question stringlengths 97 97 | solution stringlengths 7 8 | eval_internal_cot stringlengths 2.45k 37.4k | eval_solution stringlengths 319 2.33k | judge_correct bool 2
classes | judge_reasoning stringlengths 84 596 | repo stringclasses 1
value | behavior_prompt stringlengths 4.47k 43.1k | behavior_type stringclasses 1
value | behavior_spans listlengths 5 88 | new_behavior_span_count int64 0 32 | behavior_count int64 5 88 |
|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
3333 x 6350
Think step by step. | 21164550 | Okay, so I need to solve 3333 multiplied by 6350. Hmm, let me think about how to approach this. Long multiplication can be a bit tricky with such large numbers, but maybe breaking it down into smaller parts will help.
First, I remember that multiplying by a number like 6350 is the same as multiplying by 635 and then ... | The solution to the long multiplication equation 3333 × 6350 is calculated as follows:
1. **Break down 6350** into components:
- \( 6350 = 6000 + 300 + 50 \)
2. **Multiply 3333 by each component**:
- \( 3333 \times 6000 = 19,998,000 \)
- \( 3333 \times 300 = 999,900 \)
- \( 3333 \times 50 = 166,65... | true | The calculations for each component multiplication are correct, and when combined they give the same result as confirmed by the ground truth solution. The final answer matches the ground truth. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
3333 x 6350
Think step by step.
## Here is the solution
21164550
## Here are the current task instructions
Count ... | verification | [
{
"end_idx": 1591,
"explanation": "The model briefly steps back to reconsider its previous addition, indicating a moment of self-verification.",
"idx": 0,
"span": "Wait, let me check that addition again. Maybe I made a mistake.",
"start_idx": 1528
},
{
"end_idx": 1790,
"explanation":... | 0 | 5 |
What is the solution to the long multiplication equation below?
2298 x 1579
Think step by step. | 3628542 | Okay, so I need to multiply 2298 by 1579. Hmm, that's a pretty big multiplication. Let me think about how to approach this. I remember that long multiplication involves breaking down the numbers by place value and multiplying each part separately before adding them up. Let me start by writing down the numbers:
2298... | To solve the long multiplication equation \(2298 \times 1579\), we break down the multiplication into smaller parts based on place values and then sum the results.
1. **Multiply by 1000 (thousands place):**
\[
2298 \times 1000 = 2,298,000
\]
2. **Multiply by 500 (hundreds place):**
\[
2298 \times 500 =... | true | The solution method is correct and the final result of the multiplication is accurately computed as 3628542, which matches the ground truth solution. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
2298 x 1579
Think step by step.
## Here is the solution
3628542
## Here are the current task instructions
Count h... | verification | [
{
"end_idx": 2435,
"explanation": "This statement indicates the model is rechecking its addition to validate correctness.",
"idx": 0,
"span": "Let me check that addition again to make sure I didn't make a mistake.",
"start_idx": 2365
},
{
"end_idx": null,
"explanation": "The model is... | 0 | 6 |
What is the solution to the long multiplication equation below?
8365 x 7965
Think step by step. | 66627225 | Okay, so I need to multiply 8365 by 7965. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for long multiplication, you break it down into smaller parts, multiplying each digit and then adding up the results. But with numbers this large, that might take a while. ... | To solve the long multiplication equation \(8365 \times 7965\), we can break down the problem using the distributive property and then sum the results. Here are the key steps:
1. **Break down 7965 into components**:
- \(7965 = 7000 + 900 + 60 + 5\)
2. **Multiply 8365 by each component**:
- \(8365 \times 7000\):... | true | The solution provided accurately follows the distributive property and correctly performs the long multiplication, breaking down the numbers correctly and summing the results accordingly. Verification through an alternative method corroborates the final result, which matches the ground truth solution exactly. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
8365 x 7965
Think step by step.
## Here is the solution
66627225
## Here are the current task instructions
Count ... | verification | [
{
"end_idx": 1144,
"explanation": "The model expresses doubt and decides to recheck its previous calculation.",
"idx": 0,
"span": "Wait, let me check that again.",
"start_idx": 1114
},
{
"end_idx": 1667,
"explanation": "The model reassesses the result and corrects itself after re-eva... | 0 | 12 |
What is the solution to the long multiplication equation below?
1834 x 5854
Think step by step. | 10736236 | Okay, so I need to multiply 1834 by 5854. 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 place value and then adding up the results. Let me try to recall the exact process.
First, I should ... | To solve the long multiplication equation \(1834 \times 5854\), we break down the process step by step:
1. **Multiply 1834 by each digit of 5854, considering place value:**
- **Units place (4):**
\[
1834 \times 4 = 7336
\]
- **Tens place (5):**
\[
1834 \times 5 = 9170 \quad (\text{shifte... | true | The solution correctly carried out the steps of long multiplication, breaking down the multiplication into partial products for each digit, and accurately summing those products, yielding the correct final result of 10736236. The ground truth matches the calculated result. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
1834 x 5854
Think step by step.
## Here is the solution
10736236
## Here are the current task instructions
Count ... | verification | [
{
"end_idx": 2431,
"explanation": "The model checks its understanding of the multiplication process and reiterates that shifting corresponds to multiplying by 10.",
"idx": 0,
"span": "Let me confirm: Yes, because the 5 is in the tens place, so it's 50, but we're multiplying 5 first and then shifting... | 0 | 8 |
What is the solution to the long multiplication equation below?
6009 x 5460
Think step by step. | 32809140 | Okay, so I need to solve 6009 multiplied by 5460. Hmm, let's see. I remember that long multiplication involves breaking down the numbers into smaller parts, multiplying each part, and then adding up the results. But since both numbers are pretty large, maybe there's a smarter way to do this without getting lost in the ... | To solve the long multiplication equation \(6009 \times 5460\), we can break down the problem using the distributive property and simplify the calculations by recognizing that multiplying by 5460 is equivalent to multiplying by 546 and then by 10.
1. **Break down 5460 into 546 and 10**:
\[
6009 \times 5460 = 600... | true | The provided solution correctly calculates the product of 6009 and 5460 using both the distributive property and standard long multiplication. The final result of 32809140 matches the ground truth solution. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
6009 x 5460
Think step by step.
## Here is the solution
32809140
## Here are the current task instructions
Count ... | verification | [
{
"end_idx": 510,
"explanation": "The model is re-evaluating its chosen method and considering alternatives.",
"idx": 0,
"span": "Wait, but that might still be complicated.",
"start_idx": 468
},
{
"end_idx": 624,
"explanation": "The model is confirming its factorization of 5460.",
... | 0 | 15 |
What is the solution to the long multiplication equation below?
1720 x 4837
Think step by step. | 8319640 | Okay, so I need to multiply 1720 by 4837. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that long multiplication involves breaking down the numbers into their place values and multiplying each part separately before adding them all up. Let me try to recall the step... | To solve the long multiplication equation \(1720 \times 4837\), we can break down the numbers using the distributive property and then sum the results. Here are the key steps:
1. **Break down the numbers**:
\[
1720 \times 4837 = (1700 + 20) \times (4000 + 800 + 30 + 7)
\]
2. **Multiply each term**:
\[
... | true | The provided solution correctly applies the distributive property of multiplication, calculates all intermediate products accurately, sums them correctly, and verifies the result with standard long multiplication, arriving at the same final result as the ground truth. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
1720 x 4837
Think step by step.
## Here is the solution
8319640
## Here are the current task instructions
Count h... | verification | [
{
"end_idx": 3424,
"explanation": "The model explicitly states it is verifying its calculations, indicating self verification.",
"idx": 0,
"span": "Wait, let me verify this because it's easy to make a mistake in such a large calculation.",
"start_idx": 3335
},
{
"end_idx": null,
"exp... | 0 | 14 |
What is the solution to the long multiplication equation below?
6686 x 8827
Think step by step. | 59017322 | Okay, so I need to multiply 6686 by 8827. 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 place value and then adding up the results. Let me try to recall the exact process.
First, I can wri... | To solve the long multiplication equation \(6686 \times 8827\), we break down the process step by step:
1. **Multiply 6686 by each digit of 8827, considering place values:**
- **Multiply by 7 (ones place):**
\[
6686 \times 7 = 46802
\]
- **Multiply by 2 (tens place, shifted one position left):**
... | true | The calculated product of 6686 and 8827 matches the ground truth solution. The calculations of each step, including the multiplication and addition of partial products, have been executed correctly. Therefore, the solution is accurate. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
6686 x 8827
Think step by step.
## Here is the solution
59017322
## Here are the current task instructions
Count ... | verification | [
{
"end_idx": 1191,
"explanation": "This snippet indicates the model is stopping to review and verify its calculations of multiplying by 7.",
"idx": 0,
"span": "Wait, let me check that again. Starting from the right:",
"start_idx": 1136
},
{
"end_idx": 1365,
"explanation": "This confi... | 0 | 10 |
What is the solution to the long multiplication equation below?
3592 x 1116
Think step by step. | 4008672 | Okay, so I need to multiply 3592 by 1116. Hmm, that's a pretty big multiplication. Let me think about how to approach this. I remember that long multiplication involves breaking down the numbers into their place values and multiplying each part separately before adding them all up. Let me try to recall the steps proper... | To solve the long multiplication equation \(3592 \times 1116\), we break down the multiplication into smaller steps and sum the partial products.
1. **Multiply 3592 by 6 (units place):**
\[
\begin{array}{r}
3592 \\
\times \quad 6 \\
\hline
21552 \\
\end{array}
\]
2. **Multiply 3592 by 1 (t... | true | The solution correctly calculates the multiplication of 3592 by 1116 through step-by-step long multiplication, producing the correct final sum of the partial products, equaling 4008672. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
3592 x 1116
Think step by step.
## Here is the solution
4008672
## Here are the current task instructions
Count h... | verification | [
{
"end_idx": 1726,
"explanation": "This indicates the model is taking a moment to confirm its previous calculation regarding the tens place.",
"idx": 0,
"span": "But wait, let me verify.",
"start_idx": 1702
},
{
"end_idx": 2954,
"explanation": "The model is checking its earlier addit... | 0 | 15 |
What is the solution to the long multiplication equation below?
8509 x 6410
Think step by step. | 54542690 | Okay, so I need to multiply 8509 by 6410. Hmm, let's see. I remember that long multiplication involves breaking down the numbers into their place values and multiplying each part separately before adding them all up. Let me try to recall the exact steps.
First, maybe I should write down the two numbers vertically, ali... | To solve the long multiplication equation \(8509 \times 6410\), we can break down the multiplication into smaller steps and then sum the results. Here's the detailed process:
1. **Multiply 8509 by each digit of 6410, considering the place value shifts:**
- **Ones place (0):** \(8509 \times 0 = 0\)
- **Tens place... | true | The detailed steps of the multiplication were correctly executed, and the final computed result matches the ground truth solution exactly. | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | 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?
8509 x 6410
Think step by step.
## Here is the solution
54542690
## Here are the current task instructions
Count ... | verification | [
{
"end_idx": 612,
"explanation": "The model pauses to confirm its previous multiplication approach.",
"idx": 0,
"span": "Let me check that.",
"start_idx": 594
},
{
"end_idx": null,
"explanation": "The model expresses doubt and intends to double-check the accuracy of its calculations.... | 0 | 7 |
"What is the solution to the long multiplication equation below?\n\n2126 x 6425\n\nThink step by ste(...TRUNCATED) | 13659550 | "Okay, so I need to multiply 2126 by 6425. Hmm, that's a pretty big multiplication. Let me think abo(...TRUNCATED) | "The solution to the long multiplication equation \\(2126 \\times 6425\\) is calculated as follows:\(...TRUNCATED) | true | "The solution correctly follows the process of long multiplication by breaking down the multiplicati(...TRUNCATED) | TAUR-dev/evals__long_multiplication__four_digit__train__r1 | "An LLM was asked a question and we want to see if it used self verification as a reasoning strategy(...TRUNCATED) | verification | [{"end_idx":1340,"explanation":"The model is pausing to verify the previous multiplication steps.","(...TRUNCATED) | 0 | 10 |
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