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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" }, ...
[ [ "We are given the numbers: \n**12, 4, 7, 1, 2, 5, 21, 88** \nWe must use **each number exactly once** and combine them using **+**, **-**, **\\***, **/** to make an expression that equals **109**.\n\n---\n\nLet’s look for a strategy.\n\nWe notice that **88** is a large number, and 109 is only 21 more than 8...
[ 33040 ]
[ 27 ]
[ [ "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...
[ [ "We are given the numbers: \n**12, 4, 7, 1, 2, 5, 21, 88** \nWe must use **each number exactly once** and combine them using **+**, **-**, **\\***, **/** to make an expression that equals **109**.\n\n---\n\nLet’s look for a strategy.\n\nWe notice that **88** is a large number, and 109 is only 21 more than 8...
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[ [ [ "88 + 21 + (5 - 4 - 2 + 1) × (12 - 7)" ], [ "88 + 21 + (12 - 7 - 5) × (4 + 1 + 2)", "88 + 21 + (12 - 7 - 5) × (4 + 1 + 2)" ], [ "88 + 21 + ( (12 ÷ (4 + 2)) - (7 - 5) ) × 1", "88 + 21 + ( (12 ÷ (4 + 2)) - (7 - 5) ) × 1" ], [ "88 + 21 + ( (12 ÷ (4 + ...
[ [ [ true ], [ true, true ], [ true, true ], [ true ], [ true ], [ true ], [ true ], [ true ], [ true ], [ true ], [ true ], [ true ], ...
[ [ [ { "answer_block": "88 + 21 + (5 - 4 - 2 + 1) * (12 - 7)", "error": null, "final_answer": 109, "is_correct": true } ], [ { "answer_block": "88 + 21 + (12 - 7 - 5) * (4 + 1 + 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)
[["We are given the numbers: \n**25, 69, 58, 14, 55, 24, 36, 60** \nWe must use **each number exac(...TRUNCATED)
[ 33299 ]
[ 18 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**25, 69, 58, 14, 55, 24, 36, 60** \nWe must use **each number exac(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["60 + 58 + 55 + (69 - 36) / (25 - 14)","60 + 58 + 55 + (69 - 36) / (25 - 14)","60 + 58 + 55 + (69(...TRUNCATED)
[[[false,false,false,false],[true],[true],[true],[true],[true],[true],[true],[true],[true],[true,tru(...TRUNCATED)
[[[{"answer_block":"60 + 58 + 55 + (69 - 36) / (25 - 14)","error":"Expression must use ALL available(...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)
[["We are given the numbers: \n**55, 36, 6, 3, 14, 99, 17, 82** \nWe must use **each number exactl(...TRUNCATED)
[ 32984 ]
[ 20 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**55, 36, 6, 3, 14, 99, 17, 82** \nWe must use **each number exactl(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["99 + 82 + 55 + 6 + 3 = 245","99 + 82 + 55 + 6 + 3 = 245","3 * 82 + 55 - 36 - 14 - 6 = 245","3 * (...TRUNCATED)
[[[false,false,false,false,false,false,false],[false],[false],[false],[false,false],[false,false],[f(...TRUNCATED)
[[[{"answer_block":"99 + 82 + 55 + 6 + 3 = 245","error":"Expression must use ALL available numbers. (...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)
[["We are given the numbers: \n**87, 87, 29, 2, 19, 4, 1, 1** \nWe must use **each number exactly (...TRUNCATED)
[ 33025 ]
[ 32 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**87, 87, 29, 2, 19, 4, 1, 1** \nWe must use **each number exactly (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["87 + 87 + 19 * 4 + 29 + 2 + 1 - 1 = 281"],["87 + 87 + 19 * 4 + 29 + 2 + 1 - 1 = 281"],["(29 + 19(...TRUNCATED)
[[[true],[true],[false,false],[true],[false],[false],[false],[true],[false],[false],[false],[false],(...TRUNCATED)
[[[{"answer_block":"87 + 87 + 19 * 4 + 29 + 2 + 1 - 1 = 281","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)
[["We are given the numbers: \n**56, 63, 7, 50, 44, 1, 87, 52** \nWe must use **each number exactl(...TRUNCATED)
[ 32963 ]
[ 60 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**56, 63, 7, 50, 44, 1, 87, 52** \nWe must use **each number exactl(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["87 + 44 + 1 + (63 - 56 - 7) × (52 - 50)"],["87 + 56 - (63 - 52) + (50 - 44) - (7 - 1)"],["(87 +(...TRUNCATED)
[[[true],[true],[false],[true],[true],[true],[true],[true],[true],[true],[true],[true],[true],[true](...TRUNCATED)
[[[{"answer_block":"87 + 44 + 1 + (63 - 56 - 7) * (52 - 50)","error":null,"final_answer":132.0,"is_c(...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)
[["We are given the numbers: \n**7, 1, 49, 7, 28, 59, 3, 44** \nWe must use **each number exactly (...TRUNCATED)
[ 32996 ]
[ 16 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**7, 1, 49, 7, 28, 59, 3, 44** \nWe must use **each number exactly (...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["44 \\times (59 - 49 + 3 - 1) - 7 = 521"],["\\left(44 \\times \\left(\\frac{49 - 28}{7} \\times ((...TRUNCATED)
[[[false],[false],[false],[false],[false],[false],[false],[false],[false],[false],[false],[false],[f(...TRUNCATED)
[[[{"answer_block":"44 * (59 - 49 + 3 - 1) - 7 = 521","error":"Expression must use ALL available num(...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)
[["We are given the numbers: \n**97, 4, 93, 26, 3, 24, 20, 31** \nWe must use **each number exactl(...TRUNCATED)
[ 32803 ]
[ 29 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**97, 4, 93, 26, 3, 24, 20, 31** \nWe must use **each number exactl(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["(20 \\times 31) + (97 - 97) + (26 - 26) + (24 - 24) + (4 - 4) + (3 - 3) = 620","20 \\times 31 + (...TRUNCATED)
[[[false,false,false],[false,false,false,false,false],[false,false,false,false],[false,false,false],(...TRUNCATED)
[[[{"answer_block":"(20 * 31) + (97 - 97) + (26 - 26) + (24 - 24) + (4 - 4) + (3 - 3) = 620","error"(...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)
[["We are given the numbers: \n**45, 69, 55, 40, 1, 9, 8, 83** \nWe must use **each number exactly(...TRUNCATED)
[ 32858 ]
[ 38 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**45, 69, 55, 40, 1, 9, 8, 83** \nWe must use **each number exactly(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["83 * (55 - 45 + 1) = 913","83 * (55 - 45 + 1) + (8 + 9 - 40 - 69) = 913","83 * (55 - 45 + 1) = 9(...TRUNCATED)
[[[false,false,false,false],[false,false,false],[false,false],[false,false],[false],[false,false],[f(...TRUNCATED)
[[[{"answer_block":"83 * (55 - 45 + 1) = 913","error":"Expression must use ALL available numbers. Un(...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)
[["We are given the numbers: \n**72, 3, 67, 1, 43, 1, 93, 53** \nWe must use **each number exactly(...TRUNCATED)
[ 33423 ]
[ 18 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**72, 3, 67, 1, 43, 1, 93, 53** \nWe must use **each number exactly(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["(93 + 53 - 1) + (67 - (72 / 3) - 43) * 1 = 145"],["(93 + 53 - 1) + (67 - (72 / 3) - 43) * 1 = 14(...TRUNCATED)
[[[true],[true],[true],[true],[true],[true],[true],[true],[true],[true,true],[true,true],[true,true](...TRUNCATED)
[[[{"answer_block":"(93 + 53 - 1) + (67 - (72 / 3) - 43) * 1 = 145","error":null,"final_answer":145.(...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)
[["We are given the numbers: \n**13, 1, 13, 68, 2, 2, 93, 62** \nWe must use **each number exactly(...TRUNCATED)
[ 32840 ]
[ 36 ]
[["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED)
[["We are given the numbers: \n**13, 1, 13, 68, 2, 2, 93, 62** \nWe must use **each number exactly(...TRUNCATED)
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[[["(93 + 68 - 62 + 2 + 1) + (13 - 13) * 2 = 102"],["68 + (93 - 62 + 1 + 2) + (13 - 13) × 2 = 102",(...TRUNCATED)
[[[true],[true,true],[true,true],[true],[true],[true],[true],[true],[true],[true],[true],[true],[tru(...TRUNCATED)
[[[{"answer_block":"(93 + 68 - 62 + 2 + 1) + (13 - 13) * 2 = 102","error":null,"final_answer":102.0,(...TRUNCATED)
End of preview. Expand in Data Studio

EAS-Qwen3-30B-A3B-Instruct-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-Instruct-2507<api_base>http://10.32.37.25:9080/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": "2025-12-26T12:20:00.562844"
}

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-Instruct-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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