query listlengths 2 2 | nums sequencelengths 2 4 | target int64 10 25 | eval_prompt listlengths 2 2 | eval_internal_cot stringlengths 398 12.5k | eval_solution stringlengths 19 385 | raw_eval_prompt listlengths 2 2 | is_correct bool 2
classes | error stringclasses 3
values | measurement_type stringclasses 1
value | measurement_prompt stringlengths 1.42k 1.78k | row_id int64 0 99 | measurement_answer_verification_final_count int64 0 16 | measurement_answer_verification_reasoning stringlengths 338 1.66k | measurement_answer_verification_metadata sequencelengths 0 10 | measurement_answer_verification_raw_response null | measurement_step_verification_final_count int64 0 20 | measurement_step_verification_reasoning stringlengths 424 1.85k | measurement_step_verification_metadata sequencelengths 0 20 | measurement_step_verification_raw_response null | measurement_reasoning_deliberation_final_count int64 0 20 | measurement_reasoning_deliberation_reasoning stringlengths 700 1.74k | measurement_reasoning_deliberation_metadata sequencelengths 0 21 | measurement_reasoning_deliberation_raw_response null |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"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... | To solve this problem, I need to use the numbers 15, 19, and 9 with basic arithmetic operations (+, -, *, /) to reach the target number 13. Each number can only be used once.
First, I'll consider the possible operations:
1. Addition: 15 + 19 + 9 = 43 (too high), 15 + 19 = 34, 15 + 9 = 24, 19 + 9 = 28. None of these a... | <answer>
Step 1: 15 - 9 = 6
Step 2: 19 - 6 = 13
</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 | 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.
The trace is:... | [
"13"
] | null | 0 | 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 ... | [] | null | 0 | 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 ap... | [] | null |
[
{
"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... | To create an equation that equals 10 using the numbers [20, 9, 2, 24] with each number used only once, I'll try different combinations of operations:
1. First, I'll try subtracting numbers: 24 - 20 = 4. Then, 9 - 2 = 7. But 4 and 7 don't combine to make 10.
2. Next, I'll try dividing: 20 / 2 = 10. Then, I have 9 and 2... | <answer>
Step 1: 24 - 20 = 4
Step 2: 9 - 4 = 5
Step 3: 5 * 2 = 10
</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 | 0 | 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, or attempts to verify it using an alternative method. Let’s step through the trace.
The trace show... | [] | null | 0 | 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 ... | [] | null | 0 | 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 ap... | [] | null |
[
{
"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... | [
13,
3,
18,
10
] | 24 | [
{
"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... | To solve this problem, I need to use the numbers [13, 3, 18, 10] exactly once with basic arithmetic operations to reach the target number 24. Here's how I can approach it:
1. First, I notice that 18 and 10 are large numbers. Subtracting them might give a useful intermediate result:
- 18 - 10 = 8
2. Now, I have the... | <final_answer>
Step 1: 18 - 10 = 8
Step 2: 13 + 3 = 16
Step 3: 16 + 8 = 24
</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... | 2 | 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.
The trace sho... | [
"8",
"16",
"24"
] | null | 0 | 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.
The trace shows three steps:
Step 1: 18 - 10 = 8
Step 2: 13 + 3 = 16
Step 3: 16 + 8 = 24
In each step, the model performs... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
23,
3,
2,
22
] | 21 | [
{
"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... | To solve this problem, I need to use the numbers [23, 3, 2, 22] exactly once each, along with basic arithmetic operations, to reach the target number 21. Here's how I can approach it:
1. First, I notice that 23 and 22 are close in value. Subtracting them gives 1 (23 - 22 = 1), but this doesn't seem immediately useful ... | <answer>
Step 1: 23 * 2 = 46
Step 2: 22 + 3 = 25
Step 3: 46 - 25 = 21
</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... | 3 | 0 | 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.
The trace con... | [] | null | 0 | 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 ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
3,
8,
4,
13
] | 17 | [
{
"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... | To reach the target number 17 using the numbers [3, 8, 4, 13], I need to find a combination of operations that results in 17. Here's how I can approach it:
1. First, I notice that 13 is the largest number. If I subtract one of the other numbers from 13, I might get close to 17. However, 13 - 3 = 10, 13 - 4 = 9, and 13... | <final_answer>
Step 1: 3 * 4 = 12
Step 2: 12 + 13 = 25
Step 3: 25 - 8 = 17
</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... | 4 | 0 | 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 given ... | [] | null | 0 | 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 c... | [] | null | 0 | 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 ap... | [] | null |
[
{
"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... | [
12,
6,
12
] | 18 | [
{
"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... | To solve this problem, I need to use the numbers [12, 6, 12] exactly once each with basic arithmetic operations to reach the target number 18. Here's how I can approach it:
1. First, I can try adding two of the numbers and see if the result is 18 or can be manipulated to 18 using the third number.
- 12 + 6 = 18, bu... | <answer>
Step 1: 12 + 12 = 24
Step 2: 24 - 6 = 18
</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... | 5 | 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.
The reasoning... | [
"18"
] | null | 0 | 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 ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
6,
15,
13,
9
] | 21 | [
{
"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... | To reach the target number of 21 using the numbers [6, 15, 13, 9], I need to find a combination of operations that will result in 21. Here's how I can approach it:
1. First, I notice that 15 and 6 are numbers that can be combined to get close to 21. For example, 15 + 6 = 21, but this would leave 13 and 9 unused, which... | <final_answer>
Step 1: 15 - 13 = 2
Step 2: 6 * 2 = 12
Step 3: 12 + 9 = 21
</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... | 6 | 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, or attempts to verify it using an alternative method. Let’s step through the trace. The trace provi... | [
"21"
] | null | 0 | 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 c... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
2,
8,
2,
11
] | 17 | [
{
"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... | To reach the target number 17 using the numbers [2, 8, 2, 11], I need to find a combination of operations that results in 17. Here's how I can approach it:
1. First, I notice that 11 is the largest number. If I subtract one of the other numbers from 11, I might get close to 17.
- 11 - 2 = 9 (too low)
- 11 - 8 = ... | <answer>
Step 1: 11 + 8 = 19
Step 2: 19 - 2 = 17
</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... | 7 | 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.
The trace is:... | [
"17"
] | null | 0 | 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.
In the provided reasoning, we see two steps:
- Step 1: 11 + 8 = 19
- Step 2: 19 - 2 = 17
Neither step explicitly shows the... | [] | null | 0 | 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 appr... | [] | null |
[
{
"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... | [
21,
15,
5,
9
] | 22 | [
{
"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... | To solve this problem, I need to use the numbers [21, 15, 5, 9] exactly once with basic arithmetic operations to reach the target number 22. Here's how I can approach it:
1. First, I notice that 21 and 15 are large numbers, so subtracting them might not be useful. Instead, I can try adding or multiplying smaller numbe... | <final_answer>
Step 1: 21 - 9 = 12
Step 2: 12 + 15 = 27
Step 3: 27 - 5 = 22
</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... | 8 | 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. Step 1: 21 - 9... | [
"12",
"27",
"22"
] | null | 0 | 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 ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
6,
22,
14
] | 14 | [
{
"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... | To create an equation that equals 14 using the numbers [6, 22, 14], we can consider the following steps:
1. First, observe that one of the numbers is already 14, so we might not need to perform any operations if we can just return 14. However, the problem likely expects us to use all the numbers in some way.
2. Altern... | <answer>
Step 1: 14 - 6 = 8
Step 2: 22 - 8 = 14
</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... | 9 | 2 | 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.
The trace pro... | [
"8",
"14"
] | null | 0 | 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 ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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,
15,
17
] | 12 | [
{
"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... | To solve this problem, I need to use the numbers 20, 15, and 17 with basic arithmetic operations (+, -, *, /) to reach the target number 12. Each number can only be used once. Here's how I can approach it:
1. First, I'll look for combinations where subtraction might give me a smaller number. For example, 20 - 15 = 5 o... | <answer>
Step 1: 20 - 17 = 3
Step 2: 15 - 3 = 12
</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... | 10 | 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.
The trace giv... | [
"12"
] | null | 0 | 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 ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
18,
9,
21,
11
] | 18 | [
{
"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... | To create an equation that equals 18 using the numbers [18, 9, 21, 11], I need to find a combination of operations that results in 18. Here's how I can approach it:
1. First, I notice that one of the numbers is already 18, so perhaps I can use it directly and cancel out the other numbers. For example, I could subtract... | <answer>
Step 1: 21 - 9 = 12
Step 2: 12 - 11 = 1
Step 3: 18 * 1 = 18
</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... | 11 | 0 | 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.
The trace sho... | [] | null | 0 | 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 c... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
24,
9,
17,
6
] | 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... | To create an equation that equals 13 using the numbers [24, 9, 17, 6] with each number used only once, I'll try different combinations of operations:
1. First, I'll try subtracting numbers:
- 17 - 6 = 11 (not 13)
- 24 - 9 = 15 (not 13)
- 24 - 17 = 7 (not 13)
2. Next, I'll try adding numbers:
- 9 + 6 = 15 ... | <answer>
Step 1: 24 - 17 = 7
Step 2: 7 + 6 = 13
</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... | 12 | 0 | 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.
The trace shows... | [] | null | 0 | 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 ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
10,
21,
17,
20
] | 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... | To reach the target number 13 using the numbers [10, 21, 17, 20], I need to find a combination of operations that results in 13. Here's how I can approach it:
1. First, I notice that 21 - 17 = 4, which is close to 13 but not quite there.
2. Next, I consider 20 - 10 = 10, which is also not 13.
3. Then, I think about co... | <answer>
It is not possible to reach the target number 13 using the numbers [10, 21, 17, 20] with basic arithmetic operations (+, -, *, /) and each number used only once.
</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... | false | Expected a single '=' separating expression and result | 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... | 13 | 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. The trace only con... | [
"It is not possible to reach the target number 13 using the numbers [10, 21, 17, 20] with basic arithmetic operations (+, -, *, /) and each number used only once."
] | null | 0 | 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 ... | [] | null | 0 | 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 ap... | [] | null |
[
{
"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,
11,
16,
1
] | 16 | [
{
"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... | To solve this problem, I need to use the numbers [20, 11, 16, 1] exactly once with basic arithmetic operations to reach the target number 16. Here's how I can approach it:
1. Since 16 is already one of the numbers in the list, the simplest solution might involve using 16 directly and ensuring the other numbers cancel ... | <answer>16</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... | false | Expected a single '=' separating expression and result | 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... | 14 | 16 | 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.
Since the tra... | [] | null | 16 | 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 look for every instance where the model does a subtask, then doubts or double-checks and redoes or confirms that subtask... | [
"\"Wait, I think I made a mistake in calculating this step, let me check again...\"",
"\"Let me re-calculate the sum to be sure...\"",
"\"I should verify this multiplication once more...\"",
"\"This derivative seems off, I'll re-derive it...\"",
"\"Double-checking the simplification to avoid errors...\"",
... | null | 16 | 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 ap... | [
"\"Is this approach the best way to tackle this problem or should I try an alternative method?\"",
"\"I need to double-check if continuing with this strategy is efficient.\"",
"\"Does it make sense to proceed with this step or would abandoning it lead to a clearer path?\"",
"\"I should pause and consider if m... | null |
[
{
"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... | [
10,
8,
2,
8
] | 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... | To reach the target number 13 using the numbers [10, 8, 2, 8], I need to find a combination of operations that results in 13. Here's how I can approach it:
1. First, I notice that 10 is the largest number. If I subtract something from 10, I might get close to 13. But 10 - 8 = 2, which is too low. 10 - 2 = 8, which is ... | <final_answer>
Step 1: 8 / 8 = 1
Step 2: 10 + 2 = 12
Step 3: 12 + 1 = 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... | 15 | 0 | 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, or attempts to verify it using an alternative method. Let’s step through the trace. The provided rea... | [] | null | 0 | 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.
Looking at the trace:
- Step 1: "8 / 8 = 1" (a direct calculation, no sign of checking or redoing)
- Step 2: "10 + 2 = 12" ... | [] | null | 0 | 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 app... | [] | null |
[
{
"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... | [
18,
6,
9
] | 12 | [
{
"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... | To solve this problem, I need to use the numbers 18, 6, and 9 with basic arithmetic operations (+, -, *, /) to reach the target number 12. Each number can only be used once.
First, I'll consider the possible operations:
1. Addition: 18 + 6 + 9 = 33 (too high), 18 + 6 = 24, 18 + 9 = 27, 6 + 9 = 15 (none of these are 1... | <answer>
(18 / 9) * 6
</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... | false | Expected a single '=' separating expression and result | 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... | 16 | 0 | To determine how many times the model proposed a final answer, we look for each explicit computation and presentation of a final result, restatement or confirmation of that result, or attempts to verify it using an alternative method. The trace only shows the expression (18 / 9) * 6 without further evaluation, restatem... | [] | null | 0 | 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.
The given trace is:
"(18 / 9) * 6"
This is just a simple expression without any accompanying reasoning steps, recalculatio... | [] | null | 0 | 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 appr... | [] | null |
[
{
"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... | [
18,
24,
23,
7
] | 23 | [
{
"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... | To create an equation that equals 23 using the numbers [18, 24, 23, 7], I need to find a combination of operations that results in 23. Here's how I can approach it:
1. First, observe that 23 is one of the given numbers. So, I can consider using 23 directly in the equation, but I need to ensure that the other numbers a... | <answer>
Step 1: 24 - 18 = 6
Step 2: 7 - 6 = 1
Step 3: 23 * 1 = 23
</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... | 17 | 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.
The given rea... | [
"23"
] | null | 0 | 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 ... | [] | null | 0 | To answer your question 2—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) 2—we need to identify all moments in the reasoning trace where: The model questions its current method or... | [] | null |
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