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Using ALL of the numbers 13, 85, 56, 2, 55, 53, 60, 94, 7, 1, 84, 13, create an expression that equals 311. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [13, 85, 56, 2, 55, 53, 60, 94, 7, 1, 84, 13], "target": 311, "operators_used": ["+", "+", "/", "*", "+", "-", "-", "-", "/", "-", "/"], "expression": "13 + 85 + 56 / 2 * 55 + 53 - 60 - 94 - 7 / 1 - 84 / 13"}
countdown
[ { "content": "You are solving a countdown arithmetic problem. You must find an expression using the given numbers (each exactly once) that equals the target.\n\nREASON USING STRUCTURED HEURISTIC SEARCH. Do not just guess — systematically search for the answer using the format below. This is critical: use the ex...
[ "<think>\nThe user wants me to solve a countdown arithmetic problem. I need to find an expression using the numbers [13, 85, 56, 2, 55, 53, 60, 94, 7, 1, 84, 13] that equals 311.\n\nLet me first note that there are 12 numbers here:\n- 13 appears twice\n- 85, 56, 2, 55, 53, 60, 94, 7, 1, 84\n\nTarget is 311.\n\nLet ...
[ { "endpoint_type": "chat", "litellm_function": "acompletion", "model": "together_ai/moonshotai/Kimi-K2.5", "raw_prompt": [ { "content": "You are solving a countdown arithmetic problem. You must find an expression using the given numbers (each exactly once) that equals the target.\n\nRE...
[ { "cost": 0.0455029, "finish_reason": "stop", "input_tokens": 1165, "model": "together_ai/moonshotai/Kimi-K2.5", "output_tokens": 16043, "raw_response": { "choices": [ { "finish_reason": "stop", "index": 0, "message": { "content": "=== ...
[ [ "56 * (7 - 2) + 60 + 13 + 13 - 55 + (85 - 1 - 84) * 94 * 53 = 311" ] ]
[ [ { "end_index": 33078, "end_phrase": "</answer>", "start_index": 32997, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[ [ { "answer_block": "56 * (7 - 2) + 60 + 13 + 13 - 55 + (85 - 1 - 84) * 94 * 53 = 311", "error": null, "final_answer": 311, "is_correct": true } ] ]
"Using ALL of the numbers 57, 3, 19, 7, 3, 70, 2, 2, 97, 2, 22, 11, create an expression that equals(...TRUNCATED)
"{\"numbers\": [57, 3, 19, 7, 3, 70, 2, 2, 97, 2, 22, 11], \"target\": 130, \"operators_used\": [\"/(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nThe user wants me to solve a countdown arithmetic problem. I need to use ALL of the numbe(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.026474099999999997,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonsh(...TRUNCATED)
[ [ "19 * 7 + 70 + 57 - 97 - 22 - 11 + (3 - 3) + 2 * (2 - 2) = 130" ] ]
[ [ { "end_index": 18835, "end_phrase": "</answer>", "start_index": 18757, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"19 * 7 + 70 + 57 - 97 - 22 - 11 + (3 - 3) + 2 * (2 - 2) = 130","error":null,"fina(...TRUNCATED)
"Using ALL of the numbers 29, 26, 3, 1, 1, 32, 61, 79, 99, 10, 59, 54, create an expression that equ(...TRUNCATED)
"{\"numbers\": [29, 26, 3, 1, 1, 32, 61, 79, 99, 10, 59, 54], \"target\": 747, \"operators_used\": [(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["Let's solve this step-by-step using the required format.\n\nTarget: 23\nNumbers: [4, 7, 3, 1]\n\nL(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0244021,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[ [ "4 * (3 + 1) + 7", "7 + 4 * (3 + 1)", "4 * (1 + 3) + 7" ] ]
[[{"end_index":16907,"end_phrase":"</answer>","start_index":16875,"start_phrase":"<answer>"},{"end_i(...TRUNCATED)
[ [ false, false, false ] ]
[[{"answer_block":"4 * (3 + 1) + 7","error":"Expression does not equal stated result","final_answer"(...TRUNCATED)
"Using ALL of the numbers 76, 89, 81, 15, 14, 90, 99, 39, 93, 25, 16, 1, create an expression that e(...TRUNCATED)
"{\"numbers\": [76, 89, 81, 15, 14, 90, 99, 39, 93, 25, 16, 1], \"target\": 551, \"operators_used\":(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nThis is a complex Countdown problem with 12 numbers. I need to find an expression using a(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0407149,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[ [ "90 × (99 - 93) + 25 - 14 + (16 - 15 - 1) × (76 + 89 + 81 + 39) = 551" ] ]
[ [ { "end_index": 30451, "end_phrase": "</answer>", "start_index": 30366, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"90 * (99 - 93) + 25 - 14 + (16 - 15 - 1) * (76 + 89 + 81 + 39) = 551","error":nul(...TRUNCATED)
"Using ALL of the numbers 82, 97, 63, 21, 2, 74, 1, 1, 62, 57, 44, 24, create an expression that equ(...TRUNCATED)
"{\"numbers\": [82, 97, 63, 21, 2, 74, 1, 1, 62, 57, 44, 24], \"target\": 664, \"operators_used\": [(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nWe need to find an expression using all numbers: 82, 97, 63, 21, 2, 74, 1, 1, 62, 57, 44,(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.039200099999999995,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonsh(...TRUNCATED)
[ [ "(82 - 74) * (63 + 21 - 1) + (97 - 57) * 1 - (62 - 44 + 24 - 2) = 664" ] ]
[ [ { "end_index": 41066, "end_phrase": "</answer>", "start_index": 40981, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"(82 - 74) * (63 + 21 - 1) + (97 - 57) * 1 - (62 - 44 + 24 - 2) = 664","error":nul(...TRUNCATED)
"Using ALL of the numbers 7, 7, 1, 1, 80, 7, 87, 11, 32, 57, 85, 85, create an expression that equal(...TRUNCATED)
"{\"numbers\": [7, 7, 1, 1, 80, 7, 87, 11, 32, 57, 85, 85], \"target\": 112, \"operators_used\": [\"(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nThe user wants me to solve a Countdown arithmetic problem. I need to use ALL of the numbe(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0191801,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[ [ "80 + 32 + 7 + 7 + 7 + 11 + 57 + 85 - 85 - 87 - 1 - 1 = 112" ] ]
[ [ { "end_index": 14406, "end_phrase": "</answer>", "start_index": 14331, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"80 + 32 + 7 + 7 + 7 + 11 + 57 + 85 - 85 - 87 - 1 - 1 = 112","error":null,"final_a(...TRUNCATED)
"Using ALL of the numbers 52, 26, 45, 29, 28, 8, 43, 43, 47, 38, 19, 97, create an expression that e(...TRUNCATED)
"{\"numbers\": [52, 26, 45, 29, 28, 8, 43, 43, 47, 38, 19, 97], \"target\": 551, \"operators_used\":(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nThis is a countdown arithmetic problem. I need to use all 12 numbers: 52, 26, 45, 29, 28,(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0403817,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[ [ "43 * 52 / (47 - 43) - 8 + (26 + 19 - 45) * 29 * 28 * 38 * 97 = 551" ] ]
[ [ { "end_index": 31278, "end_phrase": "</answer>", "start_index": 31195, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"43 * 52 / (47 - 43) - 8 + (26 + 19 - 45) * 29 * 28 * 38 * 97 = 551","error":null,(...TRUNCATED)
"Using ALL of the numbers 5, 1, 5, 1, 1, 33, 72, 15, 74, 30, 34, 53, create an expression that equal(...TRUNCATED)
"{\"numbers\": [5, 1, 5, 1, 1, 33, 72, 15, 74, 30, 34, 53], \"target\": 198, \"operators_used\": [\"(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nWe need to find an expression using numbers: 5, 1, 5, 1, 1, 33, 72, 15, 74, 30, 34, 53. T(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0206417,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[["1 + 1 + 1 + 33 + 72 + 15 + 74 + 30 + 34 - 53 - 5 - 5 = 198","EXPRESSION = TARGET","1 + 1 + 1 + 33(...TRUNCATED)
[[{"end_index":17230,"end_phrase":"</answer>","start_index":17155,"start_phrase":"<answer>"},{"end_i(...TRUNCATED)
[ [ true, false, true, true ] ]
[[{"answer_block":"1 + 1 + 1 + 33 + 72 + 15 + 74 + 30 + 34 - 53 - 5 - 5 = 198","error":null,"final_a(...TRUNCATED)
"Using ALL of the numbers 100, 47, 96, 76, 67, 58, 1, 22, 24, 3, 96, 94, create an expression that e(...TRUNCATED)
"{\"numbers\": [100, 47, 96, 76, 67, 58, 1, 22, 24, 3, 96, 94], \"target\": 147, \"operators_used\":(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nWe need to find an expression using all numbers: 100, 47, 96, 76, 67, 58, 1, 22, 24, 3, 9(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0276445,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[["tags.\n\nThe expression: 100 + 47 + (96 + 96 + 76 - 67 - 58 - 22 - 24 - 3 - 94) * 1 = 147.\n\nBut(...TRUNCATED)
[ [ { "end_index": 28153, "end_phrase": "</answer>", "start_index": 20476, "start_phrase": "<answer>" } ] ]
[ [ false ] ]
[[{"answer_block":"tags.\n\nThe expression: 100 + 47 + (96 + 96 + 76 - 67 - 58 - 22 - 24 - 3 - 94) *(...TRUNCATED)
"Using ALL of the numbers 67, 98, 18, 2, 37, 61, 69, 2, 89, 1, 53, 5, create an expression that equa(...TRUNCATED)
"{\"numbers\": [67, 98, 18, 2, 37, 61, 69, 2, 89, 1, 53, 5], \"target\": 919, \"operators_used\": [\(...TRUNCATED)
countdown
[{"content":"You are solving a countdown arithmetic problem. You must find an expression using the g(...TRUNCATED)
["<think>\nThe user wants me to solve a countdown arithmetic problem using the numbers: 67, 98, 18, (...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2.5"(...TRUNCATED)
[{"cost":0.0220053,"finish_reason":"stop","input_tokens":1165,"model":"together_ai/moonshotai/Kimi-K(...TRUNCATED)
[ [ "89 * (67 - 61 + 5) - (98 - 37 - 1) + (18 + 53 - 69 - 2) * 2 = 919" ] ]
[ [ { "end_index": 16659, "end_phrase": "</answer>", "start_index": 16577, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"89 * (67 - 61 + 5) - (98 - 37 - 1) + (18 + 53 - 69 - 2) * 2 = 919","error":null,"(...TRUNCATED)

t1-structured-reasoning-full-together_ai-moonshotai-kimi-k2-5-6921f297

Structured reasoning evaluation: instead of injecting synthesized facts, this uses a static system prompt that teaches the model a heuristic search FORMAT with explicit structural markers ([STEP], [PRUNE], [BACKTRACK], [REVIEW OPTIONS], [SOLUTION FOUND]).

Inspired by HandCraftedCountdownSearch — models SFT'd on structured search traces significantly outperform free-form CoT. This tests whether prompt-time format instruction alone can capture some of that benefit.

Performance Comparison

Comparison Chart

Metric Base Structured Delta
pass@1 0.9000 (90.0%) 0.8000 (80.0%) -0.1000 (-10.0%)

Experimental Details

Parameter Value
Inference model together_ai/moonshotai/Kimi-K2.5
Prompt style full
Temperature 0.7
Top-p 0.95
Max tokens 32768
Samples per problem 1
Enable thinking True
Total problems 10
Base eval source t1-base-eval-together_ai-qwen-qwen3-235b-a22b-thinkin-12arg

System Prompt Used (full style)

You are solving a countdown arithmetic problem. You must find an expression using the given numbers (each exactly once) that equals the target.

REASON USING STRUCTURED HEURISTIC SEARCH. Do not just guess — systematically search for the answer using the format below. This is critical: use the exact markers shown to organize your reasoning.

=== REASONING FORMAT ===

Use these markers to structure every step of your thinking:

[STEP N: COMBINE] — Try combining two numbers with an operation. Show: a OP b = result. State remaining numbers and how far from target.

[PRUNE] — BEFORE trying an operation, check if it's useful. Skip it if:
  - Division doesn't produce an integer
  - The result moves AWAY from target (current < target? don't subtract/divide. current > target? don't add/multiply)
  Say what you're skipping and why.

[BACKTRACK] — Current path is stuck or getting worse. State why (too high? too low? no numbers left?) and go back to try a different combination.

[REVIEW OPTIONS] — When stuck, list ALL remaining possible combinations, score each by |result - target|, and pick the best one to try next.

[SOLUTION FOUND] — You hit the target! Verify: recompute the expression, confirm each number is used exactly once, then give the answer.

=== KEY HEURISTIC ===

DIRECTIONAL SEARCH: At every step, check if your current value is above or below the target.
  - Below target → only try + and * (go UP)
  - Above target → only try - and / (go DOWN)
This cuts your search space in half and prevents wasted exploration.

=== WORKED EXAMPLE ===

Target: 23, Numbers: [4, 7, 3]

[STEP 1: COMBINE]
Let me scan first moves. Best candidates by closeness to 23:
  4 * 7 = 28 (distance 5) ← closest
  4 + 7 = 11 (distance 12)
  7 * 3 = 21 (distance 2) ← very close!
  7 + 3 = 10 (distance 13)
Try: 7 * 3 = 21. Remaining: [4]. Current: 21, need 23.

[STEP 2: COMBINE]
Current 21 < target 23, so only try + and *.
21 + 4 = 25 (distance 2)
21 * 4 = 84 (distance 61)
[PRUNE] 21 * 4 = 84 — way t...

Dataset Info

  • Rows: Structured reasoning evaluation results (one row per problem)
  • Columns: question, metadata, task_source, formatted_prompt, response, eval_correct, and associated metadata

Usage

from datasets import load_dataset

dataset = load_dataset("reasoning-degeneration-dev/t1-structured-reasoning-full-together_ai-moonshotai-kimi-k2-5-6921f297", split="train")
print(f"Loaded {len(dataset)} rows")

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

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