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question stringclasses 10 values	solution stringclasses 10 values	eval_solution stringclasses 10 values	judge_correct bool 2 classes	judge_reasoning stringclasses 10 values	rewritten_eval_solution stringclasses 10 values	modified bool 2 classes	repo stringclasses 1 value	behavior_prompt stringlengths 2.56k 8.97k	behavior_type stringclasses 3 values	behavior_spans listlengths 0 21	behavior_count int64 0 21
What is the solution to the long multiplication equation below? 3063 x 1377 Think step by step.	4217751	### Understanding the Problem First, I need to multiply two large numbers: 3063 and 1377. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multipl...	true	The solution thoroughly breaks down the multiplication of two large numbers using the distributive property, calculates each partial product correctly, sums them accurately, and verifies the final result using standard multiplication. The final answer matches the ground truth (4217751). Therefore, the solution is corre...	### Understanding the Problem First, I need to multiply two large numbers: 3063 and 1377. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multipl...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3063 x 1377 Think step by step. ## Here is the solution 4217751 ## Here are the current task instructions Count how ma...	backtracking	[]	0
What is the solution to the long multiplication equation below? 7657 x 6641 Think step by step.	50850137	To solve the multiplication problem \( 7657 \times 6641 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 7657 \) by each digit of \( 6641 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{al...	false	The solution provided arrives at the total of 50,862,137 for the multiplication of 7657 and 6641. However, the ground truth solution states that the correct answer is 50,850,137. This indicates that there is an error in the addition of the partial results in the solution, confirming that the solution is incorrect.	To solve the multiplication problem \( 7657 \times 6641 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 7657 \) by each digit of \( 6641 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{al...	false	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 7657 x 6641 Think step by step. ## Here is the solution 50850137 ## Here are the current task instructions Count ...	verification	[]	0
What is the solution to the long multiplication equation below? 7657 x 6641 Think step by step.	50850137	To solve the multiplication problem \( 7657 \times 6641 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 7657 \) by each digit of \( 6641 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{al...	false	The solution provided arrives at the total of 50,862,137 for the multiplication of 7657 and 6641. However, the ground truth solution states that the correct answer is 50,850,137. This indicates that there is an error in the addition of the partial results in the solution, confirming that the solution is incorrect.	To solve the multiplication problem \( 7657 \times 6641 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 7657 \) by each digit of \( 6641 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{al...	false	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 7657 x 6641 Think step by step. ## Here is the solution 50850137 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 9857 x 4502 Think step by step.	44376214	### Understanding the Problem First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9857 and 4502. The goal is to find the product of these two numbers. Since both numbers are four-digit, the standard long multiplication method seems appropriate. ### Breaking Down the Mul...	true	The solution correctly applies long multiplication and verification techniques, resulting in the correct final product of 44,376,214.	### Understanding the Problem First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9857 and 4502. The goal is to find the product of these two numbers. Since both numbers are four-digit, the standard long multiplication method seems appropriate. ### Breaking Down the Mul...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 9857 x 4502 Think step by step. ## Here is the solution 44376214 ## Here are the current task instructions Count ...	verification	[]	0
What is the solution to the long multiplication equation below? 9857 x 4502 Think step by step.	44376214	### Understanding the Problem First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9857 and 4502. The goal is to find the product of these two numbers. Since both numbers are four-digit, the standard long multiplication method seems appropriate. ### Breaking Down the Mul...	true	The solution correctly applies long multiplication and verification techniques, resulting in the correct final product of 44,376,214.	### Understanding the Problem First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9857 and 4502. The goal is to find the product of these two numbers. Since both numbers are four-digit, the standard long multiplication method seems appropriate. ### Breaking Down the Mul...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 9857 x 4502 Think step by step. ## Here is the solution 44376214 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 3764 x 9884 Think step by step.	37203376	To solve the long multiplication problem \( 3764 \times 9884 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3764 \) by each digit of \( 9884 \), starting from the rightmost digit, and then sum the partial results. ### Step 1: Break...	true	The solution computed correctly verifies that 3764 multiplied by 9884 equals 37,203,376. The result matches the ground truth given (37203376), considering it is simply formatted as a number without unnecessary leading zeros.	To solve the long multiplication problem \( 3764 \times 9884 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3764 \) by each digit of \( 9884 \), starting from the rightmost digit, and then sum the partial results. ### Step 1: Break...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3764 x 9884 Think step by step. ## Here is the solution 37203376 ## Here are the current task instructions Count ...	verification	[]	0
What is the solution to the long multiplication equation below? 3764 x 9884 Think step by step.	37203376	To solve the long multiplication problem \( 3764 \times 9884 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3764 \) by each digit of \( 9884 \), starting from the rightmost digit, and then sum the partial results. ### Step 1: Break...	true	The solution computed correctly verifies that 3764 multiplied by 9884 equals 37,203,376. The result matches the ground truth given (37203376), considering it is simply formatted as a number without unnecessary leading zeros.	To solve the long multiplication problem \( 3764 \times 9884 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3764 \) by each digit of \( 9884 \), starting from the rightmost digit, and then sum the partial results. ### Step 1: Break...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3764 x 9884 Think step by step. ## Here is the solution 37203376 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 2129 x 7692 Think step by step.	16376268	To solve the long multiplication equation \( 2129 \times 7692 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7692) by each digit of the first number (2129) and then summing the results. ### Step...	true	The solution correctly applies the distributive property of multiplication, breaks down the multiplication of 2129 and 7692 into manageable components, calculates each component accurately, sums them correctly, and arrives at the final result of 16376268, which matches the ground truth solution.	To solve the long multiplication equation \( 2129 \times 7692 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7692) by each digit of the first number (2129) and then summing the results. ### Step...	false	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 2129 x 7692 Think step by step. ## Here is the solution 16376268 ## Here are the current task instructions Count ...	verification	[]	0
What is the solution to the long multiplication equation below? 2129 x 7692 Think step by step.	16376268	To solve the long multiplication equation \( 2129 \times 7692 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7692) by each digit of the first number (2129) and then summing the results. ### Step...	true	The solution correctly applies the distributive property of multiplication, breaks down the multiplication of 2129 and 7692 into manageable components, calculates each component accurately, sums them correctly, and arrives at the final result of 16376268, which matches the ground truth solution.	To solve the long multiplication equation \( 2129 \times 7692 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7692) by each digit of the first number (2129) and then summing the results. ### Step...	false	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 2129 x 7692 Think step by step. ## Here is the solution 16376268 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 2533 x 4974 Think step by step.	12599142	To solve the long multiplication equation \(2533 \times 4974\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then summing all the partial products. ### Step ...	true	The solution correctly applies the distributive property to break down the multiplication of 2533 and 4974 into manageable parts, accurately calculates the partial products, and sums them to derive the final result. Both the final answer and the verification via long multiplication confirm that the solution is correct.	To solve the long multiplication equation \(2533 \times 4974\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then summing all the partial products. ### Step ...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 2533 x 4974 Think step by step. ## Here is the solution 12599142 ## Here are the current task instructions Count ...	verification	[]	0
What is the solution to the long multiplication equation below? 2533 x 4974 Think step by step.	12599142	To solve the long multiplication equation \(2533 \times 4974\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then summing all the partial products. ### Step ...	true	The solution correctly applies the distributive property to break down the multiplication of 2533 and 4974 into manageable parts, accurately calculates the partial products, and sums them to derive the final result. Both the final answer and the verification via long multiplication confirm that the solution is correct.	To solve the long multiplication equation \(2533 \times 4974\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then summing all the partial products. ### Step ...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 2533 x 4974 Think step by step. ## Here is the solution 12599142 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 4409 x 7586 Think step by step.	33446674	To solve the long multiplication equation \( 4409 \times 7586 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7586) by the first number (4409) and then summing the results. ### Step 1: Break down...	true	The final answer provided in the solution, 33,446,674, matches the ground truth solution of 33446674, confirming the correctness of the calculations.	To solve the long multiplication equation \( 4409 \times 7586 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7586) by the first number (4409) and then summing the results. ### Step 1: Break down...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4409 x 7586 Think step by step. ## Here is the solution 33446674 ## Here are the current task instructions Count ...	verification	[]	0
What is the solution to the long multiplication equation below? 4409 x 7586 Think step by step.	33446674	To solve the long multiplication equation \( 4409 \times 7586 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7586) by the first number (4409) and then summing the results. ### Step 1: Break down...	true	The final answer provided in the solution, 33,446,674, matches the ground truth solution of 33446674, confirming the correctness of the calculations.	To solve the long multiplication equation \( 4409 \times 7586 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7586) by the first number (4409) and then summing the results. ### Step 1: Break down...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4409 x 7586 Think step by step. ## Here is the solution 33446674 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 9773 x 6841 Think step by step.	66857093	### Understanding the Problem First, I need to multiply two large numbers: 9773 and 6841. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts should make it easier. I recall that long multiplication involves multiplying e...	true	The solution explains the long multiplication method correctly, lays out steps clearly, performs each multiplication correctly, and accurately adds up the results. The final answer of 66,857,093 matches the ground truth solution.	### Understanding the Problem First, I need to multiply two large numbers: 9773 and 6841. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts should make it easier. I recall that long multiplication involves multiplying e...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 9773 x 6841 Think step by step. ## Here is the solution 66857093 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 4426 x 5549 Think step by step.	24559874	### Understanding the Problem First, I need to multiply two large numbers: 4426 and 5549. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. ### Breaking Down the Multiplication: The Distrib...	true	The provided solution correctly calculates the multiplication of 4426 and 5549, arriving at the final result of 24,559,874 through various verification methods. Each step in the breakdown process aligns with standard multiplication rules, ensuring the accuracy of the answer.	### Understanding the Problem First, I need to multiply two large numbers: 4426 and 5549. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. ### Breaking Down the Multiplication: The Distrib...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used backtracking as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4426 x 5549 Think step by step. ## Here is the solution 24559874 ## Here are the current task instructions Count how m...	backtracking	[]	0
What is the solution to the long multiplication equation below? 3063 x 1377 Think step by step.	4217751	### Understanding the Problem First, I need to multiply two large numbers: 3063 and 1377. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multipl...	true	The solution thoroughly breaks down the multiplication of two large numbers using the distributive property, calculates each partial product correctly, sums them accurately, and verifies the final result using standard multiplication. The final answer matches the ground truth (4217751). Therefore, the solution is corre...	### Understanding the Problem First, I need to multiply two large numbers: 3063 and 1377. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multipl...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3063 x 1377 Think step by step. ## Here is the solution 4217751 ## Here are the current task instructions Count h...	verification	[ { "end_idx": 2335, "explanation": "This indicates the model is verifying that it has correctly summed all the parts to reach the final total.", "idx": 0, "span": "Now, I add all the partial products obtained from each step:", "start_idx": 2275 } ]	1
What is the solution to the long multiplication equation below? 7657 x 6641 Think step by step.	50850137	To solve the multiplication problem \( 7657 \times 6641 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 7657 \) by each digit of \( 6641 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{al...	false	The solution provided arrives at the total of 50,862,137 for the multiplication of 7657 and 6641. However, the ground truth solution states that the correct answer is 50,850,137. This indicates that there is an error in the addition of the partial results in the solution, confirming that the solution is incorrect.	To solve the multiplication problem \( 7657 \times 6641 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 7657 \) by each digit of \( 6641 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{al...	false	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it creates and uses sub-goals as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 7657 x 6641 Think step by step. ## Here is the solution 50850137 ## Here are the current task instructions Co...	subgoals	[ { "end_idx": 182, "explanation": "This snippet shows the model setting a sub-goal to break down the multiplication process.", "idx": 0, "span": "Break down the multiplication", "start_idx": 153 }, { "end_idx": null, "explanation": "This indicates an intention to treat the multiplicat...	6
What is the solution to the long multiplication equation below? 3764 x 9884 Think step by step.	37203376	To solve the long multiplication problem \( 3764 \times 9884 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3764 \) by each digit of \( 9884 \), starting from the rightmost digit, and then sum the partial results. ### Step 1: Break...	true	The solution computed correctly verifies that 3764 multiplied by 9884 equals 37,203,376. The result matches the ground truth given (37203376), considering it is simply formatted as a number without unnecessary leading zeros.	To solve the long multiplication problem \( 3764 \times 9884 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3764 \) by each digit of \( 9884 \), starting from the rightmost digit, and then sum the partial results. ### Step 1: Break...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it creates and uses sub-goals as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3764 x 9884 Think step by step. ## Here is the solution 37203376 ## Here are the current task instructions Co...	subgoals	[ { "end_idx": 163, "explanation": "The model sets a sub-goal of breaking down the problem step by step.", "idx": 0, "span": "we'll break it down step by step using the distributive property of multiplication over addition", "start_idx": 65 }, { "end_idx": null, "explanation": "The mod...	6
What is the solution to the long multiplication equation below? 2533 x 4974 Think step by step.	12599142	To solve the long multiplication equation \(2533 \times 4974\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then summing all the partial products. ### Step ...	true	The solution correctly applies the distributive property to break down the multiplication of 2533 and 4974 into manageable parts, accurately calculates the partial products, and sums them to derive the final result. Both the final answer and the verification via long multiplication confirm that the solution is correct.	To solve the long multiplication equation \(2533 \times 4974\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then summing all the partial products. ### Step ...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it creates and uses sub-goals as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 2533 x 4974 Think step by step. ## Here is the solution 12599142 ## Here are the current task instructions Co...	subgoals	[ { "end_idx": 152, "explanation": "This is a clear indication that the model is setting a sub-goal to use a specific multiplication property for the calculations.", "idx": 0, "span": "We'll break it down using the distributive property of multiplication over addition.", "start_idx": 64 }, ...	4
What is the solution to the long multiplication equation below? 4409 x 7586 Think step by step.	33446674	To solve the long multiplication equation \( 4409 \times 7586 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7586) by the first number (4409) and then summing the results. ### Step 1: Break down...	true	The final answer provided in the solution, 33,446,674, matches the ground truth solution of 33446674, confirming the correctness of the calculations.	To solve the long multiplication equation \( 4409 \times 7586 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7586) by the first number (4409) and then summing the results. ### Step 1: Break down...	true	TAUR-dev/lmfd__no_verification_v3__train	An LLM was asked a question and we want to see if it creates and uses sub-goals as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4409 x 7586 Think step by step. ## Here is the solution 33446674 ## Here are the current task instructions Co...	subgoals	[ { "end_idx": 167, "explanation": "This statement establishes an intention to decompose the problem, setting a sub-goal of clarifying how the multiplication will be tackled.", "idx": 0, "span": "we'll break it down step by step using the distributive property of multiplication over addition.", ...	6

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