numbers.\n- The units digit of 51 is 1.\n- Multiplying 1 (units) by 1 (units): \\(1 \\times 1 = 1\\).\n\nStep 2: Multiply the tens digit of one number by the tens digit...
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[ "To solve \\( 51 \\times 51 \\), we can break it down into simpler steps using the distributive property of multiplication over addition:\n\nStep 1: Break down 51 into two parts that make it easier to multiply.\n- We know that \\( 51 = 50 + 1 \\).\n\nStep 2: Apply the distributive property.\n\\[ 51 \\times 51 = (50...
{"all_responses": ["To solve \\( 51 \\times 51 \\), we can break it down into simpler steps using the distributive property of multiplication over addition:\n\nStep 1: Break down 51 into two parts that make it easier to multiply.\n- We know that \\( 51 = 50 + 1 \\).\n\nStep 2: Apply the distributive property.\n\\[ 51 \...
[ "To solve \\( 51 \\times 51 \\), we can break it down into simpler steps using the distributive property of multiplication over addition:\n\nStep 1: Break down 51 into two parts that make it easier to multiply.\n- We know that \\( 51 = 50 + 1 \\).\n\nStep 2: Apply the distributive property.\n\\[ 51 \\times 51 = (50...
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[ "255" ]
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[ "2601", "2601", "127500" ]
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[ true, true, true, true ]
[ "2601", "2601", "2601", "2601" ]
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[ [ "2601" ], [ "indeed \\( 2601 \\)", "2601" ], [ "2601" ], [ "2601" ] ]
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[ [ true ], [ true ], [ true ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 51 x 51 = 2601.\", \"answer\": \"2601\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{2601}" ]
[ true ]
[ "2601" ]
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[ [ true ] ]
[ [ "2601" ] ]
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What is the solution to the long multiplication equation below? 57 x 42 Think step by step.
2394
"{\"arg1\": 57, \"arg2\": 42, \"solution\": 2394}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n57 x 42\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(57 \\times 42\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 57\n × 42\n ```\n\n2. **Multiply 57 by 2 (the ones digit of 42):**\n - Multiply 57 by 2:\n ```\n 57\n × 2\n _______\n 114\n ```\...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "To solve the long multiplication problem \\(57 \\times 42\\), we can break it down into smaller steps:\n\n1. **Multiply 57 by 2 (the units digit of 42):**\n - \\(57 \\times 2 = 114\\)\n - Write down 4 and carry over 1.\n\n2. **Multiply 57 by 40 (the tens digit of 42, which is 4 multiplied by 10):**\n - \\(57...
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[ "Certainly! Let's break down the multiplication of 57 and 42 into steps:\n\n1. **Break it down:**\n - First, multiply 50 (the tens place of 57) by 42.\n - Then, multiply 7 (the ones place of 57) by 42.\n\n2. **Calculate each part separately:**\n\n - For 50 x 42:\n \\[\n 50 \\times 42 = 50 \\times (40 ...
{"continuation_phrases": ["Wait, this result is", "Wait, how?"], "continuations": [" incorrect. I made an error in my calculations for the first part. Let me correct that:\n\n - Correct calculation for 50 x 42 should be:\n \\[\n 50 \\times 42 = 50 \\times (40 + 2) = (50 \\times 40) + (50 \\times 2)\n \\]\...
[ "Certainly! Let's break down the multiplication of 57 and 42 into steps:\n\n1. **Break it down:**\n - First, multiply 50 (the tens place of 57) by 42.\n - Then, multiply 7 (the ones place of 57) by 42.\n\n2. **Calculate each part separately:**\n\n - For 50 x 42:\n \\[\n 50 \\times 42 = 50 \\times (40 ...
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[ "Certainly! Let's solve the long multiplication problem \\(57 \\times 42\\) step by step.\n\n### Step 1: Set up the multiplication vertically.\n```\n 57\n × 42\n ------\n```\n\n### Step 2: Multiply 57 by 2 (the ones digit of 42).\n- Multiply 57 by 2:\n ```\n 57\n × 2\n ------\n 114\n ```\n\n### ...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\(57 \\times 42\\) step by step.\n\n### Step 1: Set up the multiplication vertically.\n```\n 57\n \u00d7 42\n ------\n```\n\n### Step 2: Multiply 57 by 2 (the ones digit of 42).\n- Multiply 57 by 2:\n ```\n 57\n \u00d7 2\n -----...
[ "Certainly! Let's solve the long multiplication problem \\(57 \\times 42\\) step by step.\n\n### Step 1: Set up the multiplication vertically.\n```\n 57\n × 42\n ------\n```\n\n### Step 2: Multiply 57 by 2 (the ones digit of 42).\n- Multiply 57 by 2:\n ```\n 57\n × 2\n ------\n 114\n ```\n\n### ...
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[ [ true ] ]
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[ false, true, true ]
[ "2286", "2394", "2394" ]
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[ [ false ], [ true ], [ true ] ]
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[ [ true ] ]
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[ "2436", "2494", "2394", "2394" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 57 x 42 is\", \"answer\": \"2394\"}]}" ]
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[ "\\boxed{2394}" ]
[ true ]
[ "2394" ]
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[ [ true ] ]
[ [ "2394" ] ]
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What is the solution to the long multiplication equation below? 64 x 32 Think step by step.
2048
"{\"arg1\": 64, \"arg2\": 32, \"solution\": 2048}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n64 x 32\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(64 \\times 32\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(64\\) can be broken down into \\(60 + 4\\).\n - \\(32\\) remains as it is.\n\n2. **Multiply each part of the first number by the second number:**\n - Multiply \\(60\...
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[ "To solve the long multiplication problem \\(64 \\times 32\\), let's break it down into steps:\n\n1. **Set up the multiplication:**\n ```\n 64\n × 32\n ------\n ```\n\n2. **Multiply 64 by 2 (the units digit of 32):**\n - \\(64 \\times 2 = 128\\)\n - Write down 8 and carry over 1.\n\n3. **Multipl...
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[ "To solve the long multiplication problem \\( 64 \\times 32 \\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\n### Step-by-Step Solution:\n\n1. **Multiply 60 (from 64) by 32:**\n - \\( 60 \\times 32 = 60 \\times (30 + 2) = 60 \\times 30 + 60 \...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But according to"], "continuations": [" I made an error in my previous calculation.\n \nLet's correct the final addition:\n- Correctly adding the results gives us: \n\\[ 1920 + 128 = 2048 \\]\n\nSo, the correct solution to the long multiplication probl...
[ "To solve the long multiplication problem \\( 64 \\times 32 \\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\n### Step-by-Step Solution:\n\n1. **Multiply 60 (from 64) by 32:**\n - \\( 60 \\times 32 = 60 \\times (30 + 2) = 60 \\times 30 + 60 \...
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[ "To solve the long multiplication problem \\( 64 \\times 32 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 64\n × 32\n ------\n ```\n\n2. **Multiply 64 by 2 (the ones digit of 32):**\n - Multiply 64 by 2:\n \\[\n 64 \\times 2 = 128\n \\]\n - Write down ...
{"all_responses": ["To solve the long multiplication problem \\( 64 \\times 32 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 64\n \u00d7 32\n ------\n ```\n\n2. **Multiply 64 by 2 (the ones digit of 32):**\n - Multiply 64 by 2:\n \\[\n 64 \\times 2 = 128\n \...
[ "To solve the long multiplication problem \\( 64 \\times 32 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 64\n × 32\n ------\n ```\n\n2. **Multiply 64 by 2 (the ones digit of 32):**\n - Multiply 64 by 2:\n \\[\n 64 \\times 2 = 128\n \\]\n - Write down ...
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[ [ true ] ]
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[ "2048", "2048", "2048" ]
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[ [ "896" ], [ "15368" ], [ "15368" ], [ "\\( 2048 \\)", "2048" ] ]
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[ [ true ], [ true ], [ true ] ]
[ [ "2048" ], [ "2048" ], [ "2048" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 64 x 32 is\", \"answer\": \"2048\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
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[ "\\boxed{2048}" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 55 x 76 Think step by step.
4180
"{\"arg1\": 55, \"arg2\": 76, \"solution\": 4180}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n55 x 76\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(55 \\times 76\\), we will break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(55\\) can be broken down into \\(50 + 5\\).\n - \\(76\\) can be broken down into \\(70 + 6\\).\n\n2. **Multiply each part of the first number by each part of the seco...
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[ "To solve the long multiplication of \\(55 \\times 76\\), we can break it down into simpler steps:\n\n1. **Break down 76 into tens and ones:**\n - \\(76 = 70 + 6\\)\n\n2. **Multiply each part of 76 by 55 separately:**\n\n First, multiply 55 by 70:\n \\[\n 55 \\times 70 = 3850\n \\]\n\n Next, multiply 55...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(55 \\times 76\\), follow these steps:\n\n1. **Write down the numbers:**\n ```\n 55\n x 76\n ```\n\n2. **Multiply 55 by 6 (the units digit of 76):**\n - Multiply 55 by 6:\n ```\n 330\n ```\n\n3. **Multiply 55 by 70 (the tens digit of 76, which is...
{"continuation_phrases": ["But according to", "Wait, this result is"], "continuations": [" our original setup, it should be:\n ```\n 330\n + 4350\n ------\n 4350\n ```\n\nSo, the final answer is \\(4350\\).", " incorrect because I made an error in my previous explanation. Let's correct it.\n\n**Correcti...
[ "To solve the long multiplication problem \\(55 \\times 76\\), follow these steps:\n\n1. **Write down the numbers:**\n ```\n 55\n x 76\n ```\n\n2. **Multiply 55 by 6 (the units digit of 76):**\n - Multiply 55 by 6:\n ```\n 330\n ```\n\n3. **Multiply 55 by 70 (the tens digit of 76, which is...
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[ "To solve the long multiplication problem \\(55 \\times 76\\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\nStep 1: Multiply 55 by 6 (the units digit of 76).\n\\[55 \\times 6 = 330\\]\n\nStep 2: Multiply 55 by 70 (the tens digit of 76, which is...
{"all_responses": ["To solve the long multiplication problem \\(55 \\times 76\\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\nStep 1: Multiply 55 by 6 (the units digit of 76).\n\\[55 \\times 6 = 330\\]\n\nStep 2: Multiply 55 by 70 (the tens digit ...
[ "To solve the long multiplication problem \\(55 \\times 76\\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\nStep 1: Multiply 55 by 6 (the units digit of 76).\n\\[55 \\times 6 = 330\\]\n\nStep 2: Multiply 55 by 70 (the tens digit of 76, which is...
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[ [ true ] ]
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[ true, true, false ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 55 x 76 is\", \"answer\": \"4180\"}]}" ]
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What is the solution to the long multiplication equation below? 63 x 19 Think step by step.
1197
"{\"arg1\": 63, \"arg2\": 19, \"solution\": 1197}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n63 x 19\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(63 \\times 19\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 19 into tens and ones.\n\\[ 19 = 10 + 9 \\]\n\n#### Step 2: Multiply 63 by each part of 19 separately.\n\n**First part:**\n\\[ 63 \\times 10 \\]\nThis is s...
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[ "Certainly! Let's solve this problem step by step.\n\n### Step 1: Understand the Problem\nWe need to multiply two numbers:\n- The first number is 63.\n- The second number is 19.\n\n### Step 2: Break Down the Multiplication\nTo make it easier, we can break down the multiplication into smaller parts:\n\n\\[ 63 \\time...
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[ "To solve \\(63 \\times 19\\) using long multiplication, follow these steps:\n\nStep 1: Set up the problem:\n```\n 63\n × 19\n _______\n```\n\nStep 2: Multiply 63 by 9 (the ones digit of 19):\n```\n 567\n × 9\n _______\n```\n(63 × 9 = 567)\n\nStep 3: Multiply 63 by 10 (the tens digit of 19), but remem...
{"continuation_phrases": ["However,", "But to confirm,"], "continuations": [" there seems to be an error in my previous explanation. Let me correct that.\n\nThe correct process for 63 x 19 should be:\n\n- First, multiply 63 by 9 (the ones digit): \\(63 \\times 9 = 567\\)\n- Then, multiply 63 by 10 (the tens digit) but ...
[ "To solve \\(63 \\times 19\\) using long multiplication, follow these steps:\n\nStep 1: Set up the problem:\n```\n 63\n × 19\n _______\n```\n\nStep 2: Multiply 63 by 9 (the ones digit of 19):\n```\n 567\n × 9\n _______\n```\n(63 × 9 = 567)\n\nStep 3: Multiply 63 by 10 (the tens digit of 19), but remem...
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[ "To solve the long multiplication problem \\(63 \\times 19\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's rewrite 19 as \\(20 - 1\\). This allows us to use the distributive property:\n\n\\[63 \\times 19 = 63 \\times (20 - 1)\\]\n\nNow, di...
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[ "To solve the long multiplication problem \\(63 \\times 19\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's rewrite 19 as \\(20 - 1\\). This allows us to use the distributive property:\n\n\\[63 \\times 19 = 63 \\times (20 - 1)\\]\n\nNow, di...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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What is the solution to the long multiplication equation below? 61 x 18 Think step by step.
1098
"{\"arg1\": 61, \"arg2\": 18, \"solution\": 1098}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n61 x 18\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(61 \\times 18\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 18 into tens and ones.\n\\[ 18 = 10 + 8 \\]\n\n#### Step 2: Multiply 61 by each part of 18 separately.\n\n**First part:**\n\\[ 61 \\times 10 \\]\nThis is s...
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[ "To solve the long multiplication problem \\(61 \\times 18\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 61\n × 18\n ```\n\n2. **Multiply 61 by 8 (the rightmost digit of 18):**\n - Multiply 61 by 8:\n ```\n 488\n ```\n - Write down 8 and carry over 4.\n\n3....
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[ "To solve the long multiplication of 61 and 18, we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Multiply 61 by 8 (the units digit of 18):**\n - \\(61 \\times 8 = 488\\)\n \n2. **Multiply 61 by 10 (the tens digit of 18) and then add the result from step 1:**\n - First, multiply 6...
{"continuation_phrases": ["But I need to verify this.", "Wait, this result is"], "continuations": [" Let's do it correctly.\n\n3. **Correctly Multiply 61 by 10 first:**\n - \\(61 \\times 10 = 610\\)\n\n4. **Now, add the result of multiplying 61 by 8:**\n - \\(610 + 488 = 1098\\)\n\nSo, the final answer is \\(1098\\...
[ "To solve the long multiplication of 61 and 18, we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Multiply 61 by 8 (the units digit of 18):**\n - \\(61 \\times 8 = 488\\)\n \n2. **Multiply 61 by 10 (the tens digit of 18) and then add the result from step 1:**\n - First, multiply 6...
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[ "To solve the long multiplication problem \\( 61 \\times 18 \\), we will break it down into simpler steps:\n\n### Step 1: Break down the numbers\nFirst, let's rewrite 61 and 18 in a way that makes it easier to multiply them:\n- \\( 61 = 60 + 1 \\)\n- \\( 18 = 10 + 8 \\)\n\n### Step 2: Multiply each part of one numb...
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[ "To solve the long multiplication problem \\( 61 \\times 18 \\), we will break it down into simpler steps:\n\n### Step 1: Break down the numbers\nFirst, let's rewrite 61 and 18 in a way that makes it easier to multiply them:\n- \\( 61 = 60 + 1 \\)\n- \\( 18 = 10 + 8 \\)\n\n### Step 2: Multiply each part of one numb...
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[ "1098" ]
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[ "1098", "1100", "1108" ]
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[ [ "1098" ], [ "1100" ], [ "**1108**", "1108" ] ]
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[ [ "\\(1098\\)", "indeed \\(1098\\), but given the constraint that 18 is less than 61, the correct interpretation leads to a different understanding of the multiplication process", "61" ] ]
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[ [ "1098" ], [ "\\(1098\\)", "1098" ], [ "indeed \\(1098\\), but given the constraint that 18 is less than 61, the correct interpretation leads to a different understanding of the multiplication process", "61" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"This is straightforward:\", \"answer\": \"610\"}, {\"context\": \"Now let's add these two numbers:\", \"answer\": \"1098\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{610}", "\\boxed{1098}" ]
[ false, true ]
[ "610", "1098" ]
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[ [ "610" ], [ "1098" ] ]
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What is the solution to the long multiplication equation below? 11 x 96 Think step by step.
1056
"{\"arg1\": 11, \"arg2\": 96, \"solution\": 1056}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n11 x 96\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(11 \\times 96\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Write the numbers vertically:**\n ```\n 11\n × 96\n ```\n\n2. **Multiply 11 by 6 (the units digit of 96):**\n - \\(11 \\times 6 = 66\\)\n - Write 66 below the l...
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[ "To solve the long multiplication problem \\(11 \\times 96\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 11\n x 96\n ```\n\n2. **Multiply 11 by each digit of 96 separately:**\n\n - First, multiply 11 by 6 (the units place of 96):\n ...
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[ "To solve \\(11 \\times 96\\), we can break it down into simpler steps:\n\nStep 1: Break down 96 into its place values.\n\\[96 = 90 + 6\\]\n\nStep 2: Multiply 11 by each part of 96 separately.\n\nFirst part:\n\\[11 \\times 90 = 11 \\times (9 \\times 10) = (11 \\times 9) \\times 10 = 99 \\times 10 = 990\\]\n\nSecond...
{"continuation_phrases": ["Wait, how?", "Wait, let me try"], "continuations": [" Let me correct this. \n\nI made an error in my initial breakdown and calculation. The correct way to do this is to use the distributive property of multiplication over addition.\n\nLet's do it correctly now:\n\nStep 1: Break down 96 into i...
[ "To solve \\(11 \\times 96\\), we can break it down into simpler steps:\n\nStep 1: Break down 96 into its place values.\n\\[96 = 90 + 6\\]\n\nStep 2: Multiply 11 by each part of 96 separately.\n\nFirst part:\n\\[11 \\times 90 = 11 \\times (9 \\times 10) = (11 \\times 9) \\times 10 = 99 \\times 10 = 990\\]\n\nSecond...
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[ "To solve the long multiplication problem \\(11 \\times 96\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Multiply 11 by 6 (the units digit of 96):**\n - \\(11 \\times 6 = 66\\)\n \n2. **Multiply 11 by 90 (the tens digit of 96) and remember to shift one place to the left:**\n...
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[ "To solve the long multiplication problem \\(11 \\times 96\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Multiply 11 by 6 (the units digit of 96):**\n - \\(11 \\times 6 = 66\\)\n \n2. **Multiply 11 by 90 (the tens digit of 96) and remember to shift one place to the left:**\n...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 11 x 96 = 1056.\", \"answer\": \"1056\"}, {\"context\": \"Therefore, the final answer is 1056.\", \"answer\": \"1056\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1056}", "\\boxed{1056}" ]
[ true, true ]
[ "1056", "1056" ]
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[ [ true ], [ true ] ]
[ [ "1056" ], [ "1056" ] ]
[ [ { "all_extracted_answers": [ "1056" ], "all_extractions": [ "{'content': '1056', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '1056'}" ], "confidence": 0.9500000000000001, "extracted_answer": "1056", "extractor": "...
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What is the solution to the long multiplication equation below? 48 x 64 Think step by step.
3072
"{\"arg1\": 48, \"arg2\": 64, \"solution\": 3072}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n48 x 64\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(48 \\times 64\\), we can break it down into simpler steps:\n\n1. **Break down 48 and 64:**\n - 48 = 40 + 8\n - 64 = 60 + 4\n\n2. **Multiply each part of 48 by 64 separately:**\n\n First, multiply 40 by 64:\n \\[\n 40 \\times 64 = 40 \\times (60 + 4) = 40 \\time...
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[ "To solve the long multiplication problem \\( 48 \\times 64 \\), we'll break it down into smaller steps:\n\n1. **Multiply 48 by 4:**\n - 48 × 4 = 192\n\n2. **Multiply 48 by 60 (which is 6 × 10):**\n - First, multiply 48 by 6: \n - 48 × 6 = 288\n - Then, multiply 288 by 10:\n - 288 × 10 = 2880\n\n3. **...
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[ "Certainly! Let's solve this long multiplication problem step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n & 48 \\\\\n \\times & 64 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 48 by 4 (the ones digit of 64):**\n \\[\n 48 \\times 4 = 192\n \\]\n Write down 192 an...
{"continuation_phrases": ["However,", "Wait, let me try"], "continuations": [" it seems there was an error in the initial setup or interpretation of the question. The correct answer should be \\(3072\\). Let me correct that:\n\nTo find the correct product:\n- Multiply 48 by 4 (the ones place):\n \\[\n 48 \\times 4 = ...
[ "Certainly! Let's solve this long multiplication problem step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n & 48 \\\\\n \\times & 64 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 48 by 4 (the ones digit of 64):**\n \\[\n 48 \\times 4 = 192\n \\]\n Write down 192 an...
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[ "To solve the long multiplication problem \\( 48 \\times 64 \\), we'll break it down into steps:\n\n### Step-by-Step Solution:\n1. **Multiply 48 by 4 (the units digit of 64):**\n - \\( 48 \\times 4 = 192 \\)\n \n2. **Multiply 48 by 60 (the tens digit of 64, which is 6 * 10):**\n - \\( 48 \\times 60 = 48 \\tim...
{"all_responses": ["To solve the long multiplication problem \\( 48 \\times 64 \\), we'll break it down into steps:\n\n### Step-by-Step Solution:\n1. **Multiply 48 by 4 (the units digit of 64):**\n - \\( 48 \\times 4 = 192 \\)\n \n2. **Multiply 48 by 60 (the tens digit of 64, which is 6 * 10):**\n - \\( 48 \\time...
[ "To solve the long multiplication problem \\( 48 \\times 64 \\), we'll break it down into steps:\n\n### Step-by-Step Solution:\n1. **Multiply 48 by 4 (the units digit of 64):**\n - \\( 48 \\times 4 = 192 \\)\n \n2. **Multiply 48 by 60 (the tens digit of 64, which is 6 * 10):**\n - \\( 48 \\times 60 = 48 \\tim...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the...
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[ "3072" ]
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[ [ true ] ]
[ [ "3072" ] ]
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[ "3072", "2872", "5952" ]
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[ [ "3072" ], [ "2872" ], [ "5952" ] ]
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[ [ false, false, true ] ]
[ [ "297", "\\(3072\\)", "3072" ] ]
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[ true, true, true, true ]
[ "3072", "3072", "3072", "3072" ]
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[ [ "3072" ], [ "indeed \\( 48 \\times 64 = 3072 \\)", "3072" ], [ "indeed:", "3072" ], [ "indeed:", "3072" ] ]
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[ "297", "3072", "3072" ]
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[ [ false ], [ true ], [ false, true ] ]
[ [ "297" ], [ "3072" ], [ "\\(3072\\)", "3072" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 48 x 64 is\", \"answer\": \"3072\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{3072}" ]
[ true ]
[ "3072" ]
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[ [ true ] ]
[ [ "3072" ] ]
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What is the solution to the long multiplication equation below? 95 x 58 Think step by step.
5510
"{\"arg1\": 95, \"arg2\": 58, \"solution\": 5510}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n95 x 58\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
null
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[ "To solve the long multiplication problem \\(95 \\times 58\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 95\n × 58\n ```\n\n2. **Multiply 95 by 8 (the units digit of 58):**\n - Multiply 95 by 8:\n ```\n 760\n + 950\n ------\n 7600\n ``...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "To solve the long multiplication problem \\( 95 \\times 58 \\), we will follow these steps:\n\n1. **Multiply 95 by 8 (the units digit of 58):**\n - \\( 95 \\times 8 = 760 \\)\n\n2. **Multiply 95 by 5 (the tens digit of 58) and add a zero at the end:**\n - First, calculate \\( 95 \\times 5 = 475 \\)\n - Then,...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "Certainly! Let's solve this long multiplication problem step by step.\n\n### Step 1: Set up the multiplication\nWe need to multiply 95 by 58.\n\n```\n 95\nx 58\n------\n```\n\n### Step 2: Multiply 95 by 8 (the units digit of 58)\n```\n 95\nx 8\n------\n 760\n```\nSo far, we have:\n```\n 95\nx 58\n----...
{"continuation_phrases": ["Wait, this result is", "Wait, let me try"], "continuations": [" incorrect because we made an error in setting it up. Let's correct that and continue from the rightmost digit.\n\n### Step 3: Correct setup:\nSince 58 has two digits, we'll set up our multiplication as follows:\n\n```\n 95\nx ...
[ "Certainly! Let's solve this long multiplication problem step by step.\n\n### Step 1: Set up the multiplication\nWe need to multiply 95 by 58.\n\n```\n 95\nx 58\n------\n```\n\n### Step 2: Multiply 95 by 8 (the units digit of 58)\n```\n 95\nx 8\n------\n 760\n```\nSo far, we have:\n```\n 95\nx 58\n----...
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[ "Certainly! Let's solve the long multiplication problem \\( 95 \\times 58 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 95\n × 58\n ```\n\n2. **Multiply 95 by 8 (the ones digit of 58):**\n - Multiply 95 by 8:\n ```\n 95\n × 8\n ------\n ...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\( 95 \\times 58 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 95\n \u00d7 58\n ```\n\n2. **Multiply 95 by 8 (the ones digit of 58):**\n - Multiply 95 by 8:\n ```\n 95\n \u00...
[ "Certainly! Let's solve the long multiplication problem \\( 95 \\times 58 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 95\n × 58\n ```\n\n2. **Multiply 95 by 8 (the ones digit of 58):**\n - Multiply 95 by 8:\n ```\n 95\n × 8\n ------\n ...
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[ "12350" ]
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[ [ false ] ]
[ [ "12350" ] ]
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[ true, false, false ]
[ "5510", "1311", "95" ]
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[ [ true ], [ false ], [ false ] ]
[ [ "5510" ], [ "1311" ], [ "95" ] ]
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[ [ "\\( 95 \\times 58 = 5410 \\)", "\\( 95 \\times 58 = 5410 \\)", "5410" ] ]
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[ [ "6085" ], [ "\\( 95 \\times 58 = 5410 \\)", "5410" ], [ "\\( 95 \\times 58 = 5410 \\)", "5410" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 95 x 8 = 7600.\", \"answer\": \"7600\"}, {\"context\": \"Since this is multiplied by 5 (which is in the tens place), we shift it one place to the left: 4750\", \"answer\": \"4750\"}, {\"context\": \"So, 95 x 58 = 12350.\", \"answer\": \"12350\"}]}" ]
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[ [ "7600" ], [ "4750" ], [ "12350" ] ]
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What is the solution to the long multiplication equation below? 94 x 25 Think step by step.
2350
"{\"arg1\": 94, \"arg2\": 25, \"solution\": 2350}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n94 x 25\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(94 \\times 25\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(94\\) can be broken down into \\(90 + 4\\).\n - \\(25\\) remains as it is.\n\n2. **Multiply each part of the first number by the second number:**\n - Multiply \\(90\...
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[ "To solve the long multiplication problem \\( 94 \\times 25 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 25 as \\( 10 + 15 \\). This gives us:\n\\[ 94 \\times 25 = 94 \\times (10 + 15) \\]\n\nNow, distribute 94 across both term...
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[ "To solve the long multiplication problem \\(94 \\times 25\\), we can break it down into simpler steps:\n\n1. **Multiply 94 by 5 (the units digit of 25):**\n - \\(94 \\times 5 = 470\\)\n\n2. **Multiply 94 by 20 (which is the same as multiplying by 2 and then adding another zero at the end):**\n - First, calcula...
{"continuation_phrases": ["However,", "Wait, this result is"], "continuations": [" since we multiplied by 20, which adds two zeros, we need to adjust for that:\n - Instead of 2350, we actually have \\(470 \\times 20 = 9400\\)\n\nSo, the final answer is \\(9400\\).", " not correct based on our breakdown. Let's re-ev...
[ "To solve the long multiplication problem \\(94 \\times 25\\), we can break it down into simpler steps:\n\n1. **Multiply 94 by 5 (the units digit of 25):**\n - \\(94 \\times 5 = 470\\)\n\n2. **Multiply 94 by 20 (which is the same as multiplying by 2 and then adding another zero at the end):**\n - First, calcula...
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[ "To solve the long multiplication problem \\(94 \\times 25\\), we can break it down into simpler steps:\n\n1. **Multiply 94 by 5 (the units digit of 25):**\n - \\(94 \\times 5 = 470\\)\n\n2. **Multiply 94 by 20 (which is 2 times 10, so we need to add two zeros at the end of the product from the previous step):**\...
{"all_responses": ["To solve the long multiplication problem \\(94 \\times 25\\), we can break it down into simpler steps:\n\n1. **Multiply 94 by 5 (the units digit of 25):**\n - \\(94 \\times 5 = 470\\)\n\n2. **Multiply 94 by 20 (which is 2 times 10, so we need to add two zeros at the end of the product from the pre...
[ "To solve the long multiplication problem \\(94 \\times 25\\), we can break it down into simpler steps:\n\n1. **Multiply 94 by 5 (the units digit of 25):**\n - \\(94 \\times 5 = 470\\)\n\n2. **Multiply 94 by 20 (which is 2 times 10, so we need to add two zeros at the end of the product from the previous step):**\...
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[ [ true ], [ false, true ], [ true ] ]
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[ [ false, false, false, true ] ]
[ [ "\\(9400\\)", "indeed \\(2350\\)", "\\(2350\\)", "2350" ] ]
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[ false, false, false, true ]
[ "19270", "19270", "19270", "2350" ]
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[ [ true ], [ false, false ], [ false, false, true ] ]
[ [ "2350" ], [ "\\(9400\\)", "9400" ], [ "indeed \\(2350\\)", "\\(2350\\)", "2350" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 94 x 25 is\", \"answer\": \"1900\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1900}" ]
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[ "1900" ]
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[ [ false ] ]
[ [ "1900" ] ]
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What is the solution to the long multiplication equation below? 40 x 61 Think step by step.
2440
"{\"arg1\": 40, \"arg2\": 61, \"solution\": 2440}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n40 x 61\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(40 \\times 61\\), we can break it down into simpler steps:\n\nStep 1: Multiply 40 by 1 (the units digit of 61).\n\\[40 \\times 1 = 40\\]\n\nStep 2: Multiply 40 by 6 (the tens digit of 61).\n\\[40 \\times 6 = 240\\]\nSince this result has two digits, we need to carry over...
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[ "To solve the long multiplication problem \\(40 \\times 61\\), let's break it down into steps:\n\nStep 1: Write down the numbers vertically.\n```\n 40\nx 61\n```\n\nStep 2: Multiply 40 by 1 (the ones digit of 61).\n```\n 40\nx 61\n-----\n 400 (because 40 x 1 = 40)\n```\n\nStep 3: Multiply 40 by 6 (the ...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(40 \\times 61\\), we can break it down into simpler steps:\n\nStep 1: Multiply 40 by 1 (the ones digit of 61).\n - \\(40 \\times 1 = 40\\)\n\nStep 2: Multiply 40 by 6 (the tens digit of 61).\n - First, multiply 40 by 6:\n - \\(40 \\times 6 = 240\\) (write down 40...
{"continuation_phrases": ["Wait, this result is", "But I need to verify this."], "continuations": [" too large for one place value, so we need to adjust our approach.\n - Instead, let's think about multiplying 40 by 6 as if there were no decimal point involved initially. We'll then divide the product by 10 at the e...
[ "To solve the long multiplication problem \\(40 \\times 61\\), we can break it down into simpler steps:\n\nStep 1: Multiply 40 by 1 (the ones digit of 61).\n - \\(40 \\times 1 = 40\\)\n\nStep 2: Multiply 40 by 6 (the tens digit of 61).\n - First, multiply 40 by 6:\n - \\(40 \\times 6 = 240\\) (write down 40...
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[ "Certainly! Let's break down the multiplication of 40 and 61 step by step.\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nWe can think of 40 as \\( 4 \\times 10 \\) and 61 as \\( 60 + 1 \\).\n\n#### Step 2: Multiply 40 by each digit in 61\n- First, multiply 40 by 1 (the units place of 61):\n ...
{"all_responses": ["Certainly! Let's break down the multiplication of 40 and 61 step by step.\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nWe can think of 40 as \\( 4 \\times 10 \\) and 61 as \\( 60 + 1 \\).\n\n#### Step 2: Multiply 40 by each digit in 61\n- First, multiply 40 by 1 (the units p...
[ "Certainly! Let's break down the multiplication of 40 and 61 step by step.\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nWe can think of 40 as \\( 4 \\times 10 \\) and 61 as \\( 60 + 1 \\).\n\n#### Step 2: Multiply 40 by each digit in 61\n- First, multiply 40 by 1 (the units place of 61):\n ...
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[ [ "indeed 2440", "2440" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 40 x 61 is\", \"answer\": \"280\"}]}" ]
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[ "\\boxed{280}" ]
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[ "280" ]
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What is the solution to the long multiplication equation below? 55 x 57 Think step by step.
3135
"{\"arg1\": 55, \"arg2\": 57, \"solution\": 3135}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n55 x 57\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(55 \\times 57\\), we can break it down into simpler steps:\n\n1. **Multiply 55 by 7:**\n - \\(55 \\times 7 = 385\\)\n\n2. **Multiply 55 by 50 (which is the same as multiplying by 5 and then adding a zero at the end):**\n - \\(55 \\times 50 = 2750\\) (because \\(55 \\...
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[ "To solve the long multiplication problem \\(55 \\times 57\\), we can break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n```\n 55\n × 57\n ----\n```\n\nWe can think of this as:\n- Multiplying 55 by 7 (the rightmost digit of 57)\n- Then multiplying 55 by 50 (the leftmost digit of...
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[ "To solve \\(55 \\times 57\\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication**: Write 55 and 57 one under each other.\n\n```\n 55\n × 57\n ----\n```\n\n2. **Multiply 55 by 7 (the units digit of 57)**:\n - Multiply 55 by 7: \n ```\n 385\n ```\n - Write this do...
{"continuation_phrases": ["But according to", "But according to"], "continuations": [" the problem statement, there was no need for shifting since both numbers had more than one digit.\n\nSo the final answer is \\(27885\\).", " the original question's context, it seems there might have been a misunderstanding as the co...
[ "To solve \\(55 \\times 57\\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication**: Write 55 and 57 one under each other.\n\n```\n 55\n × 57\n ----\n```\n\n2. **Multiply 55 by 7 (the units digit of 57)**:\n - Multiply 55 by 7: \n ```\n 385\n ```\n - Write this do...
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[ "To solve the long multiplication problem \\(55 \\times 57\\), we can break it down into smaller steps:\n\n### Step 1: Break down 55 and 57 into tens and ones.\n- \\(55 = 50 + 5\\)\n- \\(57 = 50 + 7\\)\n\n### Step 2: Multiply each part of 55 by each part of 57.\n\n#### Multiplying 50 by 57:\n\\[ 50 \\times 57 \\]\n...
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[ "To solve the long multiplication problem \\(55 \\times 57\\), we can break it down into smaller steps:\n\n### Step 1: Break down 55 and 57 into tens and ones.\n- \\(55 = 50 + 5\\)\n- \\(57 = 50 + 7\\)\n\n### Step 2: Multiply each part of 55 by each part of 57.\n\n#### Multiplying 50 by 57:\n\\[ 50 \\times 57 \\]\n...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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[ "\\boxed{3135}", "\\boxed{385}", "\\boxed{2750}", "\\boxed{3135}" ]
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What is the solution to the long multiplication equation below? 81 x 71 Think step by step.
5751
"{\"arg1\": 81, \"arg2\": 71, \"solution\": 5751}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n81 x 71\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(81 \\times 71\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nFirst, let's rewrite 81 and 71 as:\n\\[ 80 + 1 \\]\nand\n\\[ 70 + 1 \\]\n\nSo,\n\\[ 81 = 80 + 1 \\]\n\\[ 71 = 70 + 1 \\]\n\n#### Step 2: Multi...
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[ "To solve the long multiplication problem \\(81 \\times 71\\), we will break it down into steps and multiply each digit of one number by each digit of the other number.\n\nLet's start with the first step:\n\n### Step 1: Multiply 80 (from 81) by 71\n\\[ 80 \\times 71 = 5680 \\]\n\nNow let's move on to the second ste...
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[ "To solve the long multiplication of 81 and 71, follow these steps:\n\n```\n 81\n × 71\n ------\n 81 (81×1)\n+ 5690 (81×70, shift one place to the left)\n------\n 5721\n```\n\nSo, 81 x 71 = 5721. Wait! I can double check this answer. Let's do it again properly.\n\nLet's break down 81 into its tens and...
{"continuation_phrases": ["Wait! I can double check this answer.", "Wait, let me try"], "continuations": [" Let's do it again properly.\n\nLet's break down 81 into its tens and ones:\n- 81 = 80 + 1\n- 71 = 70 + 1\n\nNow we multiply each part separately and then add them together:\n\n1. Multiply 80 by 70:\n 80 \u00d7 ...
[ "To solve the long multiplication of 81 and 71, follow these steps:\n\n```\n 81\n × 71\n ------\n 81 (81×1)\n+ 5690 (81×70, shift one place to the left)\n------\n 5721\n```\n\nSo, 81 x 71 = 5721.", " Let's do it again properly.\n\nLet's break down 81 into its tens and ones:\n- 81 = 80 + 1\n- 71 = 70 ...
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[ "To solve the long multiplication of 81 and 71, we will follow these steps:\n\n1. **Multiply the ones digit of each number:**\n - The ones digit of 81 is 1.\n - The ones digit of 71 is 1.\n - Multiply 1 (from 81) by 1 (from 71): \n \\[\n 1 \\times 1 = 1\n \\]\n So, the rightmost digit of our ans...
{"all_responses": ["To solve the long multiplication of 81 and 71, we will follow these steps:\n\n1. **Multiply the ones digit of each number:**\n - The ones digit of 81 is 1.\n - The ones digit of 71 is 1.\n - Multiply 1 (from 81) by 1 (from 71): \n \\[\n 1 \\times 1 = 1\n \\]\n So, the rightmost d...
[ "To solve the long multiplication of 81 and 71, we will follow these steps:\n\n1. **Multiply the ones digit of each number:**\n - The ones digit of 81 is 1.\n - The ones digit of 71 is 1.\n - Multiply 1 (from 81) by 1 (from 71): \n \\[\n 1 \\times 1 = 1\n \\]\n So, the rightmost digit of our ans...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Therefore, the final answer to 81 x 71 is:\", \"answer\": \"10650\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{10650}" ]
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[ "10650" ]
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What is the solution to the long multiplication equation below? 94 x 65 Think step by step.
6110
"{\"arg1\": 94, \"arg2\": 65, \"solution\": 6110}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n94 x 65\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(94 \\times 65\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 94\n × 65\n ------\n ```\n\n2. **Multiply 94 by 5 (the units digit of 65):**\n - Multiply 94 by 5:\n ```\n 94\n × 5\n ------\n 470...
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[ "To solve the long multiplication of 94 and 65, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 94\n × 65\n ```\n\n2. **Multiply 94 by 5 (the ones digit of 65):**\n - \\( 94 \\times 5 = 470 \\)\n Write down 470 under the line.\n\n3. **Multiply 94 by 60 (the tens digit of 65), whic...
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[ "Certainly! Let's break down the multiplication of 94 and 65 into steps.\n\n### Step-by-Step Solution:\n\n1. **Break it Down:**\n - First, let's break each number into tens and ones:\n - \\(94\\) can be written as \\(90 + 4\\)\n - \\(65\\) can be written as \\(60 + 5\\)\n\n2. **Multiply Each Part:**\n -...
{"continuation_phrases": ["But to confirm,", "Wait, this result is"], "continuations": [" we should also add the carry from multiplying \\(90\\) by \\(5\\) (which was \\(450\\)):\n \\[\n 5400 + 450 = 5850\n \\]\n Then add \\(240\\):\n \\[\n 5850 + 240 = 6090\n \\]\n Finally, add \\(20\\)...
[ "Certainly! Let's break down the multiplication of 94 and 65 into steps.\n\n### Step-by-Step Solution:\n\n1. **Break it Down:**\n - First, let's break each number into tens and ones:\n - \\(94\\) can be written as \\(90 + 4\\)\n - \\(65\\) can be written as \\(60 + 5\\)\n\n2. **Multiply Each Part:**\n -...
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[ "To solve the long multiplication of \\(94 \\times 65\\), let's break it down into steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 94\n × 65\n ```\n\n2. **Multiply 94 by 5 (the units digit of 65):**\n - \\(94 \\times 5 = 470\\)\n - Write 470 under the first row.\n\n3....
{"all_responses": ["To solve the long multiplication of \\(94 \\times 65\\), let's break it down into steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 94\n \u00d7 65\n ```\n\n2. **Multiply 94 by 5 (the units digit of 65):**\n - \\(94 \\times 5 = 470\\)\n - Write 470 under ...
[ "To solve the long multiplication of \\(94 \\times 65\\), let's break it down into steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 94\n × 65\n ```\n\n2. **Multiply 94 by 5 (the units digit of 65):**\n - \\(94 \\times 5 = 470\\)\n - Write 470 under the first row.\n\n3....
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[ [ false, false, true ] ]
[ [ ":", "indeed:", "6110" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 94 x 65 is\", \"answer\": \"56870\"}]}" ]
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What is the solution to the long multiplication equation below? 14 x 17 Think step by step.
238
"{\"arg1\": 14, \"arg2\": 17, \"solution\": 238}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n14 x 17\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(14 \\times 17\\), we can break it down into simpler steps:\n\nStep 1: Multiply 14 by 7 (the units digit of 17).\n\\[ 14 \\times 7 = 98 \\]\n\nStep 2: Multiply 14 by 10 (since 17 has one more digit than 14, and we need to account for this in our final result).\n\\[ 14 \\t...
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[ "To solve the long multiplication of 14 and 17, let's break it down into steps:\n\n### Step 1: Multiply the ones digit of 14 (which is 4) by each digit in 17.\n- \\(4 \\times 7 = 28\\)\n- Write down 8 and carry over 2.\n\n### Step 2: Multiply the tens digit of 14 (which is 1) by each digit in 17.\n- \\(1 \\times 7 ...
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[ "To solve the long multiplication of 14 and 17, follow these steps:\n\n1. **Write down the numbers:**\n ```\n 14\n × 17\n ```\n\n2. **Multiply 14 by 7 (the ones digit of 17):**\n - \\( 14 \\times 7 = 98 \\)\n Write 8 in the ones place and carry over 9.\n\n3. **Multiply 14 by 10 (the tens digit of 17),...
{"continuation_phrases": ["Wait, let me try", "Wait, this result is"], "continuations": [" again:\n - Correctly add 9 to 140:\n - \\( 140 + 9 = 149 \\) But I made an error here. Let's correct it.\n - Actually, we should have added 9 to 140 correctly as follows:\n - \\( 140 + 9 = 149 \\) but this...
[ "To solve the long multiplication of 14 and 17, follow these steps:\n\n1. **Write down the numbers:**\n ```\n 14\n × 17\n ```\n\n2. **Multiply 14 by 7 (the ones digit of 17):**\n - \\( 14 \\times 7 = 98 \\)\n Write 8 in the ones place and carry over 9.\n\n3. **Multiply 14 by 10 (the tens digit of 17),...
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[ "To solve the multiplication problem \\( 14 \\times 17 \\), we can use the standard algorithm for multiplying numbers.\n\nStep 1: Multiply 14 by 7 (the ones digit of 17).\n\\[ 14 \\times 7 = 98 \\]\nWrite down 98.\n\nStep 2: Multiply 14 by 10 (the tens digit of 17, which is just 1 in this case because it's not writ...
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[ "To solve the multiplication problem \\( 14 \\times 17 \\), we can use the standard algorithm for multiplying numbers.\n\nStep 1: Multiply 14 by 7 (the ones digit of 17).\n\\[ 14 \\times 7 = 98 \\]\nWrite down 98.\n\nStep 2: Multiply 14 by 10 (the tens digit of 17, which is just 1 in this case because it's not writ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 14 x 17 is\", \"answer\": \"238\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{238}" ]
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What is the solution to the long multiplication equation below? 92 x 92 Think step by step.
8464
"{\"arg1\": 92, \"arg2\": 92, \"solution\": 8464}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n92 x 92\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(92 \\times 92\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(92\\) can be written as \\(90 + 2\\).\n - So, \\(92 \\times 92 = (90 + 2) \\times (90 + 2)\\).\n\n2. **Use the distributive property of multiplication over addition:**...
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[ "To solve \\( 92 \\times 92 \\), we can break it down into simpler steps:\n\n1. **Break down 92**: \n - 92 can be written as \\( (100 - 8) \\).\n\n2. **Use the distributive property**:\n - Multiply 92 by each part of the breakdown separately and then add them together.\n \n3. **Calculate**:\n - First, calcu...
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[ "To solve \\( 92 \\times 92 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express \\( 92 \\times 92 \\) as:\n\\[ (100 - 8)(100 - 8) \\]\n\nNow, expand this expression:\n\\[ (100 - 8)^2 = 100^2 - 2 \\cdot 100 \\cdot 8 + 8^2 \\]\n\nCalcul...
{"continuation_phrases": ["But according to", "Wait, let me try"], "continuations": [" our original problem, there was an error in simplifying further because we should not simplify until after all multiplications are done correctly for verification purposes.\n\nSo the correct calculation is:\n\\[ (100 - 8)^2 = 100^2 -...
[ "To solve \\( 92 \\times 92 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express \\( 92 \\times 92 \\) as:\n\\[ (100 - 8)(100 - 8) \\]\n\nNow, expand this expression:\n\\[ (100 - 8)^2 = 100^2 - 2 \\cdot 100 \\cdot 8 + 8^2 \\]\n\nCalcul...
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[ "To solve \\( 92 \\times 92 \\), we can break it down into simpler steps:\n\nStep 1: Break down 92 into its tens and units digits.\n- 92 = 90 + 2\n\nStep 2: Multiply each part of 92 by itself (i.e., 90 * 90 and 2 * 2).\n- 90 * 90 = 8100\n- 2 * 2 = 4\n\nStep 3: Add these two products together.\n- 8100 + 4 = 8104\n\n...
{"all_responses": ["To solve \\( 92 \\times 92 \\), we can break it down into simpler steps:\n\nStep 1: Break down 92 into its tens and units digits.\n- 92 = 90 + 2\n\nStep 2: Multiply each part of 92 by itself (i.e., 90 * 90 and 2 * 2).\n- 90 * 90 = 8100\n- 2 * 2 = 4\n\nStep 3: Add these two products together.\n- 8100...
[ "To solve \\( 92 \\times 92 \\), we can break it down into simpler steps:\n\nStep 1: Break down 92 into its tens and units digits.\n- 92 = 90 + 2\n\nStep 2: Multiply each part of 92 by itself (i.e., 90 * 90 and 2 * 2).\n- 90 * 90 = 8100\n- 2 * 2 = 4\n\nStep 3: Add these two products together.\n- 8100 + 4 = 8104\n\n...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 92 x 92 is\", \"answer\": \"8464\"}]}" ]
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What is the solution to the long multiplication equation below? 60 x 81 Think step by step.
4860
"{\"arg1\": 60, \"arg2\": 81, \"solution\": 4860}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n60 x 81\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(60 \\times 81\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 60 and 81 into their place values.\n- \\(60\\) can be broken down as \\(6 \\times 10\\).\n- \\(81\\) can be broken down as \\(8 \\times 10 + 1 \\times 1\\)...
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[ "To solve \\(60 \\times 81\\), you can break it down into simpler steps using the distributive property of multiplication over addition:\n\n\\[60 \\times 81 = 60 \\times (80 + 1)\\]\n\nNow distribute the 60:\n\n\\[= 60 \\times 80 + 60 \\times 1\\]\n\nCalculate each part separately:\n\n\\[60 \\times 80 = 4800\\]\n\\...
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[ "To solve the long multiplication problem \\(60 \\times 81\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication\n```\n 60\n × 81\n ------\n```\n\n### Step 2: Multiply 60 by 1 (the units digit of 81)\n```\n 60\n × 81\n ------\n 600 (because 60 * 1 = 60)\n```\n\n### Step 3:...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But to confirm,"], "continuations": [" Let's do it again carefully.\n\n#### Corrected Calculation:\n1. **First Multiplication**:\n - Multiply 60 by 1: \n ```\n 60\n \u00d7 1\n ------\n 60\n ```\n\n2. **Second Multiplication**:\n -...
[ "To solve the long multiplication problem \\(60 \\times 81\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication\n```\n 60\n × 81\n ------\n```\n\n### Step 2: Multiply 60 by 1 (the units digit of 81)\n```\n 60\n × 81\n ------\n 600 (because 60 * 1 = 60)\n```\n\n### Step 3:...
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[ "To solve the long multiplication problem \\(60 \\times 81\\), we can break it down into simpler steps:\n\nStep 1: Break down 60 into 6 and 0.\n So, \\(60 \\times 81 = (6 \\times 81) + (0 \\times 81)\\)\n\nStep 2: Calculate \\(6 \\times 81\\).\n - First, multiply 6 by 1:\n \\[\n 6 \\times 1 = 6\n \\...
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[ "To solve the long multiplication problem \\(60 \\times 81\\), we can break it down into simpler steps:\n\nStep 1: Break down 60 into 6 and 0.\n So, \\(60 \\times 81 = (6 \\times 81) + (0 \\times 81)\\)\n\nStep 2: Calculate \\(6 \\times 81\\).\n - First, multiply 6 by 1:\n \\[\n 6 \\times 1 = 6\n \\...
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[ [ false, false, true ] ]
[ [ "\\(4860\\)", "indeed **4860**", "4860" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Therefore, the solution to 60 x 81 is\", \"answer\": \"4848\"}]}" ]
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[ "\\boxed{4848}" ]
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What is the solution to the long multiplication equation below? 62 x 93 Think step by step.
5766
"{\"arg1\": 62, \"arg2\": 93, \"solution\": 5766}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n62 x 93\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(62 \\times 93\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n × 93\n ------\n ```\n\n2. **Multiply 62 by 3 (the ones digit of 93):**\n - \\(62 \\times 3 = 186\\)\n - Write down 6 and carry over 18.\n\n```\n 62\n ...
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[ "To solve the long multiplication problem \\( 62 \\times 93 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n × 93\n ------\n ```\n\n2. **Multiply 62 by 3 (the units digit of 93):**\n ```\n 62\n × 93\n ------\n 186 (62 × 3)\n ------\n 5580...
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[ "Certainly! Let's solve this step by step.\n\n### Step 1: Set up the problem\nWe need to multiply \\( 62 \\) by \\( 93 \\).\n\n```\n 62\n× 93\n------\n```\n\n### Step 2: Multiply 62 by 3 (the ones digit of 93)\n- \\( 62 \\times 3 = 186 \\)\n- Write down 6 and carry over 1.\n\n```\n 62\n× 93\n------\n 6\n186\...
{"continuation_phrases": ["Wait! I can double check this answer.", "Hold on, let me verify this answer."], "continuations": [" Let's go back to Step 1.\n```\n\n### Step 4: Double-check using another method or verify manually if needed\nLet's do it again:\n\n```\n 62\n\u00d7 93\n------\n 186 (from 62 \u00d7 3)\n+55...
[ "Certainly! Let's solve this step by step.\n\n### Step 1: Set up the problem\nWe need to multiply \\( 62 \\) by \\( 93 \\).\n\n```\n 62\n× 93\n------\n```\n\n### Step 2: Multiply 62 by 3 (the ones digit of 93)\n- \\( 62 \\times 3 = 186 \\)\n- Write down 6 and carry over 1.\n\n```\n 62\n× 93\n------\n 6\n186\...
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[ "To solve the long multiplication problem \\( 62 \\times 93 \\), we can break it down into simpler steps.\n\n### Step-by-Step Solution:\n\n1. **Multiply 62 by 3:**\n - \\( 62 \\times 3 = 186 \\)\n\n2. **Multiply 62 by 90 (which is 9 times 10):**\n - \\( 62 \\times 90 = 5580 \\) (because \\( 62 \\times 9 = 558 \...
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[ "To solve the long multiplication problem \\( 62 \\times 93 \\), we can break it down into simpler steps.\n\n### Step-by-Step Solution:\n\n1. **Multiply 62 by 3:**\n - \\( 62 \\times 3 = 186 \\)\n\n2. **Multiply 62 by 90 (which is 9 times 10):**\n - \\( 62 \\times 90 = 5580 \\) (because \\( 62 \\times 9 = 558 \...
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What is the solution to the long multiplication equation below? 29 x 10 Think step by step.
290
"{\"arg1\": 29, \"arg2\": 10, \"solution\": 290}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n29 x 10\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(29 \\times 10\\), let's break it down into steps:\n\nStep 1: Understand that multiplying any number by 10 simply means adding a zero at the end of that number.\n\nStep 2: Take the number 29 and add a zero after it.\n - So, 29 becomes 290 when we add a zero at the end.\...
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[ "To solve the long multiplication problem \\(29 \\times 10\\), let's break it down step by step:\n\nStep 1: Understand what the question is asking.\nWe need to multiply 29 by 10.\n\nStep 2: Recognize that multiplying any number by 10 simply adds a zero at the end of that number.\nSo, when we multiply 29 by 10, we'r...
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[ "To solve the long multiplication problem \\(29 \\times 10\\), let's break it down into steps:\n\n### Step 1: Understand the Problem\nWe need to multiply 29 by 10.\n\n### Step 2: Break Down the Multiplication\n- When you multiply any number by 10, you simply add a zero at the end of that number.\n- For example, \\(...
{"continuation_phrases": ["However,", "Wait, how?"], "continuations": [" this isn't correct because we made a mistake in our reasoning. Let's correct it.\n\n### Correct Approach\nWhen multiplying any two-digit number (like 29) by 10, you don't actually \"add\" anything; rather, you shift the digits one place to the lef...
[ "To solve the long multiplication problem \\(29 \\times 10\\), let's break it down into steps:\n\n### Step 1: Understand the Problem\nWe need to multiply 29 by 10.\n\n### Step 2: Break Down the Multiplication\n- When you multiply any number by 10, you simply add a zero at the end of that number.\n- For example, \\(...
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[ "To solve the long multiplication problem \\(29 \\times 10\\), let's break it down into steps:\n\n1. **Understand the Problem:**\n - We need to multiply 29 by 10.\n\n2. **Break Down the Multiplication:**\n - When you multiply any number by 10, you simply add a zero at the end of that number.\n - For example, ...
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[ "To solve the long multiplication problem \\(29 \\times 10\\), let's break it down into steps:\n\n1. **Understand the Problem:**\n - We need to multiply 29 by 10.\n\n2. **Break Down the Multiplication:**\n - When you multiply any number by 10, you simply add a zero at the end of that number.\n - For example, ...
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[ "\\boxed{290}" ]
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[ [ true ] ]
[ [ "290" ] ]
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What is the solution to the long multiplication equation below? 48 x 85 Think step by step.
4080
"{\"arg1\": 48, \"arg2\": 85, \"solution\": 4080}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n48 x 85\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(48 \\times 85\\), we will follow these steps:\n\n1. **Multiply 48 by 5 (the units digit of 85):**\n - \\(48 \\times 5 = 240\\)\n - Write down 240.\n\n2. **Multiply 48 by 8 (the tens digit of 85) and add the result from step 1:**\n - First, multiply 48 by 8:\n \...
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[ "To solve the long multiplication problem \\( 48 \\times 85 \\), we can break it down into simpler steps:\n\n1. **Break down 85 into tens and ones:**\n - \\( 85 = 80 + 5 \\)\n\n2. **Multiply 48 by each part of 85 separately:**\n\n - First, multiply 48 by 80:\n \\[\n 48 \\times 80 = 48 \\times (8 \\times...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
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[ "To solve the long multiplication problem \\(48 \\times 85\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down 85 into its tens and ones place values.\n\\[ 85 = 80 + 5 \\]\n\nStep 2: Multiply each part of 85 by 48 separately.\n\\[ 48 \\t...
{"continuation_phrases": ["However,", "But to confirm,"], "continuations": [" there was an error in my initial breakdown. Let's correct this:\n\nStep 4: Correctly add the two products together:\n\\[ 48 \\times 80 = 3840 \\]\n\\[ 48 \\times 5 = 240 \\]\n\\[ 3840 + 240 = 4080 \\]\n\nBut actually, I should have added them...
[ "To solve the long multiplication problem \\(48 \\times 85\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down 85 into its tens and ones place values.\n\\[ 85 = 80 + 5 \\]\n\nStep 2: Multiply each part of 85 by 48 separately.\n\\[ 48 \\t...
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[ "To solve the long multiplication problem \\( 48 \\times 85 \\), we will follow these steps:\n\n1. **Multiply 48 by 5 (the units digit of 85):**\n - \\( 48 \\times 5 = 240 \\)\n\n2. **Multiply 48 by 80 (the tens digit of 85, which is 8 times 10):**\n - \\( 48 \\times 80 = 48 \\times 8 \\times 10 = 384 \\times 1...
{"all_responses": ["To solve the long multiplication problem \\( 48 \\times 85 \\), we will follow these steps:\n\n1. **Multiply 48 by 5 (the units digit of 85):**\n - \\( 48 \\times 5 = 240 \\)\n\n2. **Multiply 48 by 80 (the tens digit of 85, which is 8 times 10):**\n - \\( 48 \\times 80 = 48 \\times 8 \\times 10 ...
[ "To solve the long multiplication problem \\( 48 \\times 85 \\), we will follow these steps:\n\n1. **Multiply 48 by 5 (the units digit of 85):**\n - \\( 48 \\times 5 = 240 \\)\n\n2. **Multiply 48 by 80 (the tens digit of 85, which is 8 times 10):**\n - \\( 48 \\times 80 = 48 \\times 8 \\times 10 = 384 \\times 1...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the...
[ false ]
[ "624" ]
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[ [ false ] ]
[ [ "624" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}]"}]
[ true, true, true ]
[ "4080", "4080", "4080" ]
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[ [ true ], [ true ], [ true ] ]
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[ [ false, false, true ] ]
[ [ "indeed:", "indeed **4080**", "4080" ] ]
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[ true, true, true, true ]
[ "4080", "4080", "4080", "4080" ]
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[ [ true ], [ true ], [ false, true ], [ false, true ] ]
[ [ "4080" ], [ "4080" ], [ "indeed \\(4080\\)", "4080" ], [ ":", "4080" ] ]
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[ true, true, true ]
[ "4080", "4080", "4080" ]
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[ [ true ], [ false, true ], [ false, true ] ]
[ [ "4080" ], [ "indeed:", "4080" ], [ "indeed **4080**", "4080" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 48 x 85 is\", \"answer\": \"624\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{624}" ]
[ false ]
[ "624" ]
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[ [ false ] ]
[ [ "624" ] ]
[ [ { "all_extracted_answers": [ "624" ], "all_extractions": [ "{'content': '624', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '624'}" ], "confidence": 0.9500000000000001, "extracted_answer": "624", "extractor": "stri...
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What is the solution to the long multiplication equation below? 69 x 41 Think step by step.
2829
"{\"arg1\": 69, \"arg2\": 41, \"solution\": 2829}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n69 x 41\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(69 \\times 41\\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 69\n × 41\n```\n\n### Step 2: Multiply 69 by 1 (the units digit of 41)\n- Multiply 69 by 1: \n ```\n 69\n × 1\n ------...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "To solve the long multiplication problem \\(69 \\times 41\\), we will follow these steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 69\n × 41\n _______\n```\n\n### Step 2: Multiply 69 by 1 (the units digit of 41).\n```\n 69\n × 41\n _______\n 690 (because 69 × 1 = 69)\n```\n\n##...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(69 \\times 41\\), we will follow these steps:\n\n### Step-by-Step Solution:\n\n#### 1. Set up the multiplication:\n```\n 69\n × 41\n```\n\n#### 2. Multiply 69 by 1 (the ones digit of 41):\n```\n 69\n × 41\n ------\n 690 (69 times 1)\n```\n\n#### 3. Mult...
{"continuation_phrases": ["But I need to verify this.", "Wait! I can double check this answer."], "continuations": [" Let's do it again properly.\n\n#### Correct Step-by-Step Solution:\n\n1. **Multiply 69 by 1:**\n ```\n 69\n \u00d7 41\n ------\n 690\n ```\n\n2. **Multiply 69 by 4 (shifted one p...
[ "To solve the long multiplication problem \\(69 \\times 41\\), we will follow these steps:\n\n### Step-by-Step Solution:\n\n#### 1. Set up the multiplication:\n```\n 69\n × 41\n```\n\n#### 2. Multiply 69 by 1 (the ones digit of 41):\n```\n 69\n × 41\n ------\n 690 (69 times 1)\n```\n\n#### 3. Mult...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the...
[ "To solve the long multiplication of 69 and 41, we'll break it down into steps:\n\nStep 1: Multiply 69 by 1 (the units digit of 41).\n69 x 1 = 69\n\nStep 2: Multiply 69 by 40 (since 41 has a tens digit of 4).\n69 x 40 = 2760\n\nNow add these two results together:\n69 + 2760 = 2829\n\nSo, the product of 69 and 41 is...
{"all_responses": ["To solve the long multiplication of 69 and 41, we'll break it down into steps:\n\nStep 1: Multiply 69 by 1 (the units digit of 41).\n69 x 1 = 69\n\nStep 2: Multiply 69 by 40 (since 41 has a tens digit of 4).\n69 x 40 = 2760\n\nNow add these two results together:\n69 + 2760 = 2829\n\nSo, the product ...
[ "To solve the long multiplication of 69 and 41, we'll break it down into steps:\n\nStep 1: Multiply 69 by 1 (the units digit of 41).\n69 x 1 = 69\n\nStep 2: Multiply 69 by 40 (since 41 has a tens digit of 4).\n69 x 40 = 2760\n\nNow add these two results together:\n69 + 2760 = 2829\n\nSo, the product of 69 and 41 is...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the...
[ false ]
[ "2859" ]
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[ [ false ] ]
[ [ "2859" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}]"}]
[ false, true, false ]
[ "2859", "2829", "2849" ]
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[{"answer_block": null, "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": "legacy", "extracted_answer": null, "final_answer": null, "is_correct": null, "is_equivalent": null, "legacy_result": false}, {"answer_block": null, "comparison_type": null, "correct_answer": null, "error": null...
[ [ false ], [ true ], [ false ] ]
[ [ "2859" ], [ "2829" ], [ "2849" ] ]
[{"value": "[{'all_extracted_answers': None, 'all_extractions': None, 'all_matches': [\"('2859', 682)\", \"('4', 504)\", \"('276', 417)\", \"('69', 282)\"], 'all_numbers_in_line': None, 'choice_labels': None, 'confidence': 0.9934876989869754, 'extracted_answer': '2859', 'extracted_choice_letter': None, 'extracted_choic...
[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}]"}, {"value": "[{'answer_block': None, 'comparison_type': None, 'correct_a...
[ false ]
[ "345" ]
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[ [ false, false, false ] ]
[ [ "\\(2859\\)", "\\(345\\)", "345" ] ]
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[ true, true, true, true ]
[ "2829", "2829", "2829", "2829" ]
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[ [ true ], [ true ], [ true ], [ true ] ]
[ [ "2829" ], [ "2829" ], [ "2829" ], [ "2829" ] ]
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[ false, false, false ]
[ "2859", "69", "345" ]
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[ [ false ], [ false, false ], [ false, false ] ]
[ [ "2859" ], [ "\\(2859\\)", "69" ], [ "\\(345\\)", "345" ] ]
[{"value": "[{'all_extracted_answers': None, 'all_extractions': None, 'all_matches': [\"('2859', 604)\"], 'all_numbers_in_line': None, 'choice_labels': None, 'confidence': 0.9926590538336052, 'extracted_answer': '2859', 'extracted_choice_letter': None, 'extracted_choice_text': None, 'extractor': 'pattern_based', 'full_...
[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}]"}, {"value": "[{'answer_block': None, 'comparison_type': None, 'correct_a...
We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Now add the two results together:\", \"answer\": \"2859\"}, {\"context\": \"So, 69 x 41 =\", \"answer\": \"2859\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{2859}", "\\boxed{2859}" ]
[ false, false ]
[ "2859", "2859" ]
[ { "all_matches": [ "('2859', 1)", "('2859', 0)" ], "all_numbers_in_line": null, "choice_labels": null, "confidence": 0.5416666666666666, "extracted_answer": "2859", "extracted_choice_letter": null, "extracted_choice_text": null, "extractor": "pattern_based", "full...
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[ [ false ], [ false ] ]
[ [ "2859" ], [ "2859" ] ]
[ [ { "all_extracted_answers": [ "2859" ], "all_extractions": [ "{'content': '2859', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '2859'}" ], "confidence": 0.9500000000000001, "extracted_answer": "2859", "extractor": "...
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What is the solution to the long multiplication equation below? 21 x 61 Think step by step.
1281
"{\"arg1\": 21, \"arg2\": 61, \"solution\": 1281}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n21 x 61\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
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[ "To solve the long multiplication problem \\(21 \\times 61\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nFirst, let's rewrite the numbers as:\n\\[ 21 = 20 + 1 \\]\n\\[ 61 = 60 + 1 \\]\n\n#### Step 2: Multiply each part of the first number by each ...
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[ "To solve the long multiplication problem \\(21 \\times 61\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the multiplication vertically:\n\n```\n 21\n × 61\n ------\n```\n\nWe can split this into two parts: \\(21 \\times...
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[ "To solve the long multiplication problem \\(21 \\times 61\\), we can break it down into simpler steps:\n\nStep 1: Multiply 21 by 1 (the units digit of 61).\n - \\(21 \\times 1 = 21\\)\n - Write down 21.\n\nStep 2: Multiply 21 by 60 (the tens digit of 61).\n - \\(21 \\times 60 = 1260\\)\n - Since this is in...
{"continuation_phrases": ["Wait, let me try", "But according to"], "continuations": [" again with proper addition:\n - Correctly combine them as follows:\n - First, multiply 21 by 60 (which gives 1260) and then add the carry-over 21 to get 1281.\n\nTherefore, the final answer is 1281.", " the first step's...
[ "To solve the long multiplication problem \\(21 \\times 61\\), we can break it down into simpler steps:\n\nStep 1: Multiply 21 by 1 (the units digit of 61).\n - \\(21 \\times 1 = 21\\)\n - Write down 21.\n\nStep 2: Multiply 21 by 60 (the tens digit of 61).\n - \\(21 \\times 60 = 1260\\)\n - Since this is in...
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[ "Certainly! Let's solve the long multiplication problem \\(21 \\times 61\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 21\n × 61\n ```\n\n2. **Multiply 21 by 1 (the rightmost digit of 61):**\n - Multiply 21 by 1: \n \\[\n 21 \\times 1 = 21\n \\]\n ...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\(21 \\times 61\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 21\n \u00d7 61\n ```\n\n2. **Multiply 21 by 1 (the rightmost digit of 61):**\n - Multiply 21 by 1: \n \\[\n 21 \\times ...
[ "Certainly! Let's solve the long multiplication problem \\(21 \\times 61\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 21\n × 61\n ```\n\n2. **Multiply 21 by 1 (the rightmost digit of 61):**\n - Multiply 21 by 1: \n \\[\n 21 \\times 1 = 21\n \\]\n ...
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[ true ]
[ "1281" ]
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[ [ true ] ]
[ [ "1281" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': True}]"}]
[ true, false, false ]
[ "1281", "147", "12621" ]
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[ [ true ], [ false ], [ false ] ]
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[ [ true, false, true ] ]
[ [ "1281", "indeed 1281", "1281" ] ]
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[ true, true, false, true ]
[ "1281", "1281", "126", "1281" ]
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[ [ true ], [ false, true ], [ false ], [ false, true ] ]
[ [ "1281" ], [ "indeed \\(1281\\)", "1281" ], [ "126" ], [ "\\(1281\\)", "1281" ] ]
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[ false, true, true ]
[ "1261", "1281", "1281" ]
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[ [ false ], [ true ], [ false, true ] ]
[ [ "1261" ], [ "1281" ], [ "indeed 1281", "1281" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 21 x 61 is:\", \"answer\": \"1281\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1281}" ]
[ true ]
[ "1281" ]
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[ [ true ] ]
[ [ "1281" ] ]
[ [ { "all_extracted_answers": [ "1281" ], "all_extractions": [ "{'content': '1281', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '1281'}" ], "confidence": 0.9500000000000001, "extracted_answer": "1281", "extractor": "...
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What is the solution to the long multiplication equation below? 86 x 86 Think step by step.
7396
"{\"arg1\": 86, \"arg2\": 86, \"solution\": 7396}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n86 x 86\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
null
null
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[ "To solve the long multiplication problem \\(86 \\times 86\\), we can break it down into simpler steps:\n\n1. **Write the numbers vertically:**\n ```\n 86\n × 86\n ----\n ```\n\n2. **Multiply each digit of the bottom number by the top number:**\n\n - Multiply 8 (from 86) by 6:\n ```\n 8\n ...
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[ "To solve the long multiplication of \\(86 \\times 86\\), we can break it down into simpler steps:\n\n1. **Break down 86**: \n - We know that \\(86 = 80 + 6\\).\n\n2. **Multiply each part by 86**:\n - First, multiply 80 by 86.\n \\[\n 80 \\times 86 = (80 \\times 80) + (80 \\times 6)\n \\]\n - Ca...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve \\(86 \\times 86\\), we can break it down into simpler steps:\n\n1. **Square each number separately:**\n - First, square 86:\n \\[\n 86^2 = (80 + 6)^2\n \\]\n - Use the binomial expansion formula \\((a+b)^2 = a^2 + 2ab + b^2\\) where \\(a = 80\\) and \\(b = 6\\):\n \\[\n 86^2 = 80^...
{"continuation_phrases": ["But I need to verify this.", "Wait, this result is"], "continuations": [" Let's do it correctly:\n \\[\n 86^2 = 7396\n \\]\n\nSo, \\(86 \\times 86 = 7396\\).\n\nTherefore, the correct answer is \\(7396\\).", " incorrect because it doesn't match our previous calculation using the o...
[ "To solve \\(86 \\times 86\\), we can break it down into simpler steps:\n\n1. **Square each number separately:**\n - First, square 86:\n \\[\n 86^2 = (80 + 6)^2\n \\]\n - Use the binomial expansion formula \\((a+b)^2 = a^2 + 2ab + b^2\\) where \\(a = 80\\) and \\(b = 6\\):\n \\[\n 86^2 = 80^...
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[ "To solve \\(86 \\times 86\\), we can use the formula for squaring a number: \\((a + b)^2 = a^2 + 2ab + b^2\\). Here, we can think of 86 as \\(80 + 6\\).\n\nLet's break it down:\n\n1. Square the first digit (80):\n \\[\n 80^2 = 6400\n \\]\n\n2. Double the product of the two digits:\n \\[\n 2 \\times 80 \\...
{"all_responses": ["To solve \\(86 \\times 86\\), we can use the formula for squaring a number: \\((a + b)^2 = a^2 + 2ab + b^2\\). Here, we can think of 86 as \\(80 + 6\\).\n\nLet's break it down:\n\n1. Square the first digit (80):\n \\[\n 80^2 = 6400\n \\]\n\n2. Double the product of the two digits:\n \\[\n ...
[ "To solve \\(86 \\times 86\\), we can use the formula for squaring a number: \\((a + b)^2 = a^2 + 2ab + b^2\\). Here, we can think of 86 as \\(80 + 6\\).\n\nLet's break it down:\n\n1. Square the first digit (80):\n \\[\n 80^2 = 6400\n \\]\n\n2. Double the product of the two digits:\n \\[\n 2 \\times 80 \\...
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[ true ]
[ "7396" ]
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[ [ "\\(7396\\)", "indeed \\(7396\\)", "7396" ] ]
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[ [ "7400" ], [ "\\(7396\\)", "7396" ], [ "indeed \\(7396\\)", "7396" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 86 x 86 =\", \"answer\": \"7396\"}]}" ]
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[ "\\boxed{7396}" ]
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[ "7396" ]
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[ [ true ] ]
[ [ "7396" ] ]
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What is the solution to the long multiplication equation below? 84 x 46 Think step by step.
3864
"{\"arg1\": 84, \"arg2\": 46, \"solution\": 3864}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n84 x 46\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(84 \\times 46\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 84\n × 46\n ```\n\n2. **Multiply 84 by 6 (the ones digit of 46):**\n - Multiply 84 by 6:\n ```\n 84\n × 6\n ------\n 504\n ```\n - Write...
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[ "Certainly! Let's solve the multiplication problem \\(84 \\times 46\\) step by step.\n\n### Step 1: Break down the numbers into smaller parts.\nWe can break down \\(84\\) and \\(46\\) into more manageable parts:\n- \\(84 = 80 + 4\\)\n- \\(46 = 40 + 6\\)\n\n### Step 2: Multiply each part of one number by each part o...
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[ "To solve the long multiplication problem \\(84 \\times 46\\), we will follow these steps:\n\n1. **Multiply 84 by 6 (the units digit of 46):**\n - \\(84 \\times 6 = 504\\)\n\n2. **Multiply 84 by 40 (the tens digit of 46, which is 4 times 10):**\n - First, multiply 84 by 4: \n \\[\n 84 \\times 4 = 336\n ...
{"continuation_phrases": ["However,", "But to confirm,"], "continuations": [" this sum is not correct because we need to align the numbers correctly for subtraction in the next step.\n\nLet's correct the process and do it properly:\n\n**Step-by-step correction:**\n\n1. Multiply 84 by 6 (units digit):\n - \\(84 \\time...
[ "To solve the long multiplication problem \\(84 \\times 46\\), we will follow these steps:\n\n1. **Multiply 84 by 6 (the units digit of 46):**\n - \\(84 \\times 6 = 504\\)\n\n2. **Multiply 84 by 40 (the tens digit of 46, which is 4 times 10):**\n - First, multiply 84 by 4: \n \\[\n 84 \\times 4 = 336\n ...
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[ "To solve the long multiplication of 84 and 46, follow these steps:\n\n1. **Multiply the ones digit of 84 by the ones digit of 46:**\n - The ones digit of 84 is 4.\n - The ones digit of 46 is 6.\n - So, \\(4 \\times 6 = 24\\).\n - Write down 4 and carry over 2.\n\n2. **Multiply the ones digit of 84 by the t...
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[ "To solve the long multiplication of 84 and 46, follow these steps:\n\n1. **Multiply the ones digit of 84 by the ones digit of 46:**\n - The ones digit of 84 is 4.\n - The ones digit of 46 is 6.\n - So, \\(4 \\times 6 = 24\\).\n - Write down 4 and carry over 2.\n\n2. **Multiply the ones digit of 84 by the t...
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[ false, true, true ]
[ "5520", "3864", "3864" ]
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[ [ false ], [ true ], [ true ] ]
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[ [ false, false, true ] ]
[ [ "\\(3864\\)", "indeed \\(3864\\)", "3864" ] ]
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[ false, false, true, true ]
[ "848", "3984", "3864", "3864" ]
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[ [ "848" ], [ "3984" ], [ "3864" ], [ "indeed 3864, but I will now restate it properly:", "3864" ] ]
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[ [ true ], [ false, true ], [ false, true ] ]
[ [ "3864" ], [ "\\(3864\\)", "3864" ], [ "indeed \\(3864\\)", "3864" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 84 x 46 is\", \"answer\": \"34104\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{34104}" ]
[ false ]
[ "34104" ]
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[ [ false ] ]
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What is the solution to the long multiplication equation below? 11 x 99 Think step by step.
1089
"{\"arg1\": 11, \"arg2\": 99, \"solution\": 1089}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n11 x 99\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(11 \\times 99\\), we can break it down into simpler steps:\n\nStep 1: Break down 99 into 100 - 1.\nSo, \\(11 \\times 99 = 11 \\times (100 - 1)\\).\n\nStep 2: Use the distributive property of multiplication over subtraction:\n\\(11 \\times (100 - 1) = 11 \\times 100 - 11 ...
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[ "To solve \\(11 \\times 99\\), we can use the distributive property of multiplication over addition. This means we can break down the problem into simpler parts:\n\n\\[11 \\times 99 = 11 \\times (100 - 1)\\]\n\nNow, distribute the 11 across the terms inside the parentheses:\n\n\\[= 11 \\times 100 - 11 \\times 1\\]\...
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[ "Certainly! Let's solve the multiplication problem \\(11 \\times 99\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 11\n x 99\n ```\n\n2. **Multiply 11 by each digit of 99 separately:**\n\n - Multiply 11 by 9 (the ones place in 99):\n \\[\n 11 \\times 9 ...
{"continuation_phrases": ["Wait, how?", "But to confirm,"], "continuations": [" We'll multiply 11 by 9 and then add a zero at the end.\n \\[\n 11 \\times 9 = 99\n \\]\n Now, since 90 becomes 9 multiplied by 10, which is just adding another zero to 99:\n \\[\n 99 \\times 10 = 990\n \\]\n\n3. ...
[ "Certainly! Let's solve the multiplication problem \\(11 \\times 99\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 11\n x 99\n ```\n\n2. **Multiply 11 by each digit of 99 separately:**\n\n - Multiply 11 by 9 (the ones place in 99):\n \\[\n 11 \\times 9 ...
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[ "Certainly! Let's solve the long multiplication problem \\( 11 \\times 99 \\) step by step.\n\n### Step 1: Break down the numbers\nFirst, let's break down each number into tens and ones:\n- \\( 11 = 10 + 1 \\)\n- \\( 99 = 100 - 1 \\)\n\n### Step 2: Multiply each part of the first number by the second number\nNow, w...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\( 11 \\times 99 \\) step by step.\n\n### Step 1: Break down the numbers\nFirst, let's break down each number into tens and ones:\n- \\( 11 = 10 + 1 \\)\n- \\( 99 = 100 - 1 \\)\n\n### Step 2: Multiply each part of the first number by the second...
[ "Certainly! Let's solve the long multiplication problem \\( 11 \\times 99 \\) step by step.\n\n### Step 1: Break down the numbers\nFirst, let's break down each number into tens and ones:\n- \\( 11 = 10 + 1 \\)\n- \\( 99 = 100 - 1 \\)\n\n### Step 2: Multiply each part of the first number by the second number\nNow, w...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 11 x 99 = 11 x (100 - 1).\", \"answer\": \"11 x 99 = 11 x (100 - 1)\"}, {\"context\": \"Step 2: Use the distributive property of multiplication over subtraction: 11 x (100 - 1) = 11 x 100 - 11 x 1.\", \"answer\": \"11 x (100 - 1) = 11 x 100 - 11 x 1\"}, {\"context\": \"- 11 ...
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[ "\\boxed{11 x 99 = 11 x (100 - 1)}", "\\boxed{11 x (100 - 1) = 11 x 100 - 11 x 1}", "\\boxed{11 x 100 = 1100}", "\\boxed{11 x 1 = 11}", "\\boxed{1100 - 11 = 1089}", "\\boxed{11 x 99 = 1089}" ]
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[ "11", "11", "1100", "11", "1089", "1089" ]
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[ [ false ], [ false ], [ false ], [ false ], [ true ], [ true ] ]
[ [ "11 x 99 = 11 x (100 - 1)" ], [ "11 x (100 - 1) = 11 x 100 - 11 x 1" ], [ "11 x 100 = 1100" ], [ "11 x 1 = 11" ], [ "1100 - 11 = 1089" ], [ "11 x 99 = 1089" ] ]
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What is the solution to the long multiplication equation below? 42 x 27 Think step by step.
1134
"{\"arg1\": 42, \"arg2\": 27, \"solution\": 1134}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n42 x 27\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(42 \\times 27\\), we can break it down into simpler steps:\n\n1. **Multiply 42 by 7 (the units digit of 27):**\n - \\(42 \\times 7 = 294\\)\n\n2. **Multiply 42 by 20 (the tens digit of 27, which is 2 times 10):**\n - \\(42 \\times 20 = 840\\) (because \\(42 \\times 2...
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[ "To solve the long multiplication problem \\(42 \\times 27\\), we can break it down into smaller steps:\n\n1. **Break down the numbers:**\n - \\(42\\) can be broken down into \\(40 + 2\\).\n - \\(27\\) can be broken down into \\(20 + 7\\).\n\n2. **Multiply each part of one number by each part of the other numbe...
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[ "Certainly! Let's break down the multiplication of 42 and 27 step by step.\n\n1. **Multiply the ones digit of each number:**\n - The ones digit of 42 is 2.\n - The ones digit of 27 is 7.\n - Multiply these two numbers: \\(2 \\times 7 = 14\\).\n - Write down 4 and carry over 1.\n\n2. **Multiply the tens digi...
{"continuation_phrases": ["Wait, let me try", "Wait, how?"], "continuations": [" again: \\(5 + 36 = 41\\).\n\nSo, the final answer is:\n\n\\[ 42 \\times 27 = 1134 \\]\n\nLet's verify it with another method for clarity:\n\n1. **Break down 42 into 40 and 2:**\n - Calculate \\(40 \\times 27\\):\n - Multiply 27 by 0:...
[ "Certainly! Let's break down the multiplication of 42 and 27 step by step.\n\n1. **Multiply the ones digit of each number:**\n - The ones digit of 42 is 2.\n - The ones digit of 27 is 7.\n - Multiply these two numbers: \\(2 \\times 7 = 14\\).\n - Write down 4 and carry over 1.\n\n2. **Multiply the tens digi...
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[ "To solve the long multiplication problem \\(42 \\times 27\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication\n```\n 42\n × 27\n ------\n```\n\n### Step 2: Multiply 42 by 7 (the units digit of 27)\n```\n 42\n × 27\n ------\n 294 (This is 42 times 7)\n```\n\n### Step ...
{"all_responses": ["To solve the long multiplication problem \\(42 \\times 27\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication\n```\n 42\n \u00d7 27\n ------\n```\n\n### Step 2: Multiply 42 by 7 (the units digit of 27)\n```\n 42\n \u00d7 27\n ------\n 294 (This is 42 t...
[ "To solve the long multiplication problem \\(42 \\times 27\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication\n```\n 42\n × 27\n ------\n```\n\n### Step 2: Multiply 42 by 7 (the units digit of 27)\n```\n 42\n × 27\n ------\n 294 (This is 42 times 7)\n```\n\n### Step ...
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[ "41", "1134", "1134" ]
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[ [ "41" ], [ ":", "\\(1134\\)", "1134" ], [ "indeed \\(1134\\)", "1134" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 42 x 27 is\", \"answer\": \"1134\"}, {\"context\": \"42 x 7 =\", \"answer\": \"294\"}, {\"context\": \"42 x 20 =\", \"answer\": \"840\"}, {\"context\": \"Add the two results together:\", \"answer\": \"1134\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1134}", "\\boxed{294}", "\\boxed{840}", "\\boxed{1134}" ]
[ true, false, false, true ]
[ "1134", "294", "840", "1134" ]
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[ [ true ], [ false ], [ false ], [ true ] ]
[ [ "1134" ], [ "294" ], [ "840" ], [ "1134" ] ]
[ [ { "all_extracted_answers": [ "1134" ], "all_extractions": [ "{'content': '1134', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '1134'}" ], "confidence": 0.9500000000000001, "extracted_answer": "1134", "extractor": "...
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What is the solution to the long multiplication equation below? 22 x 85 Think step by step.
1870
"{\"arg1\": 22, \"arg2\": 85, \"solution\": 1870}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n22 x 85\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(22 \\times 85\\), we can break it down into simpler steps:\n\n1. **Multiply 22 by 5 (the units digit of 85):**\n - \\(22 \\times 5 = 110\\)\n\n2. **Multiply 22 by 80 (the tens digit of 85, which is 8 times 10):**\n - First, calculate \\(22 \\times 8 = 176\\)\n - Th...
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[ "To solve the long multiplication problem \\(22 \\times 85\\), we will break it down into smaller steps.\n\n1. **Break down the numbers:**\n - \\(22\\) can be written as \\(20 + 2\\).\n - \\(85\\) can be written as \\(80 + 5\\).\n\n2. **Multiply each part of \\(22\\) by each part of \\(85\\):**\n\n - Multiply...
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[ "To solve the long multiplication problem \\(22 \\times 85\\), we will break it down into smaller steps:\n\n1. **Multiply 22 by 5 (the units digit of 85):**\n - \\(22 \\times 5 = 110\\)\n\n2. **Multiply 22 by 80 (the tens digit of 85, which is 8 times 10):**\n - \\(22 \\times 80 = 1760\\) (This can be calculate...
{"continuation_phrases": ["Wait, this result is", "Wait, how?"], "continuations": [" incorrect because I made an error in my initial explanation. Let's correct it:\n - The correct way to add these products is to align them properly and then add column-wise.\n - First, multiply 22 by 5 (units place):\n \\[...
[ "To solve the long multiplication problem \\(22 \\times 85\\), we will break it down into smaller steps:\n\n1. **Multiply 22 by 5 (the units digit of 85):**\n - \\(22 \\times 5 = 110\\)\n\n2. **Multiply 22 by 80 (the tens digit of 85, which is 8 times 10):**\n - \\(22 \\times 80 = 1760\\) (This can be calculate...
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[ "To solve the long multiplication problem \\(22 \\times 85\\), we will follow these steps:\n\n1. **Write down the numbers**: \n ```\n 22\n × 85\n ```\n\n2. **Multiply 22 by 5 (the units digit of 85)**:\n - Multiply 22 by 5: \n ```\n 22\n × 5\n ------\n 110\n ```\n So...
{"all_responses": ["To solve the long multiplication problem \\(22 \\times 85\\), we will follow these steps:\n\n1. **Write down the numbers**: \n ```\n 22\n \u00d7 85\n ```\n\n2. **Multiply 22 by 5 (the units digit of 85)**:\n - Multiply 22 by 5: \n ```\n 22\n \u00d7 5\n ------\n ...
[ "To solve the long multiplication problem \\(22 \\times 85\\), we will follow these steps:\n\n1. **Write down the numbers**: \n ```\n 22\n × 85\n ```\n\n2. **Multiply 22 by 5 (the units digit of 85)**:\n - Multiply 22 by 5: \n ```\n 22\n × 5\n ------\n 110\n ```\n So...
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[ "1760" ]
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[ [ false ] ]
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[ "1870", "1870", "1960" ]
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[ [ "1870" ], [ "1870" ], [ "\\(1960\\)", "1960" ] ]
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[ [ false, false, true ] ]
[ [ "\\(1870\\)", "indeed \\(1870\\)", "1870" ] ]
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[ false, true, true, true ]
[ "176", "1870", "1870", "1870" ]
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[ [ false, false, false, false ], [ false, true ], [ false, true ], [ false, true ] ]
[ [ "0", "6", "\\(1106\\)", "176" ], [ "indeed:", "1870" ], [ ":", "1870" ], [ ":", "1870" ] ]
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[ true, true, true ]
[ "1870", "1870", "1870" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 22 x 85 is\", \"answer\": \"1870\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1870}" ]
[ true ]
[ "1870" ]
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[ [ true ] ]
[ [ "1870" ] ]
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What is the solution to the long multiplication equation below? 73 x 76 Think step by step.
5548
"{\"arg1\": 73, \"arg2\": 76, \"solution\": 5548}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n73 x 76\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(73 \\times 76\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(73\\) can be written as \\(70 + 3\\).\n - \\(76\\) can be written as \\(70 + 6\\).\n\n2. **Multiply each part of the first number by each part of the second number:**\...
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[ "To solve the long multiplication problem \\( 73 \\times 76 \\), we can break it down into simpler steps:\n\n1. **Break Down the Numbers:**\n - \\( 73 = 70 + 3 \\)\n - \\( 76 = 70 + 6 \\)\n\n2. **Multiply Each Part of the First Number by Each Part of the Second Number:**\n - Multiply 70 by 70:\n \\[\n ...
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[ "To solve the long multiplication problem \\(73 \\times 76\\), we can break it down into smaller steps:\n\n1. **Multiply 73 by 6 (the units digit of 76):**\n - \\(73 \\times 6 = 438\\)\n\n2. **Multiply 73 by 70 (the tens digit of 76, which is 7 times 10):**\n - \\(73 \\times 70 = 5110\\) (because \\(73 \\times ...
{"continuation_phrases": ["But to confirm,", "Hold on, let me verify this answer."], "continuations": [" we need to align them correctly for addition.\n\nSo, let's write it out as a sum:\n\\[ 73 \\times 76 = 73 \\times (70 + 6) = 73 \\times 70 + 73 \\times 6 \\]\n\\[ = 5110 + 438 \\]\n\\[ = 5548 \\]\n\nTherefore, the s...
[ "To solve the long multiplication problem \\(73 \\times 76\\), we can break it down into smaller steps:\n\n1. **Multiply 73 by 6 (the units digit of 76):**\n - \\(73 \\times 6 = 438\\)\n\n2. **Multiply 73 by 70 (the tens digit of 76, which is 7 times 10):**\n - \\(73 \\times 70 = 5110\\) (because \\(73 \\times ...
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[ "To solve \\(73 \\times 76\\), you can use the standard algorithm for multiplying numbers:\n\n1) Multiply 73 by 6 (the ones digit of 76):\n - \\(73 \\times 6 = 438\\)\n \n2) Multiply 73 by 70 (the tens digit of 76, which is 7 times 10):\n - \\(73 \\times 70 = 5110\\) \n \n3) Add the two results together:\n ...
{"all_responses": ["To solve \\(73 \\times 76\\), you can use the standard algorithm for multiplying numbers:\n\n1) Multiply 73 by 6 (the ones digit of 76):\n - \\(73 \\times 6 = 438\\)\n \n2) Multiply 73 by 70 (the tens digit of 76, which is 7 times 10):\n - \\(73 \\times 70 = 5110\\) \n \n3) Add the two resul...
[ "To solve \\(73 \\times 76\\), you can use the standard algorithm for multiplying numbers:\n\n1) Multiply 73 by 6 (the ones digit of 76):\n - \\(73 \\times 6 = 438\\)\n \n2) Multiply 73 by 70 (the tens digit of 76, which is 7 times 10):\n - \\(73 \\times 70 = 5110\\) \n \n3) Add the two results together:\n ...
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[ [ true ] ]
[ [ "5548" ] ]
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[ true, true, false ]
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[ [ true ], [ false, true ], [ true ], [ true ] ]
[ [ "5548" ], [ "verified and correct", "5548" ], [ "5548" ], [ "5548" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 73 x 76 is:\", \"answer\": \"5548\"}]}" ]
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[ "\\boxed{5548}" ]
[ true ]
[ "5548" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 65 x 45 Think step by step.
2925
"{\"arg1\": 65, \"arg2\": 45, \"solution\": 2925}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n65 x 45\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(65 \\times 45\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(65\\) can be broken down into \\(60 + 5\\).\n - \\(45\\) can be broken down into \\(40 + 5\\).\n\n2. **Multiply each part of the first number by each part of the secon...
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[ "Certainly! Let's solve the long multiplication problem step by step for \\(65 \\times 45\\).\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 65\n × 45\n```\n\n### Step 2: Multiply 65 by 5 (the ones digit of 45)\n- Multiply 65 by 5:\n ```\n 65\n × 5\n ---...
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[ "Certainly! Let's solve this step by step:\n\n1) First, let's write down the numbers we're multiplying:\n 65\n × 45\n -----\n\n2) To multiply these numbers, we can use the standard algorithm for long multiplication.\n\n3) Multiply 65 by 5 (the units digit of 45):\n 65 × 5 = 325\n Write 5 in the units plac...
{"continuation_phrases": ["Wait, this result is", "However,"], "continuations": [" actually 2632 which means we need to add another zero at the end since there was no carrying over from the first column.\n So, 2632 becomes 26320 when we add the zero.\n\nTherefore, the product of 65 and 45 is 2775.", " upon reviewing ...
[ "Certainly! Let's solve this step by step:\n\n1) First, let's write down the numbers we're multiplying:\n 65\n × 45\n -----\n\n2) To multiply these numbers, we can use the standard algorithm for long multiplication.\n\n3) Multiply 65 by 5 (the units digit of 45):\n 65 × 5 = 325\n Write 5 in the units plac...
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[ "To solve the long multiplication of \\(65 \\times 45\\), we can break it down into simpler steps:\n\n1. **Break it into parts:**\n - First, multiply 65 by 40 (since 45 = 40 + 5).\n - Then, multiply 65 by 5.\n\n2. **Calculate each part separately:**\n\n - For 65 multiplied by 40:\n \\[\n 65 \\times 40...
{"all_responses": ["To solve the long multiplication of \\(65 \\times 45\\), we can break it down into simpler steps:\n\n1. **Break it into parts:**\n - First, multiply 65 by 40 (since 45 = 40 + 5).\n - Then, multiply 65 by 5.\n\n2. **Calculate each part separately:**\n\n - For 65 multiplied by 40:\n \\[\n ...
[ "To solve the long multiplication of \\(65 \\times 45\\), we can break it down into simpler steps:\n\n1. **Break it into parts:**\n - First, multiply 65 by 40 (since 45 = 40 + 5).\n - Then, multiply 65 by 5.\n\n2. **Calculate each part separately:**\n\n - For 65 multiplied by 40:\n \\[\n 65 \\times 40...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 65 x 45 is\", \"answer\": \"4500\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{4500}" ]
[ false ]
[ "4500" ]
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[ [ false ] ]
[ [ "4500" ] ]
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What is the solution to the long multiplication equation below? 49 x 83 Think step by step.
4067
"{\"arg1\": 49, \"arg2\": 83, \"solution\": 4067}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n49 x 83\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(49 \\times 83\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 49\n × 83\n ```\n\n2. **Multiply 49 by 3 (the ones digit of 83):**\n - Multiply 49 by 3:\n ```\n 49\n × 3\n _______\n 147\n ```\...
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[ "To solve the long multiplication problem \\(49 \\times 83\\), we will break it down into smaller steps.\n\nFirst, let's write out the numbers:\n\n```\n 49\n × 83\n ----\n```\n\nNow, let's multiply each digit of 49 by each digit of 83:\n\n1. Multiply 49 by 3 (the units digit of 83):\n ```\n 49\n ×...
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[ "To solve the long multiplication problem \\(49 \\times 83\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 49 and 83 aligned vertically.\n\n```\n 49\n × 83\n ------\n```\n\n2. **Multiply 49 by 3 (the units digit of 83)**:\n - Multiply 49 by 3: \n ```\n 49\n × ...
{"continuation_phrases": ["However,", "Wait, let me try"], "continuations": [" there was an error in combining the numbers correctly. Let's correct that:\n\n ```\n 7\n 458\n ------\n 4117\n ```\n\nSo, the final answer to \\(49 \\times 83\\) is \\(4117\\).", " again carefully:\n\n- First multiply...
[ "To solve the long multiplication problem \\(49 \\times 83\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 49 and 83 aligned vertically.\n\n```\n 49\n × 83\n ------\n```\n\n2. **Multiply 49 by 3 (the units digit of 83)**:\n - Multiply 49 by 3: \n ```\n 49\n × ...
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[ "To solve the long multiplication problem \\(49 \\times 83\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers vertically:\n\n```\n 49\n × 83\n_______\n```\n\nNow, distribute the multiplication across each digit in ...
{"all_responses": ["To solve the long multiplication problem \\(49 \\times 83\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers vertically:\n\n```\n 49\n \u00d7 83\n_______\n```\n\nNow, distribute the multiplication a...
[ "To solve the long multiplication problem \\(49 \\times 83\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers vertically:\n\n```\n 49\n × 83\n_______\n```\n\nNow, distribute the multiplication across each digit in ...
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[ false ]
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[ [ false ] ]
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[ false, false, true, true ]
[ "3969", "3967", "4067", "4067" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the product of 49 x 83 is\", \"answer\": \"4067\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{4067}" ]
[ true ]
[ "4067" ]
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[ [ true ] ]
[ [ "4067" ] ]
[ [ { "all_extracted_answers": [ "4067" ], "all_extractions": [ "{'content': '4067', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '4067'}" ], "confidence": 0.9500000000000001, "extracted_answer": "4067", "extractor": "...
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What is the solution to the long multiplication equation below? 44 x 60 Think step by step.
2640
"{\"arg1\": 44, \"arg2\": 60, \"solution\": 2640}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n44 x 60\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(44 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply 44 by 0**: \n - Any number multiplied by 0 equals 0.\n - So, \\(44 \\times 0 = 0\\).\n\n2. **Multiply 44 by 6**:\n - To do this, multiply 44 by 6 directly: \n \\[\n 44 \\times 6 = (...
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[ "To solve the long multiplication problem \\( 44 \\times 60 \\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 44\n × 60\n ------\n ```\n\n2. **Multiply 44 by 0 (the units digit of 60):**\n - Multiply 44 by 0:\n ```\n 44\n × 0\n ------\n ...
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[ "To solve the long multiplication problem \\( 44 \\times 60 \\), follow these steps:\n\n1. **Set up the multiplication**: Write down the numbers one above the other:\n ```\n 44\n × 60\n ```\n\n2. **Multiply 44 by 0 (the ones place of 60)**:\n - Multiply 44 by 0: \\( 44 \\times 0 = 0 \\)\n - Write this...
{"continuation_phrases": ["Hold on, let me verify this answer.", "Hold on, let me verify this answer."], "continuations": [" Let's break it down:\n - \\( 44 \\times 6 = 264 \\) \u2192 This should be written as 264, but since it's multiplied by 6 (which is 60 with a zero at the end), you need to consider that each d...
[ "To solve the long multiplication problem \\( 44 \\times 60 \\), follow these steps:\n\n1. **Set up the multiplication**: Write down the numbers one above the other:\n ```\n 44\n × 60\n ```\n\n2. **Multiply 44 by 0 (the ones place of 60)**:\n - Multiply 44 by 0: \\( 44 \\times 0 = 0 \\)\n - Write this...
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[ "To solve the long multiplication problem \\(44 \\times 60\\), let's break it down into steps:\n\n1. **Multiply the ones digit of the first number by the second number:**\n - The ones digit of 44 is 4.\n - Multiply 4 by 60:\n \\[\n 4 \\times 60 = 240\n \\]\n\n2. **Write down the result and add any c...
{"all_responses": ["To solve the long multiplication problem \\(44 \\times 60\\), let's break it down into steps:\n\n1. **Multiply the ones digit of the first number by the second number:**\n - The ones digit of 44 is 4.\n - Multiply 4 by 60:\n \\[\n 4 \\times 60 = 240\n \\]\n\n2. **Write down the resul...
[ "To solve the long multiplication problem \\(44 \\times 60\\), let's break it down into steps:\n\n1. **Multiply the ones digit of the first number by the second number:**\n - The ones digit of 44 is 4.\n - Multiply 4 by 60:\n \\[\n 4 \\times 60 = 240\n \\]\n\n2. **Write down the result and add any c...
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[ [ false, false ] ]
[ [ "\\(264\\)", "264" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer is\", \"answer\": \"264\"}]}" ]
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What is the solution to the long multiplication equation below? 38 x 83 Think step by step.
3154
"{\"arg1\": 38, \"arg2\": 83, \"solution\": 3154}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n38 x 83\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(38 \\times 83\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 38\n × 83\n ------\n ```\n\n2. **Multiply 38 by 3 (the units digit of 83):**\n - Multiply 38 by 3:\n ```\n 38\n × 3\n ------\n 114\n...
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[ "To solve the long multiplication of 38 and 83, we'll break it down into steps:\n\n1) First, let's multiply 38 by 3 (the units digit of 83):\n 38 x 3 = 114\n2) Now, let's multiply 38 by 80 (the tens digit of 83). We can think of this as:\n 38 x 80 = 38 x (8 x 10) = (38 x 8) x 10 = 304 x 10 = 3040\n3) Finally, a...
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[ "Certainly! Let's break down the multiplication of 38 and 83 step by step.\n\n1. **Multiply 38 by 3:**\n \\[\n 38 \\times 3 = 114\n \\]\n\n2. **Multiply 38 by 80 (which is 8 times 10):**\n \\[\n 38 \\times 80 = 38 \\times (8 \\times 10) = (38 \\times 8) \\times 10\n \\]\n First, calculate \\(38 \\time...
{"continuation_phrases": ["Wait! I can double check this answer.", "But to confirm,"], "continuations": [" Let's use another method for verification.\n \nLet's do it using the standard long multiplication method:\n\n- Multiply 83 by 3 (the ones digit of 38):\n \\[\n 83 \\times 3 = 249\n \\]\n\n- Now, multiply 83 b...
[ "Certainly! Let's break down the multiplication of 38 and 83 step by step.\n\n1. **Multiply 38 by 3:**\n \\[\n 38 \\times 3 = 114\n \\]\n\n2. **Multiply 38 by 80 (which is 8 times 10):**\n \\[\n 38 \\times 80 = 38 \\times (8 \\times 10) = (38 \\times 8) \\times 10\n \\]\n First, calculate \\(38 \\time...
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[ "Certainly! Let's solve the long multiplication problem \\( 38 \\times 83 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 38\n × 83\n ------\n ```\n\n2. **Multiply 38 by 3 (the ones digit of 83):**\n - \\( 38 \\times 3 = 114 \\)\n - Write down 114 under...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\( 38 \\times 83 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 38\n \u00d7 83\n ------\n ```\n\n2. **Multiply 38 by 3 (the ones digit of 83):**\n - \\( 38 \\times 3 = 114 \\)\n - ...
[ "Certainly! Let's solve the long multiplication problem \\( 38 \\times 83 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n ```\n 38\n × 83\n ------\n ```\n\n2. **Multiply 38 by 3 (the ones digit of 83):**\n - \\( 38 \\times 3 = 114 \\)\n - Write down 114 under...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"- Combine them:\", \"answer\": \"318\"}, {\"context\": \"Therefore, the product of 38 x 83 is\", \"answer\": \"318\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{318}", "\\boxed{318}" ]
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[ "318", "318" ]
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What is the solution to the long multiplication equation below? 56 x 42 Think step by step.
2352
"{\"arg1\": 56, \"arg2\": 42, \"solution\": 2352}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n56 x 42\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(56 \\times 42\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(56\\) can be broken down into \\(50 + 6\\).\n - \\(42\\) can be broken down into \\(40 + 2\\).\n\n2. **Multiply each part of the first number by each part of the secon...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "To solve the long multiplication problem \\( 56 \\times 42 \\), we will break it down into steps:\n\n### Step 1: Multiply 56 by 2 (the units digit of 42)\n- \\( 56 \\times 2 = 112 \\)\n\n### Step 2: Multiply 56 by 40 (the tens digit of 42, which is 4 with an extra zero at the end)\n- \\( 56 \\times 40 = 56 \\times...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(56 \\times 42\\), let's break it down into steps:\n\n1. **Set up the multiplication:**\n ```\n 56\n × 42\n ----\n ```\n\n2. **Multiply 56 by 2 (the units digit of 42):**\n - Multiply 56 by 2:\n ```\n 56\n × 2\n ------\n ...
{"continuation_phrases": ["But I need to verify this.", "But according to"], "continuations": [" Let's do it correctly:\n ```\n 56\n \u00d7 40\n ------\n 2240\n ```\n\n4. **Add the two results together:**\n - We have 112 and 2240 from our previous steps.\n - Add them vertically:\n ...
[ "To solve the long multiplication problem \\(56 \\times 42\\), let's break it down into steps:\n\n1. **Set up the multiplication:**\n ```\n 56\n × 42\n ----\n ```\n\n2. **Multiply 56 by 2 (the units digit of 42):**\n - Multiply 56 by 2:\n ```\n 56\n × 2\n ------\n ...
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[ "Certainly! Let's solve this step-by-step.\n\n### Step 1: Set up the problem\nWe need to multiply two numbers:\n\\[ 56 \\times 42 \\]\n\n### Step 2: Break down each number into tens and ones\n- \\( 56 = 50 + 6 \\)\n- \\( 42 = 40 + 2 \\)\n\n### Step 3: Multiply each part of the first number by each part of the secon...
{"all_responses": ["Certainly! Let's solve this step-by-step.\n\n### Step 1: Set up the problem\nWe need to multiply two numbers:\n\\[ 56 \\times 42 \\]\n\n### Step 2: Break down each number into tens and ones\n- \\( 56 = 50 + 6 \\)\n- \\( 42 = 40 + 2 \\)\n\n### Step 3: Multiply each part of the first number by each pa...
[ "Certainly! Let's solve this step-by-step.\n\n### Step 1: Set up the problem\nWe need to multiply two numbers:\n\\[ 56 \\times 42 \\]\n\n### Step 2: Break down each number into tens and ones\n- \\( 56 = 50 + 6 \\)\n- \\( 42 = 40 + 2 \\)\n\n### Step 3: Multiply each part of the first number by each part of the secon...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 56 x 42 is\", \"answer\": \"2352\"}]}" ]
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[ "\\boxed{2352}" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 35 x 25 Think step by step.
875
"{\"arg1\": 35, \"arg2\": 25, \"solution\": 875}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n35 x 25\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(35 \\times 25\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(35\\) can be broken down into \\(30 + 5\\).\n - \\(25\\) remains as it is.\n\n2. **Multiply each part of the first number by the second number:**\n - Multiply \\(30\...
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[ "To solve the long multiplication problem \\(35 \\times 25\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. **Break down the numbers:**\n - \\(35\\) can be broken down into \\(30 + 5\\).\n - \\(25\\) remains as \\(25\\).\n\n2. **Apply the distrib...
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[ "To solve the long multiplication problem \\(35 \\times 25\\), you can break it down into simpler steps:\n\n1. **Multiply 35 by 5:**\n - 35 × 5 = 175\n\n2. **Multiply 35 by 20 (which is the same as multiplying by 2 and then adding zero):**\n - First, multiply 35 by 2: \n - 35 × 2 = 70\n - Then add another...
{"continuation_phrases": ["Hold on, let me verify this answer.", "Wait, this result is"], "continuations": [" Let's calculate it correctly.\n\nLet's do it again carefully:\n\n1. Multiply 35 by 5 directly:\n - 35 \u00d7 5 = 175\n\n2. Now, multiply 35 by 20:\n - 35 \u00d7 2 = 70\n - Add another 0 at the end:\n ...
[ "To solve the long multiplication problem \\(35 \\times 25\\), you can break it down into simpler steps:\n\n1. **Multiply 35 by 5:**\n - 35 × 5 = 175\n\n2. **Multiply 35 by 20 (which is the same as multiplying by 2 and then adding zero):**\n - First, multiply 35 by 2: \n - 35 × 2 = 70\n - Then add another...
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[ "To solve the long multiplication problem \\(35 \\times 25\\), we can break it down into simpler steps:\n\n1. **Break down 35**: We know that 35 can be written as \\(30 + 5\\).\n\n2. **Multiply each part by 25**:\n - First, multiply 30 by 25.\n - Then, multiply 5 by 25.\n\nLet's do this step-by-step:\n\n### Ste...
{"all_responses": ["To solve the long multiplication problem \\(35 \\times 25\\), we can break it down into simpler steps:\n\n1. **Break down 35**: We know that 35 can be written as \\(30 + 5\\).\n\n2. **Multiply each part by 25**:\n - First, multiply 30 by 25.\n - Then, multiply 5 by 25.\n\nLet's do this step-by-s...
[ "To solve the long multiplication problem \\(35 \\times 25\\), we can break it down into simpler steps:\n\n1. **Break down 35**: We know that 35 can be written as \\(30 + 5\\).\n\n2. **Multiply each part by 25**:\n - First, multiply 30 by 25.\n - Then, multiply 5 by 25.\n\nLet's do this step-by-step:\n\n### Ste...
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[ true ]
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[ [ true ] ]
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[ "875", "875", "875" ]
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[ true, true, true ]
[ "875", "875", "875" ]
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[ [ true ], [ true ], [ false, true ] ]
[ [ "875" ], [ "875" ], [ "indeed 875", "875" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 35 x 25 is\", \"answer\": \"875\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{875}" ]
[ true ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 90 x 58 Think step by step.
5220
"{\"arg1\": 90, \"arg2\": 58, \"solution\": 5220}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n90 x 58\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\( 90 \\times 58 \\), we can break it down into simpler steps:\n\n1. **Break down 90 and 58:**\n - 90 = 9 × 10\n - 58 = 5 × 10 + 8\n\n2. **Multiply each part of 90 by 58:**\n - First, multiply 9 by 58:\n \\[\n 9 \\times 58 = 9 \\times (50 + 8) = 9 \\times 50 ...
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[ "To solve the long multiplication problem \\( 90 \\times 58 \\), we can break it down into simpler steps:\n\n1. **Multiply 90 by 8 (the units digit of 58):**\n - \\( 90 \\times 8 = 720 \\)\n \n2. **Multiply 90 by 50 (the tens digit of 58):**\n - First, multiply 90 by 5: \n - \\( 90 \\times 5 = 450 \\)\n ...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\( 90 \\times 58 \\), let's break it down into steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 90\n x 58\n ----\n ```\n\n2. **Multiply 90 by 8 (the units digit of 58):**\n - \\( 90 \\times 8 = 720 \\)\n - Write down 720.\n\...
{"continuation_phrases": ["But I need to verify this.", "Wait, how?"], "continuations": [" Let me do it correctly now:\n \n - Correctly add them:\n - Align the numbers vertically for easier addition.\n ```\n 90\n x 58\n -----\n 720 (90x8)\n 4500 (90x5 shifted one place to the left)\n...
[ "To solve the long multiplication problem \\( 90 \\times 58 \\), let's break it down into steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 90\n x 58\n ----\n ```\n\n2. **Multiply 90 by 8 (the units digit of 58):**\n - \\( 90 \\times 8 = 720 \\)\n - Write down 720.\n\...
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[ "To solve the long multiplication problem \\( 90 \\times 58 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 90\n × 58\n ```\n\n2. **Multiply 90 by 8 (the units digit of 58):**\n - Multiply 90 by 8:\n \\[\n 90 \\times 8 = 720\n \\]\n - Write down 720.\n\n3. **...
{"all_responses": ["To solve the long multiplication problem \\( 90 \\times 58 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 90\n \u00d7 58\n ```\n\n2. **Multiply 90 by 8 (the units digit of 58):**\n - Multiply 90 by 8:\n \\[\n 90 \\times 8 = 720\n \\]\n - Writ...
[ "To solve the long multiplication problem \\( 90 \\times 58 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 90\n × 58\n ```\n\n2. **Multiply 90 by 8 (the units digit of 58):**\n - Multiply 90 by 8:\n \\[\n 90 \\times 8 = 720\n \\]\n - Write down 720.\n\n3. **...
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[ [ false ] ]
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[ [ "\\( 5220 \\)", "indeed \\( 5220 \\) but let's confirm that by another method:", "\\( 5220 \\)", "5220" ] ]
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[ [ "5220" ], [ "\\( 5220 \\)", "5220" ], [ "indeed \\( 5220 \\) but let's confirm that by another method:", "\\( 5220 \\)", "5220" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 90 x 58 is\", \"answer\": \"1102\"}]}" ]
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[ "\\boxed{1102}" ]
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[ "1102" ]
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[ [ false ] ]
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What is the solution to the long multiplication equation below? 88 x 65 Think step by step.
5720
"{\"arg1\": 88, \"arg2\": 65, \"solution\": 5720}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n88 x 65\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(88 \\times 65\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 88\n × 65\n ```\n\n2. **Multiply 88 by 5 (the units digit of 65):**\n - Multiply 88 by 5:\n ```\n 440\n ```\n - Write down 440.\n\n3. **Multiply 88 by ...
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[ "To solve the long multiplication problem \\(88 \\times 65\\), we can break it down into simpler steps.\n\n### Step-by-Step Solution:\n\n1. **Multiply 88 by 5:**\n - 88 × 5 = 440\n\n2. **Multiply 88 by 60 (which is 6 tens):**\n - First, multiply 88 by 6:\n \\[\n 88 \\times 6 = 528\n \\]\n - Now, m...
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[ "To solve the long multiplication problem \\( 88 \\times 65 \\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 88\n × 65\n ------\n ```\n\n2. **Multiply 88 by 5 (the units digit of 65):**\n - Multiply 88 by 5:\n ```\n 88\n × 5\n ------\n 440\n ...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But I need to verify this."], "continuations": [" Let's break it down again carefully.\n \n To get \\(88 \\times 65\\):\n - First, multiply 88 by 5 (units place) = 440.\n - Then, multiply 88 by 60 (tens place) = 5280.\n - Now add them together:...
[ "To solve the long multiplication problem \\( 88 \\times 65 \\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 88\n × 65\n ------\n ```\n\n2. **Multiply 88 by 5 (the units digit of 65):**\n - Multiply 88 by 5:\n ```\n 88\n × 5\n ------\n 440\n ...
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[ "To solve the long multiplication problem \\(88 \\times 65\\), we will break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Break down 65 into tens and ones:**\n - 65 = 60 + 5\n\n2. **Multiply 88 by each part of 65 separately:**\n\n - First, multiply 88 by 60:\n \\[\n 88 \\times 60 = ...
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[ "To solve the long multiplication problem \\(88 \\times 65\\), we will break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Break down 65 into tens and ones:**\n - 65 = 60 + 5\n\n2. **Multiply 88 by each part of 65 separately:**\n\n - First, multiply 88 by 60:\n \\[\n 88 \\times 60 = ...
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[ true, true, true ]
[ "5720", "5720", "5720" ]
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[ [ true ], [ true ], [ true ] ]
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[ [ false, false, true ] ]
[ [ "\\(5720\\)", "indeed \\(5720\\)", "5720" ] ]
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[ "5720", "5720", "5720", "5720" ]
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[ [ "5720" ], [ "\\(5720\\)", "5720" ], [ "indeed \\(5720\\)", "5720" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 88 x 65 is\", \"answer\": \"5720\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{5720}" ]
[ true ]
[ "5720" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 90 x 22 Think step by step.
1980
"{\"arg1\": 90, \"arg2\": 22, \"solution\": 1980}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n90 x 22\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\( 90 \\times 22 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 90 = 9 \\times 10 \\)\n - \\( 22 = 2 \\times 11 \\)\n\n2. **Multiply each part separately:**\n - First, multiply \\( 9 \\) by \\( 2 \\):\n \\[\n 9 \\times...
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[ "To solve the long multiplication problem \\(90 \\times 22\\), let's break it down into steps:\n\n1. **Write down the numbers:**\n ```\n 90\n x 22\n ```\n\n2. **Multiply 90 by 2 (the ones digit of 22):**\n - \\(90 \\times 2 = 180\\) \n Write down 0 and carry over 18.\n\n3. **Multiply 90 by 2 (the te...
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[ "To solve the long multiplication problem \\(90 \\times 22\\), we can break it down into simpler steps:\n\n1. **Break down 90 and 22:**\n - \\(90\\) can be broken down into \\(9 \\times 10\\).\n - \\(22\\) can be broken down into \\(2 \\times 11\\).\n\n2. **Multiply each part separately:**\n - First, multiply...
{"continuation_phrases": ["Wait! I can double check this answer.", "Hold on, let me verify this answer."], "continuations": [" Let's do it another way.\n\n4. **Recompute using distributive property:**\n - Instead of multiplying directly, use the distributive property:\n \\[\n 90 \\times 22 = (90 \\times 2) \\...
[ "To solve the long multiplication problem \\(90 \\times 22\\), we can break it down into simpler steps:\n\n1. **Break down 90 and 22:**\n - \\(90\\) can be broken down into \\(9 \\times 10\\).\n - \\(22\\) can be broken down into \\(2 \\times 11\\).\n\n2. **Multiply each part separately:**\n - First, multiply...
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[ "To solve the long multiplication problem \\( 90 \\times 22 \\), we can break it down into simpler steps:\n\n1. **Break down 90 and 22:**\n - 90 = 9 × 10\n - 22 = 2 × 11\n\n2. **Multiply each part separately:**\n - First, multiply 9 by 2:\n \\[\n 9 \\times 2 = 18\n \\]\n - Next, multiply 9 by 10...
{"all_responses": ["To solve the long multiplication problem \\( 90 \\times 22 \\), we can break it down into simpler steps:\n\n1. **Break down 90 and 22:**\n - 90 = 9 \u00d7 10\n - 22 = 2 \u00d7 11\n\n2. **Multiply each part separately:**\n - First, multiply 9 by 2:\n \\[\n 9 \\times 2 = 18\n \\]\n ...
[ "To solve the long multiplication problem \\( 90 \\times 22 \\), we can break it down into simpler steps:\n\n1. **Break down 90 and 22:**\n - 90 = 9 × 10\n - 22 = 2 × 11\n\n2. **Multiply each part separately:**\n - First, multiply 9 by 2:\n \\[\n 9 \\times 2 = 18\n \\]\n - Next, multiply 9 by 10...
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[ true ]
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[ "1980", "540", "540" ]
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[ [ "1980" ], [ "540" ], [ "540" ] ]
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[ [ "\\(1980\\)", "\\(1980\\)", "1980" ] ]
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[ "1080", "1980", "1980", "1980" ]
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[ "1120", "1980", "1980" ]
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[ [ "1120" ], [ "\\(1980\\)", "1980" ], [ "\\(1980\\)", "1980" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 90 x 22 is:\", \"answer\": \"1980\"}]}" ]
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[ "\\boxed{1980}" ]
[ true ]
[ "1980" ]
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[ [ true ] ]
[ [ "1980" ] ]
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What is the solution to the long multiplication equation below? 62 x 45 Think step by step.
2790
"{\"arg1\": 62, \"arg2\": 45, \"solution\": 2790}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n62 x 45\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(62 \\times 45\\), we can break it down into simpler steps:\n\n1. **Multiply 62 by 5 (the units digit of 45):**\n - \\(62 \\times 5 = 310\\)\n\n2. **Multiply 62 by 40 (the tens digit of 45, which is 4 times 10):**\n - First, calculate \\(62 \\times 4 = 248\\).\n - T...
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[ "To solve the long multiplication of 62 and 45, we'll break it down into simpler steps:\n\n1) First, let's write out the numbers vertically:\n ```\n 62\n x 45\n ```\n\n2) Now, multiply each digit in 62 by 5 (the rightmost digit of 45):\n - 62 * 5 = 310\n\n3) Next, multiply each digit in 62 by 4 (the lef...
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[ "To solve the long multiplication problem \\(62 \\times 45\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n × 45\n ```\n\n2. **Multiply 62 by 5 (the units digit of 45):**\n - Multiply 62 by 5:\n ```\n 310\n ```\n - Write down 310.\n\n3. **Multiply 62 by 40 (the t...
{"continuation_phrases": ["Wait! I can double check this answer.", "But I need to verify this."], "continuations": [" Let's break it down again carefully.\n \n - First, let's multiply 62 by 5:\n ```\n 62 \u00d7 5 = 310\n ```\n\n - Now, let's multiply 62 by 40:\n ```\n 62 \u00d7 40 = 2480\n ...
[ "To solve the long multiplication problem \\(62 \\times 45\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n × 45\n ```\n\n2. **Multiply 62 by 5 (the units digit of 45):**\n - Multiply 62 by 5:\n ```\n 310\n ```\n - Write down 310.\n\n3. **Multiply 62 by 40 (the t...
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[ "To solve the long multiplication problem \\( 62 \\times 45 \\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n × 45\n ------\n ```\n\n2. **Multiply 62 by 5 (the units digit of 45):**\n - Multiply 62 by 5:\n ```\n 310\n - 62×5 = 310\n ```\n - Write d...
{"all_responses": ["To solve the long multiplication problem \\( 62 \\times 45 \\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n \u00d7 45\n ------\n ```\n\n2. **Multiply 62 by 5 (the units digit of 45):**\n - Multiply 62 by 5:\n ```\n 310\n - 62\u00d75 = 31...
[ "To solve the long multiplication problem \\( 62 \\times 45 \\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 62\n × 45\n ------\n ```\n\n2. **Multiply 62 by 5 (the units digit of 45):**\n - Multiply 62 by 5:\n ```\n 310\n - 62×5 = 310\n ```\n - Write d...
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[ "2890", "2790", "2790" ]
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[ [ "25110" ], [ "indeed \\( 62 \\times 45 = 2510 \\)", "2510" ], [ "\\( 62 \\times 45 = 2790 \\)", "2790" ], [ "\\( 62 \\times 45 = 2790 \\)", "2790" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 62 x 45 is\", \"answer\": \"2790\"}]}" ]
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[ "\\boxed{2790}" ]
[ true ]
[ "2790" ]
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[ [ true ] ]
[ [ "2790" ] ]
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What is the solution to the long multiplication equation below? 15 x 17 Think step by step.
255
"{\"arg1\": 15, \"arg2\": 17, \"solution\": 255}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n15 x 17\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(15 \\times 17\\), we can break it down into simpler steps:\n\nStep 1: Multiply 15 by 7 (the units digit of 17).\n\\[ 15 \\times 7 = 105 \\]\n\nStep 2: Multiply 15 by 10 (which is the same as multiplying by 1 and then adding a zero at the end).\n\\[ 15 \\times 10 = 150 \\...
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[ "To solve the long multiplication problem \\(15 \\times 17\\), we can break it down into simpler steps:\n\nStep 1: Multiply 15 by 7 (the ones digit of 17).\n\\[ 15 \\times 7 = 105 \\]\n\nStep 2: Multiply 15 by 10 (which is the same as multiplying by 1 and then adding a zero at the end).\n\\[ 15 \\times 10 = 150 \\]...
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[ "To solve the long multiplication problem \\(15 \\times 17\\), we can break it down into simpler steps:\n\n### Step 1: Break down the numbers\nFirst, let's write out the numbers:\n- \\(15\\) (which means 1 ten and 5 ones)\n- \\(17\\) (which means 1 ten and 7 ones)\n\n### Step 2: Multiply each digit of one number by...
{"continuation_phrases": ["Wait, let me try", "But I need to verify this."], "continuations": [" again for clarity:\n- Multiply 15 by 7:\n\\[ 15 \\times 7 = 105 \\]\n- Multiply 15 by 10 (remember that this is just adding another zero at the end):\n\\[ 15 \\times 10 = 150 \\]\n\n### Step 3: Add up all these products\nNo...
[ "To solve the long multiplication problem \\(15 \\times 17\\), we can break it down into simpler steps:\n\n### Step 1: Break down the numbers\nFirst, let's write out the numbers:\n- \\(15\\) (which means 1 ten and 5 ones)\n- \\(17\\) (which means 1 ten and 7 ones)\n\n### Step 2: Multiply each digit of one number by...
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[ "Certainly! Let's solve this problem step by step.\n\n### Step-by-Step Solution:\n\n#### 1. Write down the numbers:\n \\[\n 15 \\\\\n \\times 17 \\\\\n ------\n \\]\n\n#### 2. Multiply 15 by 7 (the ones digit of 17):\n \\[\n 15 \\times 7 = 105\n \\]\n Write 5 in the ones place and carry over 10 to...
{"all_responses": ["Certainly! Let's solve this problem step by step.\n\n### Step-by-Step Solution:\n\n#### 1. Write down the numbers:\n \\[\n 15 \\\\\n \\times 17 \\\\\n ------\n \\]\n\n#### 2. Multiply 15 by 7 (the ones digit of 17):\n \\[\n 15 \\times 7 = 105\n \\]\n Write 5 in the ones place and c...
[ "Certainly! Let's solve this problem step by step.\n\n### Step-by-Step Solution:\n\n#### 1. Write down the numbers:\n \\[\n 15 \\\\\n \\times 17 \\\\\n ------\n \\]\n\n#### 2. Multiply 15 by 7 (the ones digit of 17):\n \\[\n 15 \\times 7 = 105\n \\]\n Write 5 in the ones place and carry over 10 to...
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[ true ]
[ "255" ]
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[ [ true ] ]
[ [ "255" ] ]
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[ true, true, true ]
[ "255", "255", "255" ]
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[ [ true ], [ true ], [ true ] ]
[ [ "255" ], [ "255" ], [ "255" ] ]
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[ "340" ]
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[ [ false, false ] ]
[ [ "indeed **340**", "340" ] ]
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[ "255", "255", "255", "360" ]
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[ [ "255" ], [ "270" ], [ "indeed **340**", "340" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 15 x 17 is\", \"answer\": \"255\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{255}" ]
[ true ]
[ "255" ]
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[ [ true ] ]
[ [ "255" ] ]
[ [ { "all_extracted_answers": [ "255" ], "all_extractions": [ "{'content': '255', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '255'}" ], "confidence": 0.9500000000000001, "extracted_answer": "255", "extractor": "stri...
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What is the solution to the long multiplication equation below? 20 x 20 Think step by step.
400
"{\"arg1\": 20, \"arg2\": 20, \"solution\": 400}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n20 x 20\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
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null
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null
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[ "To solve the long multiplication problem \\(20 \\times 20\\), let's break it down into steps:\n\n1. **Write the numbers vertically:**\n ```\n 20\n × 20\n ----\n ```\n\n2. **Multiply each digit of the bottom number by the top number:**\n\n - Multiply 2 (from 20) by 0:\n ```\n 20\n × 20\n...
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[ "To solve the long multiplication problem \\( 20 \\times 20 \\), we can follow these steps:\n\n1. **Write down the numbers:**\n \\[\n 20 \\\\\n \\times 20 \\\\\n ------\n \\]\n\n2. **Multiply each digit of the bottom number by the top number:**\n\n - Multiply 2 (from 20) by 0:\n \\[\n 2 \\times ...
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[ "Certainly! Let's solve this step by step:\n\n1) First, let's write down the problem:\n 20 x 20\n\n2) Now, let's break it down into simpler parts:\n - We can think of 20 as 2 tens (because 2 * 10 = 20)\n - So we have: 2 tens x 2 tens\n\n3) When you multiply two numbers that each have one zero in them, you get...
{"continuation_phrases": ["But I need to verify this.", "Wait, let me try"], "continuations": [" If we multiply 20 by 2, we get 40.\n - So, 20 x 20 should be 400.\n\n3) To double-check, let's do it another way:\n - 20 x 20 means we're multiplying 20 by itself.\n - That's like having 20 groups of 20 things each.\n...
[ "Certainly! Let's solve this step by step:\n\n1) First, let's write down the problem:\n 20 x 20\n\n2) Now, let's break it down into simpler parts:\n - We can think of 20 as 2 tens (because 2 * 10 = 20)\n - So we have: 2 tens x 2 tens\n\n3) When you multiply two numbers that each have one zero in them, you get...
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[ "To solve the long multiplication problem \\( 20 \\times 20 \\), let's break it down into steps:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\hline\n & 20 \\\\\n \\end{array}\n \\]\n\n2. **Multiply each digit of the bottom number (20) by the top number (20):**\n\...
{"all_responses": ["To solve the long multiplication problem \\( 20 \\times 20 \\), let's break it down into steps:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\hline\n & 20 \\\\\n \\end{array}\n \\]\n\n2. **Multiply each digit of the bottom number (20) by the top nu...
[ "To solve the long multiplication problem \\( 20 \\times 20 \\), let's break it down into steps:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n \\hline\n & 20 \\\\\n \\end{array}\n \\]\n\n2. **Multiply each digit of the bottom number (20) by the top number (20):**\n\...
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[ [ true ] ]
[ [ "400" ] ]
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[ true, true, true ]
[ "400", "400", "400" ]
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[ [ true ], [ false, true ], [ true ] ]
[ [ "400" ], [ "\\(400\\)", "400" ], [ "400" ] ]
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[ true ]
[ "400" ]
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[ [ false, false, true ] ]
[ [ ": 20 x 20 = 400", "indeed 400", "400" ] ]
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[ "400", "400", "400", "400" ]
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[ [ "\\( 400 \\)", "400" ], [ "indeed \\( 400 \\)", "\\( \\boxed{400} \\)", "400" ], [ "\\( \\boxed{400} \\)", "400" ], [ "indeed \\(400\\)", "400" ] ]
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[ [ "400" ], [ ": 20 x 20 = 400", "400" ], [ "indeed 400", "400" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 20 x 20 = 400.\", \"answer\": \"400\"}, {\"context\": \"Therefore, the solution to the long multiplication equation 20 x 20 is 400.\", \"answer\": \"400\"}]}" ]
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What is the solution to the long multiplication equation below? 55 x 40 Think step by step.
2200
"{\"arg1\": 55, \"arg2\": 40, \"solution\": 2200}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n55 x 40\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(55 \\times 40\\), we can break it down into simpler steps:\n\n1. **Multiply 55 by 0**: \n - Any number multiplied by 0 equals 0.\n - So, \\(55 \\times 0 = 0\\).\n\n2. **Multiply 55 by 4**:\n - To do this, you can think of it as adding 55 four times: \\(55 + 55 + 55...
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[ "To solve the long multiplication problem \\(55 \\times 40\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(55\\) can be thought of as \\(50 + 5\\).\n - \\(40\\) remains the same.\n\n2. **Multiply each part by 40:**\n - First, multiply \\(50\\) by \\(40\\):\n \\[\n ...
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[ "To solve the long multiplication problem \\( 55 \\times 40 \\), we can break it down into simpler steps.\n\n### Step-by-Step Solution:\n\n1. **Break down the numbers:**\n - \\( 55 \\) can be written as \\( 50 + 5 \\).\n - \\( 40 \\) remains the same because it's already in its simplest form.\n\n2. **Multiply e...
{"continuation_phrases": ["Hold on, let me verify this answer.", "Wait, this result is"], "continuations": [" The correct product should be calculated as follows:\n\\[\n55 \\times 40 = 55 \\times (4 \\times 10) = (5 \\times 4) \\times 10 = 20 \\times 10 = 200\n\\]\nIt seems there was an error in my previous explanation...
[ "To solve the long multiplication problem \\( 55 \\times 40 \\), we can break it down into simpler steps.\n\n### Step-by-Step Solution:\n\n1. **Break down the numbers:**\n - \\( 55 \\) can be written as \\( 50 + 5 \\).\n - \\( 40 \\) remains the same because it's already in its simplest form.\n\n2. **Multiply e...
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[ "To solve the long multiplication problem \\(55 \\times 40\\), we can break it down into simpler steps.\n\nStep 1: Break down the numbers.\n- 55 can be seen as 5 tens and 5 ones.\n- 40 can be seen as 4 tens.\n\nStep 2: Multiply each part of the first number by the second number.\n- First, multiply 5 (tens) by 40:\n...
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[ "To solve the long multiplication problem \\(55 \\times 40\\), we can break it down into simpler steps.\n\nStep 1: Break down the numbers.\n- 55 can be seen as 5 tens and 5 ones.\n- 40 can be seen as 4 tens.\n\nStep 2: Multiply each part of the first number by the second number.\n- First, multiply 5 (tens) by 40:\n...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Thus, the solution to the long multiplication equation 55 x 40 is\", \"answer\": \"220\"}]}" ]
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[ "\\boxed{220}" ]
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[ [ false ] ]
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What is the solution to the long multiplication equation below? 70 x 60 Think step by step.
4200
"{\"arg1\": 70, \"arg2\": 60, \"solution\": 4200}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n70 x 60\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(70 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply the units digits**: \n - The units digit of 70 is 0.\n - The units digit of 60 is 0.\n - So, \\(0 \\times 0 = 0\\).\n\n2. **Multiply the tens digits**:\n - The tens digit of 70 is 7 (sinc...
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[ "To solve the long multiplication problem \\( 70 \\times 60 \\), let's break it down into steps:\n\n1. **Write the numbers vertically:**\n ```\n 70\n × 60\n ```\n\n2. **Multiply 70 by 0 (the ones digit of 60):**\n - 70 × 0 = 0\n Write 0 in the units place.\n\n3. **Multiply 70 by 6 (the tens digit of 6...
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[ "To solve the long multiplication problem \\(70 \\times 60\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 70\n × 60\n _______\n```\n\n### Step 2: Multiply 70 by 0 (the units digit of 60).\n- \\(70 \\times 0 = 0\\)\n- Write this result under the line.\n\n```\n...
{"continuation_phrases": ["Wait, this result is", "Wait, let me try"], "continuations": [" incorrect. Let me correct that.\n\n### Corrected Step 3: Multiply 70 by 6 and then add zero for the carry-over from the previous multiplication.\n- \\(70 \\times 6 = 420\\) (This is already done above).\n\nNow, add the result of ...
[ "To solve the long multiplication problem \\(70 \\times 60\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 70\n × 60\n _______\n```\n\n### Step 2: Multiply 70 by 0 (the units digit of 60).\n- \\(70 \\times 0 = 0\\)\n- Write this result under the line.\n\n```\n...
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[ "To solve the long multiplication problem \\( 70 \\times 60 \\), let's break it down into steps:\n\n1. **Understand the numbers:**\n - 70 can be thought of as \\( 7 \\times 10 \\).\n - 60 can be thought of as \\( 6 \\times 10 \\).\n\n2. **Multiply each part separately:**\n - First, multiply 7 by 10:\n \\[...
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[ "To solve the long multiplication problem \\( 70 \\times 60 \\), let's break it down into steps:\n\n1. **Understand the numbers:**\n - 70 can be thought of as \\( 7 \\times 10 \\).\n - 60 can be thought of as \\( 6 \\times 10 \\).\n\n2. **Multiply each part separately:**\n - First, multiply 7 by 10:\n \\[...
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[ "4200", "4200", "4200" ]
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[ [ true ], [ true ], [ true ] ]
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[ [ false, false, true ] ]
[ [ "\\(4200\\)", "\\(4200\\)", "4200" ] ]
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[ false, true, true, true ]
[ "130", "4200", "4200", "4200" ]
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[ [ false ], [ true ], [ false, true ], [ true ] ]
[ [ "130" ], [ "4200" ], [ "indeed 4200", "4200" ], [ "4200" ] ]
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[ true, false, true ]
[ "4200", "4620", "4200" ]
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[ [ true ], [ false, false ], [ false, true ] ]
[ [ "4200" ], [ "\\(4200\\)", "4620" ], [ "\\(4200\\)", "4200" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, combining them gives us:\", \"answer\": \"42\"}, {\"context\": \"Therefore, the product of 70 x 60 is\", \"answer\": \"4200\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{42}", "\\boxed{4200}" ]
[ false, true ]
[ "42", "4200" ]
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[ [ false ], [ true ] ]
[ [ "42" ], [ "4200" ] ]
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What is the solution to the long multiplication equation below? 23 x 23 Think step by step.
529
"{\"arg1\": 23, \"arg2\": 23, \"solution\": 529}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n23 x 23\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(23 \\times 23\\), we can break it down into simpler steps:\n\n1. **Break down the numbers**: We can think of 23 as \\(20 + 3\\). So, \\(23 \\times 23\\) becomes \\((20 + 3) \\times (20 + 3)\\).\n\n2. **Use the distributive property**: The distributive property states tha...
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[ "To solve the long multiplication problem \\(23 \\times 23\\), we can break it down into smaller steps:\n\n1. **Multiply each digit of the bottom number by the first digit of the top number:**\n - \\(23 \\times 2 = 46\\)\n\n2. **Multiply each digit of the bottom number by the next digit of the top number and add ...
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[ "Certainly! Let's solve the problem of multiplying 23 by 23 step by step.\n\nStep 1: Write down the numbers to be multiplied.\n```\n 23\nx 23\n```\n\nStep 2: Multiply each digit of the bottom number (23) by the top number (23), starting from the rightmost digit and moving left.\n- Multiply 3 (from 23) by 3 (the l...
{"continuation_phrases": ["Hold on, let me verify this answer.", "But according to"], "continuations": [" When we add 9 and 60, we get 69, not 529. It looks like there was a mistake in my previous explanation. Let's correct it:\n\nThe correct way to do this is to consider that 23 is actually 20 + 3. So we can break it ...
[ "Certainly! Let's solve the problem of multiplying 23 by 23 step by step.\n\nStep 1: Write down the numbers to be multiplied.\n```\n 23\nx 23\n```\n\nStep 2: Multiply each digit of the bottom number (23) by the top number (23), starting from the rightmost digit and moving left.\n- Multiply 3 (from 23) by 3 (the l...
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[ "To solve the long multiplication problem \\(23 \\times 23\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 23\n× 23\n_____\n```\n\n### Step 2: Multiply each digit of the top number by the first digit of the bottom number (2).\n- Multiply 3 by 3:\n ```\n 3\n × ...
{"all_responses": ["To solve the long multiplication problem \\(23 \\times 23\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 23\n\u00d7 23\n_____\n```\n\n### Step 2: Multiply each digit of the top number by the first digit of the bottom number (2).\n- Multiply 3 by 3:...
[ "To solve the long multiplication problem \\(23 \\times 23\\), let's break it down into steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 23\n× 23\n_____\n```\n\n### Step 2: Multiply each digit of the top number by the first digit of the bottom number (2).\n- Multiply 3 by 3:\n ```\n 3\n × ...
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[ true ]
[ "529" ]
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[ [ true ] ]
[ [ "529" ] ]
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[ true, true, true ]
[ "529", "529", "529" ]
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[ [ true ], [ true ], [ true ] ]
[ [ "529" ], [ "529" ], [ "529" ] ]
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[ [ false, true ] ]
[ [ "\\( 23 \\times 23 = 529 \\)", "529" ] ]
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[ true, true, true, true ]
[ "529", "529", "529", "529" ]
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[ true, true, true ]
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[ [ true ], [ false, true ], [ true ] ]
[ [ "529" ], [ "\\( 23 \\times 23 = 529 \\)", "529" ], [ "529" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 23 x 23 is\", \"answer\": \"529\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{529}" ]
[ true ]
[ "529" ]
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[ [ true ] ]
[ [ "529" ] ]
[ [ { "all_extracted_answers": [ "529" ], "all_extractions": [ "{'content': '529', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '529'}" ], "confidence": 0.9500000000000001, "extracted_answer": "529", "extractor": "stri...
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What is the solution to the long multiplication equation below? 91 x 61 Think step by step.
5551
"{\"arg1\": 91, \"arg2\": 61, \"solution\": 5551}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n91 x 61\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(91 \\times 61\\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 91\n × 61\n```\n\n### Step 2: Multiply 91 by 1 (the units digit of 61)\n- Multiply 91 by 1: \n ```\n 91\n × 1\n ------...
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[ "To solve the long multiplication problem \\(91 \\times 61\\), we will follow these steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 91\n × 61\n ----\n```\n\n### Step 2: Multiply 91 by 1 (the units digit of 61).\n```\n 91\n × 61\n ----\n 91 (91 × 1)\n```\n\n### Step 3: Multiply 91 by ...
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[ "Certainly! Let's solve the multiplication problem \\(91 \\times 61\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 91 \\\\\n \\times & 61 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 91 by 1 (the rightmost digit of 61):**\n \\[\n 91...
{"continuation_phrases": ["Wait, let me try", "Wait, this result is"], "continuations": [" that again more carefully.\n\nLet's do it one last time for clarity:\n\n1. Multiply 91 by 1:\n \\[\n 91 \\times 1 = 91\n \\]\n \n2. Multiply 91 by 6 and add the carry-over from the first step:\n \\[\n 91 \\times 6 = 5...
[ "Certainly! Let's solve the multiplication problem \\(91 \\times 61\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 91 \\\\\n \\times & 61 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 91 by 1 (the rightmost digit of 61):**\n \\[\n 91...
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[ "To solve the long multiplication problem \\(91 \\times 61\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down 61 into 60 + 1.\n\\[91 \\times 61 = 91 \\times (60 + 1)\\]\n\nStep 2: Distribute 91 to both terms inside the parentheses.\n\\[...
{"all_responses": ["To solve the long multiplication problem \\(91 \\times 61\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down 61 into 60 + 1.\n\\[91 \\times 61 = 91 \\times (60 + 1)\\]\n\nStep 2: Distribute 91 to both terms inside the pa...
[ "To solve the long multiplication problem \\(91 \\times 61\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down 61 into 60 + 1.\n\\[91 \\times 61 = 91 \\times (60 + 1)\\]\n\nStep 2: Distribute 91 to both terms inside the parentheses.\n\\[...
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[ false ]
[ "637" ]
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[ [ ":", "indeed:", "5461" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"- The result from multiplying 91 by 1 is 91.\", \"answer\": \"91\"}, {\"context\": \"- The result from multiplying 91 by 6 is 546.\", \"answer\": \"546\"}, {\"context\": \"Now add these two results together:\", \"answer\": \"637\"}, {\"context\": \"So, 91 x 61 = 637.\", \"answer...
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
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[ "\\boxed{91}", "\\boxed{546}", "\\boxed{637}", "\\boxed{637}" ]
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[ "91", "546", "637", "637" ]
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[ [ "91" ], [ "546" ], [ "637" ], [ "637" ] ]
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What is the solution to the long multiplication equation below? 52 x 12 Think step by step.
624
"{\"arg1\": 52, \"arg2\": 12, \"solution\": 624}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n52 x 12\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(52 \\times 12\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers\nWe can think of 52 as \\(50 + 2\\) and 12 as \\(10 + 2\\).\n\n#### Step 2: Multiply each part separately\nFirst, multiply 50 by 12:\n\\[ 50 \\...
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[ "To solve the long multiplication problem \\(52 \\times 12\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 52\n × 12\n ```\n\n2. **Multiply 52 by 2 (the units digit of 12):**\n - Multiply 52 by 2:\n ```\n 104\n ```\n - Write down 104.\n\n3. **Multiply 52 by 1 ...
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[ "To solve the long multiplication problem \\(52 \\times 12\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 52 by 2 (the ones digit of 12)\n\\[ 52 \\times 2 = 104 \\]\n\n#### Step 2: Multiply 52 by 10 (the tens digit of 12)\nSince multiplying by 10 means adding a z...
{"continuation_phrases": ["But I need to verify this.", "But to confirm,"], "continuations": [" Let's do it correctly.\n\n**Correct Method for Step 3:**\n\n\\[ 52 \\times 12 = 52 \\times (10 + 2) = 52 \\times 10 + 52 \\times 2 = 520 + 104 = 624 \\]\n\nSo, let's correct the addition in Step 3:\n\n\\[ 104 + 520 = 624 \\]...
[ "To solve the long multiplication problem \\(52 \\times 12\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 52 by 2 (the ones digit of 12)\n\\[ 52 \\times 2 = 104 \\]\n\n#### Step 2: Multiply 52 by 10 (the tens digit of 12)\nSince multiplying by 10 means adding a z...
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[ "To solve the long multiplication problem \\( 52 \\times 12 \\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 52\n × 12\n```\n\n### Step 2: Multiply 52 by 2 (the ones digit of 12)\n- Multiply 52 by 2:\n - 2 times 2 is 4.\n - 2 time...
{"all_responses": ["To solve the long multiplication problem \\( 52 \\times 12 \\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 52\n \u00d7 12\n```\n\n### Step 2: Multiply 52 by 2 (the ones digit of 12)\n- Multiply 52 by 2:\n - 2 times...
[ "To solve the long multiplication problem \\( 52 \\times 12 \\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 52\n × 12\n```\n\n### Step 2: Multiply 52 by 2 (the ones digit of 12)\n- Multiply 52 by 2:\n - 2 times 2 is 4.\n - 2 time...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 52 x 12 is **624**.\", \"answer\": \"624\"}, {\"context\": \"This confirms that our answer is correct.\", \"answer\": \"624\"}]}" ]
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[ "\\boxed{624}", "\\boxed{624}" ]
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[ "624", "624" ]
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[ [ "624" ], [ "624" ] ]
[ [ { "all_extracted_answers": [ "624" ], "all_extractions": [ "{'content': '624', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '624'}" ], "confidence": 0.9500000000000001, "extracted_answer": "624", "extractor": "stri...
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What is the solution to the long multiplication equation below? 67 x 41 Think step by step.
2747
"{\"arg1\": 67, \"arg2\": 41, \"solution\": 2747}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n67 x 41\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(67 \\times 41\\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 67\n × 41\n```\n\n### Step 2: Multiply 67 by 1 (the ones digit of 41)\n- Multiply 67 by 1: \n ```\n 67\n × 1\n ------\...
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[ "To solve the long multiplication problem \\(67 \\times 41\\), we can break it down into simpler steps:\n\n### Step 1: Break down the numbers\n- \\(67\\) can be broken down into \\(60 + 7\\)\n- \\(41\\) can be broken down into \\(40 + 1\\)\n\nSo, the problem becomes:\n\\[ (60 + 7) \\times (40 + 1) \\]\n\n### Step 2...
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[ "To solve the long multiplication of 67 and 41, let's break it down into steps:\n\n### Step 1: Multiply the ones digit of 67 (which is 7) by the ones digit of 41 (which is 1).\n\\[ 7 \\times 1 = 7 \\]\n\nWrite this result under the line.\n\n```\n 67\n × 41\n ----\n 7\n```\n\n### Step 2: Multiply the ...
{"continuation_phrases": ["However,", "Hold on, let me verify this answer."], "continuations": [" since we're multiplying by 10 later on, we can think of this as just multiplying 7 by 4.\n\\[ 7 \\times 4 = 28 \\]\nWrite this result above the line, shifted one place to the left.\n\n```\n 67\n \u00d7 41\n ----\...
[ "To solve the long multiplication of 67 and 41, let's break it down into steps:\n\n### Step 1: Multiply the ones digit of 67 (which is 7) by the ones digit of 41 (which is 1).\n\\[ 7 \\times 1 = 7 \\]\n\nWrite this result under the line.\n\n```\n 67\n × 41\n ----\n 7\n```\n\n### Step 2: Multiply the ...
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[ "To solve the long multiplication problem \\(67 \\times 41\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Write the numbers vertically:**\n ```\n 67\n × 41\n ------\n ```\n\n2. **Multiply 67 by 1 (the units digit of 41):**\n - Multiply 67 by 1:\n ```\n ...
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[ "To solve the long multiplication problem \\(67 \\times 41\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Write the numbers vertically:**\n ```\n 67\n × 41\n ------\n ```\n\n2. **Multiply 67 by 1 (the units digit of 41):**\n - Multiply 67 by 1:\n ```\n ...
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[ "2807", "2857", "2857" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Now, add the two products together:\", \"answer\": \"2857\"}, {\"context\": \"So, 67 x 41 =\", \"answer\": \"2857\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{2857}", "\\boxed{2857}" ]
[ false, false ]
[ "2857", "2857" ]
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[ [ "2857" ], [ "2857" ] ]
[ [ { "all_extracted_answers": [ "2857" ], "all_extractions": [ "{'content': '2857', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '2857'}" ], "confidence": 0.9500000000000001, "extracted_answer": "2857", "extractor": "...
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What is the solution to the long multiplication equation below? 48 x 35 Think step by step.
1680
"{\"arg1\": 48, \"arg2\": 35, \"solution\": 1680}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n48 x 35\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(48 \\times 35\\), we can break it down into simpler steps:\n\n1. **Multiply 48 by 5:**\n - 48 × 5 = 240\n\n2. **Multiply 48 by 30 (which is 3 times 10):**\n - First, multiply 48 by 3:\n - 48 × 3 = 144\n - Then, since we multiplied by 10 (which is 1 followed by ...
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[ "To solve the long multiplication problem \\(48 \\times 35\\), we can break it down into simpler steps:\n\n1. **Break down 48 and 35:**\n - 48 = 40 + 8\n - 35 = 30 + 5\n\n2. **Multiply each part of 48 by each part of 35:**\n\n - Multiply 40 by 35:\n \\[\n 40 \\times 35 = (40 \\times 30) + (40 \\times ...
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[ "Certainly! Let's break down the multiplication of 48 and 35 step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n & 48 \\\\\n \\times & 35 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 48 by 5 (the units digit of 35):**\n \\[\n 48 \\times 5 = 240\n \\]\n ...
{"continuation_phrases": ["However,", "Wait, let me try"], "continuations": [" since we already have 8 in the tens place, it doesn't affect the final result.\n\nSo, putting everything together, we get:\n\n\\[\n\\begin{array}{c@{}c}\n & 48 \\\\\n \\times & 35 \\\\\n \\hline\n & 240 \\\\\n+ 1680 \\\\\n\\hline...
[ "Certainly! Let's break down the multiplication of 48 and 35 step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n & 48 \\\\\n \\times & 35 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 48 by 5 (the units digit of 35):**\n \\[\n 48 \\times 5 = 240\n \\]\n ...
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[ "Certainly! Let's solve the long multiplication problem \\(48 \\times 35\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n\n```\n 48\n× 35\n------\n```\n\n### Step 2: Multiply 48 by 5 (the ones digit of 35)\n- Multiply 48 by 5:\n ```\n 48\n× 5\n---...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\(48 \\times 35\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n\n```\n 48\n\u00d7 35\n------\n```\n\n### Step 2: Multiply 48 by 5 (the ones digit of 35)\n- Multiply 48 by 5:\n ```\n...
[ "Certainly! Let's solve the long multiplication problem \\(48 \\times 35\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n\n```\n 48\n× 35\n------\n```\n\n### Step 2: Multiply 48 by 5 (the ones digit of 35)\n- Multiply 48 by 5:\n ```\n 48\n× 5\n---...
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[ [ true ] ]
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[ [ "indeed \\( 48 \\times 35 = 1680 \\)", "1680" ] ]
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[ [ "1680" ], [ "1680" ], [ "indeed \\( 48 \\times 35 = 1680 \\)", "1680" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 48 x 35 is\", \"answer\": \"1680\"}]}" ]
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What is the solution to the long multiplication equation below? 88 x 78 Think step by step.
6864
"{\"arg1\": 88, \"arg2\": 78, \"solution\": 6864}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n88 x 78\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(88 \\times 78\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 88\n × 78\n ------\n ```\n\n2. **Multiply 88 by 8 (the units digit of 78):**\n - Multiply 88 by 8:\n ```\n 88\n × 8\n ------\n 664...
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[ "To solve the multiplication problem \\(88 \\times 78\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 78 as the sum of two numbers that are easier to multiply with 88:\n\\[ 78 = 70 + 8 \\]\n\nNow, we can rewrite the original multip...
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[ "Certainly! Let's solve this long multiplication problem step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 88 \\\\\n \\times & 78 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 88 by 8 (the units digit of 78):**\n \\[\n 88 \\times 8 = 704\n...
{"continuation_phrases": ["However,", "But I need to verify this."], "continuations": [" let me correct my previous steps before proceeding with the actual multiplication.\n\n### Correcting the Multiplication Steps:\n\nWhen multiplying 88 by 8 (units digit):\n\\[\n88 \\times 8 = 704\n\\]\n\nThen when multiplying 88 by ...
[ "Certainly! Let's solve this long multiplication problem step by step.\n\n### Step-by-Step Solution:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n & 88 \\\\\n \\times & 78 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 88 by 8 (the units digit of 78):**\n \\[\n 88 \\times 8 = 704\n...
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[ "To solve the long multiplication problem \\(88 \\times 78\\), we will break it down into smaller steps and perform each multiplication separately before adding them together.\n\n### Step-by-Step Solution:\n\n1. **Multiply 88 by 8:**\n - First, multiply 88 by 8:\n \\[\n 88 \\times 8 = 664\n \\]\n\n2. ...
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[ "To solve the long multiplication problem \\(88 \\times 78\\), we will break it down into smaller steps and perform each multiplication separately before adding them together.\n\n### Step-by-Step Solution:\n\n1. **Multiply 88 by 8:**\n - First, multiply 88 by 8:\n \\[\n 88 \\times 8 = 664\n \\]\n\n2. ...
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[ "6824", "6864", "6864", "6864" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 88 x 78 is 62264.\", \"answer\": \"62264\"}]}" ]
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[ "\\boxed{62264}" ]
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[ [ false ] ]
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What is the solution to the long multiplication equation below? 43 x 95 Think step by step.
4085
"{\"arg1\": 43, \"arg2\": 95, \"solution\": 4085}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n43 x 95\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(43 \\times 95\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 43\n × 95\n ------\n ```\n\n2. **Multiply 43 by 5 (the units digit of 95):**\n - Multiply 43 by 5:\n ```\n 43\n × 5\n ------\n 2...
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[ "To solve the long multiplication problem \\( 43 \\times 95 \\), follow these steps:\n\n1. **Write down the numbers**: \n ```\n 43\n × 95\n ```\n\n2. **Multiply 43 by 5 (the ones digit of 95)**:\n - \\( 43 \\times 5 = 215 \\)\n - Write down 5 and carry over 2.\n\n3. **Multiply 43 by 9 (the tens digit ...
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[ "To solve the long multiplication problem \\(43 \\times 95\\), we can break it down into smaller steps:\n\n1. **Break it down**: We can think of multiplying 43 by 90 and then by 5 separately.\n\n2. **Multiply 43 by 90**:\n - First, multiply 43 by 9: \n \\[\n 43 \\times 9 = 387\n \\]\n - Then, since ...
{"continuation_phrases": ["Hold on, let me verify this answer.", "Wait, how?"], "continuations": [" \n\nLet's check if there was any mistake in the process or calculation. Let's do it again step-by-step more carefully.\n\n- First, multiply 43 by 9:\n \\[\n 43 \\times 9 = 387\n \\]\n \n- Next, multiply 43 by 5:\n \...
[ "To solve the long multiplication problem \\(43 \\times 95\\), we can break it down into smaller steps:\n\n1. **Break it down**: We can think of multiplying 43 by 90 and then by 5 separately.\n\n2. **Multiply 43 by 90**:\n - First, multiply 43 by 9: \n \\[\n 43 \\times 9 = 387\n \\]\n - Then, since ...
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[ "To solve the long multiplication problem \\( 43 \\times 95 \\), we will break it down into simpler steps and then multiply.\n\n1. **Break down the numbers:**\n - \\( 43 = 40 + 3 \\)\n - \\( 95 = 90 + 5 \\)\n\n2. **Multiply each part of the first number by each part of the second number:**\n\n - Multiply \\( ...
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[ "To solve the long multiplication problem \\( 43 \\times 95 \\), we will break it down into simpler steps and then multiply.\n\n1. **Break down the numbers:**\n - \\( 43 = 40 + 3 \\)\n - \\( 95 = 90 + 5 \\)\n\n2. **Multiply each part of the first number by each part of the second number:**\n\n - Multiply \\( ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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What is the solution to the long multiplication equation below? 78 x 67 Think step by step.
5226
"{\"arg1\": 78, \"arg2\": 67, \"solution\": 5226}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n78 x 67\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(78 \\times 67\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 78\n × 67\n ------\n ```\n\n2. **Multiply 78 by 7 (the units digit of 67):**\n - Multiply 78 by 7:\n ```\n 78\n × 7\n ------\n 546\n...
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[ "Certainly! Let's solve the long multiplication problem \\(78 \\times 67\\) step by step.\n\n### Step 1: Set up the multiplication\n```\n 78\n × 67\n ------\n```\n\n### Step 2: Multiply 78 by 7 (the ones digit of 67)\n```\n 78\n × 7\n ------\n 546\n```\nSo, \\(78 \\times 7 = 546\\).\n\n### Step ...
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[ "To solve the long multiplication problem \\( 78 \\times 67 \\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\n### Step-by-Step Solution:\n\n1. **Multiply 78 by 7 (the units place of 67):**\n - \\( 78 \\times 7 = 546 \\)\n\n2. **Multiply 78 by...
{"continuation_phrases": ["But I need to verify this.", "But according to"], "continuations": [" Let's do it correctly:\n - First, let's calculate \\( 78 \\times 60 \\):\n - \\( 78 \\times 60 = 78 \\times 6 \\times 10 = 468 \\times 10 = 4680 \\)\n - Now add \\( 546 \\) and \\( 4680 \\):\n - \\( 546 ...
[ "To solve the long multiplication problem \\( 78 \\times 67 \\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\n### Step-by-Step Solution:\n\n1. **Multiply 78 by 7 (the units place of 67):**\n - \\( 78 \\times 7 = 546 \\)\n\n2. **Multiply 78 by...
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[ "To solve the long multiplication problem \\( 78 \\times 67 \\), we'll follow these steps:\n\n### Step 1: Multiply 78 by 7 (the units digit of 67)\n- \\( 78 \\times 7 = 546 \\)\n\n### Step 2: Multiply 78 by 60 (the tens digit of 67, which is 6 times 10)\n- First, calculate \\( 78 \\times 6 \\):\n - \\( 78 \\times ...
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[ "To solve the long multiplication problem \\( 78 \\times 67 \\), we'll follow these steps:\n\n### Step 1: Multiply 78 by 7 (the units digit of 67)\n- \\( 78 \\times 7 = 546 \\)\n\n### Step 2: Multiply 78 by 60 (the tens digit of 67, which is 6 times 10)\n- First, calculate \\( 78 \\times 6 \\):\n - \\( 78 \\times ...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 78 x 67 is 47346.\", \"answer\": \"47346\"}]}" ]
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What is the solution to the long multiplication equation below? 70 x 48 Think step by step.
3360
"{\"arg1\": 70, \"arg2\": 48, \"solution\": 3360}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n70 x 48\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(70 \\times 48\\), we can break it down into simpler steps:\n\n1. **Break down 48**: We know that 48 can be broken down into 40 + 8.\n - So, \\(70 \\times 48 = 70 \\times (40 + 8)\\)\n\n2. **Use the distributive property**:\n - Distribute 70 across both terms inside t...
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[ "To solve the long multiplication problem \\(70 \\times 48\\), we can break it down into simpler steps:\n\n1. **Multiply 70 by 8:**\n - 70 × 8 = 560\n\n2. **Multiply 70 by 40 (which is the same as multiplying by 4 and then adding a zero at the end):**\n - 70 × 4 = 280\n - 280 × 10 = 2800\n\n3. **Add the resul...
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[ "To solve the long multiplication problem \\(70 \\times 48\\), we can break it down into simpler steps:\n\n1. **Break down 48 into its place values:**\n - 48 = 40 + 8\n\n2. **Multiply each part of 48 by 70 separately:**\n\n For 40:\n - \\(70 \\times 40 = 70 \\times (4 \\times 10) = (70 \\times 4) \\times 10\\...
{"continuation_phrases": ["Wait, let me try", "Wait, how?"], "continuations": [" this again more carefully.\n\n4. **Re-calculate properly:**\n\n Let's multiply 70 by 40 first:\n - \\(70 \\times 40 = 70 \\times (4 \\times 10) = (70 \\times 4) \\times 10\\)\n - \\(70 \\times 4 = 280\\)\n - \\(280 \\times 10 =...
[ "To solve the long multiplication problem \\(70 \\times 48\\), we can break it down into simpler steps:\n\n1. **Break down 48 into its place values:**\n - 48 = 40 + 8\n\n2. **Multiply each part of 48 by 70 separately:**\n\n For 40:\n - \\(70 \\times 40 = 70 \\times (4 \\times 10) = (70 \\times 4) \\times 10\\...
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[ "To solve \\( 70 \\times 48 \\) using long multiplication:\n\n1. **Set up the multiplication**: Write 70 under the line and 48 outside.\n\n```\n 70\n× 48\n------\n```\n\n2. **Multiply 70 by 8** (the units digit of 48):\n - \\( 70 \\times 8 = 560 \\)\n - Write 560 below the line.\n\n```\n 70\n× 48\n---...
{"all_responses": ["To solve \\( 70 \\times 48 \\) using long multiplication:\n\n1. **Set up the multiplication**: Write 70 under the line and 48 outside.\n\n```\n 70\n\u00d7 48\n------\n```\n\n2. **Multiply 70 by 8** (the units digit of 48):\n - \\( 70 \\times 8 = 560 \\)\n - Write 560 below the line.\n\n```\...
[ "To solve \\( 70 \\times 48 \\) using long multiplication:\n\n1. **Set up the multiplication**: Write 70 under the line and 48 outside.\n\n```\n 70\n× 48\n------\n```\n\n2. **Multiply 70 by 8** (the units digit of 48):\n - \\( 70 \\times 8 = 560 \\)\n - Write 560 below the line.\n\n```\n 70\n× 48\n---...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 70 x 48 is\", \"answer\": \"3360\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{3360}" ]
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[ "3360" ]
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What is the solution to the long multiplication equation below? 25 x 46 Think step by step.
1150
"{\"arg1\": 25, \"arg2\": 46, \"solution\": 1150}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n25 x 46\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(25 \\times 46\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(25\\) can be thought of as \\(20 + 5\\).\n - \\(46\\) can be thought of as \\(40 + 6\\).\n\n2. **Multiply each part separately:**\n\n - Multiply \\(20\\) by \\(46\\)...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "Certainly! Let's break down the multiplication of 25 and 46 step by step.\n\n1. **Break it into smaller parts:**\n - First, let's multiply 25 by 40 (which is \\(4 \\times 10\\)).\n - Then, we'll multiply 25 by 6 (which is just 25).\n\n2. **Calculate each part separately:**\n\n - For \\(25 \\times 40\\):\n ...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(25 \\times 46\\), we can break it down into simpler steps.\n\nFirst, let's write out the numbers:\n\n```\n 25\nx 46\n-----\n```\n\nNow, we'll multiply 25 by each digit in 46 separately and then add the results together.\n\nStep 1: Multiply 25 by 6 (the units digit of 4...
{"continuation_phrases": ["But to confirm,", "But I need to verify this."], "continuations": [" we should have added them correctly as:\n```\n 250\n```\n\nSo, the final answer is:\n\\[ 25 \\times 46 = 1150 \\]", " Let me do it again carefully.\n```\n 25\nx 46\n-----\n 150 (25 x 6)\n+ 1000 (25 x 40)\n-----\n 115...
[ "To solve the long multiplication problem \\(25 \\times 46\\), we can break it down into simpler steps.\n\nFirst, let's write out the numbers:\n\n```\n 25\nx 46\n-----\n```\n\nNow, we'll multiply 25 by each digit in 46 separately and then add the results together.\n\nStep 1: Multiply 25 by 6 (the units digit of 4...
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[ "Certainly! Let's solve the long multiplication problem \\(25 \\times 46\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 25\n × 46\n ------\n ```\n\n2. **Multiply 25 by 6 (the ones digit of 46):**\n - \\(25 \\times 6 = 150\\)\n - Write down 150 under the l...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\(25 \\times 46\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 25\n \u00d7 46\n ------\n ```\n\n2. **Multiply 25 by 6 (the ones digit of 46):**\n - \\(25 \\times 6 = 150\\)\n - Write ...
[ "Certainly! Let's solve the long multiplication problem \\(25 \\times 46\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 25\n × 46\n ------\n ```\n\n2. **Multiply 25 by 6 (the ones digit of 46):**\n - \\(25 \\times 6 = 150\\)\n - Write down 150 under the l...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 25 x 46 is\", \"answer\": \"1150\"}]}" ]
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What is the solution to the long multiplication equation below? 15 x 38 Think step by step.
570
"{\"arg1\": 15, \"arg2\": 38, \"solution\": 570}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n15 x 38\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(15 \\times 38\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 38 into tens and ones.\n\\[ 38 = 30 + 8 \\]\n\n#### Step 2: Multiply 15 by each part of 38 separately.\n\n**First part:** \\(15 \\times 30\\)\n- \\(15\\) m...
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[ "To solve the long multiplication problem \\(15 \\times 38\\), we can break it down into simpler steps:\n\n### Step 1: Break down 38 into tens and ones.\n\\[ 38 = 30 + 8 \\]\n\n### Step 2: Multiply each part of 38 by 15.\n\n#### Multiplying 30 by 15:\n\\[ 30 \\times 15 = (3 \\times 10) \\times 15 = 3 \\times (10 \\...
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[ "To solve the long multiplication problem \\( 15 \\times 38 \\), we can break it down into simpler steps:\n\n### Step 1: Break down the numbers\nWe can rewrite 38 as:\n\\[ 30 + 8 \\]\n\nSo the original problem becomes:\n\\[ 15 \\times (30 + 8) \\]\n\n### Step 2: Distribute the multiplication\nUsing the distributive...
{"continuation_phrases": ["But I need to verify this.", "However,"], "continuations": [" Let's do it again using another method for clarity.\n\n### Alternative Method - Column Multiplication\nLet's use column multiplication to find the product:\n\n```\n 15\n \u00d7 38\n ------\n 120 (15\u00d78)\n 450 (1...
[ "To solve the long multiplication problem \\( 15 \\times 38 \\), we can break it down into simpler steps:\n\n### Step 1: Break down the numbers\nWe can rewrite 38 as:\n\\[ 30 + 8 \\]\n\nSo the original problem becomes:\n\\[ 15 \\times (30 + 8) \\]\n\n### Step 2: Distribute the multiplication\nUsing the distributive...
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[ "To solve the long multiplication problem \\( 15 \\times 38 \\), we will break it down into simpler steps:\n\n### Step 1: Break down the numbers\nFirst, let's express 15 and 38 as sums of smaller numbers that are easier to multiply:\n- \\( 15 = 10 + 5 \\)\n- \\( 38 = 30 + 8 \\)\n\n### Step 2: Multiply each part sep...
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[ "To solve the long multiplication problem \\( 15 \\times 38 \\), we will break it down into simpler steps:\n\n### Step 1: Break down the numbers\nFirst, let's express 15 and 38 as sums of smaller numbers that are easier to multiply:\n- \\( 15 = 10 + 5 \\)\n- \\( 38 = 30 + 8 \\)\n\n### Step 2: Multiply each part sep...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 15 x 30 = 450.\", \"answer\": \"450\"}, {\"context\": \"So, 15 x 8 = 120.\", \"answer\": \"120\"}, {\"context\": \"Therefore, 15 x 38 = 570.\", \"answer\": \"570\"}]}" ]
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[ "\\boxed{450}", "\\boxed{120}", "\\boxed{570}" ]
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What is the solution to the long multiplication equation below? 30 x 19 Think step by step.
570
"{\"arg1\": 30, \"arg2\": 19, \"solution\": 570}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n30 x 19\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(30 \\times 19\\), we can break it down into simpler steps:\n\nStep 1: Multiply 30 by 9.\n- 30 × 9 = 270\n\nStep 2: Multiply 30 by 10 (which is just adding a zero at the end of 30).\n- 30 × 10 = 300\n\nStep 3: Add the results from Step 1 and Step 2.\n- 270 + 300 = 570\n\n...
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[ "To solve the multiplication problem \\( 30 \\times 19 \\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Break Down the Numbers:**\n - We know that \\( 30 = 3 \\times 10 \\) and \\( 19 = 20 - 1 \\).\n\n2. **Use Distributive Property (also known as the FOIL method for binomials):*...
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[ "Certainly! Let's solve this problem step by step.\n\n### Step 1: Break down the numbers\nFirst, let's break down the numbers into smaller parts:\n- \\(30\\) can be written as \\(3 \\times 10\\)\n- \\(19\\) can be written as \\(1 \\times 19\\)\n\n### Step 2: Multiply the digits\nNow, we multiply each part of the fi...
{"continuation_phrases": ["Wait, how?", "Wait, how?"], "continuations": [" I made a mistake in my initial breakdown and simplification. Let me correct that:\n\nFor \\(30 \\times 19\\), you can use the distributive property or simply multiply them directly:\n\n\\[ 30 \\times 19 = 30 \\times (20 - 1) = 30 \\times 20 - 30...
[ "Certainly! Let's solve this problem step by step.\n\n### Step 1: Break down the numbers\nFirst, let's break down the numbers into smaller parts:\n- \\(30\\) can be written as \\(3 \\times 10\\)\n- \\(19\\) can be written as \\(1 \\times 19\\)\n\n### Step 2: Multiply the digits\nNow, we multiply each part of the fi...
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[ "To solve the long multiplication problem \\(30 \\times 19\\), let's break it down into steps:\n\n### Step-by-Step Solution:\n1. **Write the numbers vertically:**\n ```\n 30\n × 19\n ------\n ```\n\n2. **Multiply 30 by 9 (the ones digit of 19):**\n - \\(30 \\times 9 = 270\\)\n - Write down 270 wi...
{"all_responses": ["To solve the long multiplication problem \\(30 \\times 19\\), let's break it down into steps:\n\n### Step-by-Step Solution:\n1. **Write the numbers vertically:**\n ```\n 30\n \u00d7 19\n ------\n ```\n\n2. **Multiply 30 by 9 (the ones digit of 19):**\n - \\(30 \\times 9 = 270\\)\n ...
[ "To solve the long multiplication problem \\(30 \\times 19\\), let's break it down into steps:\n\n### Step-by-Step Solution:\n1. **Write the numbers vertically:**\n ```\n 30\n × 19\n ------\n ```\n\n2. **Multiply 30 by 9 (the ones digit of 19):**\n - \\(30 \\times 9 = 270\\)\n - Write down 270 wi...
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[ [ true ], [ true ], [ true ] ]
[ [ "570" ], [ "570" ], [ "570" ] ]
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[ [ true ] ]
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[ false, true, true, true ]
[ "510", "570", "570", "570" ]
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[ [ false ], [ false, true ], [ true ], [ true ] ]
[ [ "510" ], [ "indeed \\(570\\)", "570" ], [ "570" ], [ "570" ] ]
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[ "76", "570", "570" ]
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[ [ "76" ], [ "570" ], [ "570" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 30 x 19 is\", \"answer\": \"570\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
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[ "\\boxed{570}" ]
[ true ]
[ "570" ]
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[ [ true ] ]
[ [ "570" ] ]
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What is the solution to the long multiplication equation below? 78 x 46 Think step by step.
3588
"{\"arg1\": 78, \"arg2\": 46, \"solution\": 3588}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n78 x 46\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(78 \\times 46\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 78\n × 46\n ```\n\n2. **Multiply 78 by 6 (the units digit of 46):**\n - Multiply 78 by 6:\n ```\n 78\n × 6\n ------\n 468\n ```\n...
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[ "To solve the long multiplication problem \\(78 \\times 46\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n1. **Break down the numbers:**\n - \\(78\\) can be broken down into \\(70 + 8\\).\n - \\(46\\) can be broken down into \\(40 + 6\\).\n\n2. **Multiply each part of the first nu...
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[ "To solve the long multiplication of 78 and 46, follow these steps:\n\n1. **Set up the problem**: Write 78 under the line and 46 outside.\n\n```\n 78\n× 46\n------\n```\n\n2. **Multiply 78 by 6**:\n - Multiply 78 by 6 in the ones place: \\(78 \\times 6 = 468\\). Write down 8 and carry over 4.\n - Multiply 78...
{"continuation_phrases": ["But I need to verify this.", "Wait, how?"], "continuations": [" Actually, it should be \\(78 \\times 4 = 312\\) and then we carry over 0 for the next step since there's no additional digit from multiplying 4 with anything else after the initial 8.\n\nSo, actually:\n- \\(78 \\times 6 = 468\\),...
[ "To solve the long multiplication of 78 and 46, follow these steps:\n\n1. **Set up the problem**: Write 78 under the line and 46 outside.\n\n```\n 78\n× 46\n------\n```\n\n2. **Multiply 78 by 6**:\n - Multiply 78 by 6 in the ones place: \\(78 \\times 6 = 468\\). Write down 8 and carry over 4.\n - Multiply 78...
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[ "Certainly! Let's solve this step-by-step:\n\n1) First, let's write out the numbers we're multiplying:\n 78\n x 46\n\n2) Now, let's multiply each digit of 78 by each digit of 46:\n \n 78\n x 46\n ----\n 3480 (This is 78 * 6)\n +3120 (This is 78 * 40, or 78 times 4 tens)\n\n3) Add these two results t...
{"all_responses": ["Certainly! Let's solve this step-by-step:\n\n1) First, let's write out the numbers we're multiplying:\n 78\n x 46\n\n2) Now, let's multiply each digit of 78 by each digit of 46:\n \n 78\n x 46\n ----\n 3480 (This is 78 * 6)\n +3120 (This is 78 * 40, or 78 times 4 tens)\n\n3) Add thes...
[ "Certainly! Let's solve this step-by-step:\n\n1) First, let's write out the numbers we're multiplying:\n 78\n x 46\n\n2) Now, let's multiply each digit of 78 by each digit of 46:\n \n 78\n x 46\n ----\n 3480 (This is 78 * 6)\n +3120 (This is 78 * 40, or 78 times 4 tens)\n\n3) Add these two results t...
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[ true ]
[ "3588" ]
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[ [ true ] ]
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[ true, true, true ]
[ "3588", "3588", "3588" ]
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[ [ false, true ], [ false, true ], [ true ] ]
[ [ ":", "3588" ], [ "\\(3588\\)", "3588" ], [ "3588" ] ]
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[ [ false, false ] ]
[ [ "\\(3568\\)", "3648" ] ]
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[ false, true, true, true ]
[ "6600", "3588", "3588", "3588" ]
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[ false, false, false ]
[ "40", "3648", "3648" ]
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[ [ false, false ], [ false ], [ false ] ]
[ [ "\\(3568\\)", "40" ], [ "3648" ], [ "3648" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Therefore, the product of 78 x 46 is\", \"answer\": \"3588\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{3588}" ]
[ true ]
[ "3588" ]
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[ [ true ] ]
[ [ "3588" ] ]
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[ [ { "answer_block": null, "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": "legacy", "extracted_answer": null, "final_answer": null, "is_correct": null, "is_equivalent": null, "legacy_result": true } ] ]
What is the solution to the long multiplication equation below? 34 x 32 Think step by step.
1088
"{\"arg1\": 34, \"arg2\": 32, \"solution\": 1088}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n34 x 32\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
null
null
null
null
null
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[ "To solve the long multiplication problem \\(34 \\times 32\\), we can break it down into simpler steps:\n\n1. **Multiply 34 by 2 (the units digit of 32):**\n - \\(34 \\times 2 = 68\\)\n\n2. **Multiply 34 by 30 (the tens digit of 32, which is 3 times 10):**\n - \\(34 \\times 30 = 34 \\times 3 \\times 10 = 102 \\...
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[ "To solve the long multiplication problem \\(34 \\times 32\\), follow these steps:\n\n1. **Set up the multiplication**: Write the numbers one under the other, aligning them on the right.\n\n ```\n 34\n × 32\n ----\n ```\n\n2. **Multiply each digit of the bottom number by the top number**:\n \n - Mu...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(34 \\times 32\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers and distribute the second number (32) across the first number (34):\n\n\\[34 \\times 32 = 34 \\times (30 + 2)\...
{"continuation_phrases": ["But according to", "Wait, how?"], "continuations": [" my calculations, the correct answer should be 1088. Let me double-check this: \n\n\\[34 \\times 32 = 34 \\times (30+2) = 34 \\times 30 + 34 \\times 2 = 1020 + 68 = 1088.\\] \n\nThe calculation is correct. The final answer is indeed 1088.",...
[ "To solve the long multiplication problem \\(34 \\times 32\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers and distribute the second number (32) across the first number (34):\n\n\\[34 \\times 32 = 34 \\times (30 + 2)\...
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[ "Certainly! Let's break down the multiplication of 34 and 32 step by step.\n\n1. **Set up the multiplication:**\n ```\n 34\n x 32\n ```\n\n2. **Multiply 34 by 2 (the units digit of 32):**\n - \\(34 \\times 2 = 68\\)\n - Write 8 in the units place and carry over 6.\n\n3. **Multiply 34 by 30 (the tens d...
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[ "Certainly! Let's break down the multiplication of 34 and 32 step by step.\n\n1. **Set up the multiplication:**\n ```\n 34\n x 32\n ```\n\n2. **Multiply 34 by 2 (the units digit of 32):**\n - \\(34 \\times 2 = 68\\)\n - Write 8 in the units place and carry over 6.\n\n3. **Multiply 34 by 30 (the tens d...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 34 x 32 is\", \"answer\": \"1088\"}]}" ]
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[ "\\boxed{1088}" ]
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What is the solution to the long multiplication equation below? 88 x 10 Think step by step.
880
"{\"arg1\": 88, \"arg2\": 10, \"solution\": 880}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n88 x 10\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(88 \\times 10\\), let's break it down into steps:\n\nStep 1: Understand that multiplying any number by 10 simply means adding a zero at the end of that number.\n\nSo, we can think of this as:\n\\[ 88 \\times 10 = 880 \\]\n\nStep 2: Alternatively, you can use the distribu...
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[ "To solve the problem \\(88 \\times 10\\), let's break it down into steps:\n\nStep 1: Understand what multiplying by 10 means.\nWhen you multiply any number by 10, you simply add a zero at the end of that number.\n\nStep 2: Apply this understanding to our specific case.\nWe have \\(88 \\times 10\\).\n\nStep 3: Add ...
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[ "To solve the long multiplication problem \\(88 \\times 10\\), let's break it down into steps:\n\nStep 1: Understand that multiplying any number by 10 simply means adding a zero to the end of that number.\n\nSo, \\(88\\) multiplied by \\(10\\) will be:\n\\[ 88 \\times 10 = 880 \\]\n\nTherefore, the solution to the ...
{"continuation_phrases": ["Wait, let me try", "But according to"], "continuations": [" this with an example.\n\nLet's take 23 and multiply it by 10:\n- 23 \u00d7 10 = 230\n\nSo, we can see that when you multiply any number by 10, you just add one zero at the end.\n\nStep 2: Apply this rule to our original problem.\n- W...
[ "To solve the long multiplication problem \\(88 \\times 10\\), let's break it down into steps:\n\nStep 1: Understand that multiplying any number by 10 simply means adding a zero to the end of that number.\n\nSo, \\(88\\) multiplied by \\(10\\) will be:\n\\[ 88 \\times 10 = 880 \\]\n\nTherefore, the solution to the ...
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[ "To solve the long multiplication problem \\( 88 \\times 10 \\), we can follow these steps:\n\nStep 1: Understand that multiplying any number by 10 simply means adding a zero to the end of that number.\n\nStep 2: Take the number 88 and add one zero to it.\n - 88 + 0 = 88 (but remember, we're actually adding two z...
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[ "To solve the long multiplication problem \\( 88 \\times 10 \\), we can follow these steps:\n\nStep 1: Understand that multiplying any number by 10 simply means adding a zero to the end of that number.\n\nStep 2: Take the number 88 and add one zero to it.\n - 88 + 0 = 88 (but remember, we're actually adding two z...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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What is the solution to the long multiplication equation below? 59 x 20 Think step by step.
1180
"{\"arg1\": 59, \"arg2\": 20, \"solution\": 1180}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n59 x 20\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(59 \\times 20\\), let's break it down into steps:\n\n1. **Write the numbers vertically:**\n ```\n 59\n × 20\n ```\n\n2. **Multiply 59 by 0 (the units digit of 20):**\n - 59 × 0 = 0\n So, we write 0 in the ones place.\n\n3. **Multiply 59 by 2 (the tens digit...
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[ "To solve the long multiplication problem \\( 59 \\times 20 \\), let's break it down into steps:\n\n1. **Multiply the ones digit of the first number by the second number:**\n - The ones digit of 59 is 9.\n - Multiply 9 by 20:\n \\[\n 9 \\times 20 = 180\n \\]\n\n2. **Write down the result:**\n - Si...
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[ "To solve the long multiplication problem \\( 59 \\times 20 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 59 \\) can be broken down into \\( 50 + 9 \\).\n - \\( 20 \\) remains as \\( 20 \\).\n\n2. **Multiply each part of \\( 59 \\) by \\( 20 \\):**\n - First, multiply...
{"continuation_phrases": ["Wait, let me try", "Wait, this result is"], "continuations": [" this again in a more detailed manner:\n\n4. **Revised breakdown and calculation:**\n\n - Multiply \\( 59 \\) (which is \\( 50 + 9 \\)) by \\( 20 \\):\n - First, calculate \\( 50 \\times 20 \\):\n \\[\n 50 \\time...
[ "To solve the long multiplication problem \\( 59 \\times 20 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 59 \\) can be broken down into \\( 50 + 9 \\).\n - \\( 20 \\) remains as \\( 20 \\).\n\n2. **Multiply each part of \\( 59 \\) by \\( 20 \\):**\n - First, multiply...
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[ "To solve the long multiplication problem \\( 59 \\times 20 \\), let's break it down into steps:\n\n1. **Write down the numbers:**\n ```\n 59\n x 20\n ```\n\n2. **Multiply each digit of the second number (20) by the first number (59):**\n\n - First, multiply 59 by 0:\n ```\n 59\n x 0\n...
{"all_responses": ["To solve the long multiplication problem \\( 59 \\times 20 \\), let's break it down into steps:\n\n1. **Write down the numbers:**\n ```\n 59\n x 20\n ```\n\n2. **Multiply each digit of the second number (20) by the first number (59):**\n\n - First, multiply 59 by 0:\n ```\n 59...
[ "To solve the long multiplication problem \\( 59 \\times 20 \\), let's break it down into steps:\n\n1. **Write down the numbers:**\n ```\n 59\n x 20\n ```\n\n2. **Multiply each digit of the second number (20) by the first number (59):**\n\n - First, multiply 59 by 0:\n ```\n 59\n x 0\n...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the...
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[ [ "\\(1180\\)", "20" ] ]
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[ "1180", "2", "1180" ]
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[ [ "\\( 1180 \\)", "indeed \\( 1180 \\)", "1180" ] ]
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[ [ "1180" ], [ "indeed \\( 1180 \\)", "1180" ], [ "\\( 1180 \\)", "1180" ], [ "indeed \\( 1180 \\)", "1180" ] ]
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[ [ true ], [ false, true ], [ false, true ] ]
[ [ "1180" ], [ "\\( 1180 \\)", "1180" ], [ "indeed \\( 1180 \\)", "1180" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer is\", \"answer\": \"1180\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1180}" ]
[ true ]
[ "1180" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 30 x 59 Think step by step.
1770
"{\"arg1\": 30, \"arg2\": 59, \"solution\": 1770}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n30 x 59\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(30 \\times 59\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(30\\) can be written as \\(3 \\times 10\\).\n - \\(59\\) can be written as \\(50 + 9\\).\n\n2. **Multiply each part of the second number by the first number:**\n - M...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 1}
[ "To solve the long multiplication problem \\(30 \\times 59\\), we can break it down into simpler steps:\n\n1. **Multiply 30 by 9 (the units digit of 59):**\n - \\(30 \\times 9 = 270\\)\n\n2. **Multiply 30 by 50 (the tens digit of 59) and then add the result from step 1:**\n - First, calculate \\(30 \\times 50\\...
{"api_url": "http://127.0.0.1:61054", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "prompt": [{"content": "What is the solution to the l...
{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\( 30 \\times 59 \\), we can break it down into simpler steps:\n\n1. **Multiply 30 by 9:**\n - \\( 30 \\times 9 = 270 \\)\n\n2. **Multiply 30 by 50 (which is the same as multiplying by 5 and then adding a zero at the end):**\n - \\( 30 \\times 50 = 30 \\times (5 \\time...
{"continuation_phrases": ["Wait! I can double check this answer.", "But to confirm,"], "continuations": [" Let's do it again using another method.\n\n### Double-checking with another method:\n\n1. **Break down 59 into tens and ones:**\n - \\( 59 = 50 + 9 \\)\n\n2. **Multiply each part by 30 separately:**\n - \\( 30...
[ "To solve the long multiplication problem \\( 30 \\times 59 \\), we can break it down into simpler steps:\n\n1. **Multiply 30 by 9:**\n - \\( 30 \\times 9 = 270 \\)\n\n2. **Multiply 30 by 50 (which is the same as multiplying by 5 and then adding a zero at the end):**\n - \\( 30 \\times 50 = 30 \\times (5 \\time...
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[ "Certainly! Let's break down the multiplication of 30 and 59 step by step.\n\n### Step 1: Multiply 30 by 9 (the units digit of 59)\n- \\( 30 \\times 9 = 270 \\)\n\n### Step 2: Multiply 30 by 50 (the tens digit of 59, which is just moving the 5 one place to the left)\n- \\( 30 \\times 50 = 30 \\times (5 \\times 10) ...
{"all_responses": ["Certainly! Let's break down the multiplication of 30 and 59 step by step.\n\n### Step 1: Multiply 30 by 9 (the units digit of 59)\n- \\( 30 \\times 9 = 270 \\)\n\n### Step 2: Multiply 30 by 50 (the tens digit of 59, which is just moving the 5 one place to the left)\n- \\( 30 \\times 50 = 30 \\times ...
[ "Certainly! Let's break down the multiplication of 30 and 59 step by step.\n\n### Step 1: Multiply 30 by 9 (the units digit of 59)\n- \\( 30 \\times 9 = 270 \\)\n\n### Step 2: Multiply 30 by 50 (the tens digit of 59, which is just moving the 5 one place to the left)\n- \\( 30 \\times 50 = 30 \\times (5 \\times 10) ...
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[ [ false ] ]
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[ [ "\\(1770\\)", "1770" ], [ "1770" ], [ "\\(357\\)", "357" ] ]
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[ true ]
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[ [ "1770", "indeed \\( \\boxed{1770} \\)", "1770" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 30 x 59 is\", \"answer\": \"207\"}]}" ]
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What is the solution to the long multiplication equation below? 56 x 32 Think step by step.
1792
"{\"arg1\": 56, \"arg2\": 32, \"solution\": 1792}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n56 x 32\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(56 \\times 32\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(56\\) can be broken down into \\(50 + 6\\).\n - \\(32\\) can be broken down into \\(30 + 2\\).\n\n2. **Multiply each part of the first number by each part of the secon...
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[ "Certainly! Let's solve this step by step.\n\n### Step 1: Break down the numbers into tens and ones.\n- \\(56\\) can be broken down into \\(50 + 6\\).\n- \\(32\\) can be broken down into \\(30 + 2\\).\n\n### Step 2: Multiply each part of one number by each part of the other number.\n- First, multiply \\(50\\) by \\...
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[ "To solve the long multiplication problem \\(56 \\times 32\\), we can break it down into simpler steps:\n\n1. **Multiply 56 by 2 (the units digit of 32):**\n \\[\n 56 \\times 2 = 112\n \\]\n Write down 112.\n\n2. **Multiply 56 by 30 (the tens digit of 32, which is 3 times 10):**\n \\[\n 56 \\times 30 = ...
{"continuation_phrases": ["Hold on, let me verify this answer.", "However,"], "continuations": [" \n\n Actually, I should multiply 56 by 30 correctly as \\(56 \\times 30\\) means adding a zero at the end of 168 because multiplying by 10 increases the number's value by one place. So,\n \\[\n 56 \\times 30 = 1680\n...
[ "To solve the long multiplication problem \\(56 \\times 32\\), we can break it down into simpler steps:\n\n1. **Multiply 56 by 2 (the units digit of 32):**\n \\[\n 56 \\times 2 = 112\n \\]\n Write down 112.\n\n2. **Multiply 56 by 30 (the tens digit of 32, which is 3 times 10):**\n \\[\n 56 \\times 30 = ...
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[ "To solve the long multiplication problem \\(56 \\times 32\\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\n### Step-by-Step Solution:\n\n1. **Multiply 56 by 2 (the units place of 32):**\n - \\(56 \\times 2 = 112\\)\n - Write down 112.\n\n2...
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[ "To solve the long multiplication problem \\(56 \\times 32\\), we will break it down into smaller steps and multiply each digit of one number by each digit of the other number.\n\n### Step-by-Step Solution:\n\n1. **Multiply 56 by 2 (the units place of 32):**\n - \\(56 \\times 2 = 112\\)\n - Write down 112.\n\n2...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 56 x 32 is:\", \"answer\": \"1792\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
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What is the solution to the long multiplication equation below? 45 x 83 Think step by step.
3735
"{\"arg1\": 45, \"arg2\": 83, \"solution\": 3735}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n45 x 83\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(45 \\times 83\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 45\n × 83\n ```\n\n2. **Multiply 45 by 3 (the ones digit of 83):**\n - Multiply 45 by 3:\n ```\n 45\n × 3\n _______\n 135\n ```\...
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[ "Certainly! Let's solve this step by step.\n\n### Step 1: Set up the problem\nWe need to multiply 45 by 83.\n\n### Step 2: Break down the numbers into tens and ones\n- 45 can be broken down into 40 (tens) + 5 (ones)\n- 83 can be broken down into 80 (tens) + 3 (ones)\n\nSo, we have:\n\\[ 45 \\times 83 = (40 + 5) \\t...
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[ "To solve the long multiplication problem \\(45 \\times 83\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\\[45 \\times 83 = 45 \\times (80 + 3)\\]\n\nNow, apply the distributive property:\n\\[45 \\times (80 + 3) =...
{"continuation_phrases": ["Wait, how?", "Wait, let me try"], "continuations": [" Let me explain this step-by-step.\n - Break it down: \n \\[45 \\times 3 = 45 \\times (2+1) = (45 \\times 2) + (45 \\times 1)\\]\n - First, calculate \\(45 \\times 2\\):\n \\[45 \\times 2 = 90\\]\n - Then, calc...
[ "To solve the long multiplication problem \\(45 \\times 83\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the numbers:\n\\[45 \\times 83 = 45 \\times (80 + 3)\\]\n\nNow, apply the distributive property:\n\\[45 \\times (80 + 3) =...
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[ "Certainly! Let's solve the long multiplication problem step by step for \\( 45 \\times 83 \\).\n\n### Step 1: Set up the multiplication\n```\n 45\n × 83\n ------\n```\n\n### Step 2: Multiply 45 by 3 (the ones digit of 83)\n```\n 45\n × 83\n ------\n 135 (45 × 3 = 135)\n```\n\n### Step 3: Multi...
{"all_responses": ["Certainly! Let's solve the long multiplication problem step by step for \\( 45 \\times 83 \\).\n\n### Step 1: Set up the multiplication\n```\n 45\n \u00d7 83\n ------\n```\n\n### Step 2: Multiply 45 by 3 (the ones digit of 83)\n```\n 45\n \u00d7 83\n ------\n 135 (45 \u00d7 3 = ...
[ "Certainly! Let's solve the long multiplication problem step by step for \\( 45 \\times 83 \\).\n\n### Step 1: Set up the multiplication\n```\n 45\n × 83\n ------\n```\n\n### Step 2: Multiply 45 by 3 (the ones digit of 83)\n```\n 45\n × 83\n ------\n 135 (45 × 3 = 135)\n```\n\n### Step 3: Multi...
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[ [ "3715" ], [ "indeed **3735**, not **3715**", "3715" ], [ "3735" ], [ "3735" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 45 x 83 is 3735.\", \"answer\": \"3735\"}]}" ]
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[ "\\boxed{3735}" ]
[ true ]
[ "3735" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 72 x 53 Think step by step.
3816
"{\"arg1\": 72, \"arg2\": 53, \"solution\": 3816}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n72 x 53\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(72 \\times 53\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 72\n × 53\n ------\n ```\n\n2. **Multiply 72 by 3 (the ones digit of 53):**\n - Multiply 72 by 3:\n ```\n 72\n × 3\n ------\n 216\...
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[ "Certainly! Let's solve the long multiplication problem \\( 72 \\times 53 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 72\n × 53\n ----\n ```\n\n2. **Multiply 72 by 3 (the ones digit of 53):**\n - Multiply 72 by 3:\n \\[\n 72 \\times 3 = 216\n ...
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[ "To solve the long multiplication problem \\(72 \\times 53\\), we can break it down into smaller steps:\n\n1. **Break down the numbers:**\n - \\(72\\) can be written as \\(70 + 2\\).\n - \\(53\\) can be written as \\(50 + 3\\).\n\n2. **Multiply each part of the first number by each part of the second number:**\...
{"continuation_phrases": ["Wait, this result is", "But I need to verify this."], "continuations": [" incorrect! Let me correct my previous mistake.\n\nI apologize for the confusion in my previous response. The correct breakdown should be:\n\n- Multiply \\(70\\) by \\(53\\):\n \\[\n 70 \\times 53 = 70 \\times (50 + 3)...
[ "To solve the long multiplication problem \\(72 \\times 53\\), we can break it down into smaller steps:\n\n1. **Break down the numbers:**\n - \\(72\\) can be written as \\(70 + 2\\).\n - \\(53\\) can be written as \\(50 + 3\\).\n\n2. **Multiply each part of the first number by each part of the second number:**\...
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[ "To solve the long multiplication problem \\(72 \\times 53\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 72 and 53 one under the other, aligning them vertically.\n\n```\n 72\n × 53\n ----\n```\n\n2. **Multiply 72 by 3 (the ones digit of 53)**:\n - Multiply 72 by 3: \n ...
{"all_responses": ["To solve the long multiplication problem \\(72 \\times 53\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 72 and 53 one under the other, aligning them vertically.\n\n```\n 72\n \u00d7 53\n ----\n```\n\n2. **Multiply 72 by 3 (the ones digit of 53)**:\n - Multi...
[ "To solve the long multiplication problem \\(72 \\times 53\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 72 and 53 one under the other, aligning them vertically.\n\n```\n 72\n × 53\n ----\n```\n\n2. **Multiply 72 by 3 (the ones digit of 53)**:\n - Multiply 72 by 3: \n ...
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[ "36216" ]
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[ "36216", "3714", "3816" ]
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[ [ false ], [ false ], [ true ] ]
[ [ "36216" ], [ "3714" ], [ "3816" ] ]
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[ [ true ] ]
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[ false, true, false, false ]
[ "38160", "3816", "576", "576" ]
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[ [ "38160" ], [ "indeed \\(3816\\)", "3816" ], [ ":", "576" ], [ ":", "576" ] ]
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[ [ true ], [ true ], [ true ] ]
[ [ "3816" ], [ "3816" ], [ "3816" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 72 x 53 is\", \"answer\": \"36216\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{36216}" ]
[ false ]
[ "36216" ]
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[ [ false ] ]
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What is the solution to the long multiplication equation below? 48 x 45 Think step by step.
2160
"{\"arg1\": 48, \"arg2\": 45, \"solution\": 2160}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n48 x 45\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(48 \\times 45\\), we can break it down into simpler steps:\n\n1. **Multiply 48 by 5:**\n - 48 × 5 = 240\n\n2. **Multiply 48 by 40 (which is 4 tens):**\n - First, multiply 48 by 4:\n - 48 × 4 = 192\n - Then, since there are two zeros in 40, add another zero to 1...
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[ "To solve the multiplication problem \\( 48 \\times 45 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 45 as the sum of two numbers that are easier to multiply with 48:\n\\[ 45 = 40 + 5 \\]\n\nNow, apply the distributive property:...
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[ "Certainly! Let's break down the long multiplication of 48 and 45 step by step.\n\n1. **Multiply 48 by 5 (the units digit of 45):**\n - \\(48 \\times 5 = 240\\)\n - Write down 0 and carry over 2.\n\n2. **Multiply 48 by 4 (the tens digit of 45), and add the carried-over 2:**\n - \\(48 \\times 4 = 192\\)\n - ...
{"continuation_phrases": ["But to confirm,", "Wait, let me try"], "continuations": [" we can multiply 48 directly by 45 using another method:\n\nLet's use the standard algorithm for direct multiplication:\n- Multiply 48 by 5 (units place):\n - \\(48 \\times 5 = 240\\)\n- Then multiply 48 by 4 (tens place) and shift on...
[ "Certainly! Let's break down the long multiplication of 48 and 45 step by step.\n\n1. **Multiply 48 by 5 (the units digit of 45):**\n - \\(48 \\times 5 = 240\\)\n - Write down 0 and carry over 2.\n\n2. **Multiply 48 by 4 (the tens digit of 45), and add the carried-over 2:**\n - \\(48 \\times 4 = 192\\)\n - ...
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[ "Certainly! Let's solve the long multiplication problem \\( 48 \\times 45 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 48\n × 45\n ----\n ```\n\n2. **Multiply 48 by 5 (the units digit of 45):**\n - \\( 48 \\times 5 = 240 \\)\n - Write down 240 and carr...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\( 48 \\times 45 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 48\n \u00d7 45\n ----\n ```\n\n2. **Multiply 48 by 5 (the units digit of 45):**\n - \\( 48 \\times 5 = 240 \\)\n - Wri...
[ "Certainly! Let's solve the long multiplication problem \\( 48 \\times 45 \\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 48\n × 45\n ----\n ```\n\n2. **Multiply 48 by 5 (the units digit of 45):**\n - \\( 48 \\times 5 = 240 \\)\n - Write down 240 and carr...
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[ "2160" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 48 x 45 = 2160.\", \"answer\": \"2160\"}, {\"context\": \"48 \\u00d7 5 = 240\", \"answer\": \"240\"}, {\"context\": \"48 \\u00d7 4 = 192\", \"answer\": \"192\"}, {\"context\": \"Then, since there are two zeros in 40, add another zero to 192: 1920\", \"answer\": \"1920\"}, {\...
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{2160}", "\\boxed{240}", "\\boxed{192}", "\\boxed{1920}", "\\boxed{2160}" ]
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[ [ true ], [ false ], [ false ], [ false ], [ true ] ]
[ [ "2160" ], [ "240" ], [ "192" ], [ "1920" ], [ "2160" ] ]
[ [ { "all_extracted_answers": [ "2160" ], "all_extractions": [ "{'content': '2160', 'start_pos': 7, 'end_pos': 11, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '2160'}" ], "confidence": 0.9500000000000001, "extracted_answer": "2160", "extractor": "...
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What is the solution to the long multiplication equation below? 35 x 87 Think step by step.
3045
"{\"arg1\": 35, \"arg2\": 87, \"solution\": 3045}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n35 x 87\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(35 \\times 87\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 35\n × 87\n ```\n\n2. **Multiply 35 by 7 (the units digit of 87):**\n - Multiply 35 by 7:\n ```\n 35\n × 7\n _______\n 245\n ```...
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[ "Certainly! Let's solve this problem step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n & 35 \\\\\n \\times & 87 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 35 by 7 (the ones digit of 87):**\n \\[\n 35 \\times 7 = 245\n \\]...
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[ "To solve the long multiplication problem \\(35 \\times 87\\), we can break it down into simpler steps:\n\n1. **Break down 87 into its tens and ones place values:**\n - 87 = 80 + 7\n\n2. **Multiply 35 by each part of 87 separately:**\n\n First part:\n \\[\n 35 \\times 80\n \\]\n Multiply 35 by 8 (the te...
{"continuation_phrases": ["Wait, let me try", "But to confirm,"], "continuations": [" again.\n\nLet's do this correctly now:\n\nFirst part:\n\\[\n35 \\times 80 = 35 \\times (8 \\times 10) = (35 \\times 8) \\times 10 = 280 \\times 10 = 2800\n\\]\n\nSecond part:\n\\[\n35 \\times 7 = 245\n\\]\n\nNow add them together:\n\\...
[ "To solve the long multiplication problem \\(35 \\times 87\\), we can break it down into simpler steps:\n\n1. **Break down 87 into its tens and ones place values:**\n - 87 = 80 + 7\n\n2. **Multiply 35 by each part of 87 separately:**\n\n First part:\n \\[\n 35 \\times 80\n \\]\n Multiply 35 by 8 (the te...
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[ "To solve the long multiplication problem \\(35 \\times 87\\), we will break it down into simpler steps and then multiply.\n\n### Step-by-Step Solution:\n\n1. **Break down the numbers:**\n - \\(35\\) can be written as \\(30 + 5\\).\n - \\(87\\) can be written as \\(80 + 7\\).\n\n2. **Multiply each part of the f...
{"all_responses": ["To solve the long multiplication problem \\(35 \\times 87\\), we will break it down into simpler steps and then multiply.\n\n### Step-by-Step Solution:\n\n1. **Break down the numbers:**\n - \\(35\\) can be written as \\(30 + 5\\).\n - \\(87\\) can be written as \\(80 + 7\\).\n\n2. **Multiply eac...
[ "To solve the long multiplication problem \\(35 \\times 87\\), we will break it down into simpler steps and then multiply.\n\n### Step-by-Step Solution:\n\n1. **Break down the numbers:**\n - \\(35\\) can be written as \\(30 + 5\\).\n - \\(87\\) can be written as \\(80 + 7\\).\n\n2. **Multiply each part of the f...
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[ [ "3045" ], [ "indeed \\(3045\\)", "correct", "3045" ], [ "indeed \\(\\boxed{3045}\\)", "3045" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the product of 35 x 87 is\", \"answer\": \"3045\"}]}" ]
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What is the solution to the long multiplication equation below? 79 x 35 Think step by step.
2765
"{\"arg1\": 79, \"arg2\": 35, \"solution\": 2765}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n79 x 35\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(79 \\times 35\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(79\\) can be broken down into \\(70 + 9\\).\n - \\(35\\) remains as it is.\n\n2. **Multiply each part of the first number by the second number:**\n - Multiply \\(70\...
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[ "Certainly! Let's solve the long multiplication problem \\(79 \\times 35\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 79\n × 35\n ```\n\n2. **Multiply 79 by 5 (the ones digit of 35):**\n - Multiply 79 by 5:\n ```\n 79\n × 5\n -----...
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[ "To solve the long multiplication problem \\(79 \\times 35\\), we can break it down into simpler steps:\n\n1. **Multiply 79 by 5:**\n - \\(79 \\times 5 = 395\\)\n\n2. **Multiply 79 by 30 (which is the same as multiplying by 3 and then adding a zero):**\n - First, multiply 79 by 3:\n \\[\n 79 \\times 3 =...
{"continuation_phrases": ["But I need to verify this.", "Wait, let me try"], "continuations": [" Let's do it correctly now.\n\n4. **Correctly add 395 and 2370:**\n - Align the numbers vertically for easier addition:\n ```\n 395\n +2370\n ------\n ```\n\n - Start from the rightmost digit and ad...
[ "To solve the long multiplication problem \\(79 \\times 35\\), we can break it down into simpler steps:\n\n1. **Multiply 79 by 5:**\n - \\(79 \\times 5 = 395\\)\n\n2. **Multiply 79 by 30 (which is the same as multiplying by 3 and then adding a zero):**\n - First, multiply 79 by 3:\n \\[\n 79 \\times 3 =...
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[ "To solve the long multiplication problem \\( 79 \\times 35 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 79\n × 35\n ```\n\n2. **Multiply 79 by 5 (the units digit of 35):**\n - Multiply 79 by 5:\n ```\n 79\n × 5\n ------\n 395\n ```\n\n3. **...
{"all_responses": ["To solve the long multiplication problem \\( 79 \\times 35 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 79\n \u00d7 35\n ```\n\n2. **Multiply 79 by 5 (the units digit of 35):**\n - Multiply 79 by 5:\n ```\n 79\n \u00d7 5\n ------\n ...
[ "To solve the long multiplication problem \\( 79 \\times 35 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 79\n × 35\n ```\n\n2. **Multiply 79 by 5 (the units digit of 35):**\n - Multiply 79 by 5:\n ```\n 79\n × 5\n ------\n 395\n ```\n\n3. **...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 79 x 35 is\", \"answer\": \"2765\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{2765}" ]
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What is the solution to the long multiplication equation below? 67 x 79 Think step by step.
5293
"{\"arg1\": 67, \"arg2\": 79, \"solution\": 5293}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n67 x 79\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(67 \\times 79\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 67\n × 79\n ------\n ```\n\n2. **Multiply 67 by 9 (the units digit of 79):**\n - Multiply 67 by 9:\n ```\n 67\n × 9\n ------\n 583\n...
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[ "To solve the long multiplication problem \\( 67 \\times 79 \\), we will follow these steps:\n\n1. **Set up the multiplication**: Write the numbers one under the other, aligning them by their rightmost digits.\n \n ```\n 67\n × 79\n ----\n ```\n\n2. **Multiply 67 by 9** (the ones digit of 79):\n - M...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "Certainly! Let's break down the multiplication of 67 and 79 into steps:\n\n1. **Multiply 67 by 9 (the units digit of 79):**\n - \\(67 \\times 9 = 603\\)\n\n2. **Multiply 67 by 70 (the tens digit of 79, which is 7 times 10):**\n - \\(67 \\times 70 = 4690\\) (since \\(70 = 7 \\times 10\\))\n\n3. **Add the two re...
{"continuation_phrases": ["Wait, how?", "But according to"], "continuations": [" I made a mistake in my previous calculation. Let me correct it.\n\nLet's redo this step-by-step correctly:\n\n1. **Multiply 67 by 9 (the units digit of 79):**\n - \\(67 \\times 9 = 603\\)\n\n2. **Multiply 67 by 70 (the tens digit of 79, ...
[ "Certainly! Let's break down the multiplication of 67 and 79 into steps:\n\n1. **Multiply 67 by 9 (the units digit of 79):**\n - \\(67 \\times 9 = 603\\)\n\n2. **Multiply 67 by 70 (the tens digit of 79, which is 7 times 10):**\n - \\(67 \\times 70 = 4690\\) (since \\(70 = 7 \\times 10\\))\n\n3. **Add the two re...
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[ "To solve the long multiplication of 67 and 79, we can break it down into simpler steps:\n\n1. First, let's multiply 67 by 9 (the units digit of 79):\n 67 * 9 = 603\n\n2. Now, let's multiply 67 by 70 (which is 7 times 10):\n 67 * 70 = 4690\n\n3. Finally, add these two results together:\n 603 + 4690 = 5293\n\n...
{"all_responses": ["To solve the long multiplication of 67 and 79, we can break it down into simpler steps:\n\n1. First, let's multiply 67 by 9 (the units digit of 79):\n 67 * 9 = 603\n\n2. Now, let's multiply 67 by 70 (which is 7 times 10):\n 67 * 70 = 4690\n\n3. Finally, add these two results together:\n 603 + ...
[ "To solve the long multiplication of 67 and 79, we can break it down into simpler steps:\n\n1. First, let's multiply 67 by 9 (the units digit of 79):\n 67 * 9 = 603\n\n2. Now, let's multiply 67 by 70 (which is 7 times 10):\n 67 * 70 = 4690\n\n3. Finally, add these two results together:\n 603 + 4690 = 5293\n\n...
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[ "5273", "5228", "5293" ]
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[ [ "5273" ], [ "5228" ], [ ":", "5293" ] ]
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[ [ "5293" ], [ "\\(67 \\times 79 = 5283\\)", "5283" ], [ "5293" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 67 x 79 is\", \"answer\": \"47483\"}]}" ]
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What is the solution to the long multiplication equation below? 27 x 49 Think step by step.
1323
"{\"arg1\": 27, \"arg2\": 49, \"solution\": 1323}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n27 x 49\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(27 \\times 49\\), we can break it down into simpler steps:\n\n1. **Break down 49**: We know that 49 can be broken down into 50 - 1.\n So, \\(49 = 50 - 1\\).\n\n2. **Rewrite the original problem using this breakdown**:\n \\[\n 27 \\times 49 = 27 \\times (50 - 1)\n ...
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[ "To solve the long multiplication problem \\(27 \\times 49\\), let's break it down into steps:\n\n### Step 1: Break down the numbers\n- \\(27\\) can be written as \\(20 + 7\\).\n- \\(49\\) can be written as \\(40 + 9\\).\n\n### Step 2: Multiply each part of the first number by each part of the second number\n\n####...
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[ "To solve the long multiplication problem \\(27 \\times 49\\), we can break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n\\[ 27 \\]\n× 49\n-------\n (Multiply 27 by 9)\n 243\n -2160\n------- \n 1323 \n\nNow, let's explain each step in detail:\n1. Multiply 27 by 9:...
{"continuation_phrases": ["But according to", "Wait, how?"], "continuations": [" the original setup, we need to subtract 2160 instead of adding 243.\n \nSo, combining these two results:\n\\[ 351 - 2160 = -1809 \\]\n\nHowever, there seems to be an error in the reference solution provided. The correct answer should not...
[ "To solve the long multiplication problem \\(27 \\times 49\\), we can break it down into simpler steps.\n\nFirst, let's write out the multiplication:\n\n\\[ 27 \\]\n× 49\n-------\n (Multiply 27 by 9)\n 243\n -2160\n------- \n 1323 \n\nNow, let's explain each step in detail:\n1. Multiply 27 by 9:...
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[ "To solve the long multiplication of 27 and 49, we can break it down into simpler steps:\n\n1. First, let's write out the numbers one under the other:\n ```\n 27\n 49\n ```\n\n2. Now, multiply each digit of 27 by 9 (the units digit of 49) and add them up:\n - 7 × 9 = 63\n - 2 × 9 = 18\n - Adding th...
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[ "To solve the long multiplication of 27 and 49, we can break it down into simpler steps:\n\n1. First, let's write out the numbers one under the other:\n ```\n 27\n 49\n ```\n\n2. Now, multiply each digit of 27 by 9 (the units digit of 49) and add them up:\n - 7 × 9 = 63\n - 2 × 9 = 18\n - Adding th...
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[ [ true ] ]
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[ "1323", "1323", "1323" ]
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[ [ false, false, false, false, true ] ]
[ [ "\\(351\\)", "\\( 1323 \\)", "indeed \\( 1323 \\)", "\\( 1323 \\)", "1323" ] ]
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[ [ false, false ], [ false, true ], [ false, false, true ] ]
[ [ "\\(351\\)", "351" ], [ "\\( 1323 \\)", "1323" ], [ "indeed \\( 1323 \\)", "\\( 1323 \\)", "1323" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 27 x 49 is\", \"answer\": \"1323\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1323}" ]
[ true ]
[ "1323" ]
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What is the solution to the long multiplication equation below? 34 x 27 Think step by step.
918
"{\"arg1\": 34, \"arg2\": 27, \"solution\": 918}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n34 x 27\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve the long multiplication problem \\(34 \\times 27\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 34\n × 27\n ```\n\n2. **Multiply 34 by 7 (the ones digit of 27):**\n - Multiply 34 by 7:\n ```\n 34\n × 7\n _______\n 238\n ```\...
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[ "To solve the long multiplication problem \\(34 \\times 27\\), follow these steps:\n\n1. **Multiply the ones digit of 34 by the ones digit of 27:**\n - The ones digit of 34 is 4.\n - The ones digit of 27 is 7.\n - Multiply 4 by 7:\n \\[\n 4 \\times 7 = 28\n \\]\n - Write down 8 and carry over 2....
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\(34 \\times 27\\), we can break it down into simpler steps:\n\n1. **Multiply 34 by 7 (the units digit of 27):**\n - \\(34 \\times 7 = 238\\)\n - Write down 8 and carry over 2.\n\n2. **Multiply 34 by 20 (the tens digit of 27, which is just 2 because there's no tens pla...
{"continuation_phrases": ["Hold on, let me verify this answer.", "Wait, let me try"], "continuations": [" Let's break it down again carefully:\n\n1. Multiply 34 by 7:\n - \\(34 \\times 7 = 238\\). Write down 8 and carry over 2.\n\n2. Multiply 34 by 20:\n - \\(34 \\times 20 = 680\\). Add the carried-over 2: \\(680 +...
[ "To solve the long multiplication problem \\(34 \\times 27\\), we can break it down into simpler steps:\n\n1. **Multiply 34 by 7 (the units digit of 27):**\n - \\(34 \\times 7 = 238\\)\n - Write down 8 and carry over 2.\n\n2. **Multiply 34 by 20 (the tens digit of 27, which is just 2 because there's no tens pla...
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[ "Certainly! Let's solve the long multiplication problem \\( 34 \\times 27 \\) step by step.\n\n### Step 1: Set up the multiplication\n```\n 34\n × 27\n ------\n```\n\n### Step 2: Multiply 34 by 7 (the ones digit of 27)\n- First, multiply 34 by 7:\n ```\n 34\n × 7\n ------\n 238\n ```\n\n### Step...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\( 34 \\times 27 \\) step by step.\n\n### Step 1: Set up the multiplication\n```\n 34\n \u00d7 27\n ------\n```\n\n### Step 2: Multiply 34 by 7 (the ones digit of 27)\n- First, multiply 34 by 7:\n ```\n 34\n \u00d7 7\n ------\n...
[ "Certainly! Let's solve the long multiplication problem \\( 34 \\times 27 \\) step by step.\n\n### Step 1: Set up the multiplication\n```\n 34\n × 27\n ------\n```\n\n### Step 2: Multiply 34 by 7 (the ones digit of 27)\n- First, multiply 34 by 7:\n ```\n 34\n × 7\n ------\n 238\n ```\n\n### Step...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 34 x 27 is\", \"answer\": \"918\"}]}" ]
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What is the solution to the long multiplication equation below? 36 x 93 Think step by step.
3348
"{\"arg1\": 36, \"arg2\": 93, \"solution\": 3348}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n36 x 93\n\nThink step by step.", "role": "user" } ]
longmult
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[ "To solve the long multiplication problem \\(36 \\times 93\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 36\n × 93\n ------\n ```\n\n2. **Multiply 36 by 3 (the ones digit of 93):**\n - \\(36 \\times 3 = 108\\)\n - Write down 8 and carry over 1.\n\n3. **Multiply 36 ...
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[ "To solve the long multiplication problem \\(36 \\times 93\\), we can break it down into smaller steps and multiply each digit of 36 by each digit of 93 separately before adding them together.\n\nHere's how you do it:\n\n1. Multiply 36 by 3 (the ones place in 93):\n \\[\n 36 \\times 3 = 108\n \\]\n2. Multiply...
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[ "To solve the long multiplication problem \\(36 \\times 93\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 36 and 93 one under the other, aligning the digits by place value.\n\n ```\n 36\n × 93\n ------\n ```\n\n2. **Multiply 36 by 3 (the ones digit of 93)**:\n \n ...
{"continuation_phrases": ["Wait, how?", "But according to"], "continuations": [" Let's correct that.\n \\[\n 36 \\times 3 = 108\n \\]\n Since 36 is 4 tens and 6 ones, we can break it down as follows:\n \\[\n 4 \\times 3 = 12 \\quad (\\text{write 2 and carry 1})\n \\]\n \\[\n 6 \\time...
[ "To solve the long multiplication problem \\(36 \\times 93\\), we will follow these steps:\n\n1. **Set up the multiplication**: Write down 36 and 93 one under the other, aligning the digits by place value.\n\n ```\n 36\n × 93\n ------\n ```\n\n2. **Multiply 36 by 3 (the ones digit of 93)**:\n \n ...
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[ "To solve the long multiplication problem \\(36 \\times 93\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 93 as the sum of its digits:\n\\[93 = 90 + 3\\]\n\nNow, we can use this expression in our multiplication:\n\n\\[36 \\times 9...
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[ "To solve the long multiplication problem \\(36 \\times 93\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's express 93 as the sum of its digits:\n\\[93 = 90 + 3\\]\n\nNow, we can use this expression in our multiplication:\n\n\\[36 \\times 9...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
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What is the solution to the long multiplication equation below? 75 x 60 Think step by step.
4500
"{\"arg1\": 75, \"arg2\": 60, \"solution\": 4500}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n75 x 60\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(75 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply 75 by 6:**\n - First, multiply 75 by 6 in your head or on paper:\n \\[\n 75 \\times 6 = 450\n \\]\n\n2. **Place the result in the correct place value:**\n - Since we're multiplyin...
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[ "To solve the long multiplication problem \\( 75 \\times 60 \\), we can break it down into simpler steps:\n\n1. **Multiply 75 by 0**: \n - Any number multiplied by 0 equals 0.\n - So, \\( 75 \\times 0 = 0 \\).\n\n2. **Multiply 75 by 6**:\n - To multiply 75 by 6, you can think of it as adding 75 to itself six ...
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[ "To solve the long multiplication problem \\(75 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply 75 by 0**: \n - Since any number multiplied by 0 equals 0, \\(75 \\times 0 = 0\\).\n\n2. **Multiply 75 by 6**:\n - To do this, you can think of it as multiplying 75 by 6 and then moving the d...
{"continuation_phrases": ["Wait, how?", "But according to"], "continuations": [" Let's do it step by step.\n - First, multiply 75 by 6: \\(75 \\times 6 = 450\\).\n - Now, move the decimal point in 450 one place to the left because 6 has one fewer digit than 75.\n - Moving the decimal point one place to the ...
[ "To solve the long multiplication problem \\(75 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply 75 by 0**: \n - Since any number multiplied by 0 equals 0, \\(75 \\times 0 = 0\\).\n\n2. **Multiply 75 by 6**:\n - To do this, you can think of it as multiplying 75 by 6 and then moving the d...
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[ "To solve the long multiplication problem \\(75 \\times 60\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 75\n x 60\n ```\n\n2. **Multiply 75 by 0 (the rightmost digit of 60):**\n - 75 × 0 = 0\n Write down 0 in the units place.\n\n3. **Multiply 75 by 6 (the leftmost digit of 60)...
{"all_responses": ["To solve the long multiplication problem \\(75 \\times 60\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 75\n x 60\n ```\n\n2. **Multiply 75 by 0 (the rightmost digit of 60):**\n - 75 \u00d7 0 = 0\n Write down 0 in the units place.\n\n3. **Multiply 75 by 6 (the l...
[ "To solve the long multiplication problem \\(75 \\times 60\\), follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 75\n x 60\n ```\n\n2. **Multiply 75 by 0 (the rightmost digit of 60):**\n - 75 × 0 = 0\n Write down 0 in the units place.\n\n3. **Multiply 75 by 6 (the leftmost digit of 60)...
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[ [ false ] ]
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[ "4500", "4500", "4500" ]
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[ [ "\\( 4500 \\)", "4500" ], [ "\\(4500\\)", "4500" ], [ "4500" ] ]
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[ [ false, false ] ]
[ [ "indeed \\(4500\\), but please note that breaking down the multiplication as I initially did was incorrect", "75" ] ]
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[ "4500", "450", "450", "4500" ]
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[ [ "450" ], [ "4500" ], [ "indeed \\(4500\\), but please note that breaking down the multiplication as I initially did was incorrect", "75" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"Therefore, the final answer to 75 x 60 is\", \"answer\": \"4500\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{4500}" ]
[ true ]
[ "4500" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 58 x 38 Think step by step.
2204
"{\"arg1\": 58, \"arg2\": 38, \"solution\": 2204}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n58 x 38\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(58 \\times 38\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 58\n × 38\n ```\n\n2. **Multiply 58 by 8 (the units digit of 38):**\n - Multiply 58 by 8:\n ```\n 464\n ```\n - Write down 464.\n\n3. **Multiply 5...
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[ "Certainly! Let's solve this long multiplication problem step by step.\n\n### Step 1: Set up the multiplication\n```\n 58\n × 38\n _______\n```\n\n### Step 2: Multiply 58 by 8 (the units digit of 38)\n```\n 58\n × 8\n ______\n 464\n```\n\n### Step 3: Multiply 58 by 30 (the tens digit of 38, which ...
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{"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/SIE-countdown3arg_ppo_only-rl", "n_responses": 3}
[ "To solve the long multiplication problem \\( 58 \\times 38 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 58\n × 38\n ```\n\n2. **Multiply 58 by 8 (the ones digit of 38):**\n - Multiply 58 by 8:\n \\[\n 58 \\times 8 = 464\n \\]\n - Write down 464.\n\n3. **Mu...
{"continuation_phrases": ["But according to", "But according to"], "continuations": [" the reference text, the correct answer should be \\( 2204\\). Therefore, there seems to be an error in my previous calculation or explanation. Let me recheck it carefully.\n\nUpon reviewing, I realize that I made a mistake in the sec...
[ "To solve the long multiplication problem \\( 58 \\times 38 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 58\n × 38\n ```\n\n2. **Multiply 58 by 8 (the ones digit of 38):**\n - Multiply 58 by 8:\n \\[\n 58 \\times 8 = 464\n \\]\n - Write down 464.\n\n3. **Mu...
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[ "To solve the long multiplication of \\( 58 \\times 38 \\), we can break it down into smaller steps using the distributive property of multiplication over addition.\n\nFirst, let's express \\( 38 \\) as \\( 40 - 2 \\):\n\\[ 58 \\times 38 = 58 \\times (40 - 2) \\]\n\nNow, apply the distributive property:\n\\[ 58 \\t...
{"all_responses": ["To solve the long multiplication of \\( 58 \\times 38 \\), we can break it down into smaller steps using the distributive property of multiplication over addition.\n\nFirst, let's express \\( 38 \\) as \\( 40 - 2 \\):\n\\[ 58 \\times 38 = 58 \\times (40 - 2) \\]\n\nNow, apply the distributive proper...
[ "To solve the long multiplication of \\( 58 \\times 38 \\), we can break it down into smaller steps using the distributive property of multiplication over addition.\n\nFirst, let's express \\( 38 \\) as \\( 40 - 2 \\):\n\\[ 58 \\times 38 = 58 \\times (40 - 2) \\]\n\nNow, apply the distributive property:\n\\[ 58 \\t...
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[ [ true ] ]
[ [ "2204" ] ]
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[ true, true, true ]
[ "2204", "2204", "2204" ]
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[ [ true ], [ true ], [ true ] ]
[ [ "2204" ], [ "2204" ], [ "2204" ] ]
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[ true ]
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[ [ true ] ]
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[ true, true, true, true ]
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[ [ false, true ], [ false, true ], [ true ], [ true ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 58 x 38 is\", \"answer\": \"2204\"}]}" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 73 x 16 Think step by step.
1168
"{\"arg1\": 73, \"arg2\": 16, \"solution\": 1168}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n73 x 16\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(73 \\times 16\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 16 into tens and ones.\n\\[ 16 = 10 + 6 \\]\n\n#### Step 2: Multiply 73 by each part of 16 separately.\n\n**First part:**\n\\[ 73 \\times 10 \\]\nWhen you ...
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[ "To solve the long multiplication problem \\( 73 \\times 16 \\), follow these steps:\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 73\n × 16\n ----\n ```\n\n2. **Multiply 73 by 6 (the ones digit of 16):**\n - Multiply 73 by 6:\n \\[\n 73 \\times 6 = 438\n \\]\n...
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[ "To solve the long multiplication problem \\(73 \\times 16\\), we will follow these steps:\n\n1. **Write down the numbers**: \n ```\n 73\n × 16\n ```\n\n2. **Multiply 73 by 6 (the ones digit of 16)**:\n - Multiply 73 by 6: \n ```\n 438\n + 0\n ----\n 438\n ```\n - The resul...
{"continuation_phrases": ["But to confirm,", "But to confirm,"], "continuations": [" let's break it into smaller parts.\n \n - Break it down as follows:\n - Multiply 73 by 1 (which is just 73):\n ```\n 73\n \u00d7 1\n ------\n 73\n ```\n - Then multiply 73 by 10 (which i...
[ "To solve the long multiplication problem \\(73 \\times 16\\), we will follow these steps:\n\n1. **Write down the numbers**: \n ```\n 73\n × 16\n ```\n\n2. **Multiply 73 by 6 (the ones digit of 16)**:\n - Multiply 73 by 6: \n ```\n 438\n + 0\n ----\n 438\n ```\n - The resul...
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[ "To solve the long multiplication problem \\(73 \\times 16\\), follow these steps:\n\nStep 1: Break down the numbers into tens and ones.\n- 73 can be broken down into 70 (which represents 7 tens) + 3 (which represents 3 ones).\n- 16 can be broken down into 10 (which represents 1 ten) + 6 (which represents 6 ones).\...
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[ "To solve the long multiplication problem \\(73 \\times 16\\), follow these steps:\n\nStep 1: Break down the numbers into tens and ones.\n- 73 can be broken down into 70 (which represents 7 tens) + 3 (which represents 3 ones).\n- 16 can be broken down into 10 (which represents 1 ten) + 6 (which represents 6 ones).\...
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 73 x 16 is\", \"answer\": \"1168\"}]}" ]
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{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1168}" ]
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[ "1168" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 35 x 49 Think step by step.
1715
"{\"arg1\": 35, \"arg2\": 49, \"solution\": 1715}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n35 x 49\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(35 \\times 49\\), we can break it down into simpler steps:\n\n1. **Break down 49**: We know that 49 can be broken down into 40 + 9.\n So, \\(35 \\times 49 = 35 \\times (40 + 9)\\).\n\n2. **Use the distributive property**:\n This means we need to multiply 35 by both 4...
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[ "Certainly! Let's solve this step by step.\n\n### Step 1: Set up the problem\nWe need to multiply:\n\\[ 35 \\times 49 \\]\n\n### Step 2: Break down the numbers into parts\nTo make it easier, we can break down one of the numbers into smaller parts.\nLet's use \\( 35 = 30 + 5 \\) and \\( 49 = 40 + 9 \\).\n\nSo our pr...
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[ "Certainly! Let's solve the long multiplication problem \\(35 \\times 49\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 35\n × 49\n ----\n ```\n\n2. **Multiply 35 by 9 (the ones digit of 49):**\n - \\(35 \\times 9 = 315\\)\n - Write down 315 under the lin...
{"continuation_phrases": ["Wait, how?", "Wait, let me try"], "continuations": [" I made a mistake here.\n \n Actually, let's do this correctly:\n - Multiply 35 by 40 first (as we did before) gives us 1400.\n - Now multiply 35 by 9 (the ones digit of 49) which gives us 315.\n - So, \\(1400 + 315 = 1715\\)\n\nB...
[ "Certainly! Let's solve the long multiplication problem \\(35 \\times 49\\) step by step.\n\n### Step-by-Step Solution:\n\n1. **Set up the multiplication:**\n ```\n 35\n × 49\n ----\n ```\n\n2. **Multiply 35 by 9 (the ones digit of 49):**\n - \\(35 \\times 9 = 315\\)\n - Write down 315 under the lin...
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[ "To solve the long multiplication problem \\(35 \\times 49\\), we can break it down into smaller steps:\n\n1. **Break down the numbers:**\n - \\(35\\) can be broken down into \\(30 + 5\\).\n - \\(49\\) can be broken down into \\(40 + 9\\).\n\n2. **Multiply each part of the first number by each part of the secon...
{"all_responses": ["To solve the long multiplication problem \\(35 \\times 49\\), we can break it down into smaller steps:\n\n1. **Break down the numbers:**\n - \\(35\\) can be broken down into \\(30 + 5\\).\n - \\(49\\) can be broken down into \\(40 + 9\\).\n\n2. **Multiply each part of the first number by each pa...
[ "To solve the long multiplication problem \\(35 \\times 49\\), we can break it down into smaller steps:\n\n1. **Break down the numbers:**\n - \\(35\\) can be broken down into \\(30 + 5\\).\n - \\(49\\) can be broken down into \\(40 + 9\\).\n\n2. **Multiply each part of the first number by each part of the secon...
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[ "1715", "1715", "1745" ]
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[ [ false, false, true ] ]
[ [ "\\(1715\\)", "indeed \\(1715\\)", "1715" ] ]
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[ [ "1715" ], [ "\\(1715\\)", "1715" ], [ "indeed \\(1715\\)", "1715" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 35 x 49 is\", \"answer\": \"1715\"}]}" ]
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[ "\\boxed{1715}" ]
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[ "1715" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 96 x 19 Think step by step.
1824
"{\"arg1\": 96, \"arg2\": 19, \"solution\": 1824}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n96 x 19\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(96 \\times 19\\), we can break it down into simpler steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down 19 into tens and ones.\n\\[ 19 = 10 + 9 \\]\n\n#### Step 2: Multiply 96 by each part of 19 separately.\n\n**First part:**\n\\[ 96 \\times 10 \\]\nThis is s...
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[ "To solve the long multiplication problem \\( 96 \\times 19 \\), we can break it down into simpler steps:\n\nStep 1: Break down 96 and 19 into their place values.\n- \\( 96 = 90 + 6 \\)\n- \\( 19 = 10 + 9 \\)\n\nStep 2: Multiply each part of 96 by each part of 19.\n\nFirst, multiply 90 by 19:\n\\[ 90 \\times 19 = (...
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[ "To solve \\( 96 \\times 19 \\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 96\n × 19\n ```\n\n2. **Multiply 96 by 9 (the units digit of 19):**\n - Multiply 96 by 9:\n ```\n 864\n ```\n - Write down 864.\n\n3. **Multiply 96 by 10 (the tens ...
{"continuation_phrases": ["Wait! I can double check this answer.", "However,"], "continuations": [" Let's do it again carefully.\n \n5. **Recheck the multiplication for 96 * 10:**\n - Correctly multiply 96 by 10:\n ```\n 960\n ```\n - Shift one place to the left:\n ```\n 9600\n ```\n\...
[ "To solve \\( 96 \\times 19 \\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 96\n × 19\n ```\n\n2. **Multiply 96 by 9 (the units digit of 19):**\n - Multiply 96 by 9:\n ```\n 864\n ```\n - Write down 864.\n\n3. **Multiply 96 by 10 (the tens ...
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[ "To solve the long multiplication problem \\(96 \\times 19\\), we can break it down into simpler steps:\n\nStep 1: Break down the numbers.\n\\[96 = 90 + 6\\]\n\\[19 = 10 + 9\\]\n\nStep 2: Multiply each part of the first number (90 and 6) by each part of the second number (10 and 9).\n\\[90 \\times 10 = 900\\]\n\\[9...
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[ "To solve the long multiplication problem \\(96 \\times 19\\), we can break it down into simpler steps:\n\nStep 1: Break down the numbers.\n\\[96 = 90 + 6\\]\n\\[19 = 10 + 9\\]\n\nStep 2: Multiply each part of the first number (90 and 6) by each part of the second number (10 and 9).\n\\[90 \\times 10 = 900\\]\n\\[9...
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[ true ]
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[ "1764", "1756", "1824" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the final answer to 96 x 19 is\", \"answer\": \"1824\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{1824}" ]
[ true ]
[ "1824" ]
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[ [ true ] ]
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What is the solution to the long multiplication equation below? 59 x 59 Think step by step.
3481
"{\"arg1\": 59, \"arg2\": 59, \"solution\": 3481}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n59 x 59\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication of 59 and 59, we can break it down into simpler steps:\n\n1. **Multiply the units digits**: \n - The units digit of 59 is 9.\n - Multiply 9 by 9: \\( 9 \\times 9 = 81 \\).\n\n2. **Multiply the tens digits**:\n - The tens digit of both numbers is 5.\n - Multiply 5 by 5: \\( ...
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[ "To solve the long multiplication of 59 and 59, we'll break it down into simpler steps:\n\nStep 1: Multiply the ones digit of both numbers.\n5 * 9 = 45\n\nStep 2: Write down this result as the last two digits of our answer.\n\nNow we need to multiply the tens digit of both numbers:\n50 * 50 = 2500\n\nStep 3: Add th...
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[ "To solve \\( 59 \\times 59 \\), we can use the formula for squaring a binomial: \\((a + b)^2 = a^2 + 2ab + b^2\\).\n\nHere, \\( a = 50 \\) and \\( b = 9 \\). So,\n\n\\[\n(50 + 9)^2 = 50^2 + 2 \\cdot 50 \\cdot 9 + 9^2\n\\]\n\nNow let's calculate each part:\n\n1. \\( 50^2 = 2500 \\)\n2. \\( 2 \\cdot 50 \\cdot 9 = 90...
{"continuation_phrases": ["But to confirm,", "However,"], "continuations": [" let's calculate it directly:\n\n\\( 59 \\times 59 \\)\n\n1. Multiply 59 by 59:\n - First part of the calculation: \\( 59 \\times 59 = (60 - 1)(60 - 1) = 60^2 - 2 \\cdot 60 \\cdot 1 + 1^2 \\)\n - Second part of the calculation: \\( 60^2 = ...
[ "To solve \\( 59 \\times 59 \\), we can use the formula for squaring a binomial: \\((a + b)^2 = a^2 + 2ab + b^2\\).\n\nHere, \\( a = 50 \\) and \\( b = 9 \\). So,\n\n\\[\n(50 + 9)^2 = 50^2 + 2 \\cdot 50 \\cdot 9 + 9^2\n\\]\n\nNow let's calculate each part:\n\n1. \\( 50^2 = 2500 \\)\n2. \\( 2 \\cdot 50 \\cdot 9 = 90...
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[ "To solve the long multiplication of 59 x 59, we can break it down into steps:\n\n1) First, multiply 59 by 5:\n ```\n 59\n x 5\n ------\n 295\n ```\n\n2) Now, multiply 59 by 0 (the next digit in 59):\n ```\n 59\n x 0\n ------\n 0\n ```\n\n3) Add these two results together:\n ``...
{"all_responses": ["To solve the long multiplication of 59 x 59, we can break it down into steps:\n\n1) First, multiply 59 by 5:\n ```\n 59\n x 5\n ------\n 295\n ```\n\n2) Now, multiply 59 by 0 (the next digit in 59):\n ```\n 59\n x 0\n ------\n 0\n ```\n\n3) Add these two results t...
[ "To solve the long multiplication of 59 x 59, we can break it down into steps:\n\n1) First, multiply 59 by 5:\n ```\n 59\n x 5\n ------\n 295\n ```\n\n2) Now, multiply 59 by 0 (the next digit in 59):\n ```\n 59\n x 0\n ------\n 0\n ```\n\n3) Add these two results together:\n ``...
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[ false ]
[ "331" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the product of 59 and 59 is\", \"answer\": \"331\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{331}" ]
[ false ]
[ "331" ]
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[ [ false ] ]
[ [ "331" ] ]
[ [ { "all_extracted_answers": [ "331" ], "all_extractions": [ "{'content': '331', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '331'}" ], "confidence": 0.9500000000000001, "extracted_answer": "331", "extractor": "stri...
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What is the solution to the long multiplication equation below? 60 x 22 Think step by step.
1320
"{\"arg1\": 60, \"arg2\": 22, \"solution\": 1320}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n60 x 22\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(60 \\times 22\\), we can break it down into simpler steps:\n\n1. **Multiply 60 by 2:**\n - \\(60 \\times 2 = 120\\)\n\n2. **Multiply 60 by 20 (which is the same as multiplying by 2 and then adding a zero):**\n - \\(60 \\times 20 = 1200\\) (because \\(60 \\times 2 = 1...
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[ "Certainly! Let's break down the multiplication of 60 and 22 into steps.\n\n### Step-by-Step Solution:\n\n1. **Break Down 60:**\n - 60 can be broken down into 6 tens (since \\(6 \\times 10 = 60\\)).\n\n2. **Multiply 6 tens by 22:**\n - First, multiply 6 by 22.\n \\[\n 6 \\times 22 = 132\n \\]\n - ...
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[ "To solve the long multiplication problem \\(60 \\times 22\\), we can break it down into simpler steps:\n\n1. **Multiply 60 by 2:**\n - 60 × 2 = 120\n\n2. **Multiply 60 by 20 (which is the same as multiplying by 2 and then adding a zero):**\n - 60 × 20 = 1200\n\n3. **Add the two results together:**\n - 120 + ...
{"continuation_phrases": ["However,", "However,"], "continuations": [" since 22 has one zero at the end, we need to adjust our result:\n - 60 \u00d7 22 = 1200 + 240 = 1440\n\nSo, the final answer is 1440.", " let's verify this with the standard method of long multiplication:\n\n- Multiply 60 by 2: 60 \u00d7 2 = 120...
[ "To solve the long multiplication problem \\(60 \\times 22\\), we can break it down into simpler steps:\n\n1. **Multiply 60 by 2:**\n - 60 × 2 = 120\n\n2. **Multiply 60 by 20 (which is the same as multiplying by 2 and then adding a zero):**\n - 60 × 20 = 1200\n\n3. **Add the two results together:**\n - 120 + ...
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[ "To solve the long multiplication problem \\(60 \\times 22\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(60\\) can be thought of as \\(6 \\times 10\\).\n - \\(22\\) can be broken down into \\(2 \\times 11\\).\n\n2. **Multiply each part separately:**\n - First, multiply ...
{"all_responses": ["To solve the long multiplication problem \\(60 \\times 22\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(60\\) can be thought of as \\(6 \\times 10\\).\n - \\(22\\) can be broken down into \\(2 \\times 11\\).\n\n2. **Multiply each part separately:**\n - F...
[ "To solve the long multiplication problem \\(60 \\times 22\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(60\\) can be thought of as \\(6 \\times 10\\).\n - \\(22\\) can be broken down into \\(2 \\times 11\\).\n\n2. **Multiply each part separately:**\n - First, multiply ...
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[ true ]
[ "1320" ]
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[ "264", "1320", "240" ]
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[ "1276", "1320", "1320", "1320" ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to 60 x 22 is\", \"answer\": \"1320\"}]}" ]
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[ "\\boxed{1320}" ]
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What is the solution to the long multiplication equation below? 62 x 91 Think step by step.
5642
"{\"arg1\": 62, \"arg2\": 91, \"solution\": 5642}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n62 x 91\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(62 \\times 91\\), we will follow these steps:\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 62\n × 91\n```\n\n### Step 2: Multiply 62 by 1 (the units digit of 91)\n- Multiply 62 by 1: \n ```\n 62\n × 1\n -----...
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[ "Certainly! Let's solve the long multiplication problem \\( 62 \\times 91 \\) step by step.\n\n### Step 1: Set up the multiplication vertically.\n```\n 62\n× 91\n------\n```\n\n### Step 2: Multiply 62 by 1 (the ones digit of 91).\n```\n 62\n× 91\n------\n 62 (62 × 1)\n+508 (62 × 9, shifted one place t...
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[ "To solve the long multiplication problem \\(62 \\times 91\\), we will follow these steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 62\n × 91\n```\n\n### Step 2: Multiply 62 by 1 (the units digit of 91).\n```\n 62\n × 91\n -----\n 62 (62 × 1)\n```\n\n### Step 3: Multiply 62 b...
{"continuation_phrases": ["But according to", "Wait! I can double check this answer."], "continuations": [" our setup in Step 2, it should be:\n```\n 62\n\u00d7 91\n-----\n 62\n+558\n-----\n 5702\n```\nSo the correct multiplication for Step 3 should be:\n```\n 62\n\u00d7 91\n-----\n 62\n+558\n-----\n 5702\n``...
[ "To solve the long multiplication problem \\(62 \\times 91\\), we will follow these steps:\n\n### Step 1: Set up the multiplication vertically.\n```\n 62\n × 91\n```\n\n### Step 2: Multiply 62 by 1 (the units digit of 91).\n```\n 62\n × 91\n -----\n 62 (62 × 1)\n```\n\n### Step 3: Multiply 62 b...
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[ "To solve the long multiplication problem \\(62 \\times 91\\), we can break it down into smaller steps:\n\n### Step 1: Break Down the Multiplication\nFirst, let's think about how to multiply these numbers without actually doing all the work at once.\n\n\\[ 62 \\times 91 = (60 + 2) \\times (90 + 1) \\]\n\nThis is be...
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[ "To solve the long multiplication problem \\(62 \\times 91\\), we can break it down into smaller steps:\n\n### Step 1: Break Down the Multiplication\nFirst, let's think about how to multiply these numbers without actually doing all the work at once.\n\n\\[ 62 \\times 91 = (60 + 2) \\times (90 + 1) \\]\n\nThis is be...
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[ [ "\\(5702\\)", "indeed \\(5702\\), but if you want to verify it, use the standard algorithm or another method like breaking it into parts as shown above", "620" ] ]
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[ [ "6042" ], [ "\\(5702\\)" ], [ "indeed \\(5702\\), but if you want to verify it, use the standard algorithm or another method like breaking it into parts as shown above", "620" ] ]
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We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, 62 x 91 = 620.\", \"answer\": \"620\"}, {\"context\": \"The result from multiplying by 1 is 62.\", \"answer\": \"62\"}, {\"context\": \"The result from multiplying by 9 is 558.\", \"answer\": \"558\"}]}" ]
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[ "\\boxed{620}", "\\boxed{62}", "\\boxed{558}" ]
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What is the solution to the long multiplication equation below? 13 x 29 Think step by step.
377
"{\"arg1\": 13, \"arg2\": 29, \"solution\": 377}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n13 x 29\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the long multiplication problem \\(13 \\times 29\\), we can break it down into simpler steps:\n\nStep 1: Multiply 13 by 9 (the units digit of 29).\n\\[13 \\times 9 = 117\\]\n\nStep 2: Multiply 13 by 20 (which is the same as multiplying 13 by 2 and then adding a zero at the end).\n\\[13 \\times 20 = 260\\]...
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[ "To solve the long multiplication problem \\(13 \\times 29\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's write out the multiplication vertically:\n\n```\n 13\n × 29\n ----\n```\n\nNow, distribute the multiplication across each di...
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[ "Certainly! Let's solve the multiplication problem \\( 13 \\times 29 \\) step by step.\n\n### Step 1: Break down the numbers\nFirst, we can break down the numbers into smaller parts for easier calculation:\n- \\( 13 = 10 + 3 \\)\n- \\( 29 = 20 + 9 \\)\n\nSo, our problem becomes:\n\\[ (10 + 3) \\times (20 + 9) \\]\n...
{"continuation_phrases": ["Wait! I can double check this answer.", "However,"], "continuations": [" The correct breakdown should be \\( 29 = 20 + 9 \\), but let's move forward with it.\n \n### Step 2: Use the distributive property (also known as the FOIL method for binomials)\nWe'll use the distributive property to mu...
[ "Certainly! Let's solve the multiplication problem \\( 13 \\times 29 \\) step by step.\n\n### Step 1: Break down the numbers\nFirst, we can break down the numbers into smaller parts for easier calculation:\n- \\( 13 = 10 + 3 \\)\n- \\( 29 = 20 + 9 \\)\n\nSo, our problem becomes:\n\\[ (10 + 3) \\times (20 + 9) \\]\n...
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[ "Certainly! Let's solve the long multiplication problem \\(13 \\times 29\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 13\n × 29\n ------\n```\n\n### Step 2: Multiply 13 by 9 (the ones digit of 29)\n\\[\n13 \\times 9 = 117\n\\]\nWrite this res...
{"all_responses": ["Certainly! Let's solve the long multiplication problem \\(13 \\times 29\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 13\n \u00d7 29\n ------\n```\n\n### Step 2: Multiply 13 by 9 (the ones digit of 29)\n\\[\n13 \\times 9 = 117\...
[ "Certainly! Let's solve the long multiplication problem \\(13 \\times 29\\) step by step.\n\n### Step 1: Set up the multiplication\nWrite down the numbers one under the other:\n```\n 13\n × 29\n ------\n```\n\n### Step 2: Multiply 13 by 9 (the ones digit of 29)\n\\[\n13 \\times 9 = 117\n\\]\nWrite this res...
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[ [ "\\( 377 \\)", "indeed \\( 377 \\)", "377" ] ]
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[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}, {'answer_block': None, 'comparison_type': None, 'correct_answer': None, '...
[ false, false, false, true ]
[ "2717", "2717", "2717", "377" ]
[{"all_matches": ["('2717', 662)", "('2600', 597)", "('260', 450)", "('2', 418)", "('117', 272)"], "all_numbers_in_line": null, "boxed_attempt": null, "choice_labels": null, "confidence": 0.9688385269121813, "extracted_answer": "2717", "extracted_choice_letter": null, "extracted_choice_text": null, "extraction_attempts...
[{"answer_block": null, "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": "legacy", "extracted_answer": null, "final_answer": null, "is_correct": null, "is_equivalent": null, "legacy_result": false, "reason": null}, {"answer_block": null, "comparison_type": null, "correct_answer": nul...
[ [ false, false ], [ false, false ], [ false, false ], [ false, true ] ]
[ [ "\\(2717\\)", "2717" ], [ "indeed \\(2717\\)", "2717" ], [ "indeed \\(2717\\)", "2717" ], [ "actually \\(377\\), not \\(2717\\)", "377" ] ]
[{"value": "[{'all_extracted_answers': ['\\\\(2717\\\\)'], 'all_extractions': [\"{'content': '\\\\\\\\(2717\\\\\\\\)', 'start_pos': 687, 'end_pos': 706, 'phrase_pair': ('answer is', ''), 'full_match': 'answer is \\\\\\\\(2717\\\\\\\\).'}\"], 'all_matches': None, 'all_numbers_in_line': None, 'choice_labels': None, 'conf...
[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': False}, {'answer_block': None, 'comparison_type': None, 'correct_answer': None, '...
[ true, true, true ]
[ "377", "377", "377" ]
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[ [ true ], [ false, true ], [ false, true ] ]
[ [ "377" ], [ "\\( 377 \\)", "377" ], [ "indeed \\( 377 \\)", "377" ] ]
[{"value": "[{'all_extracted_answers': None, 'all_extractions': None, 'all_matches': [\"('377', 976)\", \"('377', 877)\", \"('350', 856)\", \"('290', 835)\", \"('27', 686)\", \"('60', 662)\", \"('90', 637)\", \"('200', 611)\", \"('10', 458)\", \"('20', 227)\", \"('10', 207)\"], 'all_numbers_in_line': None, 'choice_labe...
[{"value": "[{'answer_block': None, 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': 'legacy', 'extracted_answer': None, 'final_answer': None, 'is_correct': None, 'is_equivalent': None, 'legacy_result': True}]"}, {"value": "[{'answer_block': None, 'comparison_type': None, 'correct_an...
We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. These may be within <answer> tags, \boxed{} values, or just plain text embedded in sentences like "The final answer is:". Your job is to find these spans and their context...
[ "{\"answer_spans\": [{\"context\": \"So, the solution to the long multiplication equation 13 x 29 is\", \"answer\": \"377\"}]}" ]
{ "api_url": "", "backend": "openai", "chat_template_applied": false, "generation_params": { "temperature": 0 }, "model_name": "gpt-4o-mini", "prompt": "We gave the following question to a language model. We want you to look through the response it gave and find all the answer spans it produced. \n\nT...
{ "backend": "openai", "model_name": "gpt-4o-mini", "n_responses": 1 }
[ "\\boxed{377}" ]
[ true ]
[ "377" ]
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[ [ true ] ]
[ [ "377" ] ]
[ [ { "all_extracted_answers": [ "377" ], "all_extractions": [ "{'content': '377', 'start_pos': 7, 'end_pos': 10, 'phrase_pair': ('\\\\boxed{', ['}']), 'full_match': '377'}" ], "confidence": 0.9500000000000001, "extracted_answer": "377", "extractor": "stri...
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