question string | solution string | eval_internal_cot string | eval_solution string | judge_correct bool | judge_reasoning string | eval_prompt list | eval_steps list | steps_word_count int64 | trace_word_count int64 | word_count_diff int64 | measurement_type string | measurement_prompt string | row_id int64 | measurement_answer_verification_final_count int64 | measurement_answer_verification_reasoning string | measurement_answer_verification_metadata sequence | measurement_answer_verification_raw_response null | measurement_step_verification_final_count int64 | measurement_step_verification_reasoning string | measurement_step_verification_metadata sequence | measurement_step_verification_raw_response null | measurement_reasoning_deliberation_final_count int64 | measurement_reasoning_deliberation_reasoning string | measurement_reasoning_deliberation_metadata sequence | measurement_reasoning_deliberation_raw_response null |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
8274 x 3529
Think step by step. | 29198946 | Okay, so I need to multiply 8274 by 3529. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this step by step. I remember that long multiplication involves breaking down the numbers by each digit and then adding up the results. Let me try to recall the exact process.
First, I should w... | The solution to the long multiplication equation \(8274 \times 3529\) is calculated as follows:
1. **Break down the multiplication by each digit of 3529:**
- **Ones place (9):**
\(8274 \times 9 = 74{,}466\)
- **Tens place (2, shifted one position left):**
\(8274 \times 2 = 16{,}548 \rightarrow 165{... | true | The solution accurately follows the steps of long multiplication and correctly sums the partial products to arrive at the final answer. The calculated answer matches the ground truth solution of 29198946. | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "Okay, so I need to multiply 8274 by 3529. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this step by step. I remember that long multiplication involves breaking down the numbers by each digit and then adding up the results. ... | 1,216 | 1,216 | 0 | 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 ca... | [
"29,198,946",
"29,198,946",
"29,198,946"
] | null | 6 | 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.
1. The model performs 8274 x 9 and writes down the step-by-step multiplication with carrying, arriving at 74,466. This is a... | [
"Wait, maybe breaking it down more clearly: 74,466 + 165,480 addition verification.",
"Adding 4,376,946 + 24,822,000 with careful step-by-step rechecking.",
"Let me recheck the partial products: First partial product: 8274 x 9 ...",
"Second partial product: 8274 x 2 ...",
"Third partial product: 8274 x 5 ..... | null | 3 | 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... | [
"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this step by step. I remember that long multiplication involves breaking down the numbers by each digit and then adding up the results. Let me try to recall the exact process.",
"Wait, let me verify this with another method to be... | null |
"What is the solution to the long multiplication equation below?\n\n9341 x 4130\n\nThink step by ste(...TRUNCATED) | 38578330 | "Okay, so I need to solve 9341 multiplied by 4130. Hmm, let me think about how to approach this. I r(...TRUNCATED) | "The solution to the long multiplication equation 9341 × 4130 is calculated as follows:\n\n1. **Bre(...TRUNCATED) | true | "The calculations presented in the solution are accurate, and the final result matches the ground tr(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to solve 9341 multiplied by 4130. Hmm, le(...TRUNCATED) | 929 | 936 | 7 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 1 | 4 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"38,578,330",
"38,578,330",
"38,578,330",
"38,578,330"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Wait, no, that's not right. Wait, 93,410 is 90,000 + 3,410. So adding 3,736,400 + 90,000 = 3,826,4(...TRUNCATED) | null | 4 | "To answer your question\u00151 how many times does the model verify its higher-level reasoning (i.e(...TRUNCATED) | ["\"Hmm, let me think about how to approach this. I remember that multiplying large numbers can be b(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n6637 x 5510\n\nThink step by ste(...TRUNCATED) | 36569870 | "Okay, so I need to multiply 6637 by 5510. Hmm, let's see. I remember that long multiplication invol(...TRUNCATED) | "To solve the long multiplication equation \\(6637 \\times 5510\\), we can break down the process in(...TRUNCATED) | true | "The solution provided calculates the product of 6637 and 5510 accurately by breaking down the multi(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 6637 by 5510. Hmm, let's see.(...TRUNCATED) | 878 | 1,300 | 422 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 2 | 7 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"36569870",
"36569870",
"36569870",
"36569870",
"36569870",
"36569870",
"36569870"
] | null | 6 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that again to make sure I didn't make a mistake in addition.\"","\"Let me ver(...TRUNCATED) | null | 2 | "To answer your question\u0002013 how many times does the model verify its higher-level reasoning (i(...TRUNCATED) | ["\"But wait, 5510 has a zero at the end. That might make things a bit simpler because multiplying b(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n5086 x 6642\n\nThink step by ste(...TRUNCATED) | 33781212 | "Okay, so I need to multiply 5086 by 6642. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(5086 \\times 6642\\), we break down the multiplication(...TRUNCATED) | true | "The provided solution correctly implements the long multiplication method. Each step of the multipl(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 5086 by 6642. Hmm, that's a p(...TRUNCATED) | 1,623 | 2,657 | 1,034 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 3 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"33781212",
"33781212",
"33781212"
] | null | 7 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that again step by step: ... So 5086 x 2 = 10172. That seems right.\"","\"Wai(...TRUNCATED) | null | 7 | "To answer your question\t64how many times does the model verify its higher-level reasoning (i.e., d(...TRUNCATED) | ["Usually, the larger number is on top, but since both are four-digit numbers, maybe it doesn't matt(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n8996 x 8373\n\nThink step by ste(...TRUNCATED) | 75323508 | "Okay, so I need to multiply 8996 by 8373. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(8996 \\times 8373\\), we break down the multiplication(...TRUNCATED) | true | "The solution correctly calculates the product of 8996 and 8373 using both the long multiplication m(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 8996 by 8373. Hmm, that's a p(...TRUNCATED) | 1,005 | 1,302 | 297 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 4 | 4 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"75323508",
"75323508",
"75323508",
"75323508"
] | null | 10 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that again. 8996 x 7: Starting from the right: 6*7=42, carryover 4. 9*7=63 +4(...TRUNCATED) | null | 4 | "To answer your question\u00020\u0002how many times does the model verify its higher-level reasoning(...TRUNCATED) | ["\"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this.\"","\"(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n9275 x 6116\n\nThink step by ste(...TRUNCATED) | 56725900 | "Okay, so I need to multiply 9275 by 6116. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(9275 \\times 6116\\), we can break down the multiplier(...TRUNCATED) | true | "The solution correctly breaks down the multiplication of 9275 by each part of 6116, calculates each(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 9275 by 6116. Hmm, that's a p(...TRUNCATED) | 1,177 | 1,617 | 440 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 5 | 5 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"56725900",
"56725900",
"56725900",
"56725900",
"56725900"
] | null | 2 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Wait, let me check that addition again to make sure I didn't make a mistake.","Compute 9275 x 16: (...TRUNCATED) | null | 7 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this.\"","\"(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n1556 x 1996\n\nThink step by ste(...TRUNCATED) | 3105776 | "Okay, so I need to multiply 1556 by 1996. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(1556 \\times 1996\\), we can use the distributive prop(...TRUNCATED) | true | "The solution correctly applies the distributive property to simplify the multiplication, accurately(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 1556 by 1996. Hmm, that's a p(...TRUNCATED) | 961 | 1,026 | 65 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 5 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"3105776",
"3105776",
"3105776",
"3105776",
"3105776"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that subtraction again to be sure.\" (rechecking subtraction 3,112,000 - 6,22(...TRUNCATED) | null | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, that's a pretty big multiplication problem. Let me think about the best way to approach this.(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n3622 x 5165\n\nThink step by ste(...TRUNCATED) | 18707630 | "Okay, so I need to multiply 3622 by 5165. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(3622 \\times 5165\\), we can break down the multiplier(...TRUNCATED) | true | "The provided solution correctly performs the long multiplication of 3622 and 5165 by breaking down (...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 3622 by 5165. Hmm, that's a p(...TRUNCATED) | 875 | 1,636 | 761 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 7 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"18707630",
"18707630",
"18707630",
"18707630",
"18707630",
"18707630",
"18707630"
] | null | 2 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that addition again to make sure I didn't make a mistake. So starting with 18(...TRUNCATED) | null | 16 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this step by(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n6624 x 7409\n\nThink step by ste(...TRUNCATED) | 49077216 | "Okay, so I need to multiply 6624 by 7409. Hmm, that's a pretty big multiplication. Let me think abo(...TRUNCATED) | "To solve the long multiplication equation \\(6624 \\times 7409\\), we break down the multiplication(...TRUNCATED) | true | "The breakdown of the multiplication is accurately executed, and the final sum of the products yield(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 6624 by 7409. Hmm, that's a p(...TRUNCATED) | 1,346 | 2,091 | 745 | 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) | [
"49077216",
"49077216"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["'Wait, no, 26,496 with two zeros is 2,649,600? Wait, 26,496 x 100 = 2,649,600. Yes, that's correct(...TRUNCATED) | null | 2 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Let me verify this with another method to make sure I didn't make a mistake. Maybe using the stand(...TRUNCATED) | null |
"What is the solution to the long multiplication equation below?\n\n2861 x 2656\n\nThink step by ste(...TRUNCATED) | 7598816 | "Okay, so I need to multiply 2861 by 2656. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(2861 \\times 2656\\), we break down the multiplication(...TRUNCATED) | true | "The solution correctly breaks down the long multiplication into manageable parts, accurately calcul(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 2861 by 2656. Hmm, that's a p(...TRUNCATED) | 921 | 1,466 | 545 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 5 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"7598816",
"7598816",
"7598816",
"7598816",
"7598816"
] | null | 8 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, 6 is in the hundreds place, so it's actually 600 x 2861. So, 6 x 2861 is 17166, then times(...TRUNCATED) | null | 9 | "To answer your question\u0002014 how many times does the model verify its higher-level reasoning (i(...TRUNCATED) | ["\"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I reme(...TRUNCATED) | null |
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