doc_id int64 | doc dict | target string | arguments dict | resps sequence | filtered_resps sequence | doc_hash string | prompt_hash string | target_hash string | exact_match int64 | extracted_answers sequence | source_file string | model_name string | measurement_answer_verification_reasoning string | measurement_answer_verification_final_count int64 | measurement_answer_verification_metadata sequence | measurement_answer_verification_raw_response string | metadata_answers_correct sequence | metadata_answers_correct_judge_data list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | {
"answer": "27920880",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 27920880 | {
"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\n2983 x 9360\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2983 \\times 9360\\), we can break it down into simpler steps by first multiplying 2983 by 9000 and then by 360, and finally adding the two results together.\n\nStep 1: Calculate \\(2983 \\times 9000\\).\n\\[2983 \\times 9000 = 26247000\\]\n\nStep 2: Calculate \\(... | [
"To solve the long multiplication equation \\(2983 \\times 9360\\), we can break it down into simpler steps by first multiplying 2983 by 9000 and then by 360, and finally adding the two results together.\n\nStep 1: Calculate \\(2983 \\times 9000\\).\n\\[2983 \\times 9000 = 26247000\\]\n\nStep 2: Calculate \\(2983 \... | 049b734fc33b4d136be3940d181cef03c74ac3683c0b8e7532b8a741d83152e9 | 8a73ad045d104953ef589b56ac66669f0147b013b439daba0d0e513b5d9b5f41 | 1524b58d71fd3c67a0c7fa073af5f0a366117855afc1af1e1a3a3f74fcf69775 | 0 | [
"To solve the long multiplication equation \\(2983 \\times 9360\\), we can break it down into simpler steps by first multiplying 2983 by 9000 and then by 360, and finally adding the two results together.\n\nStep 1: Calculate \\(2983 \\times 9000\\).\n\\[2983 \\times 9000 = 26247000\\]\n\nStep 2: Calculate \\(2983 \... | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 2983 x 9360 is 27279880." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"27279880"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 2983 by 9360, we can perform the calculation step by step:\n\n1. Break down the multiplication:\n - 2983 x 9360 can be calculated as:\n - 2983 x (9000 + 360) = 2983 x 9000 + 2983 x 360\n\n2. Calculate 2983 x 9000:\n - 2983 x 9000 = 2684... | |
1 | {
"answer": "85049860",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 85049860 | {
"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\n8660 x 9821\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 8660 \\times 9821 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 8 & 6 & 6 \\\\\n \\times & 9 & 8 & 2 \\\\\n \\hline\n \\end{array}\n \\]\n\n... | [
"To solve the long multiplication equation \\( 8660 \\times 9821 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 8 & 6 & 6 \\\\\n \\times & 9 & 8 & 2 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **M... | 698aa5cb6555150eba51f5c1575ad3b425fd35594fc85b8fbc7b963752d3f11f | 831e837c58fd5ace437a4c89127b5f9b7431c9cd24cf5c9e67820a71b7136461 | 66b6db2a60e688220605acc4e362109453f11fa962fa10572630845fd83be98b | 0 | [
"862000"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'Therefore, the solution to the long multiplication equation 8660 x 9821 is \(\boxed{862000}\)'. This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"862000"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 8660 by 9821, we can perform the calculation step by step. First, we can break down the multiplication: \n\n8660 x 9821 = 8660 x (9000 + 800 + 20 + 1) \n= 8660 x 9000 + 8660 x 800 + 8660 x 20 + 8660 x 1 \n\nCalculating each part:\n1. 8660 x... | |
2 | {
"answer": "7116252",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long ... | 7116252 | {
"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\n1014 x 7018\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(1014 \\times 7018\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's the step-by-step process:\n\n1. **Break down the numbers into components:**\n - \\(1014\\) can be thought of as \\(1000 + 14\... | [
"To solve the long multiplication equation \\(1014 \\times 7018\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's the step-by-step process:\n\n1. **Break down the numbers into components:**\n - \\(1014\\) can be thought of as \\(1000 + 14\\).\n ... | 9ae7734e6d4e245781734e1ce6e41be6b3f1c4393303f1e5283239b0930cad5c | b83a891f234a26c097440bfcdee9f4d5833c37332c18c3d16d0b4da8b5d91a4e | 2011ce3c349cb8f96857b179dbe2fd74a33f85986f1ea124fba66d1a15b5950f | 0 | [
"728252"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 1014 x 7018 is \(\boxed{728252}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"728252"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 1014 and 7018, we can perform the long multiplication step by step:\n\n1. Multiply 1014 by 8 (the last digit of 7018):\n 1014 x 8 = 8112\n\n2. Multiply 1014 by 1 (the second digit of 7018, which is actually 10):\n 1014 x 1 = 1014, but sin... | |
3 | {
"answer": "18061120",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 18061120 | {
"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\n3520 x 5131\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3520 \\times 5131\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 3 & 5 & 2 & 0 \\\\\n \\times & 5 & 1 & 3 & 1 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(3520 \\times 5131\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 3 & 5 & 2 & 0 \\\\\n \\times & 5 & 1 & 3 & 1 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | a2f1bdfe252810b633d599ba3e54711d1f9e0076909a64b77e7053cd67276dc2 | a301e58ab8174fac26d55f49c8d62d2ccafc462968b15e82322890ea6d48e789 | db1efa6b28b6f0ace487532d0c48a25f16cd53366954a194bf7aa23dfe6134a7 | 0 | [
"109120"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 3520 x 5131 is \(\boxed{109120}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"109120"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3520 by 5131, we can perform the calculation step by step:\n\n1. Multiply 3520 by 1 (the last digit of 5131): 3520 x 1 = 3520\n2. Multiply 3520 by 3 (the second digit of 5131, shifted one position to the left): 3520 x 3 = 10560 (shifted giv... | |
4 | {
"answer": "8882562",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long ... | 8882562 | {
"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\n6838 x 1299\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6838 \\times 1299\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 6838 by 9 (the units digit of 1299):**\n \\[\n 6838 \\times 9 = 6132\n \\]\n\n2. **Multiply 6838 by 10 (the tens digit of 1299, w... | [
"To solve the long multiplication equation \\(6838 \\times 1299\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 6838 by 9 (the units digit of 1299):**\n \\[\n 6838 \\times 9 = 6132\n \\]\n\n2. **Multiply 6838 by 10 (the tens digit of 1299, which i... | 12affd463da3378c6575dcbfa7412dd67ab0ecd6cfd0671e1cb584428069b831 | 98d1e45af31cde86c96be980508076b0a5389b1b2fa4e9b0b683093742a49def | 607d4b82535dda4f178b0a3d3286bcd68ac497be23fdcae580c31944f48a8303 | 0 | [
"74512"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 6838 x 1299 is \(\boxed{74512}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"74512"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6838 and 1299 step by step. \n\n1. First, we multiply 6838 by each digit of 1299, starting from the rightmost digit:\n - 6838 x 9 = 61542\n - 6838 x 9 (next digit) = 61542, but th... | |
5 | {
"answer": "34661674",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 34661674 | {
"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\n4366 x 7939\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4366 \\times 7939\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the ones place of the dividend by the ones place of the multiplier:**\n \\[\n 4 \\times 9 = 36\n \\]\n Write down 6 and carry o... | [
"To solve the long multiplication equation \\(4366 \\times 7939\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the ones place of the dividend by the ones place of the multiplier:**\n \\[\n 4 \\times 9 = 36\n \\]\n Write down 6 and carry over 3.... | 32eb0514336fe04ea4a806e2382b0961b7f18fd783b7087ef5a8bc13e73ca6b7 | 5f1b01505b265eb78c13648f5f4ae414d03679a259118f1da1bb3b93904a5ccc | 44b77d8f0ec2ca4140541a3648340fc3bef9d4dad405363f64fd93d907202ec5 | 0 | [
"34667"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the final product of 4366 x 7939 is 34,667.\[\boxed{34667}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"34667"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the provided solution, we need to perform the multiplication of 4366 and 7939 step by step. \n\n1. **Multiply 4366 by 7939**: \n - 4366 x 7939 = 34661674. \n\n2. **Compare the provided solution with the ground truth**: \n - The provided so... | |
6 | {
"answer": "20024290",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 20024290 | {
"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\n7865 x 2546\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(7865 \\times 2546\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 7 & 8 & 6 & 5 \\\\\n \\times & 2 & 5 & 4 & 6 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(7865 \\times 2546\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 7 & 8 & 6 & 5 \\\\\n \\times & 2 & 5 & 4 & 6 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | 0c0484d0744c56863a540f961b0d5da34877c5a472676d49b48d825ddda11f19 | 0418beb43b585e425d4a64ec7cc11c32ed1c05d37cf38d3cf0005789a65bb832 | 222f094896bd55c0007d87b49f9eb2017ae308e1d8b66d6bbe335daa447b9c4f | 0 | [
"430240"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 7865 x 2546 is \(\boxed{430240}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"430240"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7865 and 2546 step by step. \n\n1. Multiply 7865 by 6 (the last digit of 2546): \n 7865 x 6 = 47190 \n\n2. Multiply 7865 by 4 (the second digit of 2546, shifted one position to the ... | |
7 | {
"answer": "28848365",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 28848365 | {
"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\n6461 x 4465\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 6461 \\times 4465 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 6 & 4 & 6 & 1 \\\\\n \\times & 4 & 4 & 6 & 5 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the top number by each digit of... | [
"To solve the long multiplication equation \\( 6461 \\times 4465 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 6 & 4 & 6 & 1 \\\\\n \\times & 4 & 4 & 6 & 5 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the top number by each digit of the b... | ae785a65c4eb6165405f969de764ef6bb22badcf40cf0ae69d16080d3c1e7e74 | c6d203237190063b907c3d2cb0b9562e95adb1073a99abad9a892f4595b13f25 | e928c704412b55293ef9ee56d503b77616914398a779a638eb15f4a18111d888 | 0 | [
"10270545"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | 1. The first proposal of a final answer is found in step 4: "So, the solution to the long multiplication equation 6461 x 4465 is 10270545." This clearly states the final answer, which counts as one proposal.
2. The second instance of verification occurs when the model confirms the final answer by stating: "Final answ... | 2 | [
"10270545",
"10270545"
] | [
false,
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 6461 by 4465, we can perform the long multiplication step by step:\n\n1. Multiply 6461 by 5 (the last digit of 4465):\n 6461 x 5 = 32305\n\n2. Multiply 6461 by 6 (the second digit of 4465, shifted one position to the left):\n 6461 x 6 = 3... | |
8 | {
"answer": "19675775",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 19675775 | {
"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\n3877 x 5075\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3877 \\times 5075\\), we can break it down into simpler steps:\n\n1. **Break down the numbers**: We can rewrite \\(3877\\) as \\(3000 + 800 + 70 + 7\\) and \\(5075\\) as \\(5000 + 700 + 50 + 5\\).\n \n2. **Multiply step-by-step**:\n - First, multiply \\(3000\\... | [
"To solve the long multiplication equation \\(3877 \\times 5075\\), we can break it down into simpler steps:\n\n1. **Break down the numbers**: We can rewrite \\(3877\\) as \\(3000 + 800 + 70 + 7\\) and \\(5075\\) as \\(5000 + 700 + 50 + 5\\).\n \n2. **Multiply step-by-step**:\n - First, multiply \\(3000\\) by \... | 2b3ef1ab7c2bf0ca8f488ba473346b768b779366e3feaf50b6a0e7031430b162 | 908e543b85e36bb03a03ea787911e023ccbe8affd4bb859d6aa03d494178f3cd | 38b4bab79942a4fed0c1f2af71c965c30f3dd4b84e22b76c8aadae05e799c074 | 0 | [
"To solve the long multiplication equation \\(3877 \\times 5075\\), we can break it down into simpler steps:\n\n1. **Break down the numbers**: We can rewrite \\(3877\\) as \\(3000 + 800 + 70 + 7\\) and \\(5075\\) as \\(5000 + 700 + 50 + 5\\).\n \n2. **Multiply step-by-step**:\n - First, multiply \\(3000\\) by \... | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace concludes with a clear final answer: "So, the solution to the long multiplication equation 3877 x 5075 is 628000." This statement directly proposes the final answer to the multiplication problem, which counts as one proposal. | 1 | [
"628000"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3877 and 5075, we can perform the long multiplication step by step:\n\n1. Multiply 3877 by 5 (the units digit of 5075):\n 3877 x 5 = 19385\n\n2. Multiply 3877 by 7 (the tens digit of 5075, which is actually 70):\n 3877 x 7 = 27139, but ... | |
9 | {
"answer": "8774359",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long ... | 8774359 | {
"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\n4133 x 2123\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4133 \\times 2123\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 3 (from 4133) by 3 (from 2123).\n \\[\n 3 \\times 3 = 9\n \\]\n Write down 9.\n\n2. **Multip... | [
"To solve the long multiplication equation \\(4133 \\times 2123\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 3 (from 4133) by 3 (from 2123).\n \\[\n 3 \\times 3 = 9\n \\]\n Write down 9.\n\n2. **Multiply the... | fa5168f9f58ecce7f5cba4a002f013f83876325d1a3198e9fafb36f691b0b0b1 | e258a17e62732bb5cc4db6897fd95e1ab83eba0a2aa2b73194709f721a12a42b | 1236d3aa175712b479162a6753f65557bca804b266abc59d422be0eabf41738a | 0 | [
"To solve the long multiplication equation \\(4133 \\times 2123\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 3 (from 4133) by 3 (from 2123).\n \\[\n 3 \\times 3 = 9\n \\]\n Write down 9.\n\n2. **Multiply the... | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the final product of 4133 x 2123 is 863559." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"863559"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 4133 and 2123, we can perform the long multiplication step by step:\n\n1. Multiply 4133 by 3 (the last digit of 2123):\n 4133 x 3 = 12399\n\n2. Multiply 4133 by 2 (the second digit of 2123, which is in the tens place):\n 4133 x 2 = 8266, ... | |
10 | {
"answer": "17088288",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 17088288 | {
"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\n3017 x 5664\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3017 \\times 5664\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 3017 \\\\\n \\times & 5664 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3017 by 4 (the... | [
"To solve the long multiplication equation \\(3017 \\times 5664\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 3017 \\\\\n \\times & 5664 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3017 by 4 (the right... | f2fdc1d5ba0debd52faf6e3e7f5f33aa8c17522bb8532070354cb79877f44da5 | 5828c53cf39b65d37a8fba26ba60404bf3d5c7187d0ce5d5c2db799fdf1088ae | aac36e65554b79d7639931d148cfd4b60c3b1baa0754c87cb1f67b2934a8cba5 | 0 | [
"162688"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 3017 x 5664 is \(\boxed{162688}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"162688"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3017 and 5664, we can perform the long multiplication step by step:\n\n1. Multiply 3017 by 4 (the last digit of 5664): 3017 x 4 = 12068\n2. Multiply 3017 by 6 (the second digit of 5664, shifted one position to the left): 3017 x 6 = 18102, s... | |
11 | {
"answer": "11567042",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 11567042 | {
"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\n7066 x 1637\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(7066 \\times 1637\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 7066 by 7 (the units digit of 1637):**\n \\[\n 7066 \\times 7 = 49462\n \\]\n\n2. **Multiply 7066 by 10 (the tens digit of 1637, which is jus... | [
"To solve the long multiplication equation \\(7066 \\times 1637\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 7066 by 7 (the units digit of 1637):**\n \\[\n 7066 \\times 7 = 49462\n \\]\n\n2. **Multiply 7066 by 10 (the tens digit of 1637, which is just 1, b... | f8ace94193e2b6a4062935393de69180d16830b23892604bd5df8b9e200f4b03 | 38e0f2e6f7cb0d029b485d43f8a451305ad40972ec60e2e7cb6e907318525678 | 74507a7d3d4370ed4f3e796d9a16cfc3a71eca1fa869cd616a94a90ce9f271d0 | 0 | [
"120122"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 7066 x 1637 is \(\boxed{120122}\)." 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 | [
"120122"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7066 and 1637 step by step:\n\n1. Multiply 7066 by 7 (the units digit of 1637):\n 7066 x 7 = 49462\n\n2. Multiply 7066 by 3 (the tens digit of 1637):\n 7066 x 3 = 21198, but since... | |
12 | {
"answer": "12750510",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 12750510 | {
"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\n2346 x 5435\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2346 \\times 5435\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Multiply the digits**: We will multiply each digit of the first number by each digit of the second number, and then add the results column by column, starting... | [
"To solve the long multiplication equation \\(2346 \\times 5435\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Multiply the digits**: We will multiply each digit of the first number by each digit of the second number, and then add the results column by column, starting from ... | 9c0f756608a41e81493494e5980128ca5d5bf612d1287696b6fdbee2e7d5c843 | c398c627e82c46a7c988f7e704210279300a4dcd8b5a17b1fd08f0e975d5143a | e0737304a4b6947e5325f2c6ab36f3429acfef0f744e5e84b195c802c544d8e7 | 0 | [
"To solve the long multiplication equation \\(2346 \\times 5435\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Multiply the digits**: We will multiply each digit of the first number by each digit of the second number, and then add the results column by column, starting from ... | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 2346 x 5435 is 1386." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1386"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 2346 by 5435, we perform the long multiplication step by step:\n\n1. Multiply 2346 by 5 (the unit digit of 5435):\n 2346 x 5 = 11730\n\n2. Multiply 2346 by 3 (the tens digit of 5435), shift one position to the left:\n 2346 x 3 = 7038, s... | |
13 | {
"answer": "60429072",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 60429072 | {
"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\n9264 x 6523\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9264 \\times 6523 \\), we will follow the standard algorithm for multiplication. This involves multiplying each digit of one number by each digit of the other number and then summing all the results, taking care to align the digits correctly.\n\nLet's break it do... | [
"To solve the long multiplication equation \\( 9264 \\times 6523 \\), we will follow the standard algorithm for multiplication. This involves multiplying each digit of one number by each digit of the other number and then summing all the results, taking care to align the digits correctly.\n\nLet's break it down ste... | 9bbf91846dbe9e7fb0e141b954c8b1d5a5bb8b9120a8cc0c8407ba79ad734601 | 3bef97aec73d02be0a094b71d548bc90d8dae67dd9c55ff0d61f59459bd74553 | 8013e3638abd91ca60da26f7230d3ae9d21f58148853d8689c73a8d5bb98569b | 0 | [
"645752"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace concludes with a final answer: "Therefore, the solution to the long multiplication equation 9264 x 6523 is \boxed{645752}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"645752"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 9264 and 6523 step by step:\n\n1. Multiply 9264 by 3 (the units digit of 6523):\n 9264 x 3 = 27792\n\n2. Multiply 9264 by 2 (the tens digit of 6523), and shift one position to the l... | |
14 | {
"answer": "32035560",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 32035560 | {
"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\n7170 x 4468\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 7170 \\times 4468 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 7170 \\\\\n \\times & 4468 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 7170 by 8 (t... | [
"To solve the long multiplication equation \\( 7170 \\times 4468 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 7170 \\\\\n \\times & 4468 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 7170 by 8 (the uni... | 105349441fd899fa97f0ebdf9168ed245a30d5fcf30c7c4cdb119911efb130fb | c1e626667be5808a0fd372481fe6ee2c64e91497b2d863503a068247ea83b654 | c9f79caea0d4b141582c9ad202a50a1bdc8c3a1534a6469a1be242ce7231ca9a | 0 | [
"764060"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 7170 x 4468 is \(\boxed{764060}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"764060"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 7170 by 4468, we can perform the calculation step by step:\n\n1. First, we can break down the multiplication:\n - 7170 x 4468 = 7170 x (4000 + 400 + 60 + 8)\n - This can be calculated as:\n - 7170 x 4000 = 28680000\n - 7170 x 40... | |
15 | {
"answer": "42768863",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 42768863 | {
"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\n9749 x 4387\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9749 \\times 4387 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 7 & 4 & 9 \\\\\n \\times & 4 & 3 & 8 & 7 \\\\\n \\hline\n \\end{array}\n \\]... | [
"To solve the long multiplication equation \\( 9749 \\times 4387 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 7 & 4 & 9 \\\\\n \\times & 4 & 3 & 8 & 7 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | e0522682ad24b0aed4f34ef1e8e044a1782378c3c2f6927e87d74992c4d96074 | becad6f0f4beb11bd65e362810e50a9d19b522aa68cba6c3e14078f3a6060059 | a67723669c8da5f5ae8342b6f9d9cf8ab7e0733a595cd9dda6a064a92413a4a1 | 0 | [
"4255933"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 9749 x 4387 is: \[\boxed{4255933}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"4255933"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 9749 and 4387, we can perform the long multiplication step by step:\n\n1. Multiply 9749 by 7 (the units digit of 4387):\n 9749 x 7 = 68243\n\n2. Multiply 9749 by 8 (the tens digit of 4387), shifting one position to the left:\n 9749 x 8 = ... | |
16 | {
"answer": "44236416",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 44236416 | {
"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\n4704 x 9404\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 4704 \\times 9404 \\), we will break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. **Break down the numbers:**\n \\[\n 4704 = 4700 + 4\n \\]\n \\[\n 9404 = 9400 + 4\n \\]\n\n2. **Apply the distributi... | [
"To solve the long multiplication equation \\( 4704 \\times 9404 \\), we will break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. **Break down the numbers:**\n \\[\n 4704 = 4700 + 4\n \\]\n \\[\n 9404 = 9400 + 4\n \\]\n\n2. **Apply the distributive pro... | b24a68f7e17bec4c6ff23b4137d5d7129965297562a7708c10ec84e63bb76024 | 841a1d1dce8d0f5fd3ce41f901c534ad8be02bfe57807fc707551c88d78a620b | 20b3b771613e89e037700619d5f4ed090b3a662a348b1476ba8a487f34dbe3e2 | 0 | [
"4772116"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 4704 x 9404 is \(\boxed{4772116}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"4772116"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the correctness of the solution, we need to perform the multiplication of 4704 and 9404 step by step. \n\n1. First, we can break down the multiplication: \n 4704 x 9404 = 4704 x (9000 + 404) \n = 4704 x 9000 + 4704 x 404 \n\n2. Calculate 4704 x 9000: \n 4704... | |
17 | {
"answer": "24957688",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 24957688 | {
"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\n9772 x 2554\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(9772 \\times 2554\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 9 & 7 & 7 \\\\\n \\times & 2 & 5 & 5 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(9772 \\times 2554\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 9 & 7 & 7 \\\\\n \\times & 2 & 5 & 5 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Mul... | 8db812af311e804926677f80292c96211a3ec2ed4aea8eaeadf8c4171f904e60 | 6d4506d6b3fb1355af61dfa1b3a3e51bf01345b8f7808128943bcb96c1c3af1a | 96b801b79e8eef3a0b9f114d2317019b89f84d47e1cb383f8671f60da27c97c3 | 0 | [
"244300"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 9772 x 2554 is \(\boxed{244300}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"244300"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 9772 by 2554, we can perform the long multiplication step by step:\n\n1. Multiply 9772 by 4 (the last digit of 2554):\n 9772 x 4 = 39088\n\n2. Multiply 9772 by 5 (the second digit of 2554, which is in the tens place):\n 9772 x 5 = 48860... | |
18 | {
"answer": "25554852",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 25554852 | {
"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\n5172 x 4941\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5172 \\times 4941 \\), we will follow these steps:\n\n1. **Break down the problem using the distributive property of multiplication:**\n \\[\n 5172 \\times 4941 = 5172 \\times (4000 + 900 + 41)\n \\]\n\n2. **Distribute \\( 5172 \\) across each term in the s... | [
"To solve the long multiplication equation \\( 5172 \\times 4941 \\), we will follow these steps:\n\n1. **Break down the problem using the distributive property of multiplication:**\n \\[\n 5172 \\times 4941 = 5172 \\times (4000 + 900 + 41)\n \\]\n\n2. **Distribute \\( 5172 \\) across each term in the sum:**\... | 08266520be443262cda28d8160eed1a250e9d3338a164a50c3988ed688151774 | 810aba8947dbe5add06811a867c63dad8731128fd0f7f04562d66e65a3a2cc2d | 7f2a4c45b05e109095ed733bd4e1b402765d544ce1b3d8d56dfd761fc6834c3c | 0 | [
"27523322"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace concludes with a clear final answer: 'Therefore, the solution to the long multiplication equation 5172 x 4941 is \(\boxed{27523322}\).' This statement directly proposes the final answer to the multiplication problem, which counts as one proposal. | 1 | [
"27523322"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 5172 by 4941, we can perform the long multiplication step by step:\n\n1. Multiply 5172 by 1 (the last digit of 4941): 5172\n2. Multiply 5172 by 4 (the second digit of 4941, shifted one position to the left): 20688\n3. Multiply 5172 by 9 (the ... | |
19 | {
"answer": "30198996",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 30198996 | {
"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\n6339 x 4764\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6339 \\times 4764\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 6 & 3 & 3 & 9 \\\\\n \\times & 4 & 7 & 6 & 4 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(6339 \\times 4764\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 6 & 3 & 3 & 9 \\\\\n \\times & 4 & 7 & 6 & 4 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | bf7ac6a89ccec0a5187f14dafb8c6559cacf7d0b55b54355bcd41ff11e65cafc | dba7e6306e26a0d9bacc926d8ac32c2f1bd06db73eed8b66a08fcd46ca34c755 | 8ec945bd7a4da696c39823dad39685086470b5c9e69db3e00aa4a3f7509aa5c1 | 0 | [
"468486"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'So, the solution to the long multiplication equation 6339 x 4764 is \(\boxed{468486}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"468486"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6339 and 4764 step by step:\n\n1. Multiply 6339 by each digit of 4764, starting from the rightmost digit:\n - 6339 x 4 = 25356\n - 6339 x 6 = 38034 (shifted one position to the le... | |
20 | {
"answer": "36059446",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 36059446 | {
"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\n7222 x 4993\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(7222 \\times 4993\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 7222 by 3 (the units digit of 4993):**\n \\[\n 7222 \\times 3 = 21666\n \\]\n\n2. **Multiply 7222 by 40 (the tens digit of 4993, ... | [
"To solve the long multiplication equation \\(7222 \\times 4993\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 7222 by 3 (the units digit of 4993):**\n \\[\n 7222 \\times 3 = 21666\n \\]\n\n2. **Multiply 7222 by 40 (the tens digit of 4993, which ... | ecdf1cd125c43607d77629ed85af3c399c3128f4b19097218c6d2d3c362af5b0 | f81a68b0aad63474c340b8e091c2b768b79055538ecc2e0fc9268096d2306716 | 48db18f274b8d04206205e1fbfb74aba904b40b01b0b5ebaa0d05ef456ec7804 | 0 | [
"290546"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 7222 x 4993 is \(\boxed{290546}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"290546"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7222 and 4993 step by step. \n\n1. First, we multiply 7222 by each digit of 4993, starting from the rightmost digit:\n - 7222 x 3 = 21666\n - 7222 x 9 = 64998 (shifted one positio... | |
21 | {
"answer": "57916314",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 57916314 | {
"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\n8054 x 7191\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8054 \\times 7191\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 8054 \\\\\n \\times & 7191 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 8054 by 1 (the... | [
"To solve the long multiplication equation \\(8054 \\times 7191\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 8054 \\\\\n \\times & 7191 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 8054 by 1 (the units... | 8a6565a3d5a59536bb669a7b4cac8f363ad319a2f9d8b65c2db37110d46e9d72 | bcbd6331e8f3d28dfc01a6e3f1b4e63f45a2094f66cbdcd0396832332b58ab45 | 65d510573bd8f871adccf29ed0624dd21a5f1a7265b86ad6e8cf5d45592d1f42 | 0 | [
"732914"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 8054 x 7191 is \(\boxed{732914}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"732914"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the solution, we need to perform the multiplication of 8054 and 7191 step by step:\n\n1. Multiply 8054 by 1 (the last digit of 7191): 8054 x 1 = 8054\n2. Multiply 8054 by 9 (the second digit of 7191): 8054 x 9 = 72486, shifted one position to the left (add a zero)... | |
22 | {
"answer": "38217452",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 38217452 | {
"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\n7924 x 4823\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 7924 \\times 4823 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 7 & 9 & 2 & 4 \\\\\n \\times & 4 & 8 & 2 & 3 \\\\\n \\end{array}\n \\]\n\n2. *... | [
"To solve the long multiplication equation \\( 7924 \\times 4823 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 7 & 9 & 2 & 4 \\\\\n \\times & 4 & 8 & 2 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Multi... | 2dafa663e915dad11dbbd24f4056e4daf7677826398a22dd60b765a9a4376cd4 | d9fe5d10c14aaa6aa282cbfc04c5788c50bbff565dc5fa4fb65bbfb6939fc36d | bc7e133737810d899fdd7fe3dc50e1d23c2e0d51aacd1057d22fa2d1f6eb6686 | 0 | [
"657692"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 7924 x 4823 is: \[\boxed{657692}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"657692"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the correctness of the solution, we need to perform the long multiplication of 7924 and 4823 step by step:\n\n1. Multiply 7924 by 3 (the units digit of 4823):\n 7924 x 3 = 23772\n\n2. Multiply 7924 by 2 (the tens digit of 4823), shift one position to the left:\n... | |
23 | {
"answer": "23698528",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 23698528 | {
"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\n5264 x 4502\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5264 \\times 4502 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 5 & 2 & 6 \\\\\n \\times & 4 & 5 & 0 \\\\\n \\hline\n \\end{array}\n \\]\n\n... | [
"To solve the long multiplication equation \\( 5264 \\times 4502 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 5 & 2 & 6 \\\\\n \\times & 4 & 5 & 0 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **M... | 467efaefcd2a6254a48dba49c96348a16741d2a29cf26f9fc9ebd5ef7119ef38 | d4380623017316755389cf282ea99f42c9ca3d79503de14cda36296643bdb7f3 | 9acf84ffc74ac729ed3a04cb797425abad757abe309f5ea3cc994b6eb67415bf | 0 | [
"26220"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 5264 x 4502 is \(\boxed{26220}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"26220"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 5264 by 4502, we can perform the calculation step by step:\n\n1. First, we multiply 5264 by 2 (the last digit of 4502):\n 5264 x 2 = 10528\n\n2. Next, we multiply 5264 by 0 (the second digit of 4502):\n 5264 x 0 = 0 (this contributes no... | |
24 | {
"answer": "47262788",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 47262788 | {
"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\n8012 x 5899\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8012 \\times 5899\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 8012 \\\\\n \\times & 5899 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 8012 by 9 (the... | [
"To solve the long multiplication equation \\(8012 \\times 5899\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 8012 \\\\\n \\times & 5899 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 8012 by 9 (the units... | 86b806571fd1dcb8e7211e9415bcaa518fcd7be4a3ac4b86965395db0b8c5a11 | f7497f8512820adbc188c5d10e9c389bad3efb43b08243314d02a4102d7436e1 | 826362f36d586308dfe0409a105da0deb863df3a679364cc6ff3b6962830f81c | 0 | [
"112078"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 8012 x 5899 is \(\boxed{112078}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"112078"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 8012 and 5899 step by step. \n\n1. Multiply 8012 by 9 (the last digit of 5899): \n 8012 x 9 = 72108 \n\n2. Multiply 8012 by 90 (the second digit of 5899, which is 9, shifted one pla... | |
25 | {
"answer": "71524759",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 71524759 | {
"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\n9101 x 7859\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9101 \\times 7859 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 1 & 0 & 1 \\\\\n \\times & 7 & 8 & 5 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | [
"To solve the long multiplication equation \\( 9101 \\times 7859 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 1 & 0 & 1 \\\\\n \\times & 7 & 8 & 5 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Multiply ... | e08b4df1e4743d436329f7038d7a8b3f017d64fc0ad8b6a3f75ef3c43e12ca75 | 71864967f1a96b4ff050ae6e0039bc2fe61e9ee70af0443e33466373525cdefe | a8ef80900a80e051981803d11514709a66956f26e1f367ce084187319ecfe469 | 0 | [
"78010"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 9101 x 7859 is \boxed{78010}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"78010"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 9101 by 7859, we can perform the long multiplication step by step:\n\n1. Multiply 9101 by 9 (the last digit of 7859):\n 9101 x 9 = 81909\n\n2. Multiply 9101 by 5 (the second digit of 7859):\n 9101 x 5 = 45505, but since this is in the t... | |
26 | {
"answer": "14414517",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 14414517 | {
"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\n2197 x 6561\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2197 \\times 6561\\), we can break it down into simpler steps by first multiplying the smaller number by the first digit of the larger number, and then multiplying the larger number by the next digit of the larger number, and so on.\n\nHere's how you solve it:\n\n... | [
"To solve the long multiplication equation \\(2197 \\times 6561\\), we can break it down into simpler steps by first multiplying the smaller number by the first digit of the larger number, and then multiplying the larger number by the next digit of the larger number, and so on.\n\nHere's how you solve it:\n\n1. Mul... | ce1d1e88e5d5d1b907340415cef4033fd57feb39204445c173e104252e065039 | fd38f749b167080de657869244fd4f5dc795f1f67f902c929ea764c6c0d54743 | 6e0d197287f12c0e46ade106566a2bba77bf87e4f740924c47933c17ec8b304e | 0 | [
"To solve the long multiplication equation \\(2197 \\times 6561\\), we can break it down into simpler steps by first multiplying the smaller number by the first digit of the larger number, and then multiplying the larger number by the next digit of the larger number, and so on.\n\nHere's how you solve it:\n\n1. Mul... | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer when it states, "So, the solution to the long multiplication equation 2197 x 6561 is 15379." This is a clear proposal of the final answer after performing the calculations. There are no subsequent verifications or additional proposals in the trace, so the total count remains 1. | 1 | [
"15379"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 2197 and 6561 step by step. \n\n1. **Multiply 2197 by 1 (the units place of 6561):** \n - 2197 x 1 = 2197 \n\n2. **Multiply 2197 by 6 (the tens place of 6561):** \n - 2197 x 6 = 1... | |
27 | {
"answer": "17864665",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 17864665 | {
"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\n5135 x 3479\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(5135 \\times 3479\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 5 & 1 & 3 & 5 \\\\\n \\times & 3 & 4 & 7 & 9 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(5135 \\times 3479\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 5 & 1 & 3 & 5 \\\\\n \\times & 3 & 4 & 7 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | 0336f8ce28831a058a5798f6766bfa4a114ef1319ef59f26ae4cf95ae5955ecf | 04fe1a29876ba15b6ccf526f5bae6d9d4eab36edc53fab33ceb9196f9b2fd10b | 6dc5a61e830709e5086762e564f3546f80ec9031ea8580ddbddb7f73328dd7d8 | 0 | [
"311565"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'So, the solution to the long multiplication equation 5135 x 3479 is \(\boxed{311565}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"311565"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 5135 and 3479 step by step:\n\n1. Multiply 5135 by 9 (the last digit of 3479):\n 5135 x 9 = 46215\n\n2. Multiply 5135 by 7 (the second digit of 3479, shifted one position to the lef... | |
28 | {
"answer": "14041975",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 14041975 | {
"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\n2225 x 6311\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2225 \\times 6311\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 2225 \\\\\n \\times & 6311 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2225 by 1 (the... | [
"To solve the long multiplication equation \\(2225 \\times 6311\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 2225 \\\\\n \\times & 6311 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2225 by 1 (the units... | 89bf514387acb1b1d98e994a546a785a560ea2be66aa4370a05bcfbf7faf9225 | 3d45345d3847937572145683203af6bc9de8fc62e4fa842a3ecd43483915ceb1 | e3f88490daba280d420ae84d21d421f83acd7dbdd4d62d6e0be5ddd2bc8696c8 | 0 | [
"192475"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 2225 x 6311 is \(\boxed{192475}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"192475"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 2225 and 6311, we can perform the long multiplication step by step:\n\n1. Multiply 2225 by 1 (the last digit of 6311): 2225 x 1 = 2225\n2. Multiply 2225 by 1 (the second digit of 6311, shifted one position to the left): 2225 x 1 = 2225, shi... | |
29 | {
"answer": "19507773",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 19507773 | {
"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\n4371 x 4463\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4371 \\times 4463\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 1 (from 4371) by 3 (from 4463).\n \\[\n 1 \\times 3 = 3\n \\]\n Write down 3, and carry over... | [
"To solve the long multiplication equation \\(4371 \\times 4463\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 1 (from 4371) by 3 (from 4463).\n \\[\n 1 \\times 3 = 3\n \\]\n Write down 3, and carry over 0 to ... | 38d8fa86f6f26083a35fa1c84b9a409166fd169a33d058c7645b260e016fa8d4 | 8c01bb0307bf8dc00f4d37067e1f8337c8461f9f2fae5b8f653fcd045eb21a84 | d396bf20f54f1b1946eda26ca05b203e7db6c374c0f09c969fa7cfb0ddf58647 | 0 | [
"18643"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'Thus, the final product is 18643.' This is a clear proposal of the final answer after completing the calculations. There are no subsequent verifications or double checks of this final answer in the provided reasoning trace. | 1 | [
"18643"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 4371 and 4463 step by step. \n\n1. **Multiply 4371 by 3 (the units digit of 4463):** 4371 x 3 = 13113\n2. **Multiply 4371 by 6 (the tens digit of 4463):** 4371 x 6 = 26226, but since ... | |
30 | {
"answer": "47253360",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 47253360 | {
"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\n7671 x 6160\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 7671 \\times 6160 \\), we will follow these steps:\n\n1. **Break down the problem into manageable parts**:\n - First, consider \\( 7671 \\times 60 \\).\n - Then, consider \\( 7671 \\times 10 \\).\n - Finally, combine the results from the previous steps.\n\n... | [
"To solve the long multiplication equation \\( 7671 \\times 6160 \\), we will follow these steps:\n\n1. **Break down the problem into manageable parts**:\n - First, consider \\( 7671 \\times 60 \\).\n - Then, consider \\( 7671 \\times 10 \\).\n - Finally, combine the results from the previous steps.\n\n2. **C... | 3563fdec40cd55fcf23337eee95dae842cc243e1059830329f0c5566c5816798 | 026e10c061ce2b3e6f204bc2c5279958e2da13dad8ea495229b1d87c2455a548 | 28a6948f665cf4cb51be18ad83e7a365f7cae783a8155ab0c936ece071e6bd30 | 0 | [
"5369700"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace concludes with a clear final answer: 'Therefore, the solution to the long multiplication equation 7671 x 6160 is \(\boxed{5369700}\).' This statement directly proposes the final answer to the multiplication problem, which counts as one proposal. | 1 | [
"5369700"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7671 and 6160 step by step. \n\n1. First, we multiply 7671 by each digit of 6160, starting from the rightmost digit:\n - 7671 x 0 = 0\n - 7671 x 6 = 46026 (shifted one position to... | |
31 | {
"answer": "31522905",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 31522905 | {
"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\n3585 x 8793\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3585 \\times 8793\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 3 & 5 & 8 & 5 \\\\\n \\times & 8 & 7 & 9 & 3 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(3585 \\times 8793\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 3 & 5 & 8 & 5 \\\\\n \\times & 8 & 7 & 9 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | 14b7d25b37286f8f2f243217b6b1a60891900dfb2cb28fb80e85edb0dfa8c49b | b94a270f22e2ff8649f25e55d790139588e07a05591cdf9ea67690e3116bf28e | fad0281e18f667216c7e657cfea2c540f1687bd27a739e16a05293b4bcfa5d11 | 0 | [
"3911405"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 3585 x 8793 is \(\boxed{3911405}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"3911405"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 3585 and 8793, we can perform the long multiplication step by step:\n\n1. Multiply 3585 by 3 (the units digit of 8793):\n 3585 x 3 = 10755\n\n2. Multiply 3585 by 9 (the tens digit of 8793):\n 3585 x 9 = 32265, but since this is in the ten... | |
32 | {
"answer": "61868622",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 61868622 | {
"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\n7179 x 8618\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(7179 \\times 8618\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 7 & 1 & 7 \\\\\n \\times & 8 & 6 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(7179 \\times 8618\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 7 & 1 & 7 \\\\\n \\times & 8 & 6 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Mul... | 9e36f5b47d6b8a1552c080294fdffbb402b42181534f82836a6226aeed4411b2 | 784b48e508871f300eb24c5e9e3d1b2dfafa0606ac4a812f00de4c9acf994614 | 6507ce0feded43c83301ebc1214e22d90b369df30c3a23ebad569e58dd07fc45 | 0 | [
"573599"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 7179 x 8618 is \boxed{573599}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"573599"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 7179 and 8618 step by step. \n\n1. First, we can break down the multiplication: \n - 7179 x 8618 can be calculated directly or using the long multiplication method. \n\n2. Performing the... | |
33 | {
"answer": "55158120",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 55158120 | {
"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\n6068 x 9090\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6068 \\times 9090\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n \\[\n 6068 = 6000 + 68\n \\]\n \\[\n 9090 = 9000 + 90\n \\]\n\n2. **Multiply each part separately:**\n \\[\n (6000 + 68) \\times 9090\n \\]\n\n3. *... | [
"To solve the long multiplication equation \\(6068 \\times 9090\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n \\[\n 6068 = 6000 + 68\n \\]\n \\[\n 9090 = 9000 + 90\n \\]\n\n2. **Multiply each part separately:**\n \\[\n (6000 + 68) \\times 9090\n \\]\n\n3. **Use t... | 261157a9454e089902bcab95764c89dbcba1ea62406a3af06816ea4bef76b224 | ade1a318f1b23bc8ca582324b59692076e303298183a7d87ff74c37adf460a39 | 44917f56b50fe98a82ccd5cf367890b4c55f52a5fa0d8435c9a994ab706c8007 | 0 | [
"6012000"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace concludes with a clear final answer: 'Therefore, the solution to the long multiplication equation 6068 x 9090 is \(\boxed{6012000}\).' This statement directly proposes the final answer to the multiplication problem, which counts as one proposal. | 1 | [
"6012000"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 6068 by 9090, we can perform the calculation step by step:\n\n1. Break down the multiplication:\n - 6068 x 9090 = 6068 x (9000 + 90)\n - = 6068 x 9000 + 6068 x 90\n\n2. Calculate each part:\n - 6068 x 9000 = 54612000\n - 6068 x 90 =... | |
34 | {
"answer": "32006344",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 32006344 | {
"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\n6508 x 4918\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6508 \\times 4918\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 6 & 5 & 0 \\\\\n \\times & 4 & 9 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(6508 \\times 4918\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 6 & 5 & 0 \\\\\n \\times & 4 & 9 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Mul... | 992aa76eb41dd9c0d412124f3b536a94a7a322a8a17c9b9e0fa269f4c4d86f10 | f58370259d1498eb0d35e652106622af3a632f04848a87bb813d71f1bab46652 | c9e53082da38d0a27750cb13b30472f9f53c85ece90fa556089c00e6c83de83d | 0 | [
"293288"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'So, the solution to the long multiplication equation 6508 x 4918 is \(\boxed{293288}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"293288"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6508 and 4918 step by step:\n\n1. Multiply 6508 by 8 (the last digit of 4918):\n 6508 x 8 = 52064\n\n2. Multiply 6508 by 1 (the second digit of 4918, which is actually 10):\n 6508... | |
35 | {
"answer": "13003956",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 13003956 | {
"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\n5562 x 2338\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(5562 \\times 2338\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 5 & 5 & 6 \\\\\n \\times & 2 & 3 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Multiply ... | [
"To solve the long multiplication equation \\(5562 \\times 2338\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 5 & 5 & 6 \\\\\n \\times & 2 & 3 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5562 b... | 923c71763bc60df33faacafd60cb3344638315ee24c3abd40c7bfe614aea4d06 | 34f99b301f34f5bc6b80d1b7f90d2f431516cc3246c47360e479020cee4edc35 | 6a7da9c68366029fa97d213da6a2091c3aca782e895270dc623b06292598a00f | 0 | [
"12788"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 5562 x 2338 is \(\boxed{12788}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"12788"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 5562 by 2338, we can perform the long multiplication step by step:\n\n1. Multiply 5562 by 8 (the last digit of 2338):\n 5562 x 8 = 44496\n\n2. Multiply 5562 by 3 (the second digit of 2338, which is in the tens place):\n 5562 x 3 = 16686... | |
36 | {
"answer": "18412352",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 18412352 | {
"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\n4088 x 4504\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 4088 \\times 4504 \\), we will follow these steps:\n\n1. **Break down the problem using the distributive property of multiplication:**\n \\[\n 4088 \\times 4504 = 4088 \\times (4000 + 500 + 80 + 8)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n ... | [
"To solve the long multiplication equation \\( 4088 \\times 4504 \\), we will follow these steps:\n\n1. **Break down the problem using the distributive property of multiplication:**\n \\[\n 4088 \\times 4504 = 4088 \\times (4000 + 500 + 80 + 8)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n 4088... | 78ff4f09e22313c1dea16bfc5fb6a6f0e52b6a5518fe1e8f172d9d2e4c75ad8b | fd416b6f1935a2b87c20c18bf41073b10cc2e862b53d789643aa326622e86dda | 83dda1b91ef1697aa4765154b0052afc0b1f95dd80b4f9d86bcb64c39ce238b9 | 0 | [
"19627444"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "Therefore, the solution to the long multiplication equation 4088 x 4504 is \(\boxed{19627444}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"19627444"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the correctness of the solution, we need to perform the long multiplication of 4088 and 4504 step by step. \n\n1. First, we multiply 4088 by each digit of 4504, starting from the rightmost digit:\n - 4088 x 4 = 16352\n - 4088 x 0 = 0 (shifted one position to t... | |
37 | {
"answer": "77933040",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 77933040 | {
"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\n9385 x 8304\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9385 \\times 8304 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 9 & 3 & 8 & 5 \\\\\n \\times & 8 & 3 & 0 & 4 \\\\\n \\end{array}\n \\]\n\n... | [
"To solve the long multiplication equation \\( 9385 \\times 8304 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 9 & 3 & 8 & 5 \\\\\n \\times & 8 & 3 & 0 & 4 \\\\\n \\end{array}\n \\]\n\n2. **M... | 51421595677fb553ae15dd8d4c2cfab3f5e9e38d72ea8429fc0383f3186eb170 | f41d81077172555722fbc5671a03a73eded924deea06b5ae93553d913a54b6f4 | 8a79ab6e97d0c43149ffe3239ca72c3d86c7e39f3cd6eead049a0be84d641abf | 0 | [
"319090"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: "So, the solution to the long multiplication equation 9385 x 8304 is \(\boxed{319090}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"319090"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the provided solution, we need to perform the long multiplication of 9385 and 8304 step by step:\n\n1. Multiply 9385 by 4 (the last digit of 8304):\n 9385 x 4 = 37540\n\n2. Multiply 9385 by 0 (the second digit of 8304):\n 9385 x 0 = 0 (shi... | |
38 | {
"answer": "28478385",
"args": null,
"is_model_response_correct": null,
"is_model_response_correct__correctness_prompt": null,
"is_model_response_correct__correctness_reasoning": null,
"is_model_response_correct__final_answer": null,
"model_responses": null,
"problem": "What is the solution to the long... | 28478385 | {
"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\n3645 x 7813\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3645 \\times 7813\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 3 & 6 & 4 & 5 \\\\\n \\times & 7 & 8 & 1 & 3 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(3645 \\times 7813\\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c@{}c}\n & 3 & 6 & 4 & 5 \\\\\n \\times & 7 & 8 & 1 & 3 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | a0c1e308d45faa92afb5dbbe159d273eae03111a64548678ba789205a87a56e6 | 07292871d4dbe109329fff28ce7ca23a39c30d69f8636a5083c6fdaf24af27bd | 6c805fa38f4d20c7c15155bc975bec56859b3c9083637e3e889de25801b7af29 | 0 | [
"290135"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'Therefore, the solution to the long multiplication equation 3645 x 7813 is \(\boxed{290135}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"290135"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 3645 and 7813 step by step. \n\n1. First, we can break down the multiplication:\n - 3645 x 7813 can be calculated directly or using the long multiplication method.\n\n2. Performing the m... |
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