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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" }, ...
[ [ "<think>\nOkay, 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, that's a bit challenging. Let me start by listing out all the numbers to keep track: 12, 4, 7, 1, 2, 5, 21, 88. Eight numbers total.\n\nFirst thought: Maybe start by looking at the...
[ 33506 ]
[ 25 ]
[ [ "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies.", "Continue explo...
[ [ "<think>\nOkay, 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, that's a bit challenging. Let me start by listing out all the numbers to keep track: 12, 4, 7, 1, 2, 5, 21, 88. Eight numbers total.\n\nFirst thought: Maybe start by looking at the...
iterative
[ "budget_reached" ]
[ null ]
false
[ [ [ "88 + 21 + (12 - 5) * (7 - 4 - 2 - 1)" ], [], [ "(88 + 21) + (12 - 5) * (7 - (4 + 2 + 1))" ], [], [ "(88 + 21) - (12 - 5) * (7 - 4 - 2 - 1)", "(88 + 21) - (12 - 5) * (7 - 4 - 2 - 1)" ], [ "(88 + 21) + (5 - (12 - 7)) * (4 + 2 + 1)" ], [], ...
[ [ [ true ], [], [ true ], [], [ true, true ], [ true ], [], [ true ], [ true, true ], [], [ true ], [ true, true ], [ true ], [ true, true ...
[ [ [ { "answer_block": "88 + 21 + (12 - 5) * (7 - 4 - 2 - 1)", "error": null, "final_answer": 109, "is_correct": true } ], [], [ { "answer_block": "(88 + 21) + (12 - 5) * (7 - (4 + 2 + 1))", "error": null, "final_answer": 109, ...
"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)
[["<think>\nOkay, let's try to figure out how to make 176 using all these numbers: 25, 69, 58, 14, 5(...TRUNCATED)
[ 33453 ]
[ 17 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["<think>\nOkay, let's try to figure out how to make 176 using all these numbers: 25, 69, 58, 14, 5(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[["(69 - 58) * (25 - 14) + 60 + 55 + 36 - 24"],["(69 - 58) * (25 - 14) + 60 + 55 + 36 - 24"],["(69 (...TRUNCATED)
[[[false],[false],[false],[],[true,true],[true],[true,true],[true],[true,true],[],[],[true],[true,tr(...TRUNCATED)
[[[{"answer_block":"(69 - 58) * (25 - 14) + 60 + 55 + 36 - 24","error":"Expression does not equal st(...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)
[["<think>\nOkay, let's see. I need to use all these numbers: 55, 36, 6, 3, 14, 99, 17, 82. Each exa(...TRUNCATED)
[ 33058 ]
[ 13 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["<think>\nOkay, let's see. I need to use all these numbers: 55, 36, 6, 3, 14, 99, 17, 82. Each exa(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[["(82 * 3) - ((99 - 55 - 36) / (17 - 14 - 6))"],["( (99 - 55 - (36 / 6) - 3) * (14 / (6 / 3)) ) * (...TRUNCATED)
[[[false],[false],[false,false],[],[false],[false,false,false,false],[false],[],[false,false],[false(...TRUNCATED)
[[[{"answer_block":"(82 * 3) - ((99 - 55 - 36) / (17 - 14 - 6))","error":"Expression does not equal (...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)
[["","","<think>\nOkay, let's try to figure out how to make 281 using all the numbers 87, 87, 29, 2,(...TRUNCATED)
[ 32834 ]
[ 24 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["","","<think>\nOkay, let's try to figure out how to make 281 using all the numbers 87, 87, 29, 2,(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[[],[],["87 + 87 + 29 + 19 * 4 + 2 + 1 - 1"],[],[],["87 + 87 + 29 + 19 * 4 + 2 + 1 - 1"],[],[],[],[(...TRUNCATED)
[[[],[],[true],[],[],[true],[],[],[],[],[true],[],[true,true],[true],[true,true],[true,true],[true],(...TRUNCATED)
[[[],[],[{"answer_block":"87 + 87 + 29 + 19 * 4 + 2 + 1 - 1","error":null,"final_answer":281.0,"is_c(...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)
[["<think>\nOkay, let's see. I need to make an expression that equals 132 using all the numbers 56, (...TRUNCATED)
[ 33074 ]
[ 17 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["<think>\nOkay, let's see. I need to make an expression that equals 132 using all the numbers 56, (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[["87 + 52 - 7 + 50 - 44 - 63 + 56 + 1"],[],["(87 + 52 - 7) - (63 - 56) + (50 - 44) + 1"],[],["(87 (...TRUNCATED)
[[[true],[],[true],[],[true,true],[true],[true],[],[],[true,true],[true],[],[true,true],[],[false,fa(...TRUNCATED)
[[[{"answer_block":"87 + 52 - 7 + 50 - 44 - 63 + 56 + 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)
[["<think>\nOkay, let's try to solve this problem. We need to use all the numbers 7, 1, 49, 7, 28, 5(...TRUNCATED)
[ 32994 ]
[ 24 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["<think>\nOkay, let's try to solve this problem. We need to use all the numbers 7, 1, 49, 7, 28, 5(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[["49 - (7 / 7) + 59 * ((44 - 28) / (3 - 1)) + 1"],["49 - (7 / 7) + 59 * ((44 - 28) / (3 - 1)) + 1"(...TRUNCATED)
[[[false],[false],[false],[],[],[false,false],[false],[false,false],[false],[],[],[],[],[],[false,fa(...TRUNCATED)
[[[{"answer_block":"49 - (7 / 7) + 59 * ((44 - 28) / (3 - 1)) + 1","error":"Expression uses an unava(...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)
[["<think>\nOkay, let's try to figure out how to make 620 using all these numbers: 97, 4, 93, 26, 3,(...TRUNCATED)
[ 36309 ]
[ 1 ]
[ [] ]
[["<think>\nOkay, let's try to figure out how to make 620 using all these numbers: 97, 4, 93, 26, 3,(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ [ [ "26 * 24 - (97 - 93) + (4 - 3) * (20 - 31)" ] ] ]
[ [ [ false ] ] ]
[[[{"answer_block":"26 * 24 - (97 - 93) + (4 - 3) * (20 - 31)","error":"Expression does not equal st(...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)
[["<think>\nOkay, let's try to solve this problem. We need to use all the numbers 45, 69, 55, 40, 1,(...TRUNCATED)
[ 33037 ]
[ 33 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["<think>\nOkay, let's try to solve this problem. We need to use all the numbers 45, 69, 55, 40, 1,(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[["83 * (69 - 55 - 45 + 40 + 9 - 8 + 1)"],[],["83 * (69 - 55 - 45 + 40 + 9 - 8 + 1)"],[],[],[],[],[(...TRUNCATED)
[[[true],[],[true],[],[],[],[],[],[true,true],[],[],[true],[true,true],[],[],[true],[true,true],[],[(...TRUNCATED)
[[[{"answer_block":"83 * (69 - 55 - 45 + 40 + 9 - 8 + 1)","error":null,"final_answer":913.0,"is_corr(...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)
[["<think>\nOkay, let's see. I need to use all the numbers 72, 3, 67, 1, 43, 1, 93, 53 to make 145. (...TRUNCATED)
[ 35433 ]
[ 28 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["<think>\nOkay, let's see. I need to use all the numbers 72, 3, 67, 1, 43, 1, 93, 53 to make 145. (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[["93 + 53 - (72 / 3 - (67 - 43) + 1 * 1)","93 + 53 - (72 / 3 - (67 - 43) + 1 * 1)"],[],[],[],["93 (...TRUNCATED)
[[[true,true],[],[],[],[true],[],[true,true],[true],[],[],[],[true,true],[true],[],[],[],[],[true,tr(...TRUNCATED)
[[[{"answer_block":"93 + 53 - (72 / 3 - (67 - 43) + 1 * 1)","error":null,"final_answer":145.0,"is_co(...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)
[["","","","","","","","","<think>\nOkay, let's try to figure out how to make 102 using all the numb(...TRUNCATED)
[ 35975 ]
[ 9 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["","","","","","","","","<think>\nOkay, let's try to figure out how to make 102 using all the numb(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[[[],[],[],[],[],[],[],[],["(93 - (13 + 13 + 2)) * 2 + (68 - 62) - 1","(93 * 2) - 68 - 13 - 2 - 1 - (...TRUNCATED)
[ [ [], [], [], [], [], [], [], [], [ false, false, false, true ] ] ]
[[[],[],[],[],[],[],[],[],[{"answer_block":"(93 - (13 + 13 + 2)) * 2 + (68 - 62) - 1","error":"Expre(...TRUNCATED)
End of preview. Expand in Data Studio

EAS-Qwen3-4B-Thinking-2507-cd8arg-iterative

Countdown reasoning with iterative strategy to 32768 tokens

Dataset Info

  • Rows: 100
  • Columns: 16

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
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/Qwen3-4B-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
  },
  "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,
  "status": "completed",
  "completed_at": "2025-12-22T10:43:30.349936"
}

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-Qwen3-4B-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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