sample_index int64 0 599 | numbers listlengths 4 4 | ground_truth_solutions listlengths 1 11 | difficulty_amt float64 4.36 212 | partial_solution stringlengths 105 13k | step_number int64 1 208 | total_steps int64 14 209 | pct_complete float64 0 1 | empirical_success_rate float64 0 1 | num_continuations int64 10 10 | num_correct int64 0 10 | full_initial_generation stringlengths 2.28k 13.1k | continuations listlengths 10 10 | parsed_answers listlengths 10 10 | initial_intervention_used bool 2
classes | continuation_interventions listlengths 10 10 | num_continuations_intervened int64 0 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
50 | [
1,
2,
2,
5
] | [
"(5+1)×(2+2)",
"(5+1)×2×2"
] | 7.78 | First, I have the numbers: 1, 2, 2, 5. I need to use each exactly once with basic arithmetic operations to make 24. The operations are addition, subtraction, multiplication, and division. I can also use parentheses to group operations. | 1 | 144 | 0.006944 | 1 | 10 | 10 | First, I have the numbers: 1, 2, 2, 5. I need to use each exactly once with basic arithmetic operations to make 24. The operations are addition, subtraction, multiplication, and division. I can also use parentheses to group operations.
I should think about what combinations might get me to 24. Since 24 is a multiple o... | [
"Okay, let's see. I need to make 24 with 1, 2, 2, 5. Hmm. 24 is a pretty common target in these puzzles. Let me think about what combinations might work.\n\nFirst, I know that 24 is 4 times 6, or 3 times 8, or 12 times 2, etc. Maybe I can try to get two numbers to multiply to something that helps. Wait, I have two ... | [
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 * 2)",
"(2 * 2) * (5 + 1)",
"(5 + 1) * 2 * 2",
"(5 + 1) * (2 * 2)",
"(5 + 1) * (2 + 2)",
"(2 × 2) × (5 + 1)",
"(5 + 1) × (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 * 2)"
] | true | [
false,
false,
false,
true,
false,
false,
false,
false,
false,
false
] | 1 |
50 | [
1,
2,
2,
5
] | [
"(5+1)×(2+2)",
"(5+1)×2×2"
] | 7.78 | First, I have the numbers: 1, 2, 2, 5. I need to use each exactly once with basic arithmetic operations to make 24. The operations are addition, subtraction, multiplication, and division. I can also use parentheses to group operations.
I should think about what combinations might get me to 24. Since 24 is a multiple o... | 72 | 144 | 0.5 | 0.2 | 10 | 2 | First, I have the numbers: 1, 2, 2, 5. I need to use each exactly once with basic arithmetic operations to make 24. The operations are addition, subtraction, multiplication, and division. I can also use parentheses to group operations.
I should think about what combinations might get me to 24. Since 24 is a multiple o... | [
"Okay, so I need to solve the Game of 24 with the numbers 1, 2, 2, 5. Let me think through this carefully.\n\nFirst, I have four numbers: 1, 2, 2, 5. I must use each exactly once with +, -, ×, ÷, and parentheses to get 24.\n\nHmm, 24 is a multiple of many numbers. Let's see what combinations I can try.\n\nIf I mult... | [
"(2 * 2) * (5 + 1)",
"tags.\n\nThe <answer> tag must be at the very end, with only the expression inside.\n\nSo, I'll write:\n\nStep 1: I observe that 5 and 1 can be summed to 6.\n\nStep 2: The two 2s can be summed to 4.\n\nStep 3: Multiplying 6 and 4 gives 24, which uses all four numbers exactly once.\n\nThen, <... | true | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0 |
50 | [
1,
2,
2,
5
] | [
"(5+1)×(2+2)",
"(5+1)×2×2"
] | 7.78 | First, I have the numbers: 1, 2, 2, 5. I need to use each exactly once with basic arithmetic operations to make 24. The operations are addition, subtraction, multiplication, and division. I can also use parentheses to group operations.
I should think about what combinations might get me to 24. Since 24 is a multiple o... | 143 | 144 | 0.993056 | 1 | 10 | 10 | First, I have the numbers: 1, 2, 2, 5. I need to use each exactly once with basic arithmetic operations to make 24. The operations are addition, subtraction, multiplication, and division. I can also use parentheses to group operations.
I should think about what combinations might get me to 24. Since 24 is a multiple o... | [
"Okay, so I need to solve this Game of 24 puzzle with the numbers 1, 2, 2, 5. The goal is to use each number exactly once and the basic operations (+, -, ×, ÷) to make exactly 24. Let me think through this step by step.\n\nFirst, I'll list out the numbers: 1, 2, 2, 5. I need to combine them with operations to get 2... | [
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)",
"(5 + 1) * (2 + 2)"
] | true | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0 |
51 | [
1,
2,
2,
6
] | [
"(6+2)×(2+1)",
"6×2×2×1",
"(2+2)×6×1"
] | 4.78 | "First, I have the numbers: 1, 2, 2, 6. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | 1 | 160 | 0.00625 | 1 | 10 | 10 | "First, I have the numbers: 1, 2, 2, 6. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | ["Okay, let's see. I need to make 24 with 1, 2, 2, and 6. Hmm. Let's think about how to combine thes(...TRUNCATED) | ["(6 + 2) × (2 + 1)","( (2 × 2) × 6 ) × 1","2 ÷ (1 ÷ 6) × 2","1 × 6 × (2 + 2)","(6 + 2) × (...TRUNCATED) | true | [
true,
true,
true,
true,
true,
false,
true,
false,
false,
true
] | 7 |
51 | [
1,
2,
2,
6
] | [
"(6+2)×(2+1)",
"6×2×2×1",
"(2+2)×6×1"
] | 4.78 | "First, I have the numbers: 1, 2, 2, 6. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | 80 | 160 | 0.5 | 0 | 10 | 0 | "First, I have the numbers: 1, 2, 2, 6. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | ["First, I need to solve the Game of 24 puzzle with the numbers 1, 2, 2, 6. The goal is to use each (...TRUNCATED) | ["tag.\n\nBut let me see if there's another way, just to be thorough.\n\nSuppose I do 6 * (2 * 2) * (...TRUNCATED) | true | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0 |
51 | [
1,
2,
2,
6
] | [
"(6+2)×(2+1)",
"6×2×2×1",
"(2+2)×6×1"
] | 4.78 | "First, I have the numbers: 1, 2, 2, 6. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | 159 | 160 | 0.99375 | 0 | 10 | 0 | "First, I have the numbers: 1, 2, 2, 6. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | ["First, I need to solve the Game of 24 puzzle with the numbers 1, 2, 2, 6. The rules require using (...TRUNCATED) | ["tag.\n\nBut let me see if there's another way, just to be thorough.\n\nSuppose I do 6 * (2 * 2) * (...TRUNCATED) | true | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0 |
52 | [
1,
2,
2,
7
] | [
"(7-1)×(2+2)",
"(7-1)×2×2"
] | 8.47 | "First, I have the numbers: 1, 2, 2, 7. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | 1 | 160 | 0.00625 | 0.8 | 10 | 8 | "First, I have the numbers: 1, 2, 2, 7. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | ["Okay, let's see. I need to make 24 with 1, 2, 2, 7. Hmm. Let's think about what combinations could(...TRUNCATED) | ["(2 * 2) * (7 - 1)","(7 - 1) * (2 + 2)","(2 + 2) * (7 - 1)","(2 × 2) × (7 - 1)","(2 × 2) × (7 -(...TRUNCATED) | true | [
false,
true,
false,
false,
false,
false,
true,
true,
false,
false
] | 3 |
52 | [
1,
2,
2,
7
] | [
"(7-1)×(2+2)",
"(7-1)×2×2"
] | 8.47 | "First, I have the numbers: 1, 2, 2, 7. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | 80 | 160 | 0.5 | 0 | 10 | 0 | "First, I have the numbers: 1, 2, 2, 7. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | ["First, I need to solve the Game of 24 puzzle with the numbers 1, 2, 2, 7. I must use each number e(...TRUNCATED) | ["tag.\n\nThe problem says \"show all reasoning and intermediate work outside of <answer> tags\", an(...TRUNCATED) | true | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0 |
52 | [
1,
2,
2,
7
] | [
"(7-1)×(2+2)",
"(7-1)×2×2"
] | 8.47 | "First, I have the numbers: 1, 2, 2, 7. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | 159 | 160 | 0.99375 | 0 | 10 | 0 | "First, I have the numbers: 1, 2, 2, 7. I need to use each exactly once with basic arithmetic operat(...TRUNCATED) | ["Okay, so I need to solve the Game of 24 puzzle with the numbers 1, 2, 2, and 7. Let me think throu(...TRUNCATED) | ["tag.\n\nThe problem says \"show all reasoning and intermediate work outside of <answer> tags\", an(...TRUNCATED) | true | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0 |
53 | [
1,
2,
2,
8
] | [
"(2+2-1)×8",
"(2×2-1)×8"
] | 6.36 | "First, I have the numbers: 1, 2, 2, 8. I need to use each exactly once with +, -, ×, ÷ to make 24(...TRUNCATED) | 1 | 62 | 0.016129 | 1 | 10 | 10 | "First, I have the numbers: 1, 2, 2, 8. I need to use each exactly once with +, -, ×, ÷ to make 24(...TRUNCATED) | ["Okay, let's see. I need to get 24 from 1, 2, 2, 8. Hmm. 24 is a multiple of 8, so maybe that's a g(...TRUNCATED) | ["8 × (2 × 2 - 1)","8 × (2 + (2 - 1))","8*(2+2-1)","8×(2×2-1)","8*(2*2-1)","(8 × (2 + 2 - 1))"(...TRUNCATED) | false | [
false,
true,
false,
false,
false,
false,
false,
false,
false,
false
] | 1 |
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