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Using ALL of the numbers 12, 4, 7, 1, 2, 5, 21, 88, create an expression that equals 109. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [12, 4, 7, 1, 2, 5, 21, 88], "target": 109, "operators_used": ["/", "+", "/", "/", "/", "*", "+"], "expression": "12 / 4 + 7 / 1 / 2 / 5 * 21 + 88"}
countdown
[ { "content": "You are a helpful assistant that solves math problems by reasoning step-by-step. Show your work clearly and provide complete solutions. You MUST use ALL of the given numbers exactly once in your solution. When you have a final answer, wrap it in <answer></answer> tags.", "role": "system" }, ...
[ [ "Okay, let's see. I need to use all the numbers 12, 4, 7, 1, 2, 5, 21, 88 exactly once with +, -, *, / to make 109. Hmm, this might take a while. Let me start by listing out the numbers again to make sure I have them all: 12, 4, 7, 1, 2, 5, 21, 88. Eight numbers total. So, I need to combine them with operatio...
[ 32941 ]
[ 4 ]
[ [ "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies." ] ]
[ [ "Okay, let's see. I need to use all the numbers 12, 4, 7, 1, 2, 5, 21, 88 exactly once with +, -, *, / to make 109. Hmm, this might take a while. Let me start by listing out the numbers again to make sure I have them all: 12, 4, 7, 1, 2, 5, 21, 88. Eight numbers total. So, I need to combine them with operatio...
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[ [ [ "88 + 21 + (12 - 7 - 5) * (4 - 2 - 1)" ], [ "88 + 21 + (12 - 4 - 7 - 1) * (5 - 2)" ], [ "88 + 21 + ((7 * 2) - 12) * (5 - (4 + 1))" ], [ "88 + 5 * 4 + 1 + (21 - 12 - 7 - 2)", "88 + 5 * 4 + 1 + (21 - 12 - 7 - 2)" ] ] ]
[ [ [ true ], [ true ], [ true ], [ true, true ] ] ]
[ [ [ { "answer_block": "88 + 21 + (12 - 7 - 5) * (4 - 2 - 1)", "error": null, "final_answer": 109, "is_correct": true } ], [ { "answer_block": "88 + 21 + (12 - 4 - 7 - 1) * (5 - 2)", "error": null, "final_answer": 109, "is_...
[ [] ]
"Using ALL of the numbers 25, 69, 58, 14, 55, 24, 36, 60, create an expression that equals 176. You (...TRUNCATED)
"{\"numbers\": [25, 69, 58, 14, 55, 24, 36, 60], \"target\": 176, \"operators_used\": [\"-\", \"+\",(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 25, 69, 58, 14, 55, 24, 36, 60 exactly once with +(...TRUNCATED)
[ 39403 ]
[ 1 ]
[ [] ]
[["Okay, let's see. I need to use all the numbers 25, 69, 58, 14, 55, 24, 36, 60 exactly once with +(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[ [ [ "(69 - 55) * (25 - 14) + (60 - 58) * (36 / 24)" ] ] ]
[ [ [ false ] ] ]
[[[{"answer_block":"(69 - 55) * (25 - 14) + (60 - 58) * (36 / 24)","error":"Expression does not equa(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 55, 36, 6, 3, 14, 99, 17, 82, create an expression that equals 245. You mu(...TRUNCATED)
"{\"numbers\": [55, 36, 6, 3, 14, 99, 17, 82], \"target\": 245, \"operators_used\": [\"*\", \"-\", \(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to create an expression using all the numbers 55, 36, 6, 3, 14, 99, 17, 8(...TRUNCATED)
[ 33991 ]
[ 4 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's see. I need to create an expression using all the numbers 55, 36, 6, 3, 14, 99, 17, 8(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["(82 + 99 + 55 + 14) - (17 - (36 / (6 - 3)))"],["(14 * 17) + (99 - 82) - (55 - 36 - 6 - 3)"],["(3(...TRUNCATED)
[ [ [ true ], [ true ], [ true ], [ true ] ] ]
[[[{"answer_block":"(82 + 99 + 55 + 14) - (17 - (36 / (6 - 3)))","error":null,"final_answer":245.0,"(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 87, 87, 29, 2, 19, 4, 1, 1, create an expression that equals 281. You must(...TRUNCATED)
"{\"numbers\": [87, 87, 29, 2, 19, 4, 1, 1], \"target\": 281, \"operators_used\": [\"/\", \"+\", \"/(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to create an expression using all the numbers 87, 87, 29, 2, 19, 4, 1, 1 (...TRUNCATED)
[ 38597 ]
[ 4 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's see. I need to create an expression using all the numbers 87, 87, 29, 2, 19, 4, 1, 1 (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["87 + 87 + 29 + 19 * 4 + 2 + 1 - 1"],["87 + 87 + 29 + 19 * 4 + 2 + 1 - 1"],["87 + 87 + 29 + 19 * (...TRUNCATED)
[ [ [ true ], [ true ], [ true ], [ true ] ] ]
[[[{"answer_block":"87 + 87 + 29 + 19 * 4 + 2 + 1 - 1","error":null,"final_answer":281.0,"is_correct(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 56, 63, 7, 50, 44, 1, 87, 52, create an expression that equals 132. You mu(...TRUNCATED)
"{\"numbers\": [56, 63, 7, 50, 44, 1, 87, 52], \"target\": 132, \"operators_used\": [\"-\", \"/\", \(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 56, 63, 7, 50, 44, 1, 87, 52 exactly once with +, (...TRUNCATED)
[ 37256 ]
[ 3 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 56, 63, 7, 50, 44, 1, 87, 52 exactly once with +, (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["56 + 7 + 44 + 87 + 52 - 63 - 50 - 1"],["56 + 7 + 44 + 87 + 52 - 63 - 50 - 1","56 + 50 + 1 + 87 +(...TRUNCATED)
[ [ [ true ], [ true, true, true, true, true, true ], [ true, true, true, true, true, true ] ] ]
[[[{"answer_block":"56 + 7 + 44 + 87 + 52 - 63 - 50 - 1","error":null,"final_answer":132.0,"is_corre(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 7, 1, 49, 7, 28, 59, 3, 44, create an expression that equals 521. You must(...TRUNCATED)
"{\"numbers\": [7, 1, 49, 7, 28, 59, 3, 44], \"target\": 521, \"operators_used\": [\"/\", \"*\", \"/(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 7, 1, 49, 7, 28, 59, 3, 44 exactly once to make 52(...TRUNCATED)
[ 36366 ]
[ 2 ]
[ [ "Continue exploring alternative solution strategies." ] ]
[["Okay, let's see. I need to use all the numbers 7, 1, 49, 7, 28, 59, 3, 44 exactly once to make 52(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["49*7 + 59*3 + 1 + (7 - 7)*28*44","49*7 + 59*3 + 1 + (7 - 7)*28*44"],["44*(49/7 + 3 + 1) + (59 - (...TRUNCATED)
[ [ [ false, false ], [ false ] ] ]
[[[{"answer_block":"49*7 + 59*3 + 1 + (7 - 7)*28*44","error":"Expression uses an unavailable or repe(...TRUNCATED)
[[{"class_label":"521 divisible by anything?","created_at":"2025-12-27T01:06:17.757221","description(...TRUNCATED)
"Using ALL of the numbers 97, 4, 93, 26, 3, 24, 20, 31, create an expression that equals 620. You mu(...TRUNCATED)
"{\"numbers\": [97, 4, 93, 26, 3, 24, 20, 31], \"target\": 620, \"operators_used\": [\"-\", \"/\", \(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 97, 4, 93, 26, 3, 24, 20, 31 exactly once with +, (...TRUNCATED)
[ 34087 ]
[ 6 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 97, 4, 93, 26, 3, 24, 20, 31 exactly once with +, (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["31*20 + (97 - 93 - 4)*(26 - 24 - 3)"],["31*20 + (97 - 93 - 4) / (26 - 24 - 3)"],["31*20 + ((97 -(...TRUNCATED)
[ [ [ true ], [ true ], [ true, true, true ], [ true ], [ true ], [ true ] ] ]
[[[{"answer_block":"31*20 + (97 - 93 - 4)*(26 - 24 - 3)","error":null,"final_answer":620.0,"is_corre(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 45, 69, 55, 40, 1, 9, 8, 83, create an expression that equals 913. You mus(...TRUNCATED)
"{\"numbers\": [45, 69, 55, 40, 1, 9, 8, 83], \"target\": 913, \"operators_used\": [\"*\", \"+\", \"(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 45, 69, 55, 40, 1, 9, 8, 83 to make an expression (...TRUNCATED)
[ 38035 ]
[ 6 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 45, 69, 55, 40, 1, 9, 8, 83 to make an expression (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["83 * ((69 - 55) - (9 / (8 - (45 - 40))) * 1)","83 * ((69 - 55) - (9 / (8 - (45 - 40))) * 1)"],["(...TRUNCATED)
[ [ [ true, true ], [ true ], [ true ], [ true ], [ true ], [ true ] ] ]
[[[{"answer_block":"83 * ((69 - 55) - (9 / (8 - (45 - 40))) * 1)","error":null,"final_answer":913.0,(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 72, 3, 67, 1, 43, 1, 93, 53, create an expression that equals 145. You mus(...TRUNCATED)
"{\"numbers\": [72, 3, 67, 1, 43, 1, 93, 53], \"target\": 145, \"operators_used\": [\"/\", \"-\", \"(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's try to solve this problem. We need to use all the numbers 72, 3, 67, 1, 43, 1, 93, 53(...TRUNCATED)
[ 33679 ]
[ 7 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's try to solve this problem. We need to use all the numbers 72, 3, 67, 1, 43, 1, 93, 53(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["(93 + 53 - 1) * (72 / (67 - 43) / 3 * 1)"],["(93 + 72) - (67 - 43 - 3 - 1) + (1 - 1) * 53"],["93(...TRUNCATED)
[ [ [ true ], [ false ], [ true ], [ false ], [ true ], [ false ], [ false ] ] ]
[[[{"answer_block":"(93 + 53 - 1) * (72 / (67 - 43) / 3 * 1)","error":null,"final_answer":145.0,"is_(...TRUNCATED)
[ [] ]
"Using ALL of the numbers 13, 1, 13, 68, 2, 2, 93, 62, create an expression that equals 102. You mus(...TRUNCATED)
"{\"numbers\": [13, 1, 13, 68, 2, 2, 93, 62], \"target\": 102, \"operators_used\": [\"/\", \"-\", \"(...TRUNCATED)
countdown
[{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 13, 1, 13, 68, 2, 2, 93, 62 exactly once to make 1(...TRUNCATED)
[ 35953 ]
[ 4 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["Okay, let's see. I need to use all the numbers 13, 1, 13, 68, 2, 2, 93, 62 exactly once to make 1(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["93 + 68 - 62 + 1 + 2 + (13 - 13) * 2"],["68 * 2 - (93 - 62 + 2 + 1) + (13 - 13)"],["93 + 68 - 62(...TRUNCATED)
[ [ [ true ], [ true ], [ true ], [ false ] ] ]
[[[{"answer_block":"93 + 68 - 62 + 1 + 2 + (13 - 13) * 2","error":null,"final_answer":102.0,"is_corr(...TRUNCATED)
[ [] ]
End of preview. Expand in Data Studio

EAS-Qwen3-30B-A3B-Thinking-2507-cd8arg-iterative

Countdown reasoning with iterative strategy to 32768 tokens

Dataset Info

  • Rows: 100
  • Columns: 17

Columns

Column Type Description
question Value('string') The countdown problem statement
metadata Value('string') JSON with target number, available numbers, and solution
task_source Value('string') Task type identifier (countdown)
formatted_prompt List({'content': Value('string'), 'role': Value('string')}) Initial prompt messages sent to the model
responses_by_sample List(List(Value('string'))) Full model response [sample_idx][round_idx] = response string
tokens_by_sample List(Value('int64')) Total token count for each sample (based on continuation_text)
num_rounds_by_sample List(Value('int64')) Number of continuation rounds for each sample
continuation_prompts_by_sample List(List(Value('string'))) Continuation prompts used [sample_idx][round_idx] = prompt string
continuation_text_by_sample List(List(Value('string'))) Truncated text used for continuation [sample_idx][round_idx]. For budget_forcing: truncated at first tag. For other strategies: same as responses_by_sample.
strategy_type Value('string') Prompting strategy: 'iterative', 'budget_forcing', or 'random_noise'
termination_reason_by_sample List(Value('string')) Why each sample terminated: 'max_rounds_reached', 'budget_reached', or 'answer_correct'
correct_round_by_sample List(Value('null')) Round number where correct answer was first found (None if never correct)
smart_termination_enabled Value('bool') Whether smart termination was enabled for this run
retry_count_by_sample List(Value('int64')) Total retry attempts per sample due to empty or too-short responses (0 if no retries needed)
answers_by_sample List(List(List(Value('string')))) Extracted answer spans [sample][round][answer_idx]
evals_by_sample List(List(List(Value('bool')))) Correctness evaluations [sample][round][answer_idx]
eval_metadata_by_sample List(List(List({'answer_block': Value('string'), 'error': Value('string'), 'final_answer': Value('float64'), 'is_correct': Value('bool')}))) Evaluation details [sample][round][answer_idx]

Generation Parameters

{
  "script_name": "stage_01_generate_reasoning.py",
  "model": "hosted_vllm/Qwen/Qwen3-30B-A3B-Thinking-2507<api_base>http://10.32.37.15:10080/v1",
  "hyperparameters": {
    "temperature": 0.7,
    "max_tokens_per_round": 32768,
    "target_total_tokens": 32768,
    "samples": 1,
    "strategy": "iterative",
    "max_rounds": null,
    "min_tokens": 10,
    "max_retries_per_round": -1
  },
  "input_datasets": [],
  "description": "Countdown reasoning with iterative strategy to 32768 tokens",
  "experiment": "degen_test_1_countdown",
  "strategy": "iterative",
  "arg_count": 8,
  "seed": 42,
  "smart_termination": false,
  "max_rounds": null,
  "min_tokens": 10,
  "inference_backend": "inference_engine",
  "status": "completed",
  "completed_at": "2025-12-26T11:33:30.670898"
}

Experiment Documentation

For complete experiment details, see https://github.com/TAUR-Lab/Reasoning-Horizons/tree/main/experiments/degen_test_1_countdown

Usage

from datasets import load_dataset

dataset = load_dataset("reasoning-degeneration-dev/EAS-Qwen3-30B-A3B-Thinking-2507-cd8arg-iterative", split="train")
print(f"Loaded {len(dataset)} rows")

This dataset is tracked in reasoning-degeneration-dev/PROJECT-MANIFEST

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