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classes | error stringclasses 11
values | measurement_type stringclasses 1
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[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
15,
19,
9
] | 13 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 15, 19, and 9 each exactly once with basic operations to get 13. Hmm. Let me think about possible combinations.
First, maybe subtract two numbers and then add or subtract the third. Let's try 19 minus 15. That gives 4. Then if I use the 9, maybe 4 plus 9 is 13. Wait, but that... | <final_answer>
Step 1: 15 - 9 = 6
Step 2: 19 - 6 = 13
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 0 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The model fi... | [
"13",
"13",
"13"
] | null | 2 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"\"Let me check the arithmetic: 19 minus 15 is 4, plus 9 is 13. That works!\"",
"\"Let me check the arithmetic again. For the second approach: 15 -9=6, then 19-6=13.\""
] | null | 6 | To answer your question 6 how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching) 7 we need to identify all moments in the reasoning trace where:
The model questions its current method o... | [
"Hmm. Let me think about possible combinations.",
"First, maybe subtract two numbers and then add or subtract the third. Let's try 19 minus 15.",
"But wait, the problem says \"create an equation\" and each number can only be used once... But let me make sure there's no other way. Alternatively, maybe division o... | null | [
false,
false
] | [
{
"error_explanation": "There is no error in the previous step; all calculations and logic are correct. The verification step simply reiterates the same calculation without correcting or changing any value.",
"next_step": "Let me check the arithmetic: 19 minus 15 is 4, plus 9 is 13. That works!",
"next_... | [
false,
false,
false
] | [
{
"correct": false,
"reasoning": "The given solution simply states the number '13' without showing any arithmetic operations or steps using the numbers [15, 19, 9]. The problem requires using those numbers exactly once with basic arithmetic operations to create an equation equaling 13, and the final answer ... | [
true,
true,
true,
true,
true,
true
] | [
{
"change_in_direction_explanation": "The deliberation caused the model to explicitly consider alternative arithmetic operations and decide on trying specific sequences, leading it to explore and confirm multiple solutions rather than continuing blindly. This is a meaningful shift in approach, indicating the de... |
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
20,
9,
2,
24
] | 10 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 20, 9, 2, and 24 each exactly once to make 10. Hmm. Let's start by thinking about possible combinations.
First, maybe subtract some numbers. Like 24 minus something. 24 - 14 is 10. But do I have numbers that can make 14? Let's see. 20 and 9 and 2. If I use 20 - (9 + 2) = 9, t... | <final_answer>
Step 1: 24 - 9 = 15
Step 2: 20 - 15 = 5
Step 3: 5 * 2 = 10
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 1 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
In the trace,... | [
"10"
] | null | 4 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"'If I use 20 / 2 = 10, then I still have 9 and 24 left. But I can't just leave them. So that approach might not work because all numbers must be used. Oh right, the problem says each number can only be used once. So all four numbers must be part of the equation. So I can't just use two numbers and ignore the other... | null | 8 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
- The model questions its current method or ... | [
"\"Oh, that's a good start. If I use 20 / 2 = 10, then I need to use the remaining numbers 9 and 24. But how? Because each number must be used once. Wait, but if I do 20 / 2 = 10, then I still have 9 and 24 left. But I can't just leave them. So that approach might not work because all numbers must be used.\"",
"\... | null | [
true,
true,
false,
false
] | [
{
"error_explanation": "There is no error in the previous step's calculation of 20 / 2 = 10; the partial numerical result is correct. However, the error is in the partial solution's approach to the problem, neglecting the need to use all numbers exactly once, which this verification correctly identifies.",
... | [
false
] | [
{
"correct": false,
"reasoning": "The provided solution '10' does not follow the instructions outlined in the question. The question requires the solution to be formatted with step-by-step arithmetic operations labeled as Step 1, Step 2, etc., each showing a single operation resulting in the target number. ... | [
true,
true,
true,
true,
true,
true,
true,
true
] | [
{
"change_in_direction_explanation": "The deliberation explicitly reconsidered the initial approach of simply dividing 20 by 2 to get 10, recognizing that it fails to use all numbers as required. This discarded the initial straightforward approach and prompted the model to explore alternative strategies involvi... |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
13,
3,
18,
10
] | 24 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 13, 3, 18, and 10 each exactly once with basic operation(...TRUNCATED) | "<final_answer>\nStep 1: 13 + 3 = 16 \nStep 2: 18 - 10 = 8 \nStep 3: 16 + 8 = 24 \n</final_answer(...TRUNCATED) | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 2 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"24"
] | null | 11 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"If I subtract them, 18 - 10 is 8. Then maybe multiply by 3? 8 * 3 is 24, but then I still have 1(...TRUNCATED) | null | 23 | "To answer your question\u00151 how many times does the model verify its higher-level reasoning (i.e(...TRUNCATED) | ["First, 18 and 10 are there. If I subtract them, 18 - 10 is 8. Then maybe multiply by 3? 8 * 3 is 2(...TRUNCATED) | null | [
false,
false,
false,
false,
false,
false,
false,
true,
true,
true,
true
] | [{"error_explanation":"No prior numeric calculation was established before this step, so no prior er(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The provided solution '24' does not follow the detailed instructions (...TRUNCATED) | [true,false,true,false,true,false,false,true,false,true,true,false,true,true,true,false,false,false,(...TRUNCATED) | [{"change_in_direction_explanation":"The deliberation reconsidered the prior approach's limitation o(...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
23,
3,
2,
22
] | 21 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 23, 3, 2, and 22 each exactly once to make 21. Hmm. Let (...TRUNCATED) | "<final_answer>\nStep 1: 23 * 2 = 46 \nStep 2: 46 - 22 = 24 \nStep 3: 24 - 3 = 21 \n</final_answe(...TRUNCATED) | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 3 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"21"
] | null | 6 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["23 - 2 = 21. Oh, wait, but then I have to use 3 and 22 as well. But if I do 23 - 2, that's 21, but(...TRUNCATED) | null | 16 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Oh, wait, but then I have to use 3 and 22 as well. But if I do 23 - 2, that's 21, but I still have(...TRUNCATED) | null | [
true,
false,
false,
false,
false,
false
] | [{"error_explanation":"No error occurred in the calculation of 23 - 2 = 21; the arithmetic is correc(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The solution provided is simply '21', which does not follow the instr(...TRUNCATED) | [
true,
true,
true,
true,
true,
true,
true,
true,
true,
true,
true,
true,
true,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation caused the model to reject the apparently stra(...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
3,
8,
4,
13
] | 17 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 3, 8, 4, and 13 each exactly once to make 17. Hmm. Let m(...TRUNCATED) | <final_answer>
Step 1: 3 * 4 = 12
Step 2: 13 - 8 = 5
Step 3: 12 + 5 = 17
</final_answer> | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 4 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"17"
] | null | 11 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["13 + 4 is 17, but then I have to use 3 and 8. Wait, but if I do 13 + 4 =17, but I need to use all (...TRUNCATED) | null | 6 | "To answer your question\u000123456789how many times does the model verify its higher-level reasonin(...TRUNCATED) | ["Hmm. Let me think about possible combinations.","First, maybe start by looking at the largest numb(...TRUNCATED) | null | [
false,
false,
false,
true,
false,
true,
false,
true,
false,
false,
false
] | [{"error_explanation":"The initial step did not contain an error in calculation; it correctly comput(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The solution provided is simply '17', which does not follow the requi(...TRUNCATED) | [
false,
false,
true,
false,
true,
true
] | [{"change_in_direction_explanation":"The deliberation did not change the direction meaningfully; the(...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
12,
6,
12
] | 18 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 12, 6, and 12 each exactly once to get 18. The operation(...TRUNCATED) | <final_answer>
Step 1: 12 + 12 = 24
Step 2: 24 - 6 = 18
</final_answer> | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 5 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"18",
"18"
] | null | 2 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, but the original numbers are [12, 6, 12], so there are two 12s. So each instance can be us(...TRUNCATED) | null | 7 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Wait, but that would use the second 12 again.\"","\"Wait, the problem says each number can be us(...TRUNCATED) | null | [
true,
false,
false,
false
] | [{"error_explanation":"There is no error in the previous calculation as no arithmetic value was comp(...TRUNCATED) | [
false,
false
] | [{"correct":false,"reasoning":"The solution provided is just the number 18 without showing any arith(...TRUNCATED) | [
false,
true,
true,
true,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation clarified the usage of duplicate numbers but d(...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
6,
15,
13,
9
] | 21 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 6, 15, 13, and 9 each exactly once to make 21. Hmm. Let (...TRUNCATED) | "<final_answer>\nStep 1: 15 - 13 = 2 \nStep 2: 2 * 6 = 12 \nStep 3: 12 + 9 = 21 \n</final_answer>(...TRUNCATED) | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"21"
] | null | 5 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["If I take 15 and subtract 13, that gives me 2.","Like, 13 - 9 = 4. Then 15 + 6 - (13 -9) would be (...TRUNCATED) | null | 10 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, let me start by thinking about possible combinations.","First, maybe I can subtract some numb(...TRUNCATED) | null | [
false,
false,
false,
false,
false
] | [{"error_explanation":"There is no error in the previous step. The calculation 15 - 13 = 2 is correc(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The solution provided is just the number '21', which does not satisfy(...TRUNCATED) | [
false,
true,
true,
true,
false,
true,
true,
false,
true,
true
] | [{"change_in_direction_explanation":"The deliberation repeats the initial direction without proposin(...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
2,
8,
2,
11
] | 17 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 2, 8, 2, and 11 to make 17. Each number can only be used(...TRUNCATED) | <final_answer>
Step 1: 8 / 2 = 4
Step 2: 11 + 4 = 15
Step 3: 15 + 2 = 17
</final_answer> | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"17"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["'Wait, but each number can only be used once. Oh right, the two 2s are separate numbers. Wait, the(...TRUNCATED) | null | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"First, 11 is a big number. Maybe if I subtract something from 11. Let's see. 11 plus something? (...TRUNCATED) | null | [
false,
false,
false,
true
] | [{"error_explanation":"There was no error in the previous step; it correctly recognized that the two(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The provided solution '17' is not correct because it does not follow (...TRUNCATED) | [
true,
true,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation shifted from only considering simple addition (...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
21,
15,
5,
9
] | 22 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 21, 15, 5, and 9 each exactly once to make 22. Hmm. Let (...TRUNCATED) | "<final_answer>\nStep 1: 15 - 9 = 6 \nStep 2: 21 - 5 = 16 \nStep 3: 16 + 6 = 22 \n</final_answer>(...TRUNCATED) | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 8 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"22",
"22"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Let me check that: 21-5=16, 15-9=6, 16+6=22. Yes, that works.\"","\"Step 1: 15 - 9 = 6\nStep 2: (...TRUNCATED) | null | 3 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Alternatively, maybe another way. Let me check if there's another combination.","Wait, the first i(...TRUNCATED) | null | [
false,
false,
false,
false
] | [{"error_explanation":"There is no actual error in the previous step; all arithmetic computations ar(...TRUNCATED) | [
false,
false
] | [{"correct":false,"reasoning":"The question asks to use the numbers [21, 15, 5, 9] each exactly once(...TRUNCATED) | [
false,
false,
false
] | [{"change_in_direction_explanation":"The deliberation involved exploring multiple alternative operat(...TRUNCATED) |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
6,
22,
14
] | 14 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 6, 22, and 14 to make an equation that equals 14. Each n(...TRUNCATED) | <final_answer>
Step 1: 14 - 6 = 8
Step 2: 22 - 8 = 14
</final_answer> | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"14",
"14"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["22 divided by (14 - 6), that's 22 divided by 8, which is 2.75.","14 divided by (22 - 6) is 14/16, (...TRUNCATED) | null | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, the target is 14, and one of the numbers is already 14. Maybe I can use that somehow. But I h(...TRUNCATED) | null | [
false,
false,
false,
false
] | [{"error_explanation":"","next_step":"Alternatively, 14 divided by something. 14 divided by (22 - 6)(...TRUNCATED) | [
false,
false
] | [{"correct":false,"reasoning":"The user's question requests creating an equation using the numbers [(...TRUNCATED) | [
true,
true,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation prompted the model to focus more deliberately (...TRUNCATED) |
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