doc_id int64 | doc dict | target string | arguments dict | resps list | filtered_resps list | doc_hash string | prompt_hash string | target_hash string | exact_match int64 | extracted_answers list | source_file string | model_name string | measurement_answer_verification_reasoning string | measurement_answer_verification_final_count int64 | measurement_answer_verification_metadata list | measurement_answer_verification_raw_response string | metadata_answers_correct list | metadata_answers_correct_judge_data list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | {
"answer": "6956",
"args": [
"74",
"94"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 6956 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n94 x 74\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 94 \\times 74 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n 94 & \\times 74 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 94 by 4 (the units digit of 74... | [
"To solve the long multiplication equation \\( 94 \\times 74 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n 94 & \\times 74 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 94 by 4 (the units digit of 74):**\n... | 3506920013cb62a6063a9cafecd1e30d93ef201299844c139689e60654805de5 | 95bbc2cb45309aa5d9c1587d3aae09db449d9e60fa67b1df723146901666a85f | 5edcf3b4d5f63d095b027a02182f2783e2bcdb36e2d8210617364fcce9da2df1 | 0 | [
"6616"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "The final result is 6616." This counts as the first proposal. 2. The next verification occurs when the model states: "Wait, how? I thought that I couldn't just change it to 6416 because of the carry-over." This indicates a need to verify the previous a... | 4 | [
"6616",
"6616",
"6616",
"6616"
] | [
false,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 94 and 74, we can break it down step by step:\n\n1. Multiply 94 by 4 (the units digit of 74):\n - 94 x 4 = 376\n\n2. Multiply 94 by 7 (the tens digit of 74), remembering to shift one position to the left (which is equivalent to multiplying ... | |
1 | {
"answer": "1271",
"args": [
"31",
"41"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1271 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n31 x 41\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(31 \\times 41\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. **Distribute the numbers:**\n \\[\n 31 \\times 41 = 31 \\times (40 + 1)\n \\]\n\n2. **Apply the distributive property:**\n \... | [
"To solve the long multiplication equation \\(31 \\times 41\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. **Distribute the numbers:**\n \\[\n 31 \\times 41 = 31 \\times (40 + 1)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n ... | a03e77b4cb35931279477ff67396bc4a30dd956e4376ed814c5f139dabb56ad7 | 8ccb2b6f30da4efcddbed56c09a1595fb49ccf928c02535a6102acad362a5369 | efbd1f26a54875e39972ccf7fa21a34f2491c850b2eba9636cb5478e595897b5 | 1 | [
"1271"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 31 x 41 is \(\boxed{1271}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1271"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 31 and 41, we can break it down step by step:\n\n1. Multiply 31 by 1 (the units digit of 41):\n 31 x 1 = 31\n\n2. Multiply 31 by 4 (the tens digit of 41), remembering to shift one position to the left (add a zero):\n 31 x 4 = 124, which be... | |
2 | {
"answer": "1271",
"args": [
"31",
"41"
],
"is_model_response_correct": [
false,
false,
true,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 1271 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n41 x 31\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(41 \\times 31\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Write down the numbers and align them vertically:\n \\[\n \\begin{array}{r}\n 41 \\\\\n \\times 31 \\\\... | [
"To solve the long multiplication equation \\(41 \\times 31\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Write down the numbers and align them vertically:\n \\[\n \\begin{array}{r}\n 41 \\\\\n \\times 31 \\\\\n \... | 9a95e2b6f770ad1cddc0aa76c9beb5950853c9798bc4d80e3f181e6ecf6fd8fd | 83963bc97deb94d50fa072fa21434d6a74eb6ddb6d3ab2d720629c492c0529c1 | efbd1f26a54875e39972ccf7fa21a34f2491c850b2eba9636cb5478e595897b5 | 1 | [
"1271"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 41 x 31 is 1271." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1271"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 41 and 31, we can break it down step by step:\n\n1. Multiply 41 by 1 (the units digit of 31):\n 41 x 1 = 41\n\n2. Multiply 41 by 3 (the tens digit of 31), remembering to shift one position to the left (which is equivalent to multiplying by 3... | |
3 | {
"answer": "3072",
"args": [
"48",
"64"
],
"is_model_response_correct": [
false,
true,
false,
true,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 3072 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n48 x 64\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(48 \\times 64\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 48 by 4 (the units digit of 64):**\n \\[\n 48 \\times 4 = 192\n \\]\n\n2. **Multiply 48 by 6 (the tens digit of 64, which is 60) an... | [
"To solve the long multiplication equation \\(48 \\times 64\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 48 by 4 (the units digit of 64):**\n \\[\n 48 \\times 4 = 192\n \\]\n\n2. **Multiply 48 by 6 (the tens digit of 64, which is 60) and shif... | e94a268416eba9204077a4688b5c7a1c98b71008bf6bfbee08af69f977ba8d4d | 3e1a83ac555f8f02c464e007ce67804d680f398c1ab871c272c6c03f431d591b | 82147211de4c4b846e2cf7a2edac668990dff673d07bebcb2c9eae6aeb2c5963 | 1 | [
"3072"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 48 x 64 is \(\boxed{3072}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"3072"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 48 and 64, we can break it down step by step:\n\n1. First, we can multiply 48 by 64 directly:\n - 48 x 64 = 3072.\n\n2. We can also verify this by breaking it down further:\n - 48 can be expressed as (40 + 8).\n - Therefore, 48 x 64 = (4... | |
4 | {
"answer": "3072",
"args": [
"48",
"64"
],
"is_model_response_correct": [
false,
true,
true,
true,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ab... | 3072 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n48 x 64\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(48 \\times 64\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 48 by 4 (the units digit of 64):**\n \\[\n 48 \\times 4 = 192\n \\]\n\n2. **Multiply 48 by 6 (the tens digit of 64, which is 60) an... | [
"To solve the long multiplication equation \\(48 \\times 64\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 48 by 4 (the units digit of 64):**\n \\[\n 48 \\times 4 = 192\n \\]\n\n2. **Multiply 48 by 6 (the tens digit of 64, which is 60) and shif... | 505329ab00a3c8d1267202bf0a03ebc9ca63b3e9656552959bcdedf7c17958b3 | 3e1a83ac555f8f02c464e007ce67804d680f398c1ab871c272c6c03f431d591b | 82147211de4c4b846e2cf7a2edac668990dff673d07bebcb2c9eae6aeb2c5963 | 1 | [
"3072"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 48 x 64 is \(\boxed{3072}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"3072"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the solution, we can perform the long multiplication of 48 and 64 step by step:\n\n1. Multiply 48 by 4 (the units digit of 64):\n - 48 x 4 = 192\n\n2. Multiply 48 by 6 (the tens digit of 64), remembering to shift one position to the left (add a zero):\n - 48 x ... | |
5 | {
"answer": "4554",
"args": [
"66",
"69"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 4554 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n69 x 66\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 69 \\times 66 \\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 69 by 6 (the units digit of 66):**\n \\[\n 69 \\times 6 = 414\n \\]\n\n2. **Multiply 69 by 60 (the tens digit of 66, which is 60):*... | [
"To solve the long multiplication equation \\( 69 \\times 66 \\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 69 by 6 (the units digit of 66):**\n \\[\n 69 \\times 6 = 414\n \\]\n\n2. **Multiply 69 by 60 (the tens digit of 66, which is 60):**\n ... | e0638cb89d49ee49ea55a3ad9ca7ddd6170637d72a47920527a3953f355edb16 | d28934273dc1d0c80c02161e1d0758e36d4c7f9797250ca7b1d5b70647a66931 | c59ba22287efed2c760a4823f839d75e55aca4cde59995e7f0ca4a69719c66ba | 1 | [
"4554"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 69 x 66 is \(\boxed{4554}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"4554"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 69 and 66, we can break it down step by step:\n\n1. Multiply 69 by 6 (the units digit of 66):\n - 69 x 6 = 414\n\n2. Multiply 69 by 60 (the tens digit of 66, which is 6, but we treat it as 60):\n - 69 x 60 = 4140\n\n3. Now, add the two res... | |
6 | {
"answer": "754",
"args": [
"13",
"58"
],
"is_model_response_correct": [
false,
false,
false,
true,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ab... | 754 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n58 x 13\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(58 \\times 13\\), we can break it down into simpler steps:\n\n1. **Multiplication Step-by-Step:**\n - First, multiply 58 by 3 (the ones digit of 13).\n \\[\n 58 \\times 3 = 174\n \\]\n - Next, multiply 58 by the tens digit of 13, which is 1 (since ... | [
"To solve the long multiplication equation \\(58 \\times 13\\), we can break it down into simpler steps:\n\n1. **Multiplication Step-by-Step:**\n - First, multiply 58 by 3 (the ones digit of 13).\n \\[\n 58 \\times 3 = 174\n \\]\n - Next, multiply 58 by the tens digit of 13, which is 1 (since we are... | 5fc73e50e37f3dcb77f1e8e2170849fa0336d721bd4b6487a563d3eac4cebd59 | 4e86266d260333c3af59ac66444dfd29717e2bd7b0cc3d89046a466c2f33c2e5 | 4099ed5ba70aebc5a9dc26bc2093d4b45839f99b306bd12f68cedfd351e6ab7a | 1 | [
"754"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the final answer to the equation 58 x 13 is \boxed{754}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"754"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 58 and 13, we can break it down step by step:\n\n1. Multiply 58 by 3 (the units digit of 13):\n - 58 x 3 = 174\n\n2. Multiply 58 by 1 (the tens digit of 13), remembering to shift one position to the left (which is equivalent to multiplying b... | |
7 | {
"answer": "1600",
"args": [
"20",
"80"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1600 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n20 x 80\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(20 \\times 80\\), we can break it down into simpler steps:\n\n1. **Multiply the digits without considering the zeros initially**: First, calculate \\(2 \\times 8 = 16\\).\n2. **Account for the added zero**: Since there are two zeros in the original problem (one af... | [
"To solve the long multiplication equation \\(20 \\times 80\\), we can break it down into simpler steps:\n\n1. **Multiply the digits without considering the zeros initially**: First, calculate \\(2 \\times 8 = 16\\).\n2. **Account for the added zero**: Since there are two zeros in the original problem (one after th... | a946c053b5814fe447c15bac4fed4d05c7c2b1e5cbb263f4a51773c4a9f70fa4 | 9e646a8b4c51eaa86581a9a5b906310525b28ff12e232d6b8b819c89eebcaaa6 | b458944d9ec4322f9ff0de2885ce82d580341fcf0fd688422e9929b6e7ce3b2d | 1 | [
"1600"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "Hence, the solution is \(\boxed{1600}\)." This is a clear conclusion to the problem, providing the final answer to the multiplication equation. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1600"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 20 and 80, we can break it down as follows: \n\n1. Multiply 20 by 8 (the tens digit of 80): \n 20 x 8 = 160 \n\n2. Since 80 is actually 80 (which is 8 times 10), we need to multiply the result by 10: \n 160 x 10 = 1600 \n\nThus, the final r... | |
8 | {
"answer": "1600",
"args": [
"20",
"80"
],
"is_model_response_correct": [
false,
true,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 1600 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n80 x 20\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(80 \\times 20\\), we can break it down into simpler steps:\n\n1. **Multiply 80 by 2:**\n - \\(80 \\times 2 = 160\\)\n\n2. **Multiply 80 by 20:**\n - This is the same as \\(80 \\times 20\\), which we have already calculated to be \\(1600\\).\n\nSo, the value of... | [
"To solve the long multiplication equation \\(80 \\times 20\\), we can break it down into simpler steps:\n\n1. **Multiply 80 by 2:**\n - \\(80 \\times 2 = 160\\)\n\n2. **Multiply 80 by 20:**\n - This is the same as \\(80 \\times 20\\), which we have already calculated to be \\(1600\\).\n\nSo, the value of \\(80... | 6c0c2141d0596c6b716f334e6d9389e84f36d5bfd594a7e05106023c1c7629f2 | 769affaff23cc62360da1bf80dbf8c073928ed7126e00b224fc1dd797d1daab8 | b458944d9ec4322f9ff0de2885ce82d580341fcf0fd688422e9929b6e7ce3b2d | 1 | [
"1600"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "Therefore, the answer is \(\boxed{1600}\)." This is a clear conclusion of the calculation, indicating that the final answer to the multiplication problem is 1600. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1600"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 80 and 20, we can break it down as follows: \n\n1. Multiply 80 by 2 (the units digit of 20): \n 80 x 2 = 160 \n\n2. Since 20 is actually 2 with a zero (10), we need to multiply the result by 10: \n 160 x 10 = 1600 \n\nThus, the final result... | |
9 | {
"answer": "6402",
"args": [
"66",
"97"
],
"is_model_response_correct": [
true,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 6402 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n66 x 97\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(66 \\times 97\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 66 \\\\\n \\times & 97 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 66 by 7 (the un... | [
"To solve the long multiplication equation \\(66 \\times 97\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 66 \\\\\n \\times & 97 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 66 by 7 (the units di... | b43bff8d81e370fb280925fb8f883017a4d175622c585e1d1bd31ecab26d9860 | 1d590e22b4f1b80d92c57241abfa679ebc1ef7b2f823cd5087239b40eafadb5c | e50271b2ab1592e4586f4435ccc103a76f80498eb9cb86fbb4e95a0ee54ddc4e | 1 | [
"6402"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal is when the model states, "So, the solution to the long multiplication equation 66 x 97 is \(\boxed{6402}\)." This counts as a proposal of a final answer. 2. The second proposal is when the model reaffirms, "So, the solution is indeed \(\boxed{6402}\)." This is a confirmation of the previous answe... | 5 | [
"6402",
"6402",
"6402",
"6402",
"6402"
] | [
true,
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 66 and 97, we can break it down step by step:\n\n1. Multiply 66 by 7 (the units digit of 97):\n - 66 x 7 = 462\n\n2. Multiply 66 by 90 (the tens digit of 97, which is 9, but we treat it as 90):\n - 66 x 90 = 5940\n\n3. Now, add the two res... | |
10 | {
"answer": "6402",
"args": [
"66",
"97"
],
"is_model_response_correct": [
false,
false,
false,
true,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 6402 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n97 x 66\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 97 \\times 66 \\), we will follow these steps:\n\n1. **Break down the numbers into smaller parts:**\n \\[\n 97 = 90 + 7\n \\]\n \\[\n 66 = 60 + 6\n \\]\n\n2. **Multiply each part of the first number by each part of the second number:**\n \\[\n 90 ... | [
"To solve the long multiplication equation \\( 97 \\times 66 \\), we will follow these steps:\n\n1. **Break down the numbers into smaller parts:**\n \\[\n 97 = 90 + 7\n \\]\n \\[\n 66 = 60 + 6\n \\]\n\n2. **Multiply each part of the first number by each part of the second number:**\n \\[\n 90 \\time... | 9ae6ae7342b63f662df6d684fd52b96636dd9d162b71eb6833f3fe387b170d96 | b721ccd0a77e28628bf0ed6a3ff00a3d3ac77c36b4089db72ed388a9154f2fa0 | e50271b2ab1592e4586f4435ccc103a76f80498eb9cb86fbb4e95a0ee54ddc4e | 1 | [
"6402"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'So, the solution to the long multiplication equation 97 x 66 is: \[\boxed{6402}\]'. This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"6402"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 97 and 66, we can break it down step by step:\n\n1. Multiply 97 by 6 (the units digit of 66):\n - 97 x 6 = 582\n\n2. Multiply 97 by 60 (the tens digit of 66, which is 6, but we treat it as 60):\n - 97 x 60 = 5820\n\n3. Now, add the two res... | |
11 | {
"answer": "2925",
"args": [
"45",
"65"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 2925 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n45 x 65\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(45 \\times 65\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 45 \\\\\n \\times 65 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 45 by 5 (the units digit of... | [
"To solve the long multiplication equation \\(45 \\times 65\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 45 \\\\\n \\times 65 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 45 by 5 (the units digit of 65):*... | 989070c832f5d116f20a8a3a7c9f2b2a48b9cb5f2c3e59e3d70a42ea51eed31f | 1307d88afe9d3df98959bf95d20c6e7dd70ca5d16d7c2c14329f5de286ccb44f | f0e3bd92f157f9b73ede82834286e7cea4044134b39d92ac3ee7e56392194241 | 1 | [
"2925"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 45 x 65 is \(\boxed{2925}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"2925"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 45 and 65, we can break it down step by step:\n\n1. Multiply 45 by 5 (the units digit of 65):\n 45 x 5 = 225\n\n2. Multiply 45 by 6 (the tens digit of 65), remembering to add a zero since it's in the tens place:\n 45 x 6 = 270, and then ad... | |
12 | {
"answer": "660",
"args": [
"12",
"55"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 660 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n12 x 55\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(12 \\times 55\\), we can break it down into simpler steps.\n\n1. **Break down 55:**\n \\[\n 55 = 50 + 5\n \\]\n\n2. **Multiply 12 by 50:**\n \\[\n 12 \\times 50 = 12 \\times (5 \\times 10) = (12 \\times 5) \\times 10 = 60 \\times 10 = 600\n \\]\n\n3. *... | [
"To solve the long multiplication equation \\(12 \\times 55\\), we can break it down into simpler steps.\n\n1. **Break down 55:**\n \\[\n 55 = 50 + 5\n \\]\n\n2. **Multiply 12 by 50:**\n \\[\n 12 \\times 50 = 12 \\times (5 \\times 10) = (12 \\times 5) \\times 10 = 60 \\times 10 = 600\n \\]\n\n3. **Multi... | 4468256e019dd82fe95819840d7dd46670eb2f1bdf8a997349207e37295c51c1 | ae600f1d836566e8bfbbcd59db920834efcf8247840caaca10c6a7f9180ba59e | fc9e91cc78e1817d80b4ba8c2dc9a638d0c57959825ee34f5e3d7688ad80dfb9 | 1 | [
"660"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 12 x 55 is \(\boxed{660}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"660"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 12 and 55, we can break it down step by step:\n\n1. Multiply 12 by 5 (the units digit of 55):\n 12 x 5 = 60\n\n2. Multiply 12 by 50 (the tens digit of 55, which is 5 but represents 50):\n 12 x 50 = 600\n\n3. Now, add the two results togeth... | |
13 | {
"answer": "1328",
"args": [
"16",
"83"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1328 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n16 x 83\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(16 \\times 83\\), we can break it down into simpler steps:\n\n1. **Multiply 16 by 3 (the units digit of 83):**\n \\[\n 16 \\times 3 = 48\n \\]\n\n2. **Multiply 16 by 80 (the tens digit of 83, which is 80):**\n \\[\n 16 \\times 80 = 16 \\times 8 \\times 1... | [
"To solve the long multiplication equation \\(16 \\times 83\\), we can break it down into simpler steps:\n\n1. **Multiply 16 by 3 (the units digit of 83):**\n \\[\n 16 \\times 3 = 48\n \\]\n\n2. **Multiply 16 by 80 (the tens digit of 83, which is 80):**\n \\[\n 16 \\times 80 = 16 \\times 8 \\times 10 = 12... | 0a0f4af69b70e3a54cc4c4d50c4faa9c90cd22cef6f9ebefa5d5f7468a091b20 | 338589f1edb5b2582e8bad195f927327a9088129929bd5beb18aab895d07cc3b | 040fe555cb4f5459547ee1da624040b002a012b23af44ff9005e59005b7e62ac | 1 | [
"1328"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 16 x 83 is \(\boxed{1328}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1328"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 16 and 83, we can break it down step by step:\n\n1. Multiply 16 by 3 (the units digit of 83):\n 16 x 3 = 48\n\n2. Multiply 16 by 8 (the tens digit of 83), remembering to shift one position to the left (since it's actually 80):\n 16 x 8 = 1... | |
14 | {
"answer": "4960",
"args": [
"62",
"80"
],
"is_model_response_correct": [
true,
true,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 4960 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n62 x 80\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(62 \\times 80\\), we can break it down into simpler steps:\n\n1. **Multiply 62 by 8:**\n - Perform the multiplication: \\(62 \\times 8 = 496\\).\n\n2. **Multiply 62 by 10:**\n - Perform the multiplication: \\(62 \\times 10 = 620\\).\n - Since we're multiplyi... | [
"To solve the long multiplication equation \\(62 \\times 80\\), we can break it down into simpler steps:\n\n1. **Multiply 62 by 8:**\n - Perform the multiplication: \\(62 \\times 8 = 496\\).\n\n2. **Multiply 62 by 10:**\n - Perform the multiplication: \\(62 \\times 10 = 620\\).\n - Since we're multiplying by ... | da5bfd43164d43235bb5af590485ec96fbe50936b2c9c09d287a35f521627773 | e3a09fe84e06145c912a89a4338489557cca779f18da6de924220c151ea8dd23 | cdcaf888b551e74fe7c4c6909b2216058d03a773f60aa31c5632eeba2dce71c2 | 0 | [
"1116"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is made when the model states, "So, the solution to the long multiplication equation 62 x 80 is 1116." This counts as the first proposal.
2. The first verification occurs when the model says, "But I need to verify this. Let's do it step by step again carefully:" and then repeat... | 5 | [
"1116",
"1116",
"49600",
"1116",
"1116"
] | [
false,
false,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 62 by 80, we can break it down step by step:\n\n1. First, multiply 62 by 8 (the tens digit of 80):\n - 62 x 8 = 496\n\n2. Since 80 is actually 8 with a zero at the end, we need to multiply the result by 10:\n - 496 x 10 = 4960\n\nThus, the... | |
15 | {
"answer": "4960",
"args": [
"62",
"80"
],
"is_model_response_correct": [
false,
false,
false,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 4960 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n80 x 62\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(80 \\times 62\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(80\\) is the number to multiply by \\(62\\).\n\n2. **Multiply each digit of the second number (\\(62\\)) by the carrying number part (which is simply the tens and... | [
"To solve the long multiplication equation \\(80 \\times 62\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(80\\) is the number to multiply by \\(62\\).\n\n2. **Multiply each digit of the second number (\\(62\\)) by the carrying number part (which is simply the tens and units... | a3cc9bc0526953a5b882b8c2f79f3f3dff8590a033731a8c4322f9a49bc964c1 | 2a6decb3b1b5351b54e38e8f46d23ddb097f7820b213d4823b49e681680ccd03 | cdcaf888b551e74fe7c4c6909b2216058d03a773f60aa31c5632eeba2dce71c2 | 1 | [
"4960"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "Therefore, the final product is 4960." This clearly states the final answer to the multiplication problem.
2. The verification process begins with: "Wait, how? I thought that I couldn't just change it to 4920 or 4980 because of the thousands separato... | 2 | [
"4960",
"4960"
] | [
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 80 and 62, we can break it down step by step:\n\n1. Multiply 80 by 2 (the units digit of 62):\n 80 x 2 = 160\n\n2. Multiply 80 by 60 (the tens digit of 62, which is 6, but we treat it as 60):\n 80 x 60 = 4800\n\n3. Now, add the two results... | |
16 | {
"answer": "4960",
"args": [
"62",
"80"
],
"is_model_response_correct": [
false,
false,
false,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 4960 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n80 x 62\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(80 \\times 62\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(80\\) is the number to multiply by \\(62\\).\n\n2. **Multiply each digit of the second number (\\(62\\)) by the carrying number part (which is simply the tens and... | [
"To solve the long multiplication equation \\(80 \\times 62\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(80\\) is the number to multiply by \\(62\\).\n\n2. **Multiply each digit of the second number (\\(62\\)) by the carrying number part (which is simply the tens and units... | 2ef70e8e40b7af75dff059346e5d266b64fe77089a20fd7d9d6a36bcebd37b8a | 2a6decb3b1b5351b54e38e8f46d23ddb097f7820b213d4823b49e681680ccd03 | cdcaf888b551e74fe7c4c6909b2216058d03a773f60aa31c5632eeba2dce71c2 | 1 | [
"4960"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is when the model states, "Therefore, the final product is 4960." This is a clear conclusion of the multiplication process. 2. The first verification occurs when the model says, "Wait, how? I thought that I couldn't just change it to 4920 or 4966 just because the numbers are clos... | 3 | [
"4960",
"4960",
"4960"
] | [
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 80 and 62, we can break it down step by step:\n\n1. Multiply 80 by 2 (the units digit of 62):\n 80 x 2 = 160\n\n2. Multiply 80 by 6 (the tens digit of 62), remembering that this represents 60:\n 80 x 6 = 480, but since it's in the tens pla... | |
17 | {
"answer": "4982",
"args": [
"53",
"94"
],
"is_model_response_correct": [
true,
false,
false,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 4982 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n94 x 53\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 94 \\times 53 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 4 \\\\\n \\times & 5 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 94 by 3... | [
"To solve the long multiplication equation \\( 94 \\times 53 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 4 \\\\\n \\times & 5 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 94 by 3 (the ... | 4e150285298d26b984b20343bf51e12127771f34739277560bdf94076b2ee7eb | eac4591d422e30ff77378a04b85c115a86ed460e39667b23ecf502ee533370ab | 59e1e59850940550ff0a67e34a6da30192d117b4d8619df6729f40a10865f656 | 0 | [
"5002"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "So, the solution to the long multiplication equation 94 x 53 is \boxed{5000}." This counts as the first proposal. 2. The second proposal is in the statement: "The correct answer using the distributive property is \boxed{5002}." This counts as the secon... | 2 | [
"5000",
"5002"
] | [
false,
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 94 and 53, we can break it down step by step:\n\n1. Multiply 94 by 3 (the units digit of 53):\n 94 x 3 = 282\n\n2. Multiply 94 by 50 (the tens digit of 53, which is 5, shifted one place to the left):\n 94 x 50 = 4700\n\n3. Now, add the ... | |
18 | {
"answer": "4982",
"args": [
"53",
"94"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 4982 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n53 x 94\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(53 \\times 94\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 53 \\\\\n \\times 94 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 53 by 4 (the on... | [
"To solve the long multiplication equation \\(53 \\times 94\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 53 \\\\\n \\times 94 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 53 by 4 (the ones dig... | 2f2b079bdc1de94896f2f9ad4945a2797e328abc4485965e202b0c1bbcd0682f | f4f06ad57378a6a1ca654aec34600101f8f0c536e998dfa50e8e44fc953ca67e | 59e1e59850940550ff0a67e34a6da30192d117b4d8619df6729f40a10865f656 | 0 | [
"4792"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is made when the model states, "So, the solution to the long multiplication equation 53 x 94 is \(\boxed{4792}\)." This counts as the first proposal. 2. The model then states, "But I need to verify this." This leads to a verification process where the model re-evaluates the multi... | 5 | [
"4792",
"4792",
"4792",
"4792",
"4792"
] | [
false,
false,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 53 and 94, we can break it down step by step:\n\n1. Multiply 53 by 4 (the units digit of 94):\n 53 x 4 = 212\n\n2. Multiply 53 by 9 (the tens digit of 94), remembering to shift one position to the left (which is equivalent to multiplying by... | |
19 | {
"answer": "2310",
"args": [
"33",
"70"
],
"is_model_response_correct": [
true,
false,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 2310 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n70 x 33\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(70 \\times 33\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 70 \\times 33 = 70 \\times (30 + 3)\n \\]\n\n2. **Use the distributive property:**\n \\[\n 70 \\times (30 + 3) = 70 \\times 30 + 70 \\times 3\n ... | [
"To solve the long multiplication equation \\(70 \\times 33\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 70 \\times 33 = 70 \\times (30 + 3)\n \\]\n\n2. **Use the distributive property:**\n \\[\n 70 \\times (30 + 3) = 70 \\times 30 + 70 \\times 3\n \\]\n\... | 986d80e700c7949e39abaedcbd0cdd5f07e593ae43a2de5b000372db831e51fd | 5d1c05647c52c7dfc545606a1d0a9ccb57de2b6ced57b2ab3d20cd6a79ee3d89 | 21945e7f31fb51b4fccc6947a26b2573b9bc4763ae10b6bd1b59afda8959aab3 | 1 | [
"2310"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 70 x 33 is \(\boxed{2310}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"2310"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the solution, we can perform the long multiplication of 70 and 33 step by step:\n\n1. Multiply 70 by 3 (the units digit of 33):\n 70 x 3 = 210\n\n2. Multiply 70 by 30 (the tens digit of 33, which is 3, but we need to account for its place value):\n 70 x 30 = 21... | |
20 | {
"answer": "3290",
"args": [
"35",
"94"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 3290 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n35 x 94\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(35 \\times 94\\), we can break it down into simpler steps:\n\n1. **Multiply 35 by 4 (the units digit of 94):**\n \\[\n 35 \\times 4 = 140\n \\]\n\n2. **Multiply 35 by 90 (the tens digit of 94, which is 9 x 10):**\n \\[\n 35 \\times 90 = 3150\n \\]\n\n3... | [
"To solve the long multiplication equation \\(35 \\times 94\\), we can break it down into simpler steps:\n\n1. **Multiply 35 by 4 (the units digit of 94):**\n \\[\n 35 \\times 4 = 140\n \\]\n\n2. **Multiply 35 by 90 (the tens digit of 94, which is 9 x 10):**\n \\[\n 35 \\times 90 = 3150\n \\]\n\n3. **Ad... | 1a463fcbd5629b45489b1352dc5ab295d712d245ea02baf09efe90f279ba538c | b0a3829bbd2a21fd5ed0eaf21da2ae308b7bf7081fa339cf7f7519e85af77350 | 8a9745162300f3c10294fd3df86ed83be7eae647f61dcdc3881d5c85158fe8ce | 1 | [
"3290"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "So, the solution to the long multiplication equation 35 x 94 is \(\boxed{3290}\)." This is a clear proposal of the final answer to the multiplication problem. | 1 | [
"3290"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 35 and 94, we can break it down step by step:\n\n1. Multiply 35 by 4 (the units digit of 94):\n 35 x 4 = 140\n\n2. Multiply 35 by 9 (the tens digit of 94), remembering to add a zero since we are actually multiplying by 90:\n 35 x 9 = 315, ... | |
21 | {
"answer": "3910",
"args": [
"46",
"85"
],
"is_model_response_correct": [
true,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 3910 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n46 x 85\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(46 \\times 85\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 46 \\\\\n \\times 85 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 46 by 5 (the units digit of... | [
"To solve the long multiplication equation \\(46 \\times 85\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 46 \\\\\n \\times 85 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 46 by 5 (the units digit of 85):*... | c94285d1f311cec89db7fbdc2b63fc4737830f57ba28fc9533ffe8bf86d4971e | 3c6786f730e82ab02bf9259bfa047c8747d673dcd0735720d4da200afe58bee1 | e70a396cdf3eea9df71179a4b709ee24f3b22ea2a438d30f4c1ce33f6f07cc2a | 1 | [
"3910"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is when the model states, "So, the solution to the long multiplication equation 46 x 85 is \(\boxed{3910}\)." This counts as the first proposal.
2. The first verification occurs when the model says, "But I need to verify this. Let's use the correct long multiplication again:" a... | 4 | [
"3910",
"3910",
"3910",
"3910"
] | [
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 46 and 85, we can break it down step by step:\n\n1. Multiply 46 by 5 (the units digit of 85):\n - 46 x 5 = 230\n\n2. Multiply 46 by 8 (the tens digit of 85), remembering to shift one position to the left (which is equivalent to multiplying b... | |
22 | {
"answer": "1552",
"args": [
"16",
"97"
],
"is_model_response_correct": [
true,
true,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 1552 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n97 x 16\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 97 \\times 16 \\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 97 \\times 16 = (90 + 7) \\times 16\n \\]\n\n2. **Apply the distributive property:**\n \\[\n (90 + 7) \\times 16 = 90 \\times 16 + 7 \\times 16\... | [
"To solve the long multiplication equation \\( 97 \\times 16 \\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 97 \\times 16 = (90 + 7) \\times 16\n \\]\n\n2. **Apply the distributive property:**\n \\[\n (90 + 7) \\times 16 = 90 \\times 16 + 7 \\times 16\n \\... | 56968e4ddbf363ed3d7cc5505b2f8e0773469cd757cdb3a4519f43f6a49623f6 | aa656a8e2841af3397574a0a0beaf6247c92a924893ed159239395531b593bca | 51e6811411165c04f691eb5a38cf11a7316fdd776478b4fd222fd0107973c381 | 1 | [
"1552"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 97 x 16 is \(\boxed{1552}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1552"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 97 by 16, we can break it down step by step:\n\n1. Multiply 97 by 6 (the units digit of 16):\n - 97 x 6 = 582\n\n2. Multiply 97 by 10 (the tens digit of 16):\n - 97 x 10 = 970\n\n3. Now, add the two results together:\n - 582 + 970 = 1552... | |
23 | {
"answer": "1456",
"args": [
"16",
"91"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1456 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n16 x 91\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 16 \\times 91 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 16 \\\\\n \\times 91 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 16 by 1 (the units digit of 91):**\n \\[\n 16 \\times 1 = 1... | [
"To solve the long multiplication equation \\( 16 \\times 91 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 16 \\\\\n \\times 91 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 16 by 1 (the units digit of 91):**\n \\[\n 16 \\times 1 = 16\n ... | 5e7c5de00062024b904caf5741d90c990afeb1868a870eb56d3fdcd6dae936d2 | f76724250d43300abbb26c5cfaf85db8b37a75880bb1b07d973eca1a9727bf79 | fddc599a3afe6c68b8098f7ef3db02335f7e398e3c0bd34b663f04f424886aeb | 1 | [
"1456"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 16 x 91 is \( \boxed{1456} \)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1456"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 16 and 91, we can break it down step by step:\n\n1. Multiply 16 by 1 (the units digit of 91):\n 16 x 1 = 16\n\n2. Multiply 16 by 9 (the tens digit of 91), remembering that this is actually 90:\n 16 x 9 = 144 (and since it's in the tens pla... | |
24 | {
"answer": "3741",
"args": [
"43",
"87"
],
"is_model_response_correct": [
true,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 3741 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n87 x 43\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(87 \\times 43\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 87 by 3 (the units digit of 43):**\n \\[\n 87 \\times 3 = 261\n \\]\n\n2. **Multiply 87 by 4 (the tens digit of 43) and shift the r... | [
"To solve the long multiplication equation \\(87 \\times 43\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 87 by 3 (the units digit of 43):**\n \\[\n 87 \\times 3 = 261\n \\]\n\n2. **Multiply 87 by 4 (the tens digit of 43) and shift the result ... | e1d178c67b9d7197a4dcc904b8839979f1325d9d088325a6fde5fb0d4924cce8 | ae4d6287874ae08b59cdbb088b6f85c9505b5e47bf2be90f1a7ce75de0bd7be1 | 66d0af18b66f5630cdb662ba54c992d34cf38bdb51601f52c5740a7846d11e90 | 1 | [
"3741"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'So, the solution to the long multiplication equation 87 x 43 is \(\boxed{3741}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"3741"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 87 and 43, we can break it down step by step:\n\n1. Multiply 87 by 3 (the units digit of 43):\n - 87 x 3 = 261\n\n2. Multiply 87 by 4 (the tens digit of 43), remembering to shift one position to the left (which is equivalent to multiplying b... | |
25 | {
"answer": "1150",
"args": [
"25",
"46"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1150 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n25 x 46\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(25 \\times 46\\), we can break it down into simpler steps:\n\n1. **Multiply 25 by 6:**\n \\[\n 25 \\times 6 = 150\n \\]\n\n2. **Multiply 25 by 40 (which is the same as 4 times 10):**\n \\[\n 25 \\times 40 = 25 \\times (4 \\times 10) = (25 \\times 4) \\ti... | [
"To solve the long multiplication equation \\(25 \\times 46\\), we can break it down into simpler steps:\n\n1. **Multiply 25 by 6:**\n \\[\n 25 \\times 6 = 150\n \\]\n\n2. **Multiply 25 by 40 (which is the same as 4 times 10):**\n \\[\n 25 \\times 40 = 25 \\times (4 \\times 10) = (25 \\times 4) \\times 10... | 9b35306bf9761affb7ac7fe94c4bdff83fdb24554faa6c7b35c05621d66fedc9 | 3e870ec886abad88e6105dbcd189af6b76fb59fe0f8ea938c82e38e993aeb5ee | 0eaa69a16d7c358a329a7111a809bd2f9a7ff489596bdda17538705e9e03e05d | 1 | [
"1150"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 25 x 46 is \(\boxed{1150}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1150"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 25 and 46, we can break it down step by step:\n\n1. Multiply 25 by 6 (the units digit of 46):\n 25 x 6 = 150\n\n2. Multiply 25 by 4 (the tens digit of 46), remembering to add a zero since it's in the tens place:\n 25 x 4 = 100, and then ad... | |
26 | {
"answer": "1230",
"args": [
"15",
"82"
],
"is_model_response_correct": [
true,
true,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 1230 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n82 x 15\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(82 \\times 15\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 82 \\times 15 = (80 + 2) \\times 15\n \\]\n\n2. **Use the distributive property:**\n \\[\n (80 + 2) \\times 15 = 80 \\times 15 + 2 \\times 15\n ... | [
"To solve the long multiplication equation \\(82 \\times 15\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 82 \\times 15 = (80 + 2) \\times 15\n \\]\n\n2. **Use the distributive property:**\n \\[\n (80 + 2) \\times 15 = 80 \\times 15 + 2 \\times 15\n \\]\n\... | f3f78f6259a57314c07f8fb8995a14c7419d3df77fb0626aedb8062b088c9bd2 | b5a4c12dc00ccac824c236de6b5116938eff817530f7cf5ee24f92b4c3261773 | 22a2fa7d04248931a8853a7714b86546610afd01b2b1841890e979ba7ba6bcae | 1 | [
"1230"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 82 x 15 is \(\boxed{1230}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1230"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 82 and 15, we can break it down step by step:\n\n1. Multiply 82 by 5:\n - 82 x 5 = 410\n\n2. Multiply 82 by 10:\n - 82 x 10 = 820\n\n3. Now, add the two results together:\n - 410 + 820 = 1230\n\nSince the solution provided (1230) matches... | |
27 | {
"answer": "1736",
"args": [
"28",
"62"
],
"is_model_response_correct": [
true,
true,
true,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 1736 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n28 x 62\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(28 \\times 62\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 28 \\\\\n \\times 62 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 28 by 2 (the units digit of 62):**\n \\[\n 28 \\times 2 = 56\n \\]\n ... | [
"To solve the long multiplication equation \\(28 \\times 62\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 28 \\\\\n \\times 62 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 28 by 2 (the units digit of 62):**\n \\[\n 28 \\times 2 = 56\n \\]\n Writ... | fffad29e7ff19e3ac30fdf870f5e30724ed3a1cdb2381c82b7d1bc537689aca2 | c976aa3257356bc1c179ef949c94921e59acc9e7bfc3bd35f2f6227baf9faea4 | 96a1a93e19030f5f93783143ab66d333a0ee8e97c4d2d1eccc7d831d5fb4e2d9 | 1 | [
"1736"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the multiplication 28 x 62 is \(\boxed{1736}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1736"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 28 and 62, we can break it down step by step:\n\n1. Multiply 28 by 2 (the units digit of 62):\n 28 x 2 = 56\n\n2. Multiply 28 by 6 (the tens digit of 62), remembering to shift one position to the left (which is equivalent to multiplying by 6... | |
28 | {
"answer": "4140",
"args": [
"46",
"90"
],
"is_model_response_correct": [
false,
true,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 4140 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n90 x 46\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 90 \\times 46 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 90 \\\\\n \\times 46 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 90 by 6 (the units digit of 46):**\n \\[\n 90 \\times 6 = 540\n \\]... | [
"To solve the long multiplication equation \\( 90 \\times 46 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 90 \\\\\n \\times 46 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 90 by 6 (the units digit of 46):**\n \\[\n 90 \\times 6 = 540\n \\]\n W... | c752e376ff25f5efb09104c31fb108830462ee174c405c9ab314037db69a3aca | 6b4c5a42c69e8f7373c5de31df38d5ea9e86b63e21a7696bb1f53cac39cb68a6 | 1f74494f923e9bf4bedc9968f0418824c2b298bd83009812a45e547f6733ac7b | 1 | [
"4140"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 90 x 46 is \( \boxed{4140} \)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"4140"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 90 and 46, we can break it down step by step:\n\n1. Multiply 90 by 6 (the units digit of 46):\n 90 x 6 = 540\n\n2. Multiply 90 by 4 (the tens digit of 46), remembering to shift one position to the left (which is equivalent to multiplying by ... | |
29 | {
"answer": "7084",
"args": [
"77",
"92"
],
"is_model_response_correct": [
true,
true,
false,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 7084 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n92 x 77\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 92 \\times 77 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 2 \\\\\n \\times & 7 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 92 by 7... | [
"To solve the long multiplication equation \\( 92 \\times 77 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 2 \\\\\n \\times & 7 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 92 by 7 (the ... | d235154d75437afb4a5404b912557a0bca5b275d86f3784bb906f655f4297d9d | af7266ab6bad9bfa4848d6a1721eb4f76b09c2dd94403aaedd5150529ce3ee73 | 6d57a1ee6667d05a20b1c49535662abc0bc1412dee1e42cb61948d303d39b796 | 1 | [
"7084"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 92 x 77 is \boxed{7084}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"7084"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 92 and 77, we can break it down step by step:\n\n1. Multiply 92 by 7 (the units digit of 77):\n - 92 x 7 = 644\n\n2. Multiply 92 by 70 (the tens digit of 77, which is 7, but we need to account for the place value):\n - 92 x 70 = 6440\n\n3.... | |
30 | {
"answer": "7084",
"args": [
"77",
"92"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 7084 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n77 x 92\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 77 \\times 92 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 77 \\\\\n \\times 92 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 77 by 2 (the units digit of 92):**\n \\[\n 77 \\times 2 = 154\n \\]... | [
"To solve the long multiplication equation \\( 77 \\times 92 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 77 \\\\\n \\times 92 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 77 by 2 (the units digit of 92):**\n \\[\n 77 \\times 2 = 154\n \\]\n W... | 7ca438d95052ad782dd439ccf7e3a7242fb8553154eb82d1c9f0cdccd1331008 | c3323b7ab344e1546ff229fad724fa6218b6ccace2a493703ade29311838628e | 6d57a1ee6667d05a20b1c49535662abc0bc1412dee1e42cb61948d303d39b796 | 1 | [
"7084"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 77 x 92 is: \[\boxed{7084}\]" This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"7084"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 77 and 92, we can break it down step by step:\n\n1. Multiply 77 by 2 (the units digit of 92):\n 77 x 2 = 154\n\n2. Multiply 77 by 9 (the tens digit of 92), remembering to add a zero for the tens place:\n 77 x 9 = 693, and then add a zero t... | |
31 | {
"answer": "5548",
"args": [
"73",
"76"
],
"is_model_response_correct": [
false,
true,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 5548 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n76 x 73\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 76 \\times 73 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n 76 & \\times \\quad 73 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 76 by 3 (the units digi... | [
"To solve the long multiplication equation \\( 76 \\times 73 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n 76 & \\times \\quad 73 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 76 by 3 (the units digit of 7... | 52c8cd66f5f0fd207e6aa38f27a494d21cfef258c12e5b9c4e8874a9e82b9174 | 3d74e0e90bfd43058f06e38e3d5d888d91cc116dff2c30a49371edd6d781e112 | 869ab3d28136025484ecb4235eed83d0eacef3129d0ac4cf8b23afdab847fd6f | 1 | [
"5548"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 76 x 73 is \boxed{5548}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"5548"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 76 and 73, we can break it down step by step:\n\n1. Multiply 76 by 3 (the units digit of 73):\n - 76 x 3 = 228\n\n2. Multiply 76 by 7 (the tens digit of 73), remembering to shift one position to the left (which is equivalent to multiplying b... | |
32 | {
"answer": "7740",
"args": [
"86",
"90"
],
"is_model_response_correct": [
true,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 7740 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n90 x 86\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 90 \\times 86 \\), we will follow these steps:\n\n1. **Break down the numbers:**\n \\[\n 90 = 9 \\times 10\n \\]\n \\[\n 86 = 80 + 6\n \\]\n\n2. **Multiply each part of \\( 86 \\) by \\( 9 \\):**\n \\[\n 9 \\times 80 = 720\n \\]\n \\[\n 9 \\... | [
"To solve the long multiplication equation \\( 90 \\times 86 \\), we will follow these steps:\n\n1. **Break down the numbers:**\n \\[\n 90 = 9 \\times 10\n \\]\n \\[\n 86 = 80 + 6\n \\]\n\n2. **Multiply each part of \\( 86 \\) by \\( 9 \\):**\n \\[\n 9 \\times 80 = 720\n \\]\n \\[\n 9 \\times ... | b7e211fa31118198489bf9a6266f3639505ae1c94706ba5cf0c4eff117914650 | 2c1ea6d5792fdfa6d0bf2c56758bf96d50c86a97cd251a4ab24b8b80a1cf6f2a | 4987ed252a8732b906614beddb808972bf15361de735c459d0ce2df48d14a744 | 1 | [
"7740"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 90 x 86 is \boxed{7740}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"7740"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 90 and 86, we can break it down step by step:\n\n1. Multiply 90 by 80 (which is 86 rounded down to the nearest ten):\n 90 x 80 = 7200\n\n2. Multiply 90 by 6 (the remaining part of 86):\n 90 x 6 = 540\n\n3. Now, add the two results together... | |
33 | {
"answer": "7740",
"args": [
"86",
"90"
],
"is_model_response_correct": [
true,
false,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 7740 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n86 x 90\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 86 \\times 90 \\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n \\[\n 86 \\times 90 = 86 \\times (9 \\times 10)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Multiply 86 ... | [
"To solve the long multiplication equation \\( 86 \\times 90 \\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n \\[\n 86 \\times 90 = 86 \\times (9 \\times 10)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Multiply 86 by 9:*... | 7340dc17a687c2ed190ccdf9bfb833010d2746621991363506ba27221c41fbf4 | 6ad300fed359363d07c2b4de539610fd9a9f0fa788b408ee54c4ef8b7506a5ea | 4987ed252a8732b906614beddb808972bf15361de735c459d0ce2df48d14a744 | 1 | [
"7740"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 86 x 90 is: \boxed{7740}". This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"7740"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 86 and 90, we can break it down step by step:\n\n1. First, we can multiply 86 by 9 (the tens digit of 90):\n - 86 x 9 = 774.\n\n2. Since we are actually multiplying by 90, we need to multiply the result by 10 (to account for the zero in 90):... | |
34 | {
"answer": "7740",
"args": [
"86",
"90"
],
"is_model_response_correct": [
true,
false,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 7740 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n86 x 90\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 86 \\times 90 \\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n \\[\n 86 \\times 90 = 86 \\times (9 \\times 10)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Multiply 86 ... | [
"To solve the long multiplication equation \\( 86 \\times 90 \\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n \\[\n 86 \\times 90 = 86 \\times (9 \\times 10)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Multiply 86 by 9:*... | bc509f674a3e8369c01b5c0c121cca82e1d381a6abd22dcc86aa8389360a4647 | 6ad300fed359363d07c2b4de539610fd9a9f0fa788b408ee54c4ef8b7506a5ea | 4987ed252a8732b906614beddb808972bf15361de735c459d0ce2df48d14a744 | 1 | [
"7740"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 86 x 90 is: \[\boxed{7740}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"7740"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 86 and 90, we can break it down step by step:\n\n1. First, we can multiply 86 by 9 (the tens digit of 90):\n - 86 x 9 = 774.\n\n2. Since we are actually multiplying by 90, we need to multiply the result by 10 (because 90 = 9 x 10):\n - 774... | |
35 | {
"answer": "2187",
"args": [
"27",
"81"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 2187 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n27 x 81\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(27 \\times 81\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 27 \\\\\n \\times 81 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 27 by 1 (the units digit of 81):**\n \\[\n 27 \\times 1 = 27\n \\]\n ... | [
"To solve the long multiplication equation \\(27 \\times 81\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 27 \\\\\n \\times 81 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 27 by 1 (the units digit of 81):**\n \\[\n 27 \\times 1 = 27\n \\]\n Writ... | d6af00db293f63f81cd00134bce6889a85f5f4d4525a0b6931238e6ca9306020 | b538f84dc638ae99aa88e36a55c491ea6e0183698f0146cf5f9aaab219ed3fa7 | 2d2c33c52e3df492704c04881c254aa93f37fc0b89dfbafaa9687340e0696ea9 | 0 | [
"2167"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the line: "Therefore, the solution to the long multiplication equation 27 x 81 is \(\boxed{2167}\)." This counts as a proposal because it states a final answer to the multiplication problem. 2. The second verification occurs when the model states: "But to confirm, let... | 2 | [
"2167",
"2187"
] | [
false,
true
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 27 and 81, we can break it down step by step:\n\n1. Multiply 27 by 1 (the units digit of 81):\n 27 x 1 = 27\n\n2. Multiply 27 by 8 (the tens digit of 81), remembering that this is actually 80:\n 27 x 8 = 216\n Since this is in the tens ... | |
36 | {
"answer": "2187",
"args": [
"27",
"81"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 2187 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n81 x 27\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(81 \\times 27\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Write down the numbers to be multiplied:\n \\[\n 81 \\times 27\n \\]\n\n2. Break down 27 into 20 and 7:\n \\[\n 81 \\times... | [
"To solve the long multiplication equation \\(81 \\times 27\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Write down the numbers to be multiplied:\n \\[\n 81 \\times 27\n \\]\n\n2. Break down 27 into 20 and 7:\n \\[\n 81 \\times (20 +... | 0636de6083115e2b689f45955f84822c03a54e4724903b71530f729dffb00dea | 874de2af09be8625656e454dd7c895398f9fd188432e2688ec0315c6eca582e2 | 2d2c33c52e3df492704c04881c254aa93f37fc0b89dfbafaa9687340e0696ea9 | 1 | [
"2187"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 81 x 27 is \(\boxed{2187}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"2187"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 81 and 27, we can break it down step by step:\n\n1. Multiply 81 by 7 (the units digit of 27):\n - 81 x 7 = 567\n\n2. Multiply 81 by 20 (the tens digit of 27, which is 2, but we treat it as 20):\n - 81 x 20 = 1620\n\n3. Now, add the two res... | |
37 | {
"answer": "2088",
"args": [
"24",
"87"
],
"is_model_response_correct": [
true,
false,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 2088 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n24 x 87\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(24 \\times 87\\), we can break it down into simpler steps:\n\n1. **Multiply 24 by 7 (the units digit of 87):**\n \\[\n 24 \\times 7 = 168\n \\]\n\n2. **Multiply 24 by 80 (the tens digit of 87, which is 80):**\n \\[\n 24 \\times 80 = 1920\n \\]\n\n3. **... | [
"To solve the long multiplication equation \\(24 \\times 87\\), we can break it down into simpler steps:\n\n1. **Multiply 24 by 7 (the units digit of 87):**\n \\[\n 24 \\times 7 = 168\n \\]\n\n2. **Multiply 24 by 80 (the tens digit of 87, which is 80):**\n \\[\n 24 \\times 80 = 1920\n \\]\n\n3. **Add th... | 364e539f3fefdc85f903acebd14237ddc3bfba9b85f1c63b9bfc839f1440eea9 | df769faa1656652ef78de82cce311bd1a928cc23219ccaa21a156fda313d0517 | b906e4061c4a678dd89a63a670cccdb0a034e70d456ba90a802d223deccd0f65 | 1 | [
"2088"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 24 x 87 is 2088." This is a clear proposal of the final answer, which counts as one instance. There are no verifications present in the trace, as there is no subsequent checking or confirmation of the proposed answer. | 1 | [
"2088"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 24 and 87, we can break it down step by step:\n\n1. Multiply 24 by 7 (the units digit of 87):\n - 24 x 7 = 168\n\n2. Multiply 24 by 8 (the tens digit of 87), remembering to shift one position to the left (which is equivalent to multiplying b... | |
38 | {
"answer": "9702",
"args": [
"98",
"99"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 9702 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n99 x 98\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 99 \\times 98 \\), we can break it down into simpler steps.\n\n1. **Break it into parts:**\n \\[\n 99 \\times 98 = 99 \\times (100 - 2)\n \\]\n\n2. **Distribute the multiplication:**\n \\[\n 99 \\times (100 - 2) = 99 \\times 100 - 99 \\times 2\n \\]\n... | [
"To solve the long multiplication equation \\( 99 \\times 98 \\), we can break it down into simpler steps.\n\n1. **Break it into parts:**\n \\[\n 99 \\times 98 = 99 \\times (100 - 2)\n \\]\n\n2. **Distribute the multiplication:**\n \\[\n 99 \\times (100 - 2) = 99 \\times 100 - 99 \\times 2\n \\]\n\n3. *... | e4268f5aea53f8971426287ccf8da55d7bd562c33c5d9a9a44f3d219b413195f | e31e528ed4e9049e3852f808f31627d859056f13975ec900a814b86914ada5d9 | 73352dbe01eaf5e063590356fca278158488377671555cb85a230d504a7b78d7 | 1 | [
"9702"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 99 x 98 is \(\boxed{9702}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"9702"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 99 and 98, we can break it down step by step:\n\n1. Calculate 99 x 98 using the distributive property:\n - 99 can be expressed as (100 - 1), so:\n - 99 x 98 = (100 - 1) x 98 = 100 x 98 - 1 x 98\n - 100 x 98 = 9800\n - 1 x 98 = 98\n -... | |
39 | {
"answer": "5610",
"args": [
"66",
"85"
],
"is_model_response_correct": [
true,
true,
false,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 5610 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n66 x 85\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 66 \\times 85 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 66 \\\\\n \\times 85 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 66 by 5 (the units digit ... | [
"To solve the long multiplication equation \\( 66 \\times 85 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 66 \\\\\n \\times 85 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 66 by 5 (the units digit of 85)... | 83151b361f0a0d969aeece1bd632a47e88d06f10b9ba39d1ed909b82b5f3e5ac | 82c7b9c9e444eee0b733c0b71087da83b4b817e7494478ab1633d0f46e223d4c | 83344686e2ff31c00c517b70a0d33d7ad3512ac8e8051001de5c409d902c5efa | 1 | [
"5610"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 66 x 85 is \boxed{5610}." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"5610"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 66 and 85, we can break it down step by step:\n\n1. Multiply 66 by 5 (the units digit of 85):\n 66 x 5 = 330\n\n2. Multiply 66 by 8 (the tens digit of 85), remembering to shift one position to the left (which is equivalent to multiplying by ... | |
40 | {
"answer": "611",
"args": [
"13",
"47"
],
"is_model_response_correct": [
false,
false,
false,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 611 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n47 x 13\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(47 \\times 13\\), we can break it down into simpler steps.\n\n1. **Multiply 47 by 3 (the units digit of 13):**\n \\[\n 47 \\times 3 = 141\n \\]\n\n2. **Multiply 47 by 10 (the tens digit of 13, which is the same as multiplying by 1 and then adding a zero at t... | [
"To solve the long multiplication equation \\(47 \\times 13\\), we can break it down into simpler steps.\n\n1. **Multiply 47 by 3 (the units digit of 13):**\n \\[\n 47 \\times 3 = 141\n \\]\n\n2. **Multiply 47 by 10 (the tens digit of 13, which is the same as multiplying by 1 and then adding a zero at the end... | 171265fc651fadc3ae8ba182906db9862fc9f31cba8ef7132841d7e030ef2c99 | 091c53d76ab9e6f225c7511977c9a34ebaf523be97431ccdfdd4d52c6916eaa3 | 97623535a9ed79620c0c749a7c0a785de0f8a895807195daf2b0e58893db160e | 1 | [
"611"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 47 x 13 is 611." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"611"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 47 and 13, we can break it down step by step:\n\n1. Multiply 47 by 3 (the units digit of 13):\n - 47 x 3 = 141\n\n2. Multiply 47 by 10 (the tens digit of 13):\n - 47 x 10 = 470\n\n3. Now, add the two results together:\n - 141 + 470 = 611... | |
41 | {
"answer": "4312",
"args": [
"56",
"77"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 4312 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n77 x 56\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 77 \\times 56 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 77 \\\\\n \\times 56 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 77 by 6 (the ones digit o... | [
"To solve the long multiplication equation \\( 77 \\times 56 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 77 \\\\\n \\times 56 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 77 by 6 (the ones digit of 56):... | 50b371216938e5c630306ff2ef15a3d92843ca2896c6243ab427c5f277ba5934 | a7091aadbcfab96930a5abc26544b0d6b9dbd88cff9501953eb3a88f743a898c | 9347c0c9a9a77d1df666d472577afdf194993199ff30713910b6766b2bd71aa8 | 0 | [
"4432"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal is made when the model states, "So, the solution to the long multiplication equation 77 x 56 is \boxed{4432}." This counts as a proposal of a final answer. 2. The model then verifies this answer by stating, "But to confirm, you can use the standard multiplication algorithm with digits: ..." and pr... | 4 | [
"4432",
"4432",
"4602",
"4432"
] | [
false,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 77 and 56, we can break it down step by step:\n\n1. Multiply 77 by 6 (the units digit of 56):\n - 77 x 6 = 462\n\n2. Multiply 77 by 5 (the tens digit of 56), remembering to shift one position to the left (which is equivalent to multiplying ... | |
42 | {
"answer": "377",
"args": [
"13",
"29"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 377 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n29 x 13\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(29 \\times 13\\), we can break it down into simpler steps.\n\n1. **Multiply 29 by 3 (the ones place of 13):**\n \\[\n 29 \\times 3 = 87\n \\]\n\n2. **Multiply 29 by 10 (the tens place of 13, which is the same as multiplying by 1 and then adding a zero at the... | [
"To solve the long multiplication equation \\(29 \\times 13\\), we can break it down into simpler steps.\n\n1. **Multiply 29 by 3 (the ones place of 13):**\n \\[\n 29 \\times 3 = 87\n \\]\n\n2. **Multiply 29 by 10 (the tens place of 13, which is the same as multiplying by 1 and then adding a zero at the end):... | dd3ef3be4fcd5a6e8fe08beb24b5884db447387ab23a7da8bba2d56b062cfc8f | 7e8bd1246176227377604680ac1245e5e8b87fb8b8dfcef315030f1ad78ab071 | 2c4cf657337835125bc4258d0e2e546af4185bdb70f64e1b0aa46d1d78017404 | 1 | [
"377"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 29 x 13 is 377." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"377"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 29 and 13, we can break it down step by step:\n\n1. Multiply 29 by 3 (the units digit of 13):\n 29 x 3 = 87\n\n2. Multiply 29 by 1 (the tens digit of 13), remembering to shift one position to the left (which is equivalent to multiplying by 1... | |
43 | {
"answer": "2548",
"args": [
"26",
"98"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 2548 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n98 x 26\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(98 \\times 26\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 98 \\\\\n \\times 26 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 98 by 6:**\n \\[\n \\be... | [
"To solve the long multiplication equation \\(98 \\times 26\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 98 \\\\\n \\times 26 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 98 by 6:**\n \\[\n \\begin{ar... | 8c0e33c535b7a63cb0e25777a413c42fa130c29cb118ba3c61fd859b3a9c4d6c | ebe7d31c37268e00b3e15a7d1c6fee395972cb4ee6d296359a3a4a6591d2ef77 | 299ae77a4ef350ae0dd37d6bba1c002d03444fb1edb236b341962dec14cb4bb4 | 1 | [
"2548"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'So, the solution to the long multiplication equation 98 x 26 is \(\boxed{2548}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"2548"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 98 and 26, we can break it down step by step:\n\n1. Multiply 98 by 6 (the units digit of 26):\n - 98 x 6 = 588\n\n2. Multiply 98 by 20 (the tens digit of 26, which is 2, but we treat it as 20):\n - 98 x 20 = 1960\n\n3. Now, add the two res... | |
44 | {
"answer": "2632",
"args": [
"28",
"94"
],
"is_model_response_correct": [
false,
true,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 2632 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n28 x 94\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(28 \\times 94\\), we can break it down into simpler steps:\n\n1. **Multiply 28 by 4 (the units digit of 94):**\n \\[\n 28 \\times 4 = 112\n \\]\n\n2. **Multiply 28 by 90 (the tens digit of 94, which is 9 x 10):**\n \\[\n 28 \\times 90 = 2520\n \\]\n\n3... | [
"To solve the long multiplication equation \\(28 \\times 94\\), we can break it down into simpler steps:\n\n1. **Multiply 28 by 4 (the units digit of 94):**\n \\[\n 28 \\times 4 = 112\n \\]\n\n2. **Multiply 28 by 90 (the tens digit of 94, which is 9 x 10):**\n \\[\n 28 \\times 90 = 2520\n \\]\n\n3. **Ad... | ffdbdf9654f70a733a5183d67ee9083f28979bd52a8f43b4e84b48cf9845ed5e | 8afb418759f7d62a96632f073c86be784901a304c831ff9759144b60e38c40f9 | 994aa605e86d263f1818ca1cec63a70b694f492aa906560e90ca193ef4dc181d | 1 | [
"2632"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "So, the solution to the long multiplication equation 28 x 94 is \(\boxed{2632}\)." This is a clear proposal of the final answer to the multiplication problem. | 1 | [
"2632"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 28 and 94, we can break it down step by step:\n\n1. Multiply 28 by 4 (the units digit of 94):\n - 28 x 4 = 112\n\n2. Multiply 28 by 9 (the tens digit of 94), remembering to add a zero since we are actually multiplying by 90:\n - 28 x 9 = 2... | |
45 | {
"answer": "4940",
"args": [
"52",
"95"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 4940 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n95 x 52\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 95 \\times 52 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 95 \\\\\n \\times 52 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 95 by 2 (the units digit of 52):**\n \\[\n 95 \\times 2 = 1... | [
"To solve the long multiplication equation \\( 95 \\times 52 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 95 \\\\\n \\times 52 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 95 by 2 (the units digit of 52):**\n \\[\n 95 \\times 2 = 190\n ... | 9e6d8c1875e5403a84b150505e7aeb598338a53f5ba513c3f34c4c56851cacd2 | f49cba7bc037f51765637f2709241dc04578a88c191f64e0287355aa6f03aec0 | 468aa3110cc6849759a36fda915c5f1f3b13c20c1a877a385136eec9fa8b7b2b | 1 | [
"4940"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is made when it states, "So, the solution to the long multiplication equation 95 x 52 is \(\boxed{4940}\)." This counts as the first proposal. 2. The second proposal is made again when it states, "So, the solution to the long multiplication equation 95 x 52 is indeed \(\boxed{494... | 5 | [
"4940",
"4940",
"4940",
"4940",
"4940"
] | [
true,
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 95 and 52, we can break it down step by step:\n\n1. Multiply 95 by 2:\n 95 x 2 = 190\n\n2. Multiply 95 by 50 (which is 5 with a zero):\n 95 x 50 = 4750\n\n3. Now, add the two results together:\n 190 + 4750 = 4940\n\nSince the calculated ... | |
46 | {
"answer": "1971",
"args": [
"27",
"73"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1971 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n73 x 27\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(73 \\times 27\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 73 \\\\\n \\times 27 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 73 by 7 (the units digit of... | [
"To solve the long multiplication equation \\(73 \\times 27\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 73 \\\\\n \\times 27 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 73 by 7 (the units digit of 27):*... | d66b9256ce5f722c62c16e480f38406f303e317d204732843ecee7af9b7d447a | b840c9b2dd2046991701a37aa2a5e32c4004901b8d30b860a857aca1e969f777 | 2b5d2ba5803e6fe3a2bc08b5f3965f47a92918a9c44b8090618d5d5a2876cf8c | 0 | [
"1911"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 73 x 27 is \(\boxed{1911}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1911"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 73 and 27, we can break it down step by step:\n\n1. Multiply 73 by 7 (the units digit of 27):\n - 73 x 7 = 511\n\n2. Multiply 73 by 20 (the tens digit of 27, which is 2, but we treat it as 20):\n - 73 x 20 = 1460\n\n3. Now, add the two re... | |
47 | {
"answer": "1971",
"args": [
"27",
"73"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1971 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n73 x 27\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(73 \\times 27\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 73 \\\\\n \\times 27 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 73 by 7 (the units digit of... | [
"To solve the long multiplication equation \\(73 \\times 27\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 73 \\\\\n \\times 27 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 73 by 7 (the units digit of 27):*... | 60451d740e655795fda6cc93ad0228325e1c7666481d8ea7c210953fe061480a | b840c9b2dd2046991701a37aa2a5e32c4004901b8d30b860a857aca1e969f777 | 2b5d2ba5803e6fe3a2bc08b5f3965f47a92918a9c44b8090618d5d5a2876cf8c | 0 | [
"1911"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 73 x 27 is \(\boxed{1911}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1911"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 73 and 27, we can break it down step by step:\n\n1. Multiply 73 by 7 (the units digit of 27):\n - 73 x 7 = 511\n\n2. Multiply 73 by 20 (the tens digit of 27, which is 2, but we treat it as 20):\n - 73 x 20 = 1460\n\n3. Now, add the two re... | |
48 | {
"answer": "3300",
"args": [
"55",
"60"
],
"is_model_response_correct": [
false,
false,
true,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 3300 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n60 x 55\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(60 \\times 55\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(60\\) is \\(6\\) tens.\n - \\(55\\) can be split into \\(50\\) (which is \\(5\\) tens) and \\(5\\) ones.\n\n2. **Multiply the numbers:**\n - First, multiply \... | [
"To solve the long multiplication equation \\(60 \\times 55\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(60\\) is \\(6\\) tens.\n - \\(55\\) can be split into \\(50\\) (which is \\(5\\) tens) and \\(5\\) ones.\n\n2. **Multiply the numbers:**\n - First, multiply \\(6\\)... | 2d04e708f990a2dacc3a627390f4b53d37170d1a5f0b76c8918c2f6d5832c775 | edb8975dae1a4824f7e83467f034126c806a8045072d7c859348c0340fac8960 | d3b63363e3c4234a3fa5ad9e7dac9449c7fc9a4b3c28236247d3bace953f9de7 | 1 | [
"3300"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 60 x 55 is \(\boxed{3300}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"3300"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 60 and 55, we can break it down step by step:\n\n1. Multiply 60 by 50: 60 x 50 = 3000\n2. Multiply 60 by 5: 60 x 5 = 300\n3. Add the two results together: 3000 + 300 = 3300\n\nThus, the solution provided (3300) is indeed correct and matches th... | |
49 | {
"answer": "7938",
"args": [
"81",
"98"
],
"is_model_response_correct": [
false,
false,
false,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 7938 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n81 x 98\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(81 \\times 98\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nStep 1: Break down the number 98 into 100 and 9.\n\\(81 \\times 98 = 81 \\times (100 - 2)\\)\n\nStep 2: Distribute the multiplication o... | [
"To solve the long multiplication equation \\(81 \\times 98\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nStep 1: Break down the number 98 into 100 and 9.\n\\(81 \\times 98 = 81 \\times (100 - 2)\\)\n\nStep 2: Distribute the multiplication over th... | df214ec1eb79b5b19d136c2c10c20b0e99284e63e0e880edff0e480fb0448fcf | deb99a09475f0da99bd0fa3c2f0b4265b993a878a3083ef5948cec53510d162d | 93bad48c1cec2fd81754d3b51b5bd2e53b4c838721f2019f15e9ecd20f0ddd88 | 0 | [
"8938"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 81 x 98 is \boxed{8938}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"8938"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 81 and 98, we can break it down step by step:\n\n1. Multiply 81 by 8 (the units digit of 98):\n - 81 x 8 = 648\n\n2. Multiply 81 by 9 (the tens digit of 98), remembering to shift one position to the left (which is equivalent to multiplying ... | |
50 | {
"answer": "7938",
"args": [
"81",
"98"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 7938 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n81 x 98\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(81 \\times 98\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nStep 1: Break down the number 98 into 100 and 9.\n\\(81 \\times 98 = 81 \\times (100 - 2)\\)\n\nStep 2: Distribute the multiplication o... | [
"To solve the long multiplication equation \\(81 \\times 98\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nStep 1: Break down the number 98 into 100 and 9.\n\\(81 \\times 98 = 81 \\times (100 - 2)\\)\n\nStep 2: Distribute the multiplication over th... | 284b79c1ed262f5c074eea4266b91f3b20d7c5cbda7ae205dfc69ff3a0187d04 | deb99a09475f0da99bd0fa3c2f0b4265b993a878a3083ef5948cec53510d162d | 93bad48c1cec2fd81754d3b51b5bd2e53b4c838721f2019f15e9ecd20f0ddd88 | 0 | [
"8938"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 81 x 98 is \boxed{8938}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"8938"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 81 and 98, we can break it down step by step:\n\n1. Multiply 81 by 8 (the units digit of 98):\n 81 x 8 = 648\n\n2. Multiply 81 by 9 (the tens digit of 98), remembering to shift one position to the left (which is equivalent to multiplying by... | |
51 | {
"answer": "5429",
"args": [
"61",
"89"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 5429 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n61 x 89\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(61 \\times 89\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 61 by 9 (the units digit of 89):**\n \\[\n 61 \\times 9 = 549\n \\]\n\n2. **Multiply 61 by 8 (the tens digit of 89) and shift the result one plac... | [
"To solve the long multiplication equation \\(61 \\times 89\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 61 by 9 (the units digit of 89):**\n \\[\n 61 \\times 9 = 549\n \\]\n\n2. **Multiply 61 by 8 (the tens digit of 89) and shift the result one place to t... | cb3fd0337bf41fe178b161b64be88ada5f25ce6e436865dbefe9e46dad980ee6 | b57c15b13942b48bcd4aaa06595aa9a0c177ef12a905a7192150e2001502d365 | 4681639741f445ef193092a92a0d77973f1f497144139fb45798b288edfd242e | 1 | [
"5429"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 61 x 89 is \(\boxed{5429}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"5429"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 61 and 89, we can break it down step by step:\n\n1. Multiply 61 by 9:\n - 61 x 9 = 549\n\n2. Multiply 61 by 80 (which is 8 times 10):\n - 61 x 8 = 488\n - Then, multiply 488 by 10 to account for the zero in 80:\n - 488 x 10 = 4880\n\n3... | |
52 | {
"answer": "5429",
"args": [
"61",
"89"
],
"is_model_response_correct": [
false,
false,
false,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 5429 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n61 x 89\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(61 \\times 89\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 61 by 9 (the units digit of 89):**\n \\[\n 61 \\times 9 = 549\n \\]\n\n2. **Multiply 61 by 8 (the tens digit of 89) and shift the result one plac... | [
"To solve the long multiplication equation \\(61 \\times 89\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 61 by 9 (the units digit of 89):**\n \\[\n 61 \\times 9 = 549\n \\]\n\n2. **Multiply 61 by 8 (the tens digit of 89) and shift the result one place to t... | f151f9a5efaa5a3b307c02ebfc3562754ea3ca759463130fcc2f8765cf41273f | b57c15b13942b48bcd4aaa06595aa9a0c177ef12a905a7192150e2001502d365 | 4681639741f445ef193092a92a0d77973f1f497144139fb45798b288edfd242e | 1 | [
"5429"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 61 x 89 is \(\boxed{5429}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"5429"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 61 and 89, we can break it down step by step:\n\n1. Multiply 61 by 9:\n - 61 x 9 = 549\n\n2. Multiply 61 by 80 (which is 8 times 10):\n - 61 x 8 = 488\n - Then, multiply 488 by 10 to account for the zero: 4880\n\n3. Now, add the two resu... | |
53 | {
"answer": "5429",
"args": [
"61",
"89"
],
"is_model_response_correct": [
false,
true,
false,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 5429 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n61 x 89\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(61 \\times 89\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 61 by 9 (the units digit of 89):**\n \\[\n 61 \\times 9 = 549\n \\]\n\n2. **Multiply 61 by 8 (the tens digit of 89) and shift the result one plac... | [
"To solve the long multiplication equation \\(61 \\times 89\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 61 by 9 (the units digit of 89):**\n \\[\n 61 \\times 9 = 549\n \\]\n\n2. **Multiply 61 by 8 (the tens digit of 89) and shift the result one place to t... | 1eced2dc3f1ec2177a127d36414e6d46e4afc4367fabbd173cc73b81a42949dd | b57c15b13942b48bcd4aaa06595aa9a0c177ef12a905a7192150e2001502d365 | 4681639741f445ef193092a92a0d77973f1f497144139fb45798b288edfd242e | 1 | [
"5429"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 61 x 89 is \(\boxed{5429}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or double checks of this answer in the trace, so the total count remains 1. | 1 | [
"5429"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 61 and 89, we can break it down step by step:\n\n1. Multiply 61 by 9:\n - 61 x 9 = 549\n\n2. Multiply 61 by 80 (which is 8 times 10):\n - 61 x 8 = 488\n - Since this is actually 80, we write it as 4880.\n\n3. Now, add the two results tog... | |
54 | {
"answer": "5368",
"args": [
"61",
"88"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 5368 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n88 x 61\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 88 \\times 61 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 88 \\\\\n \\times 61 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 88 by 1 (the units digit of 61):**\n \\[\n 88 \\times 1 = 88\n \\]\... | [
"To solve the long multiplication equation \\( 88 \\times 61 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 88 \\\\\n \\times 61 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 88 by 1 (the units digit of 61):**\n \\[\n 88 \\times 1 = 88\n \\]\n Wr... | d1109300fd983ce48c2e48aaf416c406c1e233b08d4ea48708aec65bffde365e | bdc481e710d9b12d71b4fe72da1f242a34e7f91dc881e4afed5a6adbd219d4b3 | e1cbed0ecbee7325a4820b48e02453e8a4e5fe0a2f47fc493814497368b95784 | 0 | [
"5168"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 88 x 61 is \boxed{5168}." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"5168"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 88 and 61, we can break it down step by step:\n\n1. Multiply 88 by 1 (the units digit of 61):\n 88 x 1 = 88\n\n2. Multiply 88 by 6 (the tens digit of 61), remembering that this is actually 60:\n 88 x 6 = 528 (since 88 x 6 = 528, and we ne... | |
55 | {
"answer": "2912",
"args": [
"52",
"56"
],
"is_model_response_correct": [
false,
false,
true,
true,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 2912 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n52 x 56\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(52 \\times 56\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 52 \\\\\n \\times 56 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 52 by 6 (the units digit of 56):**\n \\[\n 52 \\times 6 = 312\n \\]\n... | [
"To solve the long multiplication equation \\(52 \\times 56\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 52 \\\\\n \\times 56 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 52 by 6 (the units digit of 56):**\n \\[\n 52 \\times 6 = 312\n \\]\n Wri... | 8150a2a1cb13f7dc1736d03f6ced5d18064bdcf14146dc8e85db69ae655c7ade | 629b32f400c4068cd98b186d4ef5e7f93a67a28ad48aa1c331ce54f4549b740a | 5c9a7f508de2f1ec87076e88a888f9af847c69d68565ab6a6983fc8b497fa1f8 | 1 | [
"2912"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the multiplication 52 x 56 is \(\boxed{2912}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"2912"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 52 and 56, we can break it down step by step:\n\n1. Multiply 52 by 6 (the units digit of 56):\n - 52 x 6 = 312\n\n2. Multiply 52 by 50 (the tens digit of 56, which is 5, but we treat it as 50):\n - 52 x 50 = 2600\n\n3. Now, add the two res... | |
56 | {
"answer": "630",
"args": [
"15",
"42"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 630 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n15 x 42\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 15 \\times 42 \\), we can break it down into simpler steps:\n\n1. **Multiply 15 by 2:**\n \\[\n 15 \\times 2 = 30\n \\]\n\n2. **Multiply 15 by 40 (which is the same as 4 times 10):**\n \\[\n 15 \\times 40 = 15 \\times (4 \\times 10) = (15 \\times 4) \\t... | [
"To solve the long multiplication equation \\( 15 \\times 42 \\), we can break it down into simpler steps:\n\n1. **Multiply 15 by 2:**\n \\[\n 15 \\times 2 = 30\n \\]\n\n2. **Multiply 15 by 40 (which is the same as 4 times 10):**\n \\[\n 15 \\times 40 = 15 \\times (4 \\times 10) = (15 \\times 4) \\times 1... | 98fe82570e9ea4ef30be3f9dc9f198e6c4215a33370104921d16886d5b32caa9 | 352154992aade7f07d0856ecc4fb10e53d1fd758fc8ab99af8523a751b4d0206 | 21900f41ecb7b8e6cfd9250f096aad2fe7f6d8fbec9436b2d28e48c304ff8255 | 1 | [
"630"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 15 x 42 is: \[\boxed{630}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"630"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 15 and 42, we can break it down step by step:\n\n1. Multiply 15 by 2 (the units digit of 42):\n 15 x 2 = 30\n\n2. Multiply 15 by 4 (the tens digit of 42), remembering to add a zero since we are actually multiplying by 40:\n 15 x 4 = 60, an... | |
57 | {
"answer": "290",
"args": [
"10",
"29"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 290 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n29 x 10\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(29 \\times 10\\), we can follow these steps:\n\n1. **Understand the problem**: We need to multiply the number 29 by 10.\n\n2. **Understand the multiplication**: Multiplying by 10 simply means adding a zero at the end of the number. \n\n3. **Apply the multiplicatio... | [
"To solve the long multiplication equation \\(29 \\times 10\\), we can follow these steps:\n\n1. **Understand the problem**: We need to multiply the number 29 by 10.\n\n2. **Understand the multiplication**: Multiplying by 10 simply means adding a zero at the end of the number. \n\n3. **Apply the multiplication**: \... | b159defd729548d1f1707c7ff5545c6360aff66d6f53fc91e3684c3a3b5862f6 | ffb5eb35d754b35cd7c63c21d844f5b7f17fbb025be7b24625ebfc8269390f41 | 09895de0407bcb0386733daa14bdb5dfa544505530c634334a05a60f161b71fc | 1 | [
"290"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "Therefore, the solution to the equation 29 x 10 is \(\boxed{290}\)." This is a clear conclusion of the reasoning process, presenting the final answer directly. | 1 | [
"290"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 29 by 10, we can break it down as follows: 29 multiplied by 10 means we are essentially adding a zero to the end of 29. Therefore, 29 x 10 = 290. The provided solution of 290 matches the ground truth solution, confirming that it is correct."
... | |
58 | {
"answer": "2350",
"args": [
"25",
"94"
],
"is_model_response_correct": [
false,
false,
false,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 2350 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n94 x 25\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(94 \\times 25\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 94 \\times 25 = 94 \\times (20 + 5)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Distribute the multi... | [
"To solve the long multiplication equation \\(94 \\times 25\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 94 \\times 25 = 94 \\times (20 + 5)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Distribute the multiplicat... | a35d7942e1ab164975883c941e2011688d9b7d6253ac3eac41012729e2456bed | 128a7d7906e11a3e54424e7b74fb4eb21b05d436c1999dc4819eb4df63693606 | 8c0b66d905f165b50e3b6c9e0e29961c5bd9c3083cde920bf5a74c8e8dc45d59 | 1 | [
"2350"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 94 x 25 is \(\boxed{2350}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"2350"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 94 by 25, we can break it down step by step:\n\n1. Multiply 94 by 5 (the units digit of 25):\n - 94 x 5 = 470\n\n2. Multiply 94 by 20 (the tens digit of 25, which is 2, but we treat it as 20):\n - 94 x 20 = 1880\n\n3. Now, add the two resu... | |
59 | {
"answer": "2744",
"args": [
"49",
"56"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 2744 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n56 x 49\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(56 \\times 49\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nStep 1: Break down the number 49 into 50 - 1.\n\\[56 \\times 49 = 56 \\times (50 - 1)\\]\n\nStep 2: Use the distributive property to se... | [
"To solve the long multiplication equation \\(56 \\times 49\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nStep 1: Break down the number 49 into 50 - 1.\n\\[56 \\times 49 = 56 \\times (50 - 1)\\]\n\nStep 2: Use the distributive property to separate... | c66e0393b11ed4657f947a5666c809eb027bf67d7f497f44a7162d88e049928c | 96f0cf9b454a9d508f20006f87fee35b26f57f6ef5b1e8f4e9b7d11c053ea894 | c4b6fe20fadf12a363d8583f4a43eaf17bdffe8c65aa383e15cd0f38ee7acdc5 | 1 | [
"2744"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 56 x 49 is \boxed{2744}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"2744"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 56 and 49, we can break it down step by step:\n\n1. Multiply 56 by 9 (the units digit of 49):\n - 56 x 9 = 504\n\n2. Multiply 56 by 40 (the tens digit of 49, which is 4, multiplied by 10):\n - 56 x 40 = 2240\n\n3. Now, add the two results ... | |
60 | {
"answer": "624",
"args": [
"12",
"52"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 624 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n12 x 52\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(12 \\times 52\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n - First, multiply \\(10\\) by \\(52\\):\n \\[\n 10 \\times 52 = 520\n \\]\n - Next, multiply \\(2\\) by \\(52\\):\n \\[\n 2 \\times 52 = 1... | [
"To solve the long multiplication equation \\(12 \\times 52\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n - First, multiply \\(10\\) by \\(52\\):\n \\[\n 10 \\times 52 = 520\n \\]\n - Next, multiply \\(2\\) by \\(52\\):\n \\[\n 2 \\times 52 = 104\n ... | 9ed6826a8e25e9c8d9d0884f4035312340ae43fae4f92b9d052ccdb9922684ef | beca039384243192a5b71e8f752c0b67e67e56209f908f2e74835651b9ed319b | 1b3c33580f2e2094cbde0bfd58f8008ee6e29c06643ca310222045c82fe0ab0e | 1 | [
"624"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 12 x 52 is \(\boxed{624}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"624"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 12 and 52, we can break it down step by step:\n\n1. Multiply 12 by 2 (the units digit of 52):\n 12 x 2 = 24\n\n2. Multiply 12 by 5 (the tens digit of 52), remembering to add a zero since we are actually multiplying by 50:\n 12 x 5 = 60, an... | |
61 | {
"answer": "3782",
"args": [
"61",
"62"
],
"is_model_response_correct": [
false,
false,
false,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 3782 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n62 x 61\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(62 \\times 61\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. **Break down the numbers:**\n \\[\n 62 = 60 + 2\n \\]\n \\[\n 61 = 60 + 1\n \\]\n\n2. **Apply the distributive property:... | [
"To solve the long multiplication equation \\(62 \\times 61\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. **Break down the numbers:**\n \\[\n 62 = 60 + 2\n \\]\n \\[\n 61 = 60 + 1\n \\]\n\n2. **Apply the distributive property:**\n ... | f2a9099644ab2f16ea340a62637b4c0f1ad2356006e8e74179bdf17a13e8e94b | 53732e9458465c5fc0b9a025b1ea1ea9f8c1195e9b835b03b7326121e2d57517 | 408a880c854efce7b187df7599e3c8899576675878f69fe7de21a085c99cbf84 | 0 | [
"3882"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 62 x 61 is \(\boxed{3882}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"3882"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 62 and 61, we can break it down step by step:\n\n1. Multiply 62 by 1 (the units place of 61):\n 62 x 1 = 62\n\n2. Multiply 62 by 6 (the tens place of 61), remembering to shift one position to the left:\n 62 x 6 = 372 (this is actually 372... | |
62 | {
"answer": "3782",
"args": [
"61",
"62"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 3782 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n61 x 62\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 61 \\times 62 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n 6 & 1 \\\\\n \\times 6 & 2 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 61 by 2 (the unit... | [
"To solve the long multiplication equation \\( 61 \\times 62 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c}\n 6 & 1 \\\\\n \\times 6 & 2 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 61 by 2 (the units digi... | 1617f4ea6e55c86aced694e26a1fa536de5392d9afa809fe60ebb8819afce3fd | 3f30fb08e9569db157bcf055d33e49c2950bf38cbd45c849740455aa89007583 | 408a880c854efce7b187df7599e3c8899576675878f69fe7de21a085c99cbf84 | 0 | [
"488"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal is made when the model states, "So, the solution to the long multiplication equation 61 x 62 is \boxed{500}." This counts as a proposal of a final answer. 2. The model then proposes an alternative method and states, "So, the solution using the alternative method is \boxed{3782}." This is another p... | 5 | [
"500",
"3782",
"500",
"500",
"500"
] | [
false,
true,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 61 and 62, we can break it down step by step:\n\n1. First, we can use the standard multiplication method:\n - Multiply 61 by 2 (the units digit of 62): 61 x 2 = 122\n - Multiply 61 by 6 (the tens digit of 62), remembering to shift one posi... | |
63 | {
"answer": "330",
"args": [
"11",
"30"
],
"is_model_response_correct": [
true,
true,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 330 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n30 x 11\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(30 \\times 11\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n - First, multiply 30 by 1.\n - Then, multiply 30 by 10.\n\n2. **Calculate each part:**\n - \\(30 \\times 1 = 30\\)\n - \\(30 \\times 10 = 300\\)\n\n3. **A... | [
"To solve the long multiplication equation \\(30 \\times 11\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n - First, multiply 30 by 1.\n - Then, multiply 30 by 10.\n\n2. **Calculate each part:**\n - \\(30 \\times 1 = 30\\)\n - \\(30 \\times 10 = 300\\)\n\n3. **Add the... | 069826b3b66847851e4c04d24b804583068787b821609b0a98cac868594785bd | b67c7bb5e04f5e654e7812014400fd94fe8dbcea50a502d2d34d103b836a9c2d | 5426d2ca50f244fb43fe9eafc82da08f33f3b4f8d9140802bd0102e780b629d6 | 1 | [
"330"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 30 x 11 is \(\boxed{330}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"330"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 30 and 11, we can break it down as follows: \n\n1. Multiply 30 by 1, which gives us 30.\n2. Multiply 30 by 10, which gives us 300.\n3. Now, add the two results together: 30 + 300 = 330.\n\nThus, the solution of 30 x 11 is indeed 330, which matc... | |
64 | {
"answer": "4720",
"args": [
"59",
"80"
],
"is_model_response_correct": [
false,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 4720 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n59 x 80\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(59 \\times 80\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication**:\n - First, multiply \\(59\\) by \\(8\\).\n - Then, multiply \\(59\\) by \\(10\\), and add the result to the product of \\(59\\) and \\(8\\).\n\nStep-by-step:\n\... | [
"To solve the long multiplication equation \\(59 \\times 80\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication**:\n - First, multiply \\(59\\) by \\(8\\).\n - Then, multiply \\(59\\) by \\(10\\), and add the result to the product of \\(59\\) and \\(8\\).\n\nStep-by-step:\n\n1. Mu... | 4ebb040c2fa85e359432347dfd0bcf1795adfa69136243f7e16cb2fa72efed06 | 4e5308be9cf665f2b639f12d43f43fe2e88c443452675e2e950b593619d828b7 | 29d504c9de3a93087127598b41c8e80273fde962f3da43e6f0fe3dded7a3d2a8 | 0 | [
"1062"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 59 x 80 is 1062." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1062"
] | [
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 59 by 80, we can break it down step by step:\n\n1. Multiply 59 by 8 (the units digit of 80):\n - 59 x 8 = 472\n\n2. Since 80 is actually 8 with a zero at the end, we need to multiply the result by 10:\n - 472 x 10 = 4720\n\nThus, the corre... | |
65 | {
"answer": "4720",
"args": [
"59",
"80"
],
"is_model_response_correct": [
false,
true,
true,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ab... | 4720 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n80 x 59\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(80 \\times 59\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 80 \\times 59 = 80 \\times (60 - 1)\n \\]\n\n2. **Distribute the multiplication:**\n \\[\n 80 \\times 60 - 80 \\times 1\n \\]\n\n3. **Calculate ... | [
"To solve the long multiplication equation \\(80 \\times 59\\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 80 \\times 59 = 80 \\times (60 - 1)\n \\]\n\n2. **Distribute the multiplication:**\n \\[\n 80 \\times 60 - 80 \\times 1\n \\]\n\n3. **Calculate each p... | 58147de83ea12feda58c7e8d6735b76d532240bb203994cc0577f708ce0a8080 | 35a6a3b0d8f806e10397a216bb4e920f89a3548d252d1885d865e8275a4868be | 29d504c9de3a93087127598b41c8e80273fde962f3da43e6f0fe3dded7a3d2a8 | 1 | [
"4720"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 80 x 59 is \(\boxed{4720}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"4720"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 80 and 59, we can break it down step by step:\n\n1. Multiply 80 by 59 directly:\n - 80 x 59 = 80 x (50 + 9) = (80 x 50) + (80 x 9)\n - Calculate 80 x 50 = 4000\n - Calculate 80 x 9 = 720\n - Now add the two results: 4000 + 720 = 4720\n... | |
66 | {
"answer": "1281",
"args": [
"21",
"61"
],
"is_model_response_correct": [
false,
false,
true,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 1281 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n21 x 61\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(21 \\times 61\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 21 \\\\\n \\times 61 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 21 by 1 (the units digit of 61):**\n \\[\n 21 \\times 1 = 21\n \\]\n ... | [
"To solve the long multiplication equation \\(21 \\times 61\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 21 \\\\\n \\times 61 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 21 by 1 (the units digit of 61):**\n \\[\n 21 \\times 1 = 21\n \\]\n Writ... | d1946d3bbc7129aa62030af9397006d24a4b50214f092ffecc76df88960cb27d | 02f4ef2c828809162d0771ca45407b028019e03b8af4fad9b76dbf47e35f4ae2 | c2a824544a0afd72c9bfe30643efd67fa7b92401d1468625235b3b7cce716a8b | 1 | [
"1281"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer in step 5: 'So, the solution to the long multiplication equation 21 x 61 is \(\boxed{1281}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1281"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 21 and 61, we can break it down step by step:\n\n1. Multiply 21 by 1 (the units digit of 61):\n 21 x 1 = 21\n\n2. Multiply 21 by 6 (the tens digit of 61), remembering that this is actually 60 (6 in the tens place):\n 21 x 6 = 126, but sinc... | |
67 | {
"answer": "1870",
"args": [
"22",
"85"
],
"is_model_response_correct": [
false,
true,
false,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 1870 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n85 x 22\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(85 \\times 22\\), we can break it down into simpler steps.\n\n1. **First Step: Multiply 85 by 20**\n - \\(85 \\times 20 = 1700\\) (because \\(85 \\times 2 = 170\\) and then add another zero).\n\n2. **Second Step: Multiply 85 by 2** \n - \\(85 \\times 2 = 170\\... | [
"To solve the long multiplication equation \\(85 \\times 22\\), we can break it down into simpler steps.\n\n1. **First Step: Multiply 85 by 20**\n - \\(85 \\times 20 = 1700\\) (because \\(85 \\times 2 = 170\\) and then add another zero).\n\n2. **Second Step: Multiply 85 by 2** \n - \\(85 \\times 2 = 170\\) (bec... | e710e444c78398c1cc9a52b7d319176c5604c9c3b1678c0bf7d0811c77cc1a4f | 5891095ec1b73d7997c310deb45b7d7bd9859584faf0f88ed6a420e3ab6205ff | cf085574d40ec95878b1c306a9b2432d86c05f888edc87a39708000b3e58b5f9 | 1 | [
"1870"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the equation 85 x 22 is 1870." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1870"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 85 by 22, we can break it down step by step:\n\n1. Multiply 85 by 2 (the units digit of 22):\n 85 x 2 = 170\n\n2. Multiply 85 by 20 (the tens digit of 22, which is 2, but we consider it as 20):\n 85 x 20 = 1700\n\n3. Now, add the two resul... | |
68 | {
"answer": "1870",
"args": [
"22",
"85"
],
"is_model_response_correct": [
true,
true,
false,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ab... | 1870 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n22 x 85\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(22 \\times 85\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 22 \\\\\n \\times 85 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 22 by 5 (the units digit of 85):**\n \\[\n 22 \\times 5 = 110\n \\]\n... | [
"To solve the long multiplication equation \\(22 \\times 85\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 22 \\\\\n \\times 85 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 22 by 5 (the units digit of 85):**\n \\[\n 22 \\times 5 = 110\n \\]\n Wri... | b710cb335a5f072a05dd60323a4f860d5ff855f2ae3b4469cef7cfe73feb6088 | a309486d4b15808d75541bfe08bc7218cd553107019c32b5c82ec12f4ecccafa | cf085574d40ec95878b1c306a9b2432d86c05f888edc87a39708000b3e58b5f9 | 1 | [
"1870"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the multiplication 22 x 85 is \(\boxed{1870}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1870"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 22 and 85, we can break it down step by step:\n\n1. Multiply 22 by 5 (the units digit of 85):\n 22 x 5 = 110\n\n2. Multiply 22 by 8 (the tens digit of 85), remembering to shift one position to the left (which is equivalent to multiplying by ... | |
69 | {
"answer": "1440",
"args": [
"16",
"90"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 1440 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n90 x 16\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 90 \\times 16 \\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 90 \\times 16 = (90 \\times 10) \\times 1.6\n \\]\n\n2. **Calculate \\( 90 \\times 10 \\):**\n \\[\n 90 \\times 10 = 900\n \\]\n\n3. **Calcula... | [
"To solve the long multiplication equation \\( 90 \\times 16 \\), we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 90 \\times 16 = (90 \\times 10) \\times 1.6\n \\]\n\n2. **Calculate \\( 90 \\times 10 \\):**\n \\[\n 90 \\times 10 = 900\n \\]\n\n3. **Calculate \\(... | 8ce3a69860c29f6932035966c72b4b1a53f0140ef9913e1eb97c7e7c31aaa4e4 | 96307378751ec452dce5a7cb36c266e1673087aec0ce7a0060f671d750059bda | a4ff3ad278c7b0575a8e32ae08eebfb327e37762cb1a2caa793c431b9b2ca2c6 | 0 | [
"1044"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 90 x 16 is 1044." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1044"
] | [
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 90 and 16, we can break it down step by step:\n\n1. Multiply 90 by 10 to get 900.\n2. Multiply 90 by 6 to get 540.\n3. Add the two results together: 900 + 540 = 1440.\n\nThus, the correct answer is 1440, not 1044. Therefore, the provided solut... | |
70 | {
"answer": "2280",
"args": [
"30",
"76"
],
"is_model_response_correct": [
true,
true,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 2280 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n30 x 76\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(30 \\times 76\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication into smaller parts:**\n - First, multiply 30 by 6.\n - Then, multiply 30 by 70 (since 76 can be split into 70 + 6).\n - Finally, add the results of these two mul... | [
"To solve the long multiplication equation \\(30 \\times 76\\), we can break it down into simpler steps:\n\n1. **Break down the multiplication into smaller parts:**\n - First, multiply 30 by 6.\n - Then, multiply 30 by 70 (since 76 can be split into 70 + 6).\n - Finally, add the results of these two multiplic... | ecf2b2672baf634dce012fc4e8d8c3a62fc2b01e9542959516af856b0c87e19b | a4d30d9362759c970dedb9290384b7d503cb01ae7dbe2a0d6cbf523579614923 | 27bb55ca7d1e8404f09fe32cd45c380b462107b39f2dee0c3e2193e25afdf1f6 | 1 | [
"2280"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 30 x 76 is \(\boxed{2280}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"2280"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the solution, we can perform the multiplication step by step. First, we can break down the multiplication: \n\n1. Multiply 30 by 76 directly: \n - 30 x 76 = 30 x (70 + 6) \n - = 30 x 70 + 30 x 6 \n - = 2100 + 180 \n - = 2280 \n\nThe calculated result matche... | |
71 | {
"answer": "703",
"args": [
"19",
"37"
],
"is_model_response_correct": [
true,
false,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 703 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n19 x 37\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(19 \\times 37\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 19 \\\\\n \\times 37 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 19 by 7 (the un... | [
"To solve the long multiplication equation \\(19 \\times 37\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 19 \\\\\n \\times 37 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 19 by 7 (the units di... | e00d4e77240b1a0ee00e88094d08ae191130a23f8308d1fba5a03c10fc1740ca | f9bfc9e7d134d5656336979f4143db31b62c9ce54d4779d73fd0c0e72b652e80 | 769e881d85fc5d27cb4cbc8382200d95b179cfdeb56e0b439da737069eaf8a5a | 1 | [
"703"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 19 x 37 is \(\boxed{703}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"703"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 19 and 37, we can perform the calculation step by step:\n\n1. Multiply 19 by 7 (the units digit of 37):\n 19 x 7 = 133\n\n2. Multiply 19 by 3 (the tens digit of 37), remembering to shift one position to the left (which is equivalent to multi... | |
72 | {
"answer": "703",
"args": [
"19",
"37"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 703 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n37 x 19\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(37 \\times 19\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Write down the numbers and align them vertically:\n \\[\n \\begin{array}{r}\n 37 \\\\\n \\times 19 \\\\... | [
"To solve the long multiplication equation \\(37 \\times 19\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Write down the numbers and align them vertically:\n \\[\n \\begin{array}{r}\n 37 \\\\\n \\times 19 \\\\\n \... | 593bb1ef9b960d0f96fe61b90bbc52279759be1bce30d745ee0cc2a8e32c3574 | 7597f7865bc9467c65ca321e573ba450f19c2f6eec77bdcf519a5777415c4417 | 769e881d85fc5d27cb4cbc8382200d95b179cfdeb56e0b439da737069eaf8a5a | 1 | [
"703"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 37 x 19 is 703." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"703"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 37 and 19, we can break it down step by step:\n\n1. Multiply 37 by 9 (the units digit of 19):\n - 37 x 9 = 333\n\n2. Multiply 37 by 10 (the tens digit of 19, which is actually 1, but we consider it as 10):\n - 37 x 10 = 370\n\n3. Now, add ... | |
73 | {
"answer": "5510",
"args": [
"58",
"95"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 5510 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n58 x 95\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(58 \\times 95\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 58 \\\\\n \\times 95 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 58 by 5 (the units digit of... | [
"To solve the long multiplication equation \\(58 \\times 95\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 58 \\\\\n \\times 95 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 58 by 5 (the units digit of 95):*... | 4b34e2104ee1d13d969efb5806608a70415143f2ff1e7137308a6e341a3a1856 | 84e73a0373fdc7dbcd058c46fab6cda2aecd7ac2cb6ef37ebd5ec41d9491d100 | 4b177cf57484bae04e725e7718a8f17dee4768dda340ac5d160f339b35fe298c | 1 | [
"5510"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is when the model states, "So, the solution to the multiplication 58 x 95 is \(\boxed{5510}\)." This counts as the first proposal.
2. The first verification occurs when the model states, "But I need to verify this. Let's use a calculator method: \[ 58 \times 95 = 5510 \] This c... | 3 | [
"5510",
"5510",
"5510"
] | [
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 58 and 95, we can break it down step by step:\n\n1. Multiply 58 by 5 (the units digit of 95):\n - 58 x 5 = 290\n\n2. Multiply 58 by 9 (the tens digit of 95), remembering to shift one position to the left (which is equivalent to multiplying b... | |
74 | {
"answer": "5510",
"args": [
"58",
"95"
],
"is_model_response_correct": [
true,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 5510 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n58 x 95\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(58 \\times 95\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 58 \\\\\n \\times 95 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 58 by 5 (the units digit of... | [
"To solve the long multiplication equation \\(58 \\times 95\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 58 \\\\\n \\times 95 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 58 by 5 (the units digit of 95):*... | 8a8e1c73c57abaf105aee605cb0fbc90633f37e81d8152e357621c3c4a76a445 | 84e73a0373fdc7dbcd058c46fab6cda2aecd7ac2cb6ef37ebd5ec41d9491d100 | 4b177cf57484bae04e725e7718a8f17dee4768dda340ac5d160f339b35fe298c | 1 | [
"5510"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is when the model states, "So, the solution to the multiplication 58 x 95 is \(\boxed{5510}\)." This counts as a proposal because it clearly states the final answer. 2. The first verification occurs when the model says, "But I need to verify this. Let's use a calculator method: \... | 3 | [
"5510",
"5510",
"5510"
] | [
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 58 and 95, we can break it down step by step:\n\n1. Multiply 58 by 5 (the units digit of 95):\n - 58 x 5 = 290\n\n2. Multiply 58 by 9 (the tens digit of 95), remembering to shift one position to the left (which is equivalent to multiplying b... | |
75 | {
"answer": "5510",
"args": [
"58",
"95"
],
"is_model_response_correct": [
true,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 5510 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n95 x 58\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 95 \\times 58 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 95 \\\\\n \\times 58 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 95 by 8 (the ... | [
"To solve the long multiplication equation \\( 95 \\times 58 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 95 \\\\\n \\times 58 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 95 by 8 (the units ... | ae017615ccc0cbcf2b264a1f5f21758db92c6c33c36f9ef1a13db7e23abc6ba2 | ee08ad3951a497d47c48a100c3a0d5a73e7da368049913c1007330f7deb88bdd | 4b177cf57484bae04e725e7718a8f17dee4768dda340ac5d160f339b35fe298c | 1 | [
"5510"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "So, the solution to the long multiplication equation 95 x 58 is \boxed{5510}." This counts as the first proposal.
2. The first verification occurs when the model states: "But to confirm, let's use the alternative method to ensure accuracy." It then c... | 4 | [
"5510",
"5510",
"5510",
"5510"
] | [
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 95 and 58, we can break it down step by step:\n\n1. Multiply 95 by 8 (the units digit of 58):\n - 95 x 8 = 760\n\n2. Multiply 95 by 50 (the tens digit of 58, which is 5, but we treat it as 50):\n - 95 x 50 = 4750\n\n3. Now, add the two res... | |
76 | {
"answer": "370",
"args": [
"10",
"37"
],
"is_model_response_correct": [
true,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 370 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n10 x 37\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(10 \\times 37\\), follow these steps:\n\n1. Write the numbers one under the other, aligning the digits:\n ```\n 10\n x 37\n ----\n ```\n\n2. Multiply 10 by 7, which gives 70. Write down 70 below 10:\n ```\n 10\n x 37\n ----\n 70\n ```\n\n3... | [
"To solve the long multiplication equation \\(10 \\times 37\\), follow these steps:\n\n1. Write the numbers one under the other, aligning the digits:\n ```\n 10\n x 37\n ----\n ```\n\n2. Multiply 10 by 7, which gives 70. Write down 70 below 10:\n ```\n 10\n x 37\n ----\n 70\n ```\n\n3. Mult... | 7eba04c9bccccd2ed13ea589c187958e232a50fc7edabe6a87466ebe643fa63a | 92cb03a5184ff5188afbdb4d8c9c990c6dd6067aca6dc460208bd9c1f6edcf74 | f1607c19a0f910ca1b8dce18843bc34e46a533c87e3524ea75798949f7a352d5 | 1 | [
"370"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace concludes with a clear final answer: "So, the solution to the equation 10 x 37 is 370." This is a definitive statement that presents the final answer to the multiplication problem, thus counting as one proposal of a final answer. | 1 | [
"370"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 10 and 37, we can break it down as follows: 10 multiplied by 37 means we are adding 37 a total of 10 times. This can also be thought of as shifting the decimal point in 37 one place to the right, which gives us 370. Therefore, the solution prov... | |
77 | {
"answer": "370",
"args": [
"10",
"37"
],
"is_model_response_correct": [
true,
false,
false,
true,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 370 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n37 x 10\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(37 \\times 10\\), we can follow these steps:\n\n1. **Understand the problem**: We need to multiply the number 37 by 10.\n\n2. **Recall the properties of multiplication**: When you multiply a number by 10, you simply add a zero to the end of that number.\n\n3. **Pe... | [
"To solve the long multiplication equation \\(37 \\times 10\\), we can follow these steps:\n\n1. **Understand the problem**: We need to multiply the number 37 by 10.\n\n2. **Recall the properties of multiplication**: When you multiply a number by 10, you simply add a zero to the end of that number.\n\n3. **Perform ... | c46a19ab46f006740eb1c69b7cfd98c37baf1c8c87024ee195dcc06cac684f00 | a13a78cf18634cd10f8a3cee6dd9f30ff490492619210976dbdbf8b39b6d531d | f1607c19a0f910ca1b8dce18843bc34e46a533c87e3524ea75798949f7a352d5 | 1 | [
"370"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "Hence, the solution is \(\boxed{370}\)." This is a clear conclusion to the problem, presenting the final answer of 370. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"370"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 37 by 10, we can break it down as follows: 37 multiplied by 10 means we are essentially adding a zero to the end of 37. Therefore, 37 x 10 = 370. The provided solution of 370 matches the ground truth solution, confirming that it is correct."
... | |
78 | {
"answer": "4800",
"args": [
"60",
"80"
],
"is_model_response_correct": [
false,
true,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 4800 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n80 x 60\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(80 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply 80 by 6:**\n - We know that \\(80 \\times 6\\) is roughly \\(80 \\times (6 \\times 10)\\).\n - \\(6 \\times 10 = 60\\), so we have \\(80 \\times 60\\).\n - Multiplying \\(80\\) by \\... | [
"To solve the long multiplication equation \\(80 \\times 60\\), we can break it down into simpler steps:\n\n1. **Multiply 80 by 6:**\n - We know that \\(80 \\times 6\\) is roughly \\(80 \\times (6 \\times 10)\\).\n - \\(6 \\times 10 = 60\\), so we have \\(80 \\times 60\\).\n - Multiplying \\(80\\) by \\(6\\):... | e2bc93c56ec77c03b5ac646639227e6d2fd7a9ca58e8596e72d685cc8fd8341a | 65b99088aad23b47813cd1352b059f2e18055c8664612590da665915ead9631e | dea1ae8613ee2a5ef5504d98bd969bd46b4c75e9c898341f497c74684599030c | 1 | [
"4800"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The reasoning trace proposes a final answer at the end: "The final answer is \(\boxed{4800}\)." This is a clear proposal of the final answer to the multiplication problem, which counts as one instance. | 1 | [
"4800"
] | [
true
] | [
{
"correct": true,
"reasoning": "To solve the multiplication of 80 and 60, we can break it down as follows: \n\n1. Multiply the numbers directly: 80 x 60 = 4800. \n2. Alternatively, we can use the distributive property: \n - 80 can be expressed as 8 x 10, and 60 as 6 x 10. \n - Therefore, 80 x 60 = (8 x... | |
79 | {
"answer": "3108",
"args": [
"37",
"84"
],
"is_model_response_correct": [
true,
true,
true,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 3108 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n84 x 37\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(84 \\times 37\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 84 by 7 (the units digit of 37):**\n \\[\n 84 \\times 7 = 588\n \\]\n\n2. **Multiply 84 by 3 (the tens digit of 37 and shift it two... | [
"To solve the long multiplication equation \\(84 \\times 37\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 84 by 7 (the units digit of 37):**\n \\[\n 84 \\times 7 = 588\n \\]\n\n2. **Multiply 84 by 3 (the tens digit of 37 and shift it two place... | 85f1e157001de57056e7d7c420d69fd23432a0b4d28f686a497bbc348401a011 | 7cff8d1690e5512d4f703036ebbea73fb201233a1a6b3127f71a08b1037f40c5 | 50d65da5a5788e6183a480898578d672eb3f1d593a5b308e6e0b971e90fab6b9 | 1 | [
"3108"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 84 x 37 is \(\boxed{3108}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"3108"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 84 and 37, we can break it down step by step:\n\n1. Multiply 84 by 7 (the units digit of 37):\n - 84 x 7 = 588\n\n2. Multiply 84 by 30 (the tens digit of 37, which is 3, but we treat it as 30):\n - 84 x 30 = 2520\n\n3. Now, add the two res... | |
80 | {
"answer": "1980",
"args": [
"22",
"90"
],
"is_model_response_correct": [
true,
true,
true,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 1980 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n22 x 90\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(22 \\times 90\\), we can break it down into simpler steps:\n\n### Step 1: Break down 90 into tens and ones.\n- \\(90\\) can be written as \\(90 = 9 \\times 10\\).\n\n### Step 2: Multiply \\(22\\) by \\(9\\).\nThis is the primary multiplication:\n\\[ 22 \\times 9 =... | [
"To solve the long multiplication equation \\(22 \\times 90\\), we can break it down into simpler steps:\n\n### Step 1: Break down 90 into tens and ones.\n- \\(90\\) can be written as \\(90 = 9 \\times 10\\).\n\n### Step 2: Multiply \\(22\\) by \\(9\\).\nThis is the primary multiplication:\n\\[ 22 \\times 9 = ? \\]... | 5254f35a8a176d60a8b4605f14f48fd89c397b6447beb0d9ee32d9a7f4a44e41 | 36e89706aaf82c7dd2e2f176c2abcda7eafff5174efb9f98685bca96ab3fccaf | 051c2e380d07844ffaca43743957f8c0efe2bdf74c6c1e6a9dcccb8d1a3c596b | 1 | [
"1980"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer in the last step: "So, the solution to the long multiplication equation 22 x 90 is \(\boxed{1980}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1980"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 22 and 90, we can break it down step by step:\n\n1. Multiply 22 by 9 (the tens digit of 90):\n - 22 x 9 = 198\n\n2. Since 90 is 90 (which is 9 times 10), we multiply the result by 10:\n - 198 x 10 = 1980\n\nThus, the final result of 22 x 9... | |
81 | {
"answer": "1980",
"args": [
"22",
"90"
],
"is_model_response_correct": [
true,
true,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 1980 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n22 x 90\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(22 \\times 90\\), we can break it down into simpler steps:\n\n### Step 1: Break down 90 into tens and ones.\n- \\(90\\) can be written as \\(90 = 9 \\times 10\\).\n\n### Step 2: Multiply \\(22\\) by \\(9\\).\nThis is the primary multiplication:\n\\[ 22 \\times 9 =... | [
"To solve the long multiplication equation \\(22 \\times 90\\), we can break it down into simpler steps:\n\n### Step 1: Break down 90 into tens and ones.\n- \\(90\\) can be written as \\(90 = 9 \\times 10\\).\n\n### Step 2: Multiply \\(22\\) by \\(9\\).\nThis is the primary multiplication:\n\\[ 22 \\times 9 = ? \\]... | f4e396cf79c929b1c77102cbeecce4bf35b11a8429c375361b501a4c3b90b0b6 | 36e89706aaf82c7dd2e2f176c2abcda7eafff5174efb9f98685bca96ab3fccaf | 051c2e380d07844ffaca43743957f8c0efe2bdf74c6c1e6a9dcccb8d1a3c596b | 1 | [
"1980"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer in the last step: "So, the solution to the long multiplication equation 22 x 90 is \(\boxed{1980}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1980"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 22 and 90, we can break it down step by step:\n\n1. Multiply 22 by 9 (the tens place of 90):\n 22 x 9 = 198\n\n2. Since 90 is 9 times 10, we multiply the result by 10:\n 198 x 10 = 1980\n\nThus, the final result of 22 x 90 is indeed 1980, ... | |
82 | {
"answer": "2924",
"args": [
"43",
"68"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 2924 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n68 x 43\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(68 \\times 43\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 68 by 3 (the units digit of 43):**\n \\[\n 68 \\times 3 = 204\n \\]\n\n2. **Multiply 68 by 4 (the tens digit of 43) and shift the r... | [
"To solve the long multiplication equation \\(68 \\times 43\\), we will follow the standard algorithm for multiplication. Let's break it down step by step:\n\n1. **Multiply 68 by 3 (the units digit of 43):**\n \\[\n 68 \\times 3 = 204\n \\]\n\n2. **Multiply 68 by 4 (the tens digit of 43) and shift the result ... | 4b6dc1f5a7e9f7b60579154134e7d25103c57d71139493ee1dbc18848bd949f8 | 0d56917fa232406ff029602f8dad72c94c7e903b35760c2f514982482a8cb0e7 | 86d082c140779e5c1e65d1e718e76a0e6eee1ca335710b597a0caa7eb976510d | 1 | [
"2924"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 68 x 43 is \(\boxed{2924}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"2924"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 68 and 43, we can break it down step by step:\n\n1. Multiply 68 by 3 (the units digit of 43):\n - 68 x 3 = 204\n\n2. Multiply 68 by 4 (the tens digit of 43), remembering to shift one position to the left (which is equivalent to multiplying b... | |
83 | {
"answer": "782",
"args": [
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"46"
],
"is_model_response_correct": [
true,
false,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 782 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n17 x 46\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 17 \\times 46 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 17 \\\\\n \\times 46 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 17 by 6 (the units digit of 46):**\n \\[\n 17 \\times 6 = 102\n \\]... | [
"To solve the long multiplication equation \\( 17 \\times 46 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 17 \\\\\n \\times 46 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 17 by 6 (the units digit of 46):**\n \\[\n 17 \\times 6 = 102\n \\]\n W... | 72e9a24cca80695c15c3220c611866140c3413acbca7a79dc880c3b333435504 | 689b5c5e262dd649c89794141dd1f33bd53e64c653f44b1e7c7877ace0652b0a | 3da6ee6699da1eb52d358aa59b8e1cf6b5d77db224b4cec0faaa540610fb3b2e | 1 | [
"782"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal is made when the model states, "Therefore, the solution to the long multiplication equation 17 x 46 is \(\boxed{782}\)." This counts as a proposal of a final answer. 2. The first verification occurs when the model says, "But I need to verify this..." and then breaks down the multiplication again, ... | 5 | [
"782",
"782",
"782",
"782",
"782"
] | [
true,
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 17 and 46, we can break it down step by step:\n\n1. Multiply 17 by 6 (the units digit of 46):\n 17 x 6 = 102\n\n2. Multiply 17 by 4 (the tens digit of 46), remembering to shift one position to the left (which is equivalent to multiplying by ... | |
84 | {
"answer": "782",
"args": [
"17",
"46"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 782 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n46 x 17\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(46 \\times 17\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Write down the numbers to be multiplied:\n \\[\n \\begin{array}{r}\n 46 \\\\\n \\times 17 \\\\\n \\end{array}\n \\]\n\n2... | [
"To solve the long multiplication equation \\(46 \\times 17\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Write down the numbers to be multiplied:\n \\[\n \\begin{array}{r}\n 46 \\\\\n \\times 17 \\\\\n \\end{array}\n \\]\n\n2. Brea... | e8d812af2576981af71e6ebff7e35c4823d850253ba9d3c3e979038f25f106e8 | 18f98e230f0d433c9ef4fcb09b9b3eeb21190c8f624d6e43eef3720b4bf5ce49 | 3da6ee6699da1eb52d358aa59b8e1cf6b5d77db224b4cec0faaa540610fb3b2e | 1 | [
"782"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 46 x 17 is: \[\boxed{782}\]" This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"782"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 46 and 17, we can break it down step by step:\n\n1. Multiply 46 by 7 (the units digit of 17):\n - 46 x 7 = 322\n\n2. Multiply 46 by 10 (the tens digit of 17, which is actually 1 but in the tens place):\n - 46 x 10 = 460\n\n3. Now, add the ... | |
85 | {
"answer": "1152",
"args": [
"32",
"36"
],
"is_model_response_correct": [
true,
true,
false,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 1152 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n32 x 36\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(32 \\times 36\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(32\\) can be thought of as \\(30 + 2\\).\n - \\(36\\) can be thought of as \\(30 + 6\\).\n\n2. **Multiply each part separately:**\n - **For \\(30 \\times 36\\... | [
"To solve the long multiplication equation \\(32 \\times 36\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(32\\) can be thought of as \\(30 + 2\\).\n - \\(36\\) can be thought of as \\(30 + 6\\).\n\n2. **Multiply each part separately:**\n - **For \\(30 \\times 36\\):**\n... | 7fb62fff23f596f1b8ff3267a9081a459f29b5a09bfb71f3d90f55a4186f72cc | 5c09413535fa8b0bb4a3a79c26f3e2ca82293a470e807a0deb97fdbd1f8fc11b | a367613375c7fcd7402955ec5143e208948604a13765c1805450f350ba570d3d | 1 | [
"1152"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 32 x 36 is \(\boxed{1152}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1152"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 32 and 36, we can break it down step by step:\n\n1. Multiply 32 by 6 (the units digit of 36):\n - 32 x 6 = 192\n\n2. Multiply 32 by 30 (the tens digit of 36, which is 3, but we treat it as 30):\n - 32 x 30 = 960\n\n3. Now, add the two resu... | |
86 | {
"answer": "1152",
"args": [
"32",
"36"
],
"is_model_response_correct": [
false,
false,
false,
true,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 1152 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n36 x 32\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(36 \\times 32\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Write down the numbers and align them vertically:\n \\[\n \\begin{array}{r}\n 36 \\\\\n \\times 32 \\\\... | [
"To solve the long multiplication equation \\(36 \\times 32\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Write down the numbers and align them vertically:\n \\[\n \\begin{array}{r}\n 36 \\\\\n \\times 32 \\\\\n \... | b633ff8545769ede45da791303648875a349b7095eb20d9b064a688296207db3 | 80d12197cb1b08fdb304ae004979c4407fd9de2b222109366f93f61ecb81cb17 | a367613375c7fcd7402955ec5143e208948604a13765c1805450f350ba570d3d | 1 | [
"1152"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 36 x 32 is 1152." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1152"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 36 and 32, we can break it down step by step:\n\n1. Multiply 36 by 2 (the units digit of 32):\n 36 x 2 = 72\n\n2. Multiply 36 by 3 (the tens digit of 32), remembering to shift one position to the left (which is equivalent to multiplying by 3... | |
87 | {
"answer": "255",
"args": [
"15",
"17"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about ... | 255 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n15 x 17\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 15 \\times 17 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 15 \\\\\n \\times 17 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 15 by 7 (the units digit ... | [
"To solve the long multiplication equation \\( 15 \\times 17 \\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 15 \\\\\n \\times 17 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 15 by 7 (the units digit of 17)... | f7c0ee331b4a0832cdd3fd9c1407db7731c5fb5588413c3ab88ef2963ae3d3ea | 1f082901d9871b03df688b41ec2772901e61097263681fcfc0cfb18c52504d93 | 9556b82499cc0aaf86aee7f0d253e17c61b7ef73d48a295f37d98f08b04ffa7f | 1 | [
"255"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 15 x 17 is 255." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"255"
] | [
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 15 and 17, we can break it down step by step:\n\n1. Multiply 15 by 7 (the units digit of 17):\n - 15 x 7 = 105\n\n2. Multiply 15 by 10 (the tens digit of 17):\n - 15 x 10 = 150\n\n3. Now, add the two results together:\n - 105 + 150 = 255... | |
88 | {
"answer": "3888",
"args": [
"48",
"81"
],
"is_model_response_correct": [
false,
true,
true,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step a... | 3888 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n81 x 48\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(81 \\times 48\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's a step-by-step breakdown:\n\n1. **Break down the numbers:**\n \\[\n 81 = 80 + 1\n \\]\n \\[\n 48 = 40 + 8\n \\]\n\n2. *... | [
"To solve the long multiplication equation \\(81 \\times 48\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's a step-by-step breakdown:\n\n1. **Break down the numbers:**\n \\[\n 81 = 80 + 1\n \\]\n \\[\n 48 = 40 + 8\n \\]\n\n2. **Apply... | b2775f95cb43ad28cf12866aeeaeec6eff078d136b11a5d8dda6039918efafa5 | 42e34b603f293764697b5a0887de910bb95f123e51610d56fe79f641e30cbe5b | a06d4d440ba33ef1b053269761468037628424f5cf2ccf3a2004463c94fadac1 | 0 | [
"3988"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "So, the solution to the long multiplication equation 81 x 48 is \(\boxed{3988}\)." This counts as the first proposal.
2. The first verification occurs when the model states: "But to confirm, let's also perform the long multiplication directly: ... So... | 4 | [
"3988",
"3988",
"3988",
"3988"
] | [
false,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 81 and 48, we can break it down step by step:\n\n1. Multiply 81 by 8 (the units digit of 48):\n - 81 x 8 = 648\n\n2. Multiply 81 by 4 (the tens digit of 48), remembering to shift one position to the left (which is equivalent to multiplying ... | |
89 | {
"answer": "3888",
"args": [
"48",
"81"
],
"is_model_response_correct": [
false,
true,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 3888 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n81 x 48\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(81 \\times 48\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's a step-by-step breakdown:\n\n1. **Break down the numbers:**\n \\[\n 81 = 80 + 1\n \\]\n \\[\n 48 = 40 + 8\n \\]\n\n2. *... | [
"To solve the long multiplication equation \\(81 \\times 48\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's a step-by-step breakdown:\n\n1. **Break down the numbers:**\n \\[\n 81 = 80 + 1\n \\]\n \\[\n 48 = 40 + 8\n \\]\n\n2. **Apply... | bcefa033f3496163b194f5c8dd50d6f4c3be2a3f3b8f92fce1dd5ef6cbbad155 | 42e34b603f293764697b5a0887de910bb95f123e51610d56fe79f641e30cbe5b | a06d4d440ba33ef1b053269761468037628424f5cf2ccf3a2004463c94fadac1 | 0 | [
"3988"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal is made when the model states, "So, the solution to the long multiplication equation 81 x 48 is \(\boxed{3988}\)." This counts as the first final answer proposal. 2. The model then verifies this answer by stating, "But to confirm, let's also perform the long multiplication directly..." and proceed... | 5 | [
"3988",
"3988",
"3988",
"3988",
"3988"
] | [
false,
false,
false,
false,
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 81 and 48, we can break it down step by step:\n\n1. Multiply 81 by 8 (the units digit of 48):\n - 81 x 8 = 648\n\n2. Multiply 81 by 4 (the tens digit of 48), remembering to shift one position to the left (which is equivalent to multiplyin... | |
90 | {
"answer": "3888",
"args": [
"48",
"81"
],
"is_model_response_correct": [
true,
false,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abou... | 3888 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n48 x 81\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(48 \\times 81\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 48 \\\\\n \\times 81 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 48 by 1 (the units digit of 81):**\n \\[\n 48 \\times 1 = 48\... | [
"To solve the long multiplication equation \\(48 \\times 81\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 48 \\\\\n \\times 81 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 48 by 1 (the units digit of 81):**\n \\[\n 48 \\times 1 = 48\n \\... | 4781ffb611bdd8e84686853a5a2d206e727adf77aeabffebaa87e99088a0b211 | 98b5f3af4c5d9d9ebfcf60222c9a9e24404398ad48155a08d044056553bef37d | a06d4d440ba33ef1b053269761468037628424f5cf2ccf3a2004463c94fadac1 | 1 | [
"3888"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is made when the model states, "So, the solution to the long multiplication equation 48 x 81 is \(\boxed{3848}\)." This counts as the first proposal.
2. The model then verifies this answer by breaking down the calculations again, stating, "But I need to verify this. Let's break... | 4 | [
"3848",
"3888",
"3888",
"3888"
] | [
false,
true,
true,
true
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 48 and 81, we can break it down step by step:\n\n1. Multiply 48 by 1 (the units digit of 81):\n 48 x 1 = 48\n\n2. Multiply 48 by 8 (the tens digit of 81), remembering to shift one position to the left (add a zero):\n 48 x 8 = 384, and t... | |
91 | {
"answer": "5400",
"args": [
"60",
"90"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 5400 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n90 x 60\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 90 \\times 60 \\), we can break it down into simpler steps:\n\n1. **Multiply 90 by 6:**\n - We know that \\( 90 \\times 6 \\) is the same as \\( 9 \\times 60 \\) because \\( 90 \\) is \\( 9 \\) groups of \\( 10 \\).\n - \\( 9 \\times 60 = 9 \\times (6 \\times... | [
"To solve the long multiplication equation \\( 90 \\times 60 \\), we can break it down into simpler steps:\n\n1. **Multiply 90 by 6:**\n - We know that \\( 90 \\times 6 \\) is the same as \\( 9 \\times 60 \\) because \\( 90 \\) is \\( 9 \\) groups of \\( 10 \\).\n - \\( 9 \\times 60 = 9 \\times (6 \\times 10) =... | eb7bb913bc77d77e5665346df3146cf18bf4d2e233b62c586a86b3ea461b1a90 | 315e05c8b777a8b71d19c22398af7c6337824d1de83dcb2a36a380917a30ce85 | 525cfd02ce6f836ca4b1d8eeaf69a9a49cd3f0125f19ebe8cf1fda0c6ea0543a | 0 | [
"1440"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 90 x 60 is 1440." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1440"
] | [
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 90 and 60, we can break it down as follows: \n\n1. Multiply 90 by 60 directly: \n 90 x 60 = 5400. \n\n2. The solution provided (1440) is incorrect because it does not reflect the correct multiplication of these two numbers. \n\nThus, the gro... | |
92 | {
"answer": "5400",
"args": [
"60",
"90"
],
"is_model_response_correct": [
false,
false,
true,
false,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ab... | 5400 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n60 x 90\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(60 \\times 90\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(60\\) is the same as \\(6 \\times 10\\).\n - \\(90\\) is the same as \\(9 \\times 10\\).\n\n2. **Multiply the digits:**\n - First, multiply \\(6\\) by \\(9\\)... | [
"To solve the long multiplication equation \\(60 \\times 90\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(60\\) is the same as \\(6 \\times 10\\).\n - \\(90\\) is the same as \\(9 \\times 10\\).\n\n2. **Multiply the digits:**\n - First, multiply \\(6\\) by \\(9\\):\n ... | 3c0cdc40a3bb326ef7c10bf453dd521868ea1caa7acc67ae56f37fd917b1cddd | 2630647a330e619686c2904f0bb9cdfe5bbfc85ced5ecf258cb858d930f241dd | 525cfd02ce6f836ca4b1d8eeaf69a9a49cd3f0125f19ebe8cf1fda0c6ea0543a | 0 | [
"54000"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "So, the solution to the long multiplication equation 60 x 90 is \(\boxed{540}\)." This counts as a proposal because it clearly states the solution to the problem. 2. The second proposal is in the statement: "Thus, 60 x 90 = 54000. The step-by-step appr... | 2 | [
"540",
"54000"
] | [
false,
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 60 and 90, we can break it down as follows: \n\n1. Multiply the numbers directly: 60 x 90 = 5400. \n2. The solution provided (540) is incorrect because it does not account for the correct placement of the zeros in the multiplication. \n\nThus,... | |
93 | {
"answer": "286",
"args": [
"13",
"22"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 286 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n22 x 13\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(22 \\times 13\\), we can break it down into simpler steps.\n\n1. **Multiplication Step-by-Step:**\n - First, multiply 22 by 3 (the ones digit of 13).\n \\[\n 22 \\times 3 = 66\n \\]\n - Next, multiply 22 by the tens digit of 13, which is 1 (since w... | [
"To solve the long multiplication equation \\(22 \\times 13\\), we can break it down into simpler steps.\n\n1. **Multiplication Step-by-Step:**\n - First, multiply 22 by 3 (the ones digit of 13).\n \\[\n 22 \\times 3 = 66\n \\]\n - Next, multiply 22 by the tens digit of 13, which is 1 (since we are ... | 27007c81ae42c8c002d0caae0e5bce5833069fbc601e60baaa5189ce571bc271 | 18895c4b2e9bddc311e6700feb83cd0bc9268e9495ca4f093eb2561c6cc8e981 | 00328ce57bbc14b33bd6695bc8eb32cdf2fb5f3a7d89ec14a42825e15d39df60 | 1 | [
"286"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "So, the final answer to the equation 22 x 13 is \boxed{286}." This counts as the first proposal. 2. The second proposal is confirmed in the statement: "So, the correct final answer to the equation 22 x 13 is indeed \boxed{286}." This counts as the seco... | 2 | [
"286",
"286"
] | [
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 22 and 13, we can break it down step by step:\n\n1. Multiply 22 by 3 (the units digit of 13):\n - 22 x 3 = 66\n\n2. Multiply 22 by 1 (the tens digit of 13), remembering to shift one position to the left (which is equivalent to multiplying by... | |
94 | {
"answer": "286",
"args": [
"13",
"22"
],
"is_model_response_correct": [
false,
true,
true,
false,
true,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step abo... | 286 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n13 x 22\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\( 13 \\times 22 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 13 \\) can be written as \\( 10 + 3 \\).\n - \\( 22 \\) can be written as \\( 20 + 2 \\).\n\n2. **Multiply each part of the first number by each part of the ... | [
"To solve the long multiplication equation \\( 13 \\times 22 \\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\( 13 \\) can be written as \\( 10 + 3 \\).\n - \\( 22 \\) can be written as \\( 20 + 2 \\).\n\n2. **Multiply each part of the first number by each part of the second... | 9244b7a517f0f01854cf663a18565711877cc3275a373a4a5f3f3717251f999e | c39ef528b252c11d8d0ff5c1d03a9410fd953dea677877ce81ce902e37257ee4 | 00328ce57bbc14b33bd6695bc8eb32cdf2fb5f3a7d89ec14a42825e15d39df60 | 1 | [
"286"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in the statement: "Therefore, the solution to the long multiplication equation 13 x 22 is \boxed{286}." This counts as the first proposal.
2. The first verification occurs when the model states: "But to confirm, let's do the multiplication directly using the standard l... | 3 | [
"286",
"286",
"286"
] | [
true,
true,
true
] | [
{
"correct": true,
"reasoning": "To verify the multiplication of 13 and 22, we can break it down step by step:\n\n1. Multiply 13 by 2 (the units digit of 22):\n 13 x 2 = 26\n\n2. Multiply 13 by 20 (the tens digit of 22, which is 2, but we consider it as 20):\n 13 x 20 = 260\n\n3. Now, add the two result... | |
95 | {
"answer": "4500",
"args": [
"60",
"75"
],
"is_model_response_correct": [
true,
true,
true,
true,
true,
true
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step about... | 4500 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n60 x 75\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(60 \\times 75\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(60\\) is simply \\(6\\) multiplied by \\(10\\).\n - \\(75\\) can be broken down into \\(70\\) and \\(5\\).\n\n2. **Multiply the numbers in the tens place:**\n ... | [
"To solve the long multiplication equation \\(60 \\times 75\\), we can break it down into simpler steps:\n\n1. **Break down the numbers:**\n - \\(60\\) is simply \\(6\\) multiplied by \\(10\\).\n - \\(75\\) can be broken down into \\(70\\) and \\(5\\).\n\n2. **Multiply the numbers in the tens place:**\n - Mul... | f7c23e15107d54d55cf16137837481c570a2128be587b3dc4b29fe88116f0bc0 | 3bb22bfd6541c4d3690b476ce79d9aad9806abd7be847c14ae5a850740d872eb | c746ee2edf45fa00fca8d08045b2575aac17cf3eeb3f2b0da5e5301fae8d1e47 | 0 | [
"1050"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 60 x 75 is \(\boxed{1050}\)." This is a clear proposal of the final answer, which counts as one instance. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"1050"
] | [
false
] | [
{
"correct": false,
"reasoning": "To solve the multiplication of 60 and 75, we can break it down step by step:\n\n1. Multiply 60 by 75 directly:\n - 60 x 75 = 4500.\n\n2. The provided solution states that the answer is 1050, which is incorrect. \n\n3. Therefore, the ground truth solution of 4500 is the co... | |
96 | {
"answer": "6014",
"args": [
"62",
"97"
],
"is_model_response_correct": [
false,
false,
true,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step ... | 6014 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n62 x 97\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(62 \\times 97\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 6 & 2 \\\\\n \\times & 9 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 62 by 7 (... | [
"To solve the long multiplication equation \\(62 \\times 97\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 6 & 2 \\\\\n \\times & 9 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 62 by 7 (the un... | 412c3e4352de9dfd5949b481fd9b6f6aaac30fa4fa3792fe4261c55b0d0a6c07 | 385df19afcb2cdf4d2d17fbc5e89c3fed17a36cb417c6b44a98fece61f49d5dd | 5214d66710a61e72e7cd52f2a07b414be8aac7843a51b412ed0f9c952d26e96f | 0 | [
"6434"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is made when the model states, "So, the solution to the long multiplication equation 62 x 97 is \(\boxed{5698}\)." This counts as the first proposal. 2. The second proposal occurs when the model states, "The correct answer using the expanded method is \(\boxed{6434}\)." This coun... | 2 | [
"5698",
"6434"
] | [
false,
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 62 and 97, we can break it down step by step:\n\n1. Multiply 62 by 7 (the units digit of 97):\n - 62 x 7 = 434\n\n2. Multiply 62 by 9 (the tens digit of 97), remembering to shift one position to the left (which is equivalent to multiplying ... | |
97 | {
"answer": "3154",
"args": [
"38",
"83"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 3154 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n38 x 83\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(38 \\times 83\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 38 by 8 (the ones digit of 83):**\n \\[\n 38 \\times 8 = 304\n \\]\n Write down 4 in the ones place and carry over 3 to the tens pl... | [
"To solve the long multiplication equation \\(38 \\times 83\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 38 by 8 (the ones digit of 83):**\n \\[\n 38 \\times 8 = 304\n \\]\n Write down 4 in the ones place and carry over 3 to the tens place.\n... | 10b5ec5e893e8584d90670668fa3c35f7a9c6d42ba6b20365333d537ef760181 | 1918343c651e4dcf0d1f5afa1d1695b11dd367ef2ade7244d4043c1e063ceec4 | ff49a4f6ed54f15fa0954b265ad056a6f0fdab175ac8a1c3eb0a98a38e46da3d | 0 | [
"3174"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 38 x 83 is \(\boxed{3174}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"3174"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 38 and 83, we can break it down step by step:\n\n1. Multiply 38 by 3 (the units digit of 83):\n - 38 x 3 = 114\n\n2. Multiply 38 by 8 (the tens digit of 83), remembering to shift one position to the left (which is equivalent to multiplying ... | |
98 | {
"answer": "3154",
"args": [
"38",
"83"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 3154 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n38 x 83\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(38 \\times 83\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 38 by 8 (the ones digit of 83):**\n \\[\n 38 \\times 8 = 304\n \\]\n Write down 4 in the ones place and carry over 3 to the tens pl... | [
"To solve the long multiplication equation \\(38 \\times 83\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 38 by 8 (the ones digit of 83):**\n \\[\n 38 \\times 8 = 304\n \\]\n Write down 4 in the ones place and carry over 3 to the tens place.\n... | 284f739a28ffb32267f1907a1a86841eb3e8d099a62cbb4e7286820e82a7f8db | 1918343c651e4dcf0d1f5afa1d1695b11dd367ef2ade7244d4043c1e063ceec4 | ff49a4f6ed54f15fa0954b265ad056a6f0fdab175ac8a1c3eb0a98a38e46da3d | 0 | [
"3174"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 38 x 83 is \(\boxed{3174}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"3174"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 38 and 83, we can break it down step by step:\n\n1. Multiply 38 by 3 (the units digit of 83):\n - 38 x 3 = 114\n\n2. Multiply 38 by 8 (the tens digit of 83), remembering to shift one position to the left (which is equivalent to multiplying ... | |
99 | {
"answer": "3154",
"args": [
"38",
"83"
],
"is_model_response_correct": [
false,
false,
false,
false,
false,
false
],
"is_model_response_correct__correctness_prompt": [
"You are given a question, a solution, and a model output. For the current output, reason step by step... | 3154 | {
"gen_args_0": {
"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\nWhat is the solution to the long multiplication equation below?\n\n38 x 83\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_sample":... | [
[
"To solve the long multiplication equation \\(38 \\times 83\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 38 by 8 (the ones digit of 83):**\n \\[\n 38 \\times 8 = 304\n \\]\n Write down 4 in the ones place and carry over 3 to the tens pl... | [
"To solve the long multiplication equation \\(38 \\times 83\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 38 by 8 (the ones digit of 83):**\n \\[\n 38 \\times 8 = 304\n \\]\n Write down 4 in the ones place and carry over 3 to the tens place.\n... | 1666d6e729ace45d84ce9353ce514a79dc3459c1de0e1747b5942c65d7095e43 | 1918343c651e4dcf0d1f5afa1d1695b11dd367ef2ade7244d4043c1e063ceec4 | ff49a4f6ed54f15fa0954b265ad056a6f0fdab175ac8a1c3eb0a98a38e46da3d | 0 | [
"3174"
] | samples_longmult_2dig_2025-05-29T00-14-42.478454.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 38 x 83 is \(\boxed{3174}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"3174"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 38 and 83, we can break it down step by step:\n\n1. Multiply 38 by 3 (the units digit of 83):\n 38 x 3 = 114\n\n2. Multiply 38 by 8 (the tens digit of 83), remembering to shift one position to the left (which is equivalent to multiplying by... |
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