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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...
[ "I need to find an expression using all 13 numbers (13, 85, 56, 2, 55, 53, 60, 94, 7, 1, 84, 13) that equals 311.\n\n[STEP 1: COMBINE]\nLet me scan for good first combinations. I notice 311 is a moderate target, so I'll look for products that get close.\n\nLet me try: 85 + 56 = 141. Remaining: [13, 2, 55, 53, 60, 9...
[ { "endpoint_type": "chat", "litellm_function": "acompletion", "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "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 t...
[ { "cost": 0.011751000000000001, "finish_reason": "stop", "input_tokens": 1164, "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "output_tokens": 3529, "raw_response": { "choices": [ { "finish_reason": "stop", "index": 0, "message": { ...
[ [ "85 + 84 + 94 + 53 - 7 + 2 + (13 - 13) + (60 - 60) + (56 - 55 - 1) = 311" ] ]
[ [ { "end_index": 8100, "end_phrase": "</answer>", "start_index": 8012, "start_phrase": "<answer>" } ] ]
[ [ false ] ]
[ [ { "answer_block": "85 + 84 + 94 + 53 - 7 + 2 + (13 - 13) + (60 - 60) + (56 - 55 - 1) = 311", "error": "Expression uses an unavailable or repeated number", "final_answer": 311, "is_correct": false } ] ]
Using ALL of the numbers 57, 3, 19, 7, 3, 70, 2, 2, 97, 2, 22, 11, create an expression that equals 130. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [57, 3, 19, 7, 3, 70, 2, 2, 97, 2, 22, 11], "target": 130, "operators_used": ["/", "/", "-", "/", "+", "-", "/", "+", "/", "*", "/"], "expression": "57 / 3 / 19 - 7 / 3 + 70 - 2 / 2 + 97 / 2 * 22 / 11"}
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...
[ "I need to find an expression using ALL numbers [57, 3, 19, 7, 3, 70, 2, 2, 97, 2, 22, 11] that equals 130.\n\nLet me start by analyzing the target and numbers:\n- Target: 130\n- Numbers: 12 numbers total, ranging from 2 to 97\n- The sum of all numbers is quite large, so I'll need careful subtraction/division\n\n[S...
[ { "endpoint_type": "chat", "litellm_function": "acompletion", "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "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 t...
[ { "cost": 0.009072, "finish_reason": "stop", "input_tokens": 1164, "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "output_tokens": 2636, "raw_response": { "choices": [ { "finish_reason": "stop", "index": 0, "message": { "conte...
[ [ "(70 + 57 + 3 + (2 - 2)) × (3/3) × (2/2) × (19/19) × (7/7) × (97/97) × (22/22) × (11/11) = 130" ] ]
[ [ { "end_index": 5801, "end_phrase": "</answer>", "start_index": 5691, "start_phrase": "<answer>" } ] ]
[ [ false ] ]
[ [ { "answer_block": "(70 + 57 + 3 + (2 - 2)) * (3/3) * (2/2) * (19/19) * (7/7) * (97/97) * (22/22) * (11/11) = 130", "error": "Expression uses an unavailable or repeated number", "final_answer": 130, "is_correct": false } ] ]
Using ALL of the numbers 29, 26, 3, 1, 1, 32, 61, 79, 99, 10, 59, 54, create an expression that equals 747. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [29, 26, 3, 1, 1, 32, 61, 79, 99, 10, 59, 54], "target": 747, "operators_used": ["-", "/", "/", "/", "-", "-", "+", "+", "*", "-", "-"], "expression": "29 - 26 / 3 / 1 / 1 - 32 - 61 + 79 + 99 * 10 - 59 - 54"}
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...
[ "I need to find an expression using ALL numbers [29, 26, 3, 1, 1, 32, 61, 79, 99, 10, 59, 54] exactly once to equal 747.\n\nLet me start by analyzing the target and available numbers.\n\nTarget: 747\nNumbers: 29, 26, 3, 1, 1, 32, 61, 79, 99, 10, 59, 54\n\nLet me look for good starting points by checking products th...
[ { "endpoint_type": "chat", "litellm_function": "acompletion", "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "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 t...
[ { "cost": 0.008085, "finish_reason": "stop", "input_tokens": 1164, "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "output_tokens": 2307, "raw_response": { "choices": [ { "finish_reason": "stop", "index": 0, "message": { "conte...
[ [ "(26 - 1) * (29 + 1) - 3 + (54 - 54) + (59 - 59) + (10 - 10) + (99 - 99) + (79 - 79) + (61 - 61) + (32 - 32) = 747" ] ]
[ [ { "end_index": 5336, "end_phrase": "</answer>", "start_index": 5206, "start_phrase": "<answer>" } ] ]
[ [ false ] ]
[ [ { "answer_block": "(26 - 1) * (29 + 1) - 3 + (54 - 54) + (59 - 59) + (10 - 10) + (99 - 99) + (79 - 79) + (61 - 61) + (32 - 32) = 747", "error": "Expression uses an unavailable or repeated number", "final_answer": 747, "is_correct": false } ] ]
Using ALL of the numbers 76, 89, 81, 15, 14, 90, 99, 39, 93, 25, 16, 1, create an expression that equals 551. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [76, 89, 81, 15, 14, 90, 99, 39, 93, 25, 16, 1], "target": 551, "operators_used": ["+", "*", "/", "*", "+", "*", "+", "/", "/", "+", "/"], "expression": "76 + 89 * 81 / 15 * 14 + 90 * 99 + 39 / 93 / 25 + 16 / 1"}
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...
[ "I need to find an expression using all 12 numbers exactly once to equal 551. Let me start by analyzing the target and available numbers.\n\nTarget: 551\nNumbers: [76, 89, 81, 15, 14, 90, 99, 39, 93, 25, 16, 1]\n\nLet me look for promising first combinations by checking products and sums that get close to 551.\n\n[...
[ { "endpoint_type": "chat", "litellm_function": "acompletion", "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "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 t...
[ { "cost": 0.015969, "finish_reason": "stop", "input_tokens": 1164, "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "output_tokens": 4935, "raw_response": { "choices": [ { "finish_reason": "stop", "index": 0, "message": { "conte...
[ [ "89 × (15 - 9) + 16 + 1 = 551", "25 × (16 + 90 ÷ 15) + 1 = 551" ] ]
[ [ { "end_index": 8742, "end_phrase": "</answer>", "start_index": 8697, "start_phrase": "<answer>" }, { "end_index": 11044, "end_phrase": "</answer>", "start_index": 10998, "start_phrase": "<answer>" } ] ]
[ [ false, false ] ]
[ [ { "answer_block": "89 * (15 - 9) + 16 + 1 = 551", "error": "Expression uses an unavailable or repeated number", "final_answer": 551, "is_correct": false }, { "answer_block": "25 * (16 + 90 / 15) + 1 = 551", "error": "Expression must use ALL available numbers. Unused...
Using ALL of the numbers 82, 97, 63, 21, 2, 74, 1, 1, 62, 57, 44, 24, create an expression that equals 664. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [82, 97, 63, 21, 2, 74, 1, 1, 62, 57, 44, 24], "target": 664, "operators_used": ["+", "*", "/", "+", "+", "/", "/", "+", "+", "-", "-"], "expression": "82 + 97 * 63 / 21 + 2 + 74 / 1 / 1 + 62 + 57 - 44 - 24"}
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...
[ "I need to find an expression using ALL of these numbers exactly once to get 664:\n82, 97, 63, 21, 2, 74, 1, 1, 62, 57, 44, 24\n\nLet me start by analyzing the target and available numbers.\n\n[STEP 1: ANALYSIS]\nTarget: 664\nNumbers: 12 numbers total\nThis is a complex problem with many numbers. Let me look for pa...
[ { "endpoint_type": "chat", "litellm_function": "acompletion", "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "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 t...
[ { "cost": 0.031491, "finish_reason": "stop", "input_tokens": 1164, "model": "together_ai/moonshotai/Kimi-K2-Instruct-0905", "output_tokens": 10109, "raw_response": { "choices": [ { "finish_reason": "stop", "index": 0, "message": { "cont...
[ [ "(62 + 2) * (44 - (97 - 63)) + 24 + (1 - 1) * (82 + 74 + 57 + 21) = 664" ] ]
[ [ { "end_index": 21100, "end_phrase": "</answer>", "start_index": 21013, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[ [ { "answer_block": "(62 + 2) * (44 - (97 - 63)) + 24 + (1 - 1) * (82 + 74 + 57 + 21) = 664", "error": null, "final_answer": 664, "is_correct": true } ] ]
"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)
["I'll solve this step-by-step using the structured approach.\n\n=== REASONING FORMAT ===\n\n[STEP 1(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2-In(...TRUNCATED)
[{"cost":0.005952,"finish_reason":"stop","input_tokens":1164,"model":"together_ai/moonshotai/Kimi-K2(...TRUNCATED)
[ [ "80 + 32 + (7 - 7) + (1 - 1) + (85 - 85) * (87 + 11 + 57 + 7) = 112" ] ]
[ [ { "end_index": 3603, "end_phrase": "</answer>", "start_index": 3520, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"80 + 32 + (7 - 7) + (1 - 1) + (85 - 85) * (87 + 11 + 57 + 7) = 112","error":null,(...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)
["I need to find an expression using all 12 numbers exactly once to equal 551.\n\nLet me start by an(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2-In(...TRUNCATED)
[{"cost":0.006294,"finish_reason":"stop","input_tokens":1164,"model":"together_ai/moonshotai/Kimi-K2(...TRUNCATED)
[ [ "19 × 29 + ((52 - 26) + (45 - 38) + (28 - 8) - (97 - 47)) × (43 - 43) = 551" ] ]
[ [ { "end_index": 3993, "end_phrase": "</answer>", "start_index": 3902, "start_phrase": "<answer>" } ] ]
[ [ true ] ]
[[{"answer_block":"19 * 29 + ((52 - 26) + (45 - 38) + (28 - 8) - (97 - 47)) * (43 - 43) = 551","erro(...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)
["I need to find an expression using all numbers: 5, 1, 5, 1, 1, 33, 72, 15, 74, 30, 34, 53 to equal(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2-In(...TRUNCATED)
[{"cost":0.013731,"finish_reason":"stop","input_tokens":1164,"model":"together_ai/moonshotai/Kimi-K2(...TRUNCATED)
[ [ "30 + 34 + 33 + 15 + 72 + 74 - 53 - 5 - 1 - 1 + (1-1) = 198" ] ]
[ [ { "end_index": 9717, "end_phrase": "</answer>", "start_index": 9642, "start_phrase": "<answer>" } ] ]
[ [ false ] ]
[[{"answer_block":"30 + 34 + 33 + 15 + 72 + 74 - 53 - 5 - 1 - 1 + (1-1) = 198","error":"Expression u(...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)
["I need to create an expression using ALL of these numbers: [100, 47, 96, 76, 67, 58, 1, 22, 24, 3,(...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2-In(...TRUNCATED)
[{"cost":0.009798000000000001,"finish_reason":"stop","input_tokens":1164,"model":"together_ai/moonsh(...TRUNCATED)
[["(100 + 47) + (96 - 96) + (22 + 24 - 46) + (76 + 67 - 143) + (58 + 94 - 152) + 3 - 3 + 1 - 1","(10(...TRUNCATED)
[[{"end_index":4693,"end_phrase":"</answer>","start_index":4585,"start_phrase":"<answer>"},{"end_ind(...TRUNCATED)
[ [ false, false, false, false, false, false, false, false ] ]
[[{"answer_block":"(100 + 47) + (96 - 96) + (22 + 24 - 46) + (76 + 67 - 143) + (58 + 94 - 152) + 3 -(...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)
["I'll solve this step-by-step using the structured approach.\n\nTarget: 919\nNumbers: [67, 98, 18, (...TRUNCATED)
[{"endpoint_type":"chat","litellm_function":"acompletion","model":"together_ai/moonshotai/Kimi-K2-In(...TRUNCATED)
[{"cost":0.020391,"finish_reason":"stop","input_tokens":1164,"model":"together_ai/moonshotai/Kimi-K2(...TRUNCATED)
[["18 × 53 - 37 + 2 + 2 - 2 + 61 + 5 - 67 + 1 + 98 - 69 - 89 + 67 - 67 = 919","18 × 53 - 37 + 2 + (...TRUNCATED)
[[{"end_index":6102,"end_phrase":"</answer>","start_index":6012,"start_phrase":"<answer>"},{"end_ind(...TRUNCATED)
[ [ false, false, false, false, false, false, false, false, false, false ] ]
[[{"answer_block":"18 * 53 - 37 + 2 + 2 - 2 + 61 + 5 - 67 + 1 + 98 - 69 - 89 + 67 - 67 = 919","error(...TRUNCATED)

t1-structured-reasoning-full-kimi-k2-instruct-0905

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%) 0.3000 (30.0%) -0.6000 (-60.0%)

Experimental Details

Parameter Value
Inference model together_ai/moonshotai/Kimi-K2-Instruct-0905
Prompt style full
Temperature 0.7
Top-p 0.95
Max tokens 65536
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-kimi-k2-instruct-0905", split="train")
print(f"Loaded {len(dataset)} rows")

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

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