question stringlengths 138 149 | metadata stringlengths 108 142 | task_source stringclasses 1
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Using ALL of the numbers 71, 38, 81, 80, 47, create an expression that equals 147. You must use each number exactly once. You may use +, -, *, /. | {"numbers": [71, 38, 81, 80, 47], "target": 147, "operators_used": ["-", "+", "+", "-"], "expression": "71 - 38 + 81 + 80 - 47"} | countdown | [
{
"content": "You are a math problem solver. Solve the given arithmetic problem step by step. Show your work and then provide your final answer inside <answer> tags.\n\nFor example: <answer>10 + 5 * 2 = 20</answer>\n\nThe answer should be a single arithmetic expression using the given numbers that equals the ta... | [
"Okay, let's see. I need to use all the numbers 71, 38, 81, 80, 47 exactly once with +, -, *, / to make 147. Hmm, first I should probably list out all the numbers and think about possible combinations. Let me start by adding them up to see what the total is, maybe that can help. 71 + 38 is 109, plus 81 is 190, plus... | [
[
"80 + 71 + 81 - 38 - 47 = 147"
],
[
"71 + 81 - 47 - 38 + 80"
],
[
"81 + 80 - 47 + 71 - 38 = 147"
],
[
"81 + 80 + 71 - 38 - 47"
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] | [
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"answer_block": "80 + 71 + 81 - 38 - 47 = 147",
"error": null,
"final_answer": 147,
"is_correct": true
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[
{
"answer_block": "71 + 81 - 47 - 38 + 80",
"error": null,
"final_answer": 147,
"is_correct": true
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{
"answer_bloc... | original | Original 5-arg |
Using ALL of the numbers 77, 7, 50, 49, 77, create an expression that equals 676. You must use each number exactly once. You may use +, -, *, /. | {"numbers": [77, 7, 50, 49, 77], "target": 676, "operators_used": ["/", "*", "+", "+"], "expression": "77 / 7 * 50 + 49 + 77"} | countdown | [
{
"content": "You are a math problem solver. Solve the given arithmetic problem step by step. Show your work and then provide your final answer inside <answer> tags.\n\nFor example: <answer>10 + 5 * 2 = 20</answer>\n\nThe answer should be a single arithmetic expression using the given numbers that equals the ta... | [
"Okay, let's see. I need to use all the numbers 77, 7, 50, 49, 77 to make 676. Wait, there are two 77s? The problem says \"using ALL of the numbers 77, 7, 50, 49, 77\" so yes, two 77s. So the numbers are 77, 77, 7, 50, 49. Each exactly once.\n\nFirst, let's check the target: 676. Hmm. Let me think about what 676 is... | [
[
"77 / 7 * 50 + 49 + 77 = 676"
],
[],
[
"(77 / 7) * 50 + 49 + 77 = 676"
],
[]
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"answer_block": "77 / 7 * 50 + 49 + 77 = 676",
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{
"answer_block": "(77 / 7) * 50 + 49 + 77 = 676",
"error": null,
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"is_correct": true
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] | original | Original 5-arg |
Using ALL of the numbers 63, 3, 15, 47, 40, create an expression that equals 197. You must use each number exactly once. You may use +, -, *, /. | {"numbers": [63, 3, 15, 47, 40], "target": 197, "operators_used": ["*", "+", "-", "+"], "expression": "63 * 3 + 15 - 47 + 40"} | countdown | [
{
"content": "You are a math problem solver. Solve the given arithmetic problem step by step. Show your work and then provide your final answer inside <answer> tags.\n\nFor example: <answer>10 + 5 * 2 = 20</answer>\n\nThe answer should be a single arithmetic expression using the given numbers that equals the ta... | [
"Okay, let's see. I need to make 197 using all the numbers 63, 3, 15, 47, 40 exactly once with +, -, *, /. Hmm. Let me start by surveying the numbers. The target is 197, which is a bit over 200. Let's list the numbers again: 63, 3, 15, 47, 40. Maybe I can combine some of the larger numbers first.\n\nFirst thought: ... | [
[
"63*3 + 15 - 47 + 40"
],
[
"10 + 5 * 2 = 20",
"tags\", and the example has the expression and the result.\n\nBut for this, since it's to be evaluated, I think providing the expression is fine.\n\nTo be safe, I can provide the expression.\n\nI think for this problem, the expression is what matters.... | [
[
{
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"start_phrase": "<answer>"
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{
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{
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"end... | [
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{
"answer_block": "63*3 + 15 - 47 + 40",
"error": null,
"final_answer": 197,
"is_correct": true
}
],
[
{
"answer_block": "10 + 5 * 2 = 20",
"error": "Expression uses an unavailable or repeated number",
"final_answer": 20,
"is_correct": false
},
... | original | Original 5-arg |
"Using ALL of the numbers 92, 40, 5, 8, 84, create an expression that equals 176. You must use each (...TRUNCATED) | "{\"numbers\": [92, 40, 5, 8, 84], \"target\": 176, \"operators_used\": [\"*\", \"/\", \"/\", \"+\"](...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["Okay, let's try to solve this problem. We need to use all the numbers 92, 40, 5, 8, 84 to make 176(...TRUNCATED) | [["92 + 84 + 40 - 5 * 8 = 176"],["92 + 84 + 40 - 5 * 8"],["(84 + 92) * (40 / 5 / 8)"],["92 + 84 + 40(...TRUNCATED) | [[{"end_index":4605,"end_phrase":"</answer>","start_index":4562,"start_phrase":"<answer>"}],[{"end_i(...TRUNCATED) | [
[
true
],
[
true
],
[
true
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[
true
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] | [[{"answer_block":"92 + 84 + 40 - 5 * 8 = 176","error":null,"final_answer":176.0,"is_correct":true}](...TRUNCATED) | original | Original 5-arg |
"Using ALL of the numbers 53, 63, 62, 3, 52, create an expression that equals 936. You must use each(...TRUNCATED) | "{\"numbers\": [53, 63, 62, 3, 52], \"target\": 936, \"operators_used\": [\"+\", \"-\", \"/\", \"*\"(...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["Okay, let's try to solve this problem. We need to use all the numbers 53, 63, 62, 3, 52 exactly on(...TRUNCATED) | [
[],
[
"52 * (63 - (62 - 53)) / 3 = 936"
],
[
"52 * ((53 + 63 - 62) / 3)"
],
[
"52 * ((53 + 63 - 62) / 3)"
]
] | [[],[{"end_index":10286,"end_phrase":"</answer>","start_index":10238,"start_phrase":"<answer>"}],[{"(...TRUNCATED) | [
[],
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] | [[],[{"answer_block":"52 * (63 - (62 - 53)) / 3 = 936","error":null,"final_answer":936.0,"is_correct(...TRUNCATED) | original | Original 5-arg |
"Using ALL of the numbers 16, 73, 32, 11, 77, create an expression that equals 847. You must use eac(...TRUNCATED) | "{\"numbers\": [16, 73, 32, 11, 77], \"target\": 847, \"operators_used\": [\"+\", \"+\", \"/\", \"*\(...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["Okay, let's try to solve this problem. We need to use all the numbers 16, 73, 32, 11, and 77 exact(...TRUNCATED) | [["(77 / 11) * (73 + 32 + 16)"],["77 / (11 / (73 + 32 + 16)) = 847"],["(77 / 11) * (73 + 32 + 16)"],(...TRUNCATED) | [[{"end_index":13864,"end_phrase":"</answer>","start_index":13821,"start_phrase":"<answer>"}],[{"end(...TRUNCATED) | [
[
true
],
[
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[
true
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] | [[{"answer_block":"(77 / 11) * (73 + 32 + 16)","error":null,"final_answer":847.0,"is_correct":true}](...TRUNCATED) | original | Original 5-arg |
"Using ALL of the numbers 72, 2, 15, 10, 89, create an expression that equals 761. You must use each(...TRUNCATED) | "{\"numbers\": [72, 2, 15, 10, 89], \"target\": 761, \"operators_used\": [\"-\", \"+\", \"*\", \"-\"(...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["I need to create an expression using all the numbers 72, 2, 15, 10, and 89 exactly once to equal 7(...TRUNCATED) | [["tags.\"\n\nAnd \"a single arithmetic expression.\"\n\nSo, I should write: 89 * 10 - 72 * 2 + 15\n(...TRUNCATED) | [[{"end_index":9687,"end_phrase":"</answer>","start_index":8918,"start_phrase":"<answer>"},{"end_ind(...TRUNCATED) | [
[
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[
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] | [[{"answer_block":"tags.\"\n\nAnd \"a single arithmetic expression.\"\n\nSo, I should write: 89 * 10(...TRUNCATED) | original | Original 5-arg |
"Using ALL of the numbers 96, 4, 31, 21, 23, create an expression that equals 782. You must use each(...TRUNCATED) | "{\"numbers\": [96, 4, 31, 21, 23], \"target\": 782, \"operators_used\": [\"/\", \"+\", \"-\", \"*\"(...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["Okay, let's see. I need to make 782 using 96, 4, 31, 21, 23 each exactly once with +, -, *, /. Hmm(...TRUNCATED) | [["23 * (96 / 4 + (31 - 21)) = 782"],["23 * (96 / 4 + 31 - 21)"],["23 * (96 / 4 + 31 - 21)"],["23 * (...TRUNCATED) | [[{"end_index":5963,"end_phrase":"</answer>","start_index":5915,"start_phrase":"<answer>"}],[{"end_i(...TRUNCATED) | [
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"Using ALL of the numbers 34, 5, 14, 14, 56, create an expression that equals 226. You must use each(...TRUNCATED) | "{\"numbers\": [34, 5, 14, 14, 56], \"target\": 226, \"operators_used\": [\"*\", \"*\", \"/\", \"+\"(...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["Okay, let's tackle this problem. We need to use all the numbers 34, 5, 14, 14, 56 exactly once wit(...TRUNCATED) | [["34 * 5 + 56 + 14 - 14"],["34 * 5 + 56 + 14 - 14"],["34 * 5 + 56 + 14 - 14"],["tags.\"\n\nAnd \"a (...TRUNCATED) | [[{"end_index":9160,"end_phrase":"</answer>","start_index":9122,"start_phrase":"<answer>"}],[{"end_i(...TRUNCATED) | [
[
true
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[
true
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[
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false,
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] | [[{"answer_block":"34 * 5 + 56 + 14 - 14","error":null,"final_answer":226.0,"is_correct":true}],[{"a(...TRUNCATED) | original | Original 5-arg |
"Using ALL of the numbers 50, 2, 25, 90, 3, create an expression that equals 273. You must use each (...TRUNCATED) | "{\"numbers\": [50, 2, 25, 90, 3], \"target\": 273, \"operators_used\": [\"/\", \"/\", \"+\", \"*\"](...TRUNCATED) | countdown | [{"content":"You are a math problem solver. Solve the given arithmetic problem step by step. Show yo(...TRUNCATED) | ["Okay, let's try to solve this problem. We need to use all the numbers 50, 2, 25, 90, 3 exactly onc(...TRUNCATED) | [
[
"3 * (90 + 50 / (25 * 2))"
],
[],
[
"3 * (90 + 25 / (50 / 2))"
],
[
"(90 + (25 / (50 / 2))) * 3"
]
] | [[{"end_index":5704,"end_phrase":"</answer>","start_index":5663,"start_phrase":"<answer>"}],[],[{"en(...TRUNCATED) | [
[
true
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[],
[
true
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[
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] | [[{"answer_block":"3 * (90 + 50 / (25 * 2))","error":null,"final_answer":273.0,"is_correct":true}],[(...TRUNCATED) | original | Original 5-arg |
End of preview. Expand in Data Studio
t1-full-q3-30b-a3b-5arg
Full Semantic Knowledge Enhanced evaluation: base eval, knowledge synthesis, and enhanced+heldout evaluation.
Performance Comparison
| Metric | Base (original) | Enhanced: Original 5-arg | Enhanced: Heldout 5-arg | Enhanced: Easier 4-arg | Enhanced: Harder 6-arg |
|---|---|---|---|---|---|
| pass@1 | 0.7400 (74.0%) | 0.6200 (62.0%) | 0.5800 (58.0%) | 0.9000 (90.0%) | 0.5000 (50.0%) |
| pass@2 | 0.7800 (78.0%) | 0.7400 (74.0%) | 0.6600 (66.0%) | 0.9800 (98.0%) | 0.5600 (56.0%) |
| pass@3 | 0.7800 (78.0%) | 0.7400 (74.0%) | 0.7000 (70.0%) | 0.9800 (98.0%) | 0.7200 (72.0%) |
| pass@4 | 0.8600 (86.0%) | 0.7800 (78.0%) | 0.7000 (70.0%) | 0.9800 (98.0%) | 0.7400 (74.0%) |
Experimental Details
| Parameter | Value |
|---|---|
| Inference model | hosted_vllm/Qwen/Qwen3-30B-A3B-Thinking-2507 |
| Synthesis model | gpt-5-mini |
| Temperature | 0.7 |
| Top-p | 0.95 |
| Max tokens | 16384 |
| Samples per problem | 4 |
| N-args | 5 |
| Heldout sets | 4-arg, 5-arg (new), 6-arg |
| Questions per set | 50 |
| Number of facts | 20 |
| Seed (base) | 42 |
| Seed (heldout) | 137 |
Synthesized Facts
- Survey the available values and the target before making any moves.
- Prioritize combining values that approach the target in large steps.
- Keep track of intermediate results and which values remain as you explore options.
- Work backwards from the target by asking which combinations could produce it.
- Group values that produce tidy results to simplify subsequent decisions.
- Avoid repeating the same pathway when it yields no closer approach to the target.
- Test complementary pairs that together reach useful checkpoints near the target.
- Combine large and small values to bridge substantial gaps efficiently.
- Reserve flexible values that can be adapted in multiple ways for late adjustments.
- Eliminate paths early when remaining values cannot reach the target.
- Prefer operations that reduce the set of values to manage the search space.
- Store explored states mentally or on paper to prevent redundant effort.
- Divide the solution process into stages and resolve each stage with the remaining values.
- Search for factor and ratio relationships that convert available values into useful components.
- Reverse a recent step to see if an alternative prior choice would reach the target.
- Keep intermediate results simple to avoid unnecessary complexity.
- Use quick estimation to discard implausible combinations at a glance.
- Record promising partial constructions and revisit them after investigating other options.
- Favor direct matches when a partial construction leads straight to the target with remaining values.
- Train pattern recognition so common useful combinations become intuitive over time.
Usage
from datasets import load_dataset
dataset = load_dataset("reasoning-degeneration-dev/t1-full-q3-30b-a3b-5arg", split="train")
Generated by run_full_experiment.py on 2026-02-17 03:29
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