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": "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... | |
39 | {
"answer": "14712346",
"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... | 14712346 | {
"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\n6347 x 2318\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6347 \\times 2318\\), we will follow the standard long multiplication method step by step.\n\n1. **Multiply 6347 by 8 (the units digit of 2318):**\n \\[\n 6347 \\times 8 = 50936\n \\]\n\n2. **Multiply 6347 by 2 (the tens digit of 2318, but we need to shift t... | [
"To solve the long multiplication equation \\(6347 \\times 2318\\), we will follow the standard long multiplication method step by step.\n\n1. **Multiply 6347 by 8 (the units digit of 2318):**\n \\[\n 6347 \\times 8 = 50936\n \\]\n\n2. **Multiply 6347 by 2 (the tens digit of 2318, but we need to shift the res... | 2b96da2928d0bfed999f89cb98bf214b7cc9bc0f5ea580c3a9bf848ba8cb5571 | dcc17fe818b62794a074bbbe6272e6b3eb3e5be3ebbe125634fc7f7f39a1f98d | 9f7451f0f56fd5d27aff436097a244b85061fb03dbb8637f5d7a82298110ff5f | 0 | [
"177876"
] | 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 6347 x 2318 is \(\boxed{177876}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"177876"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 6347 by 2318, we can perform the long multiplication step by step:\n\n1. Multiply 6347 by 8 (the last digit of 2318):\n 6347 x 8 = 50776\n\n2. Multiply 6347 by 1 (the second digit of 2318, shifted one position to the left):\n 6347 x 1 = 6... | |
40 | {
"answer": "13613328",
"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... | 13613328 | {
"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\n5976 x 2278\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5976 \\times 2278 \\), 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 & 5976 \\\\\n \\times & 2278 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5976 by 8 (t... | [
"To solve the long multiplication equation \\( 5976 \\times 2278 \\), 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 & 5976 \\\\\n \\times & 2278 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5976 by 8 (the uni... | 874e76d8f45b5bee70b75d7538b00a389e5c1cf8fffd0118730641db5a45b4ed | 9bc45fdee765a59970bfc58c763162d3cd53499bdff21f6053bc1241b8ef4045 | 39725d027feb8b73e4536d4d391d8021664b81e2dc65438680e048302d7848a7 | 0 | [
"286288"
] | 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 5976 x 2278 is: \[ \boxed{286288} \]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"286288"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 5976 by 2278, we can perform the long multiplication step by step:\n\n1. Multiply 5976 by 8 (the last digit of 2278):\n 5976 x 8 = 47808\n\n2. Multiply 5976 by 7 (the second digit of 2278, shifted one position to the left):\n 5976 x 7 =... | |
41 | {
"answer": "50145936",
"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... | 50145936 | {
"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\n8628 x 5812\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8628 \\times 5812\\), 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 & 2 \\\\\n \\times & 5 & 8 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(8628 \\times 5812\\), 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 & 2 \\\\\n \\times & 5 & 8 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Mul... | 06680cf836c53900971cfe5dfd9475ebbc2d7840ba3acefa9bc8b102d557d262 | a51170459351065df290f2dfe6806512aae433255fdba108231218113a0b6d45 | 1e2e41162ceb6b3902e7abafb2aacd5b855ff27196f45186486cb8f347bb635c | 0 | [
"499344"
] | 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 8628 x 5812 is \(\boxed{499344}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"499344"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 8628 and 5812 step by step. \n\n1. **Multiply 8628 by 2 (the last digit of 5812):** 8628 x 2 = 17256\n2. **Multiply 8628 by 1 (the second digit of 5812, shifted one position to the le... | |
42 | {
"answer": "17540394",
"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... | 17540394 | {
"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\n5466 x 3209\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(5466 \\times 3209\\), 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 & 4 & 6 \\\\\n \\times & 3 & 2 & 0 & 9 \\\\\n \\end{array}\n \\]\n\n2. **M... | [
"To solve the long multiplication equation \\(5466 \\times 3209\\), 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 & 4 & 6 \\\\\n \\times & 3 & 2 & 0 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Multipl... | a33b4e0e33c177b6caa9e17adbfcb4525a141dc2dc1071a4d91238d263036611 | b8364f436351fb35d56fa69fd2cefe4bbae4613022c67abc8293c54438a8d078 | 62e474cceae931bd86f7090ac450cc0f1539e720666c7e618f13bb966719abf3 | 0 | [
"212834"
] | 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 5466 x 3209 is \(\boxed{212834}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"212834"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 5466 and 3209 step by step:\n\n1. **Break down the multiplication**: \n - 5466 x 3209 can be calculated as:\n - (5466 x 3000) + (5466 x 200) + (5466 x 9)\n\n2. **Calculate each part**:... | |
43 | {
"answer": "8440497",
"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 ... | 8440497 | {
"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\n1807 x 4671\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 1807 \\times 4671 \\), 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 & 1807 \\\\\n \\times & 4671 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 1807 by 1 (t... | [
"To solve the long multiplication equation \\( 1807 \\times 4671 \\), 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 & 1807 \\\\\n \\times & 4671 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 1807 by 1 (the uni... | 6de761d2605b3a2028b0147438297deade10a816c5dfd2d1469147c6f0ee0d0b | 31db4eba81ffd5b079eb8ed95ed77da101c75e5970cde973a07df3fa5a249e76 | 8bb45eb75298b7f2c239ca65ddea6adaded0956fdbe6210da81f3a4319288921 | 0 | [
"742407"
] | 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 1807 x 4671 is \(\boxed{742407}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"742407"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 1807 and 4671 step by step:\n\n1. Break down the multiplication:\n - 1807 x 4671 can be calculated as:\n - (1800 + 7) x (4600 + 71)\n - This can be expanded using the distributive pr... | |
44 | {
"answer": "35353296",
"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... | 35353296 | {
"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\n5808 x 6087\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(5808 \\times 6087\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Multiply the number by the units digit of the other number:**\n \\[\n 5808 \\times 7 = 40656\n \\]\n\n2. **Multiply the number by the tens digit of the ... | [
"To solve the long multiplication equation \\(5808 \\times 6087\\), we will follow the standard long multiplication method. Here are the steps:\n\n1. **Multiply the number by the units digit of the other number:**\n \\[\n 5808 \\times 7 = 40656\n \\]\n\n2. **Multiply the number by the tens digit of the other ... | a5ca9f56bc05f63d0fd55839c3ab340481dad3e0aba1bd147b2e43259a14369d | 8321673f0ead2c06fff25e116fb8d20b34d1fe07f299b49bb1dda223c6e27c4a | 74503802c5cc5bd78384b622bbdcff0b800e42d98db04ad924cc7e074f94c9a5 | 0 | [
"389136"
] | 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 5808 x 6087 is \(\boxed{389136}\)." 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 | [
"389136"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 5808 and 6087 step by step. \n\n1. **Multiply 5808 by 7 (the units digit of 6087):** 5808 x 7 = 40656.\n2. **Multiply 5808 by 80 (the tens digit of 6087):** 5808 x 80 = 464640 (since ... | |
45 | {
"answer": "7566568",
"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 ... | 7566568 | {
"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\n6316 x 1198\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6316 \\times 1198\\), 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 - \\(6316\\) can be written as \\(6000 + 300 + ... | [
"To solve the long multiplication equation \\(6316 \\times 1198\\), 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 - \\(6316\\) can be written as \\(6000 + 300 + 100 + ... | 719704f43a2a3c59fb685504fc22f9b0fa70b5667b3ed844a261bc7361bf5aef | 43fc9aeedf287d6fb8085c9e2c95bb271d20771a7c988248155f70d368958fa3 | 5e59d8db6f48aae83fbb2f058174d4855a9683ba8b02042551463ba9a0750db2 | 0 | [
"833328"
] | 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 6316 x 1198 is \(\boxed{833328}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"833328"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 6316 by 1198, we can perform the long multiplication step by step:\n\n1. Multiply 6316 by 8 (the last digit of 1198):\n 6316 x 8 = 50528\n\n2. Multiply 6316 by 9 (the second digit of 1198, shifted one position to the left):\n 6316 x 9 = 5... | |
46 | {
"answer": "21809400",
"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... | 21809400 | {
"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\n3345 x 6520\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3345 \\times 6520\\), we can break it down into simpler steps:\n\n1. **Multiply 3345 by 520** first:\n - \\(3345 \\times 520 = 3345 \\times (500 + 20) = (3345 \\times 500) + (3345 \\times 20)\\)\n - \\(3345 \\times 500 = 1672500\\)\n - \\(3345 \\times 20 = 6... | [
"To solve the long multiplication equation \\(3345 \\times 6520\\), we can break it down into simpler steps:\n\n1. **Multiply 3345 by 520** first:\n - \\(3345 \\times 520 = 3345 \\times (500 + 20) = (3345 \\times 500) + (3345 \\times 20)\\)\n - \\(3345 \\times 500 = 1672500\\)\n - \\(3345 \\times 20 = 66900\\... | 743b265faf6467497c9406ceacb0e03377b2a8d1e1843eab587e81a0a9e939cb | 624940a7c23e528ab428c0e24812155f3a1abdc71aefe45959e3b495807093ac | cc64dde1d4ce5a46f25ce41f178defe29363a017bab32ddb20167da48970b6cc | 0 | [
"2534500"
] | 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 3345 x 6520 is: \[\boxed{2534500}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"2534500"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3345 by 6520, we can perform the calculation step by step:\n\n1. First, we can break down the multiplication:\n - 3345 x 6520 = 3345 x (6000 + 500 + 20)\n - This can be calculated as:\n - 3345 x 6000 = 20070000\n - 3345 x 500 = ... | |
47 | {
"answer": "36384372",
"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... | 36384372 | {
"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\n6458 x 5634\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 6458 \\times 5634 \\), 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 & 4 & 5 & 8 \\\\\n \\times & 5 & 6 & 3 & 4 \\\\\n \\end{array}\n \\]\n\n... | [
"To solve the long multiplication equation \\( 6458 \\times 5634 \\), 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 & 4 & 5 & 8 \\\\\n \\times & 5 & 6 & 3 & 4 \\\\\n \\end{array}\n \\]\n\n2. **M... | 80ef65a3c46bf5bd1c9cef6eedca4a2c368fc10c4fe2aafc28e9bc9ebb143b9b | 4aaef359f829cc0cd66d72386dc5b9bcd6c525a4f4c1d9f0b226c7526f164ccc | 859ca0b2f0e793041c37c8522e6672bd8cfffae3209f13a26c884a7e47e6fa49 | 0 | [
"413312"
] | 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 6458 x 5634 is \(\boxed{413312}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"413312"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 6458 by 5634, we can perform the long multiplication step by step:\n\n1. Multiply 6458 by 4 (the last digit of 5634):\n 6458 x 4 = 25832\n\n2. Multiply 6458 by 3 (the second last digit of 5634), shift one position to the left:\n 6458 x ... | |
48 | {
"answer": "23078559",
"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... | 23078559 | {
"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\n8263 x 2793\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8263 \\times 2793\\), 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 & 2 & 6 \\\\\n \\times & 2 & 7 & 9 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(8263 \\times 2793\\), 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 & 2 & 6 \\\\\n \\times & 2 & 7 & 9 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Mul... | 2a5d54f753ddb31c5cfcea054a99313e6f06095d820906f2b3d95c241fe05f1b | 4b38e92e388341db87de412d465f6f6b246ac037303086be1f867b11f0df70e9 | 91d763247a2ecb3091d454d1311743635899ac9b01ecab724a40ab1e11144639 | 0 | [
"240837"
] | 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 8263 x 2793 is \(\boxed{240837}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"240837"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 8263 and 2793 step by step:\n\n1. Multiply 8263 by 3 (the units digit of 2793):\n 8263 x 3 = 24789\n\n2. Multiply 8263 by 9 (the tens digit of 2793), and shift one position to the l... | |
49 | {
"answer": "15006852",
"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... | 15006852 | {
"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\n4284 x 3503\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4284 \\times 3503\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 4 by 3: \\(4 \\times 3 = 12\\)\n - Write down 2 and carry over 1.\n\n2. **Multiply the tens digits... | [
"To solve the long multiplication equation \\(4284 \\times 3503\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digits:**\n - Multiply 4 by 3: \\(4 \\times 3 = 12\\)\n - Write down 2 and carry over 1.\n\n2. **Multiply the tens digits and a... | 1bc5e7e20241153e8d8ab7e48776b525515e9282335286264d9b18410786c1de | 56205bc3f05abaabc60f1c1f6195b884532807ee5b8b63c1b641bc90f2a9cf81 | f0f4713006feaa86f88a99dfe7a9034edae6fe57c4acc411c505bd3091d1785c | 0 | [
"1433212"
] | 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 4284 x 3503 is \(\boxed{1433212}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1433212"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 4284 by 3503, we can perform the calculation step by step:\n\n1. Break down the multiplication:\n - 4284 x 3 = 12852\n - 4284 x 0 = 0\n - 4284 x 5 = 21420 (shifted one position to the left)\n - 4284 x 3 = 12852 (shifted two positions ... | |
50 | {
"answer": "3356274",
"args": null,
"is_model_response_correct": null,
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"is_model_response_correct__correctness_reasoning": null,
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"model_responses": null,
"problem": "What is the solution to the long ... | 3356274 | {
"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\n2994 x 1121\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2994 \\times 1121\\), 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 - \\(2994\\) can be written as \\(2000 + 994\\)... | [
"To solve the long multiplication equation \\(2994 \\times 1121\\), 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 - \\(2994\\) can be written as \\(2000 + 994\\)\n -... | e7ba8ded213ef0b5f739b1aef119bee7ba1dd1bfda4865afa2fc4c9fe67db2ed | f72ad4193adbf0e3645dbd9356bac06a7c24c346d3bfaec7a00e93bee8e3812a | ffabdf448694b3fb5e403a1531417e046b2564e9bd3c2beef4301021ba197b01 | 0 | [
"To solve the long multiplication equation \\(2994 \\times 1121\\), 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 - \\(2994\\) can be written as \\(2000 + 994\\)\n -... | 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 2994 x 1121 is 311574." 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 | [
"311574"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 2994 by 1121, we can perform the long multiplication step by step:\n\n1. Multiply 2994 by 1 (the last digit of 1121): 2994 x 1 = 2994\n2. Multiply 2994 by 2 (the second digit of 1121, shifted one position to the left): 2994 x 2 = 5988, shifte... | |
51 | {
"answer": "29001510",
"args": null,
"is_model_response_correct": null,
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"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... | 29001510 | {
"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\n6990 x 4149\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 6990 \\times 4149 \\), 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 & 6990 \\\\\n \\times & 4149 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6990 by 9 (t... | [
"To solve the long multiplication equation \\( 6990 \\times 4149 \\), 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 & 6990 \\\\\n \\times & 4149 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6990 by 9 (the uni... | b32f9ea575f2db204a67bc5069fe8153e7400256229d32aa2bbc5b921e26fca2 | e18f378a2d10eee7636f31d55d977237c790297de1cf14cf1467fcf385b6fb59 | d787079ff7ee54366c2d20f1d3e4f3bf86cf06c3acb1f54392fc15a2447f3b48 | 0 | [
"342510"
] | 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 6990 x 4149 is \(\boxed{342510}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"342510"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 6990 and 4149 step by step. \n\n1. First, let's break down the multiplication:\n - 6990 can be expressed as 6990 = 6990 \n - 4149 can be expressed as 4149 = 4000 + 100 + 40 + 9 \n\n2. ... | |
52 | {
"answer": "10700193",
"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... | 10700193 | {
"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\n8353 x 1281\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8353 \\times 1281\\), 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 & 8 & 3 & 5 \\\\\n \\times & 1 & 2 & 8 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **M... | [
"To solve the long multiplication equation \\(8353 \\times 1281\\), 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 & 8 & 3 & 5 \\\\\n \\times & 1 & 2 & 8 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multipl... | fc0ec46fe96c64e623331aa74a185fc8812209e1c7a801b0389a150ec142ae52 | b800e26ec7b9d1399b91617bf33592657e2751990361eccddfb11c80bf376b40 | 32ba40a01065ff199d363f792cfe3e19a772b4b7ed01667d2747a648f59aeace | 0 | [
"102473"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.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 8353 x 1281 is \(\boxed{102473}\)." This clearly states the final answer, which counts as the first instance. 2. The second verification occurs when the model states: "8353 x 1281 = 102473" after per... | 2 | [
"102473",
"102473"
] | [
false,
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 8353 and 1281 step by step. \n\n1. **Multiply 8353 by 1 (the units place of 1281):** \n 8353 x 1 = 8353 \n\n2. **Multiply 8353 by 8 (the tens place of 1281):** \n 8353 x 8 = 66824... | |
53 | {
"answer": "33041066",
"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... | 33041066 | {
"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\n7039 x 4694\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 7039 \\times 4694 \\), 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 & 7039 \\\\\n \\times & 4694 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 7039 by 4 (t... | [
"To solve the long multiplication equation \\( 7039 \\times 4694 \\), 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 & 7039 \\\\\n \\times & 4694 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 7039 by 4 (tens pl... | 3c91ed3eb0a59a040cda0c065f937e99303d3135742aa0e0e22e496a02e82a6c | 857ebaa120403a9bd2278102f222137bac5cc6cd03dac9084e0782b181acfd3d | 1dba8f47a0364f3b46d3c7346e1b3d6705fb8bd49b00ff19b5c18ee30771e9da | 0 | [
"450496"
] | 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 7039 x 4694 is: \[\boxed{450496}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"450496"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7039 and 4694 step by step:\n\n1. Multiply 7039 by 4 (the units digit of 4694):\n 7039 x 4 = 28156\n\n2. Multiply 7039 by 9 (the tens digit of 4694):\n 7039 x 9 = 63251, but since... | |
54 | {
"answer": "62182155",
"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... | 62182155 | {
"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\n6585 x 9443\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6585 \\times 9443\\), 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 & 6585 \\\\\n \\times & 9443 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6585 by 3 (the... | [
"To solve the long multiplication equation \\(6585 \\times 9443\\), 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 & 6585 \\\\\n \\times & 9443 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6585 by 3 (the units... | 15a32b7cad8170c0d2ba36a881c70422c45c5526f914e7dc94ca34f5d698ea4d | 969e4c6d46c53c62968afbe386c00b5ded1e8a0c5b99e2ea9173d87f19cc5b5b | 52767d740741394087f42563a721cc8c68c6fa96f6a54520dc1b801302c3af3a | 0 | [
"283155"
] | 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 6585 x 9443 is \(\boxed{283155}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"283155"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6585 and 9443 step by step. \n\n1. First, we multiply 6585 by each digit of 9443, starting from the rightmost digit:\n - 6585 x 3 = 19755\n - 6585 x 4 = 26340 (shifted one positio... | |
55 | {
"answer": "7006496",
"args": null,
"is_model_response_correct": null,
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"is_model_response_correct__correctness_reasoning": null,
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"model_responses": null,
"problem": "What is the solution to the long ... | 7006496 | {
"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\n4036 x 1736\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4036 \\times 1736\\), we can break it down into simpler steps by first multiplying 4036 by 736 and then multiplying 4036 by 1000, and finally adding the two results together.\n\nStep 1: Multiply 4036 by 736.\n\\[4036 \\times 736 = 2953776\\]\n\nStep 2: Multiply 40... | [
"To solve the long multiplication equation \\(4036 \\times 1736\\), we can break it down into simpler steps by first multiplying 4036 by 736 and then multiplying 4036 by 1000, and finally adding the two results together.\n\nStep 1: Multiply 4036 by 736.\n\\[4036 \\times 736 = 2953776\\]\n\nStep 2: Multiply 4036 by ... | b44fa6ecbfd734aa0956ba5137f56c5f0381e57397c81c2f45290007f2153cd0 | c787e7de5356aab84edf84f3f5df73b4618ea202dfb522f9b38d848e0f9d2248 | d7ba62da3442f801edee1756f2952e05a7ead6e8235b8d419f1e7ac8c059aa55 | 0 | [
"To solve the long multiplication equation \\(4036 \\times 1736\\), we can break it down into simpler steps by first multiplying 4036 by 736 and then multiplying 4036 by 1000, and finally adding the two results together.\n\nStep 1: Multiply 4036 by 736.\n\\[4036 \\times 736 = 2953776\\]\n\nStep 2: Multiply 4036 by ... | 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 4036 x 1736 is 6989776." This is a clear proposal of the final answer, which counts as one instance. There are no verifications present in the trace, as there are no statements that check or confirm the proposed answer a... | 1 | [
"6989776"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 4036 by 1736, we can perform the long multiplication step by step:\n\n1. Multiply 4036 by 6 (the last digit of 1736):\n 4036 x 6 = 24216\n\n2. Multiply 4036 by 3 (the second digit of 1736, shifted one position to the left):\n 4036 x 3 = 1... | |
56 | {
"answer": "23014114",
"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... | 23014114 | {
"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\n4754 x 4841\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 4754 \\times 4841 \\), 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 & 4 & 7 & 5 \\\\\n \\times & 4 & 8 & 4 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 47... | [
"To solve the long multiplication equation \\( 4754 \\times 4841 \\), 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 & 4 & 7 & 5 \\\\\n \\times & 4 & 8 & 4 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 4754 by ... | 368f6a6aabd15e04b7148db31667e906fe3090e6c0488bce3e0bd1ae65853e51 | c1b4f0a7c1e3c9ea086d0b112965dddabf54afb416a65191c51731f1c81322ac | 70195460cd630b6d12ed2f23839396cb8df92a026b29b4b6faf78b2cec5efe62 | 0 | [
"218192"
] | 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 4754 x 4841 is \(\boxed{218192}\)." 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 | [
"218192"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 4754 and 4841 step by step. \n\n1. First, we can break down the multiplication: \n - 4754 x 4841 can be calculated directly or using the long multiplication method. \n\n2. Performing the... | |
57 | {
"answer": "17263554",
"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... | 17263554 | {
"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\n3311 x 5214\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3311 \\times 5214\\), 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 & 3 & 1 & 1 \\\\\n \\times & 5 & 2 & 1 & 4 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(3311 \\times 5214\\), 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 & 3 & 1 & 1 \\\\\n \\times & 5 & 2 & 1 & 4 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | 6d7864f3585c016284622d378823cb2e5411b585199c804d6cabd95555e2daf1 | 8cb6afcb9ac83c004a43906bd619164a60827b6a1f67133ebc2f38e84db92ef2 | 5692a05a45629d81f9b644e78f44bd720ea1a8e540c340b35031865f939b1049 | 0 | [
"67544"
] | 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 3311 x 5214 is \(\boxed{67544}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"67544"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3311 and 5214, we can perform the long multiplication step by step:\n\n1. Multiply 3311 by 4 (the last digit of 5214):\n 3311 x 4 = 13244\n\n2. Multiply 3311 by 1 (the second digit of 5214, shifted one position to the left):\n 3311 x 1 ... | |
58 | {
"answer": "16019024",
"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... | 16019024 | {
"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\n7288 x 2198\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(7288 \\times 2198\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 7288 by 8 (the units digit of 2198):**\n \\[\n 7288 \\times 8 = 57904\n \\]\n\n2. **Multiply 7288 by 2 (the tens digit of 2198, b... | [
"To solve the long multiplication equation \\(7288 \\times 2198\\), we will follow the standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply 7288 by 8 (the units digit of 2198):**\n \\[\n 7288 \\times 8 = 57904\n \\]\n\n2. **Multiply 7288 by 2 (the tens digit of 2198, but we ... | a51c0957f50fa15eafbff2921eb312d3c27cbf12236a91343141281c003a8ed2 | 8bdcd4e13e8dcbd9737fc289780913164ac63514d397a4a5c14391f5c7056a4f | 9206edebcc38e5031f20dd0a3b4f4b6deebc23e097872bd701e91ea7b807d576 | 0 | [
"8224704"
] | 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 7288 x 2198 is \(\boxed{8224704}\)." 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 | [
"8224704"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the correctness of the solution, we need to perform the long multiplication of 7288 and 2198 step by step. \n\n1. **Break down the multiplication**: \n - 7288 x 8 = 58264 \n - 7288 x 90 (which is 9 in the tens place) = 655920 \n - 7288 x 1000 (which is 2 in ... | |
59 | {
"answer": "8638722",
"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 ... | 8638722 | {
"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\n1341 x 6442\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 1341 \\times 6442 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n\n \\[\n \\begin{array}{c@{}c@{}c}\n & 1341 \\\\\n \\times & 6442 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 1341 by 2 ... | [
"To solve the long multiplication equation \\( 1341 \\times 6442 \\), we will follow the standard long multiplication method step by step.\n\n1. **Set up the multiplication:**\n\n \\[\n \\begin{array}{c@{}c@{}c}\n & 1341 \\\\\n \\times & 6442 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 1341 by 2 (the o... | 04d39dfd34c5e5e18c8be96f06d9b0475e3fdc7559236b0fb04cedacd436e316 | 736bff5a0560ffc15eb792334f894e3f2288f3796506f9e14505e6a464cba314 | 7224fd06ea18cca1a74a787cd21187b8ebfcae667b613c12fce350af34da5cf2 | 0 | [
"7046"
] | 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 1341 x 6442 is \(\boxed{7046}\)." 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 | [
"7046"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 1341 and 6442 step by step. \n\n1. **Multiply 1341 by 2 (the last digit of 6442):** \n - 1341 x 2 = 2682 \n\n2. **Multiply 1341 by 4 (the second digit of 6442, shifted one position ... | |
60 | {
"answer": "28932650",
"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... | 28932650 | {
"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\n6925 x 4178\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6925 \\times 4178\\), 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 & 6925 \\\\\n \\times & 4178 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6925 by 8 (the... | [
"To solve the long multiplication equation \\(6925 \\times 4178\\), 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 & 6925 \\\\\n \\times & 4178 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6925 by 8 (the units... | 390e2009a687a42c7464961cf687708fab8d10b94ed9a84eb485159fe19738d7 | 61918a826cde86b9db6c071170ab772035497f1dfe4fd98474d452c10d39f07f | ed05cd49f7024716052d13184f4c261687acf2d59f25d8c5d75c5dfcd049b203 | 0 | [
"301250"
] | 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 6925 x 4178 is \boxed{301250}." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"301250"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6925 and 4178 step by step. \n\n1. First, we multiply 6925 by each digit of 4178, starting from the rightmost digit:\n - 6925 x 8 = 55400\n - 6925 x 7 = 48575 (shifted one positio... | |
61 | {
"answer": "9849103",
"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 ... | 9849103 | {
"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\n5797 x 1699\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5797 \\times 1699 \\), 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 & 5 & 7 & 9 & 7 \\\\\n \\times & 1 & 6 & 9 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | [
"To solve the long multiplication equation \\( 5797 \\times 1699 \\), 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 & 5 & 7 & 9 & 7 \\\\\n \\times & 1 & 6 & 9 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Multiply ... | e6dff2315c327c9265214f705753796a0425499cb06183d489680628adb48041 | 1250719f34ac3854505f83869e310e3701d4344792c3b66aac2082ae9e22ecd2 | 3fb3988c5521f2d0bf4de16b2630cbbdcab505a9b0dd2b1c5712884bd8ed92c1 | 0 | [
"398993"
] | 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 5797 x 1699 is \(\boxed{398993}\)." 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 | [
"398993"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 5797 by 1699, we can perform the calculation step by step:\n\n1. Multiply 5797 by 9 (the last digit of 1699):\n 5797 x 9 = 52173\n\n2. Multiply 5797 by 90 (the second digit of 1699, which is 9, shifted one place to the left):\n 5797 x 90 ... | |
62 | {
"answer": "2346851",
"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 ... | 2346851 | {
"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\n2171 x 1081\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2171 \\times 1081\\), we can break it down into simpler steps by considering the two parts separately: \\(2171 \\times 1080\\) and \\(2171 \\times 10\\), and then adding the results together.\n\nStep 1: Calculate \\(2171 \\times 1080\\).\n\\[2171 \\times 1080 = 21... | [
"To solve the long multiplication equation \\(2171 \\times 1081\\), we can break it down into simpler steps by considering the two parts separately: \\(2171 \\times 1080\\) and \\(2171 \\times 10\\), and then adding the results together.\n\nStep 1: Calculate \\(2171 \\times 1080\\).\n\\[2171 \\times 1080 = 2171 \\t... | 429fbf70a25497b4ebc13a61f790ce87311d94970ce90da01b46c57f1e646c7c | f047254650a01855da6e271a6816b1adb47319c425b95e2571feeed50acc30de | 4c00f8817c0801383bb215c04fe14606248ff7848cf4493716408c5d66d7260c | 0 | [
"To solve the long multiplication equation \\(2171 \\times 1081\\), we can break it down into simpler steps by considering the two parts separately: \\(2171 \\times 1080\\) and \\(2171 \\times 10\\), and then adding the results together.\n\nStep 1: Calculate \\(2171 \\times 1080\\).\n\\[2171 \\times 1080 = 2171 \\t... | 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 2171 x 1081 is 412490." 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 one. | 1 | [
"412490"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 2171 by 1081, we can perform the long multiplication step by step:\n\n1. Multiply 2171 by 1 (the units place of 1081):\n 2171\n x 1\n ------\n 2171\n\n2. Multiply 2171 by 8 (the tens place of 1081):\n 2171\n x 80\n ------\n ... | |
63 | {
"answer": "50786515",
"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... | 50786515 | {
"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\n8779 x 5785\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 8779 \\times 5785 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 8779 \\\\\n \\times 5785 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 8779 by 5 (the units digit of 5785):**\n \\[\n 8779 \\times 5... | [
"To solve the long multiplication equation \\( 8779 \\times 5785 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 8779 \\\\\n \\times 5785 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 8779 by 5 (the units digit of 5785):**\n \\[\n 8779 \\times 5 = 438... | ad088451d60858f4044bbba972e7c59637b23cbeba1d25b20d71ce23687b6dc0 | 8d5b229cb0737eaf2cc4f596b807421d27907b85b94f9a61031075de0b81c9f4 | c57c2cf84f8407665e4964612ceb088da7a5c76e1ce41dfba2b8af91f195369d | 0 | [
"737015"
] | 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 8779 x 5785 is: \[\boxed{737015}\]" This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"737015"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 8779 by 5785, we can perform the long multiplication step by step:\n\n1. Multiply 8779 by 5 (the units digit of 5785):\n 8779 x 5 = 43895\n\n2. Multiply 8779 by 8 (the tens digit of 5785), shifting one position to the left:\n 8779 x 8 =... | |
64 | {
"answer": "43862210",
"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... | 43862210 | {
"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\n4930 x 8897\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4930 \\times 8897\\), 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 & 4930 \\\\\n \\times & 8897 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 4930 by 7 (the... | [
"To solve the long multiplication equation \\(4930 \\times 8897\\), 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 & 4930 \\\\\n \\times & 8897 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 4930 by 7 (the units... | eb6ed3d25164b2d00ec66dfc8d79a1ab7a4dc1f23738d15d7f24ece14f66a314 | 774ef55700e2f98a5694c22033310a05dd41c4b3faee012cae98784a1cf9ac08 | aeb73f2d31217126e241e197dbaa210f4a89e6eb946dc1d06f265a9f1b6d1350 | 0 | [
"428910"
] | 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 4930 x 8897 is \(\boxed{428910}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"428910"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 4930 and 8897 step by step. \n\n1. First, we can break down the multiplication: \n - 4930 can be expressed as 4930 = 4900 + 30. \n - 8897 can be expressed as 8897 = 8900 - 3. \n\n2. Us... | |
65 | {
"answer": "30116926",
"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... | 30116926 | {
"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\n8258 x 3647\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8258 \\times 3647\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply the units digits**: Multiply 8 by 7.\n \\[\n 8 \\times 7 = 56\n \\]\n Write down 6 and carry over 5.\n\n2. **Multiply the tens digits and a... | [
"To solve the long multiplication equation \\(8258 \\times 3647\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply the units digits**: Multiply 8 by 7.\n \\[\n 8 \\times 7 = 56\n \\]\n Write down 6 and carry over 5.\n\n2. **Multiply the tens digits and add the... | 996ec95ca3ac9d373af27e4ac12d0e635dd0e9f8b9132aa09180c7701587e4ec | e1f5c6e24e487370b5bed2d02caa5202fe9caeaf112031d2110ef2e5f94af3cf | 4b6fefe27e4b8c25759e4f38156fde360e248937600bc0f2e45524fdd9b79d39 | 0 | [
"30227226"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'Thus, the solution to the long multiplication equation 8258 x 3647 is \(\boxed{30227226}\)'. This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"30227226"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 8258 and 3647, we can perform the long multiplication step by step:\n\n1. Multiply 8258 by 7 (the last digit of 3647):\n 8258 x 7 = 57706\n\n2. Multiply 8258 by 4 (the second digit of 3647, which is actually 40):\n 8258 x 4 = 33032, and s... | |
66 | {
"answer": "3965060",
"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 ... | 3965060 | {
"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\n2959 x 1340\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2959 \\times 1340\\), we can break it down into simpler steps by first multiplying 2959 by 130 and then by 40, and finally adding the two results together.\n\nStep 1: Multiply 2959 by 130.\n\\[2959 \\times 130 = 2959 \\times (10 + 30) = (2959 \\times 10) + (2959 \... | [
"To solve the long multiplication equation \\(2959 \\times 1340\\), we can break it down into simpler steps by first multiplying 2959 by 130 and then by 40, and finally adding the two results together.\n\nStep 1: Multiply 2959 by 130.\n\\[2959 \\times 130 = 2959 \\times (10 + 30) = (2959 \\times 10) + (2959 \\times... | a3a3088a8271e7001cbea1a325b6e207c9964ef8d84c3ec428d6ffc7bbcfe9fc | a8bf3cf0445d3579d891c77f85b1aed84ea77006eb776b4c3609c12218562b1f | b06ba674928fef3a5aec17d8e09e50a8973c0f21446505e083325167602cf122 | 0 | [
"236720"
] | 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 2959 x 1340 is \(\boxed{236720}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"236720"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 2959 by 1340, we can perform the calculation step by step:\n\n1. Break down the multiplication:\n - 2959 x 1340 can be calculated as 2959 x (1000 + 300 + 40).\n\n2. Calculate each part:\n - 2959 x 1000 = 2959000\n - 2959 x 300 = 88770... | |
67 | {
"answer": "82799430",
"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... | 82799430 | {
"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\n9870 x 8389\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9870 \\times 8389 \\), 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 & 8 & 7 \\\\\n \\times & 8 & 3 & 8 & 9 \\\\\n \\end{array}\n \\]\n\n2. *... | [
"To solve the long multiplication equation \\( 9870 \\times 8389 \\), 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 & 8 & 7 \\\\\n \\times & 8 & 3 & 8 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Multi... | ae9e7e6b969a499659a1bee98e8450b110a211d9dc04c5689f82cd5be3346945 | c8ad58af76f2034a08c5358f27ad3afa2746d289a4991abc17dcd7ba3bb42f49 | ce34a85ebe917cd5776ef5cc2d4ed9f1492ccccd2cf211376c114fe2d9dccc69 | 0 | [
"176620"
] | 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 9870 x 8389 is \(\boxed{176620}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"176620"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 9870 and 8389, we can perform the calculation step by step:\n\n1. Multiply 9870 by 8389:\n - 9870 x 8389 = 82799430.\n\n2. The provided solution states that the result is 176620, which is significantly lower than the correct result of 827... | |
68 | {
"answer": "10325688",
"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... | 10325688 | {
"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\n9508 x 1086\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9508 \\times 1086 \\), 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 & 5 & 0 & 8 \\\\\n \\times & 1 & 0 & 8 & 6 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | [
"To solve the long multiplication equation \\( 9508 \\times 1086 \\), 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 & 5 & 0 & 8 \\\\\n \\times & 1 & 0 & 8 & 6 \\\\\n \\end{array}\n \\]\n\n2. **Multiply ... | d9405fece4886e57617e9a48525436f5f2ab9547f983433fe1714d1703ee428c | c93933147aa2be416d7c8d268756a564459c8cbc98e5bd3dfe07698b77862e88 | ff62f55a3d8f17d91ef7e4d1b656002294a2fcf66f690c376237964d7119db15 | 0 | [
"98748"
] | 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 9508 x 1086 is \(\boxed{98748}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"98748"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 9508 by 1086, we can perform the long multiplication step by step:\n\n1. Multiply 9508 by 6 (the units digit of 1086):\n 9508 x 6 = 57048\n\n2. Multiply 9508 by 8 (the tens digit of 1086), and shift one position to the left:\n 9508 x 8 ... | |
69 | {
"answer": "25777960",
"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... | 25777960 | {
"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\n5570 x 4628\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5570 \\times 4628 \\), 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 & 5570 \\\\\n \\times & 4628 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5570 by 8 (t... | [
"To solve the long multiplication equation \\( 5570 \\times 4628 \\), 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 & 5570 \\\\\n \\times & 4628 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5570 by 8 (the uni... | bcfb316e9add593ca6449c49149a609d78fc052577e2e5581e91ba68fa47e7ec | 78a9dbdfbe95593217b3bfb35146af68b4837aa6c4966f5a92ff22293da646ec | d16d02ae6c305a0ffe52ec7b7d3290280c3916f498438a939202e4013ffaecfc | 0 | [
"89120"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace concludes with a final answer: 'So, the solution to the long multiplication equation 5570 x 4628 is \(\boxed{89120}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"89120"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 5570 and 4628 step by step:\n\n1. Multiply 5570 by 8 (the units digit of 4628):\n 5570 x 8 = 44560\n\n2. Multiply 5570 by 2 (the tens digit of 4628), and shift one position to the l... | |
70 | {
"answer": "10793616",
"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... | 10793616 | {
"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\n2616 x 4126\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2616 \\times 4126\\), 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 & 2616 \\\\\n \\times & 4126 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2616 by 6 (the... | [
"To solve the long multiplication equation \\(2616 \\times 4126\\), 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 & 2616 \\\\\n \\times & 4126 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2616 by 6 (the units... | 15cdc11d5d1afa4b464374e7f8c43f95af2fb3add173ea0b152eeeb444cdf494 | 48d7f97da0a36ef0b00176a94148e23b1fc091218ca5f19d2d3c86f78bc0e976 | f5b3de405e2c0774f7627f16b7ade7e456e2a667cdf71be5a9a17383323a04e9 | 0 | [
"41856"
] | 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 2616 x 4126 is \(\boxed{41856}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"41856"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 2616 by 4126, we can perform the long multiplication step by step:\n\n1. Multiply 2616 by each digit of 4126, starting from the rightmost digit:\n - 2616 x 6 = 15696\n - 2616 x 2 (which is actually 20) = 52320 (shifted one position to t... | |
71 | {
"answer": "32987221",
"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... | 32987221 | {
"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\n6263 x 5267\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 6263 \\times 5267 \\), 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 & 2 & 6 \\\\\n \\times & 5 & 2 & 6 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | [
"To solve the long multiplication equation \\( 6263 \\times 5267 \\), 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 & 2 & 6 \\\\\n \\times & 5 & 2 & 6 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply ... | 44eeb7f6091056ede8c3c82e76ca5f2f050a5e967af19b208c1cac3084edf904 | 024d918ec6c46bd508a1e1b781b0282604c788936d2b734398648fa23a3e338d | 31387d881452b896688d451be74a46ea6e04769a9690cfeb49345d3592867f06 | 0 | [
"168901"
] | 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 6263 x 5267 is \(\boxed{168901}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"168901"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 6263 and 5267 step by step. \n\n1. First, we can break down the multiplication:\n - 6263 x 5267 can be calculated directly or using the long multiplication method.\n\n2. Performing the m... | |
72 | {
"answer": "14852720",
"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... | 14852720 | {
"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\n4240 x 3503\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4240 \\times 3503\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[4240 \\times 3503 = 4240 \\times (3000 + 503)\\]\n\nWe can further expand this to:\n\\[... | [
"To solve the long multiplication equation \\(4240 \\times 3503\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[4240 \\times 3503 = 4240 \\times (3000 + 503)\\]\n\nWe can further expand this to:\n\\[4240 \... | 397f4a09f227fa31cf1e7f0713d2abfe8774471e22cac60e47cd1714583c2962 | ffcd95257827c53e21c0602c655881f7da044ca6a9dc37545d74a40f761ae8dc | fbff615a503c9a5ea86bbd1b96852205aa2d3afd486e8089c73c0f18942fb0a5 | 0 | [
"To solve the long multiplication equation \\(4240 \\times 3503\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[4240 \\times 3503 = 4240 \\times (3000 + 503)\\]\n\nWe can further expand this to:\n\\[4240 \... | 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 equation 4240 x 3503 is 1484720." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1484720"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 4240 by 3503, we can break it down step by step:\n\n1. First, we can multiply 4240 by each digit of 3503, starting from the rightmost digit:\n - 4240 x 3 = 12720\n - 4240 x 0 = 0 (this contributes nothing)\n - 4240 x 5 = 21200 (shifted ... | |
73 | {
"answer": "33870096",
"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... | 33870096 | {
"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\n6031 x 5616\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6031 \\times 5616\\), 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 & 0 & 3 & 1 \\\\\n \\times & 5 & 6 & 1 & 6 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(6031 \\times 5616\\), 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 & 0 & 3 & 1 \\\\\n \\times & 5 & 6 & 1 & 6 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | a82c566ededfb8c0d8668342bb1de24d984efe944da0f2031a93e7af6086d7e8 | 2ced61a220581d2995b090f0bcb5eb43c1e1ae1746cd5afe11b514bb5e704796 | a0a16c7944aaf6db5faf120f028e24bed24c21de4a544c4cd350d519c9d49aac | 0 | [
"66321"
] | 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 6031 x 5616 is \(\boxed{66321}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"66321"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 6031 and 5616, we can perform the long multiplication step by step:\n\n1. Multiply 6031 by each digit of 5616, starting from the rightmost digit:\n - 6031 x 6 = 36186\n - 6031 x 1 = 6031 (shifted one position to the left, so it's 60310)... | |
74 | {
"answer": "71435079",
"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... | 71435079 | {
"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\n8417 x 8487\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 8417 \\times 8487 \\), we will follow these steps:\n\n1. **Break down the numbers:**\n \\[\n 8417 = 8000 + 400 + 100 + 7\n \\]\n \\[\n 8487 = 8000 + 400 + 800 + 7\n \\]\n\n2. **Multiply each part of \\( 8417 \\) by each part of \\( 8487 \\):**\n \\[... | [
"To solve the long multiplication equation \\( 8417 \\times 8487 \\), we will follow these steps:\n\n1. **Break down the numbers:**\n \\[\n 8417 = 8000 + 400 + 100 + 7\n \\]\n \\[\n 8487 = 8000 + 400 + 800 + 7\n \\]\n\n2. **Multiply each part of \\( 8417 \\) by each part of \\( 8487 \\):**\n \\[\n (... | 16a78d897666d8ea7ef806dbbbf86778904adace7a14eec06193bdf660538b68 | c7cdb6c8822e3a17922d8b74b8f46b2e91a2509023ccc40ba238630cbcaf9905 | 379d8437de84bc4bac86d9a32169819b210a543ed26ec50716aa52ed713fabf9 | 0 | [
"229273"
] | 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 8417 x 8487 is \(\boxed{229273}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"229273"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the provided solution, we need to perform the long multiplication of 8417 and 8487 step by step:\n\n1. **Multiply 8417 by 7 (the unit digit of 8487):** 8417 x 7 = 58919\n2. **Multiply 8417 by 80 (the tens digit of 8487):** 8417 x 80 = 673360 (... | |
75 | {
"answer": "22352715",
"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... | 22352715 | {
"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\n3465 x 6451\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3465 \\times 6451\\), 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 & 4 & 6 & 5 \\\\\n \\times & 6 & 4 & 5 & 1 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(3465 \\times 6451\\), 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 & 4 & 6 & 5 \\\\\n \\times & 6 & 4 & 5 & 1 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | ff6c9b873d2fff8637c170170379b755373e40832d1933d63b934821d4a8c56e | 75fb22c51ab1142da3fd5b44660a005234888b14907384b73bc0d5372c14f8d4 | 19eb9b6642aa9fe2cacf2d5d3796fc926c76b39cfbcbcc619460fed5a7523ffa | 0 | [
"245165"
] | 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 3465 x 6451 is \(\boxed{245165}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"245165"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the provided solution, we need to perform the multiplication of 3465 and 6451 step by step. \n\n1. First, we can break down the multiplication: \n - 3465 x 1 = 3465 \n - 3465 x 5 = 17325 (3465 shifted one position to the left) \n - 3465 ... | |
76 | {
"answer": "8198197",
"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 ... | 8198197 | {
"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\n1169 x 7013\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 1169 \\times 7013 \\), 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 & 1 & 1 & 6 & 9 \\\\\n \\times & 7 & 0 & 1 & 3 \\\\\n \\hline\n \\end{array}\n \\]... | [
"To solve the long multiplication equation \\( 1169 \\times 7013 \\), 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 & 1 & 1 & 6 & 9 \\\\\n \\times & 7 & 0 & 1 & 3 \\\\\n \\hline\n \\end{array}\n \\]\n\n2.... | e36997b1205c9d8a00192572b442dcdd9b21fc00ee1cf442503ae7b8dfaa47bf | 6204fbf2bec0f2f57d3f6eabc569536172c6e1bc6ba841ebf9adfdc6d3f9a0c2 | 9e411d46783b9f12b5f6db7ac6e903c763dba9aaa3cd315771e08b3035f4cd9b | 0 | [
"84237"
] | 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 1169 x 7013 is \(\boxed{84237}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"84237"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 1169 and 7013, we can perform the calculation step by step:\n\n1. Multiply 1169 by 3 (the last digit of 7013): 1169 x 3 = 3507\n2. Multiply 1169 by 1 (the second digit of 7013, shifted one position to the left): 1169 x 1 = 1169, shifted giv... | |
77 | {
"answer": "11558976",
"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... | 11558976 | {
"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\n2526 x 4576\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2526 \\times 4576\\), 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 & 2526 \\\\\n \\times & 4576 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2526 by 6 (the... | [
"To solve the long multiplication equation \\(2526 \\times 4576\\), 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 & 2526 \\\\\n \\times & 4576 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2526 by 6 (the units... | 4fdf4354c82bff0109d257d5b6764ee16963501349dff3351fc5f10081fdcbde | cb244c804796167b7f9ceb7f75988f6e4069d4401d926e57a960b0b7eb9ab52a | 8dd28f826e4804e80e18bab727240ce2f29df5145b7e76906ebc055138c244b3 | 0 | [
"1130086"
] | 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 2526 x 4576 is \(\boxed{1130086}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1130086"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the multiplication of 2526 and 4576, we can perform the long multiplication step by step:\n\n1. Multiply 2526 by 6 (the last digit of 4576):\n 2526 x 6 = 15156\n\n2. Multiply 2526 by 7 (the second digit of 4576, shifted one position to the left):\n 2526 x 7 = ... | |
78 | {
"answer": "19500360",
"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... | 19500360 | {
"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\n2040 x 9559\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2040 \\times 9559\\), 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 & 2040 \\\\\n \\times & 9559 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2040 by 9:... | [
"To solve the long multiplication equation \\(2040 \\times 9559\\), 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 & 2040 \\\\\n \\times & 9559 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 2040 by 9:**\n ... | 7f7303b9bc744b8ec4357c1a3c29e8563e794dda8341d18cf29f58334b98d942 | ac107c246a52b63f498c1d24376079fb41e28cc59d6ed19fe7cfb57b24ca4a3f | 82cfb3688bbb258c25ae3208e305911d7081671ca949a3565c1e9c7234a18a24 | 0 | [
"193600"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The reasoning trace contains one clear proposal of a final answer and no verifications. The proposal is found in the last line where it states, "Therefore, the solution to the long multiplication equation 2040 x 9559 is \(\boxed{193600}\)." This is a definitive conclusion to the problem presented, marking it as a final... | 1 | [
"193600"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 2040 and 9559 step by step. \n\n1. First, let's break down the multiplication:\n - 2040 x 9559 can be calculated directly or by using the standard long multiplication method.\n\n2. Perfo... | |
79 | {
"answer": "82387669",
"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... | 82387669 | {
"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\n8281 x 9949\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(8281 \\times 9949\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[8281 \\times 9949 = 8281 \\times (10000 - 5)\\]\n\nThis is because \\(9949\\) can be sp... | [
"To solve the long multiplication equation \\(8281 \\times 9949\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[8281 \\times 9949 = 8281 \\times (10000 - 5)\\]\n\nThis is because \\(9949\\) can be split in... | 556e1b584060b1766b49077dd0f14d86af4a067fb0f87ed09535fd6d343b1d3d | e8e0c847b98c0118be14f4cd4fa70219bc8b750651d16cf8652f9bb861940ab9 | d407b925af7e81140d15fbd20c4427ba3cbbed6c6bd2008f2136f181c51d14d5 | 0 | [
"78669995"
] | 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 equation 8281 x 9949 is \(\boxed{78669995}\)." This is a clear proposal of the final answer to the multiplication problem. | 1 | [
"78669995"
] | [
false
] | [
{
"correct": false,
"reasoning": "To verify the correctness of the solution, we need to perform the multiplication of 8281 and 9949 step by step:\n\n1. Break down the multiplication:\n - 8281 x 9949 can be calculated as:\n - 8281 x (9000 + 900 + 40 + 9)\n\n2. Calculate each part:\n - 8281 x 9000 = 745... | |
80 | {
"answer": "12950873",
"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... | 12950873 | {
"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\n5993 x 2161\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5993 \\times 2161 \\), 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 & 9 & 9 & 3 \\\\\n \\times & 2 & 1 & 6 & 1 \\\\\n \\end{array}\n \\]\n\n... | [
"To solve the long multiplication equation \\( 5993 \\times 2161 \\), 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 & 9 & 9 & 3 \\\\\n \\times & 2 & 1 & 6 & 1 \\\\\n \\end{array}\n \\]\n\n2. **M... | db918c49175bf12e3a0a4a9a8b4c675f8eab52359d4996b05727f1a63b221e4b | 90968395f8f17ea1ec8dba3c8b5f16cf9cf763299ebd4cbf679747d9689c06d0 | f59f9b0f4be6d28c920a2be502d4e00b31054875d98e89b1f30a4d4f0c15694a | 0 | [
"439373"
] | 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 5993 x 2161 is \(\boxed{439373}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"439373"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 5993 and 2161 step by step. \n\n1. First, we can break down the multiplication: \n - 5993 x 2161 can be calculated as follows:\n - 5993 x 1 = 5993 \n - 5993 x 60 = 5993 x 6 x 10 = 35... | |
81 | {
"answer": "25006175",
"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... | 25006175 | {
"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\n6371 x 3925\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6371 \\times 3925\\), 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 & 7 \\\\\n \\times & & 3 & 9 & 2 & 5 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(6371 \\times 3925\\), 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 & 7 \\\\\n \\times & & 3 & 9 & 2 & 5 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | f6755d42a963559aee55bec78a3a7639815f39209be434281a07b50c0f871e6c | 1a365e3fa99dc1845f24501b273a116e82dbbc04889abceafd0d0da34053b5b4 | 84301854687cf651508c24cd0279650fe211b78bb04a390c7e28222a0dc5a2f5 | 0 | [
"1961075"
] | 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 6371 x 3925 is \(\boxed{1961075}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1961075"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6371 and 3925 step by step:\n\n1. Multiply 6371 by 5 (the last digit of 3925):\n 6371 x 5 = 31855\n\n2. Multiply 6371 by 2 (the second digit of 3925, which is in the tens place):\n ... | |
82 | {
"answer": "39408570",
"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... | 39408570 | {
"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\n4710 x 8367\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4710 \\times 8367\\), 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 & 4 & 7 & 10 \\\\\n \\times & 8 & 3 & 6 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Mult... | [
"To solve the long multiplication equation \\(4710 \\times 8367\\), 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 & 4 & 7 & 10 \\\\\n \\times & 8 & 3 & 6 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 4... | 5edacc69dd52666e061535d55e4fdcdba49af9e73df6e9fb477e989eeede285e | 3c720008cddd25942ad622f6c86d9e1d18b9e50dfc24601477a96abadac69af4 | c924f58d055a40758756c4bdc3ba590f134dc45d25fe9a93edbb3a058405fc1b | 0 | [
"376800"
] | samples_longmult_4dig_2025-05-29T00-06-28.234064.jsonl | gpt-4o-mini | The trace proposes a final answer at the end: 'Thus, the solution to the multiplication 4710 x 8367 is \(\boxed{376800}\).' This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"376800"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 4710 by 8367, we can perform the calculation step by step. First, we can break down the multiplication: \n\n1. Multiply 4710 by 7 (the units digit of 8367): 4710 x 7 = 32970.\n2. Multiply 4710 by 60 (the tens digit of 8367, which is 6): 471... | |
83 | {
"answer": "43486080",
"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... | 43486080 | {
"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\n6960 x 6248\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6960 \\times 6248\\), 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 & 6 & 9 & 60 \\\\\n \\times & 6 & 2 & 48 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. *... | [
"To solve the long multiplication equation \\(6960 \\times 6248\\), 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 & 6 & 9 & 60 \\\\\n \\times & 6 & 2 & 48 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multi... | a7a7015c27a5067b52a18e4897f8c3fd98e1cec3982670a3c67f1ad26e8adfdb | 664cf68f804a4982b04c02d04afc9d97b00ebab63938714ba2f3fc668ab5d5ca | 24984b8feccae18537d2780beb3f3e448662df5de9e356dbe300ba27dd46075f | 0 | [
"144780"
] | 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 6960 x 6248 is \(\boxed{144780}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"144780"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6960 and 6248 step by step:\n\n1. Multiply 6960 by each digit of 6248, starting from the rightmost digit:\n - 6960 x 8 = 55680\n - 6960 x 4 = 27840 (shifted one position to the le... | |
84 | {
"answer": "30947238",
"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... | 30947238 | {
"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\n7182 x 4309\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(7182 \\times 4309\\), 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 & 1 & 8 & 2 \\\\\n \\times & 4 & 3 & 0 & 9 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(7182 \\times 4309\\), 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 & 1 & 8 & 2 \\\\\n \\times & 4 & 3 & 0 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | d281ba14066f51d914ba924280679d5a7e0f99e36782b246d6a3bda7644b10e3 | b0d9bcd726620a61dc8c74d88f2153fb37f3dbcb6a3f2a470f5ce355953886e4 | b01ac4611f17e54f4e68129547a7f1365da1f9e19cb35698981a01c1aacc12a2 | 0 | [
"291598"
] | 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 7182 x 4309 is \(\boxed{291598}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"291598"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7182 and 4309 step by step:\n\n1. Multiply 7182 by 9 (the units digit of 4309):\n 7182 x 9 = 64638\n\n2. Multiply 7182 by 0 (the tens digit of 4309):\n 7182 x 0 = 0 (shifted one p... | |
85 | {
"answer": "15605820",
"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... | 15605820 | {
"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\n3620 x 4311\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3620 \\times 4311\\), 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 & 2 & 0 \\\\\n \\times & 4 & 3 & 1 & 1 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(3620 \\times 4311\\), 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 & 2 & 0 \\\\\n \\times & 4 & 3 & 1 & 1 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | d118874df6523541a7147d5a2f8edba81c08bb784d761865ad026491e05c45fa | d11467254d2772d35d292755a7371296e7b7f0f3660e61a965b07b5a843b4476 | ab6c4caba8a820938da7b02bebee468214364be57f05d189de9f1a6ddb30ef2e | 0 | [
"1533"
] | 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 3620 x 4311 is \(\boxed{1533}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1533"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 3620 and 4311 step by step. \n\n1. First, we multiply 3620 by each digit of 4311, starting from the rightmost digit:\n - 3620 x 1 = 3620\n - 3620 x 1 (next digit) = 3620, but shif... | |
86 | {
"answer": "12608099",
"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... | 12608099 | {
"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\n1747 x 7217\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 1747 \\times 7217 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 1 & 7 & 4 & 7 \\\\\n \\times & 7 & 2 & 1 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 1747 by 7:**\n \\[\n 1747 \\tim... | [
"To solve the long multiplication equation \\( 1747 \\times 7217 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 1 & 7 & 4 & 7 \\\\\n \\times & 7 & 2 & 1 & 7 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 1747 by 7:**\n \\[\n 1747 \\times 7 =... | 95020db033e29dce76b6525ce30aa31c4027a5629fa4c21bda3c9803ed2c2d3f | 0401c86608c2957adc693936898102dbbbe511b635899003316bc5cb4531abf5 | c7d05c9830d69ce9114183a137dbcd52e1bcf8583659f23c03300bc874c1b521 | 0 | [
"53129"
] | 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 1747 x 7217 is \(\boxed{53129}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"53129"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 1747 and 7217 step by step. \n\n1. First, we multiply 1747 by each digit of 7217, starting from the rightmost digit:\n - 1747 x 7 = 12229\n - 1747 x 1 (which is actually 10) = 174... | |
87 | {
"answer": "6278208",
"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 ... | 6278208 | {
"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\n3648 x 1721\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3648 \\times 1721\\), 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 & 3 & 6 & 4 \\\\\n \\times & 1 & 7 & 2 \\\\\n \\end{array}\n \\]\n\n2. **Multiply ... | [
"To solve the long multiplication equation \\(3648 \\times 1721\\), 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 & 3 & 6 & 4 \\\\\n \\times & 1 & 7 & 2 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3648 b... | 67d599ec90538903a8260469a10ff9f26cfcb525ad91dc2f77b7119a21b05659 | 040d6556224f4fdc2f02e68d1bbb9d2312090f527d67a583eba81aadd7890046 | bb1803e8b1294e2e98c1bccdee6b98bef0785d5f4e87f1a0c0792d20a4b6dff6 | 0 | [
"61728"
] | 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 3648 x 1721 is \(\boxed{61728}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"61728"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3648 by 1721, we can perform the long multiplication step by step:\n\n1. Multiply 3648 by 1 (the units place of 1721):\n 3648 x 1 = 3648\n\n2. Multiply 3648 by 2 (the tens place of 1721):\n 3648 x 2 = 7296, but since this is in the tens... | |
88 | {
"answer": "11827597",
"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... | 11827597 | {
"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\n6157 x 1921\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(6157 \\times 1921\\), 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 & 1 & 5 \\\\\n \\times & 1 & 9 & 2 & 1 \\\\\n \\end{array}\n \\]\n\n2. **Multi... | [
"To solve the long multiplication equation \\(6157 \\times 1921\\), 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 & 1 & 5 \\\\\n \\times & 1 & 9 & 2 & 1 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 61... | 243b9c4e28d8934b924bebe8d5a457c0392061e515f13bf031dd7c48e6e1dfaf | e95a0e75e9d1aa072a098dc54c1ff612c4ef8821308fdd3fa11b47dc7a684e93 | 07c43af6fbc6be8ec559300763b04edaa9cfaa0897820ecb24d49c71ab9c329d | 0 | [
"1281547"
] | 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 6157 x 1921 is \(\boxed{1281547}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"1281547"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6157 and 1921 step by step:\n\n1. Multiply 6157 by 1 (the units place of 1921):\n 6157 x 1 = 6157\n\n2. Multiply 6157 by 2 (the tens place of 1921), shifting one position to the lef... | |
89 | {
"answer": "8122236",
"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 ... | 8122236 | {
"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\n4098 x 1982\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(4098 \\times 1982\\), 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 & 4098 \\\\\n \\times & 1982 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 4098 by 2 (the... | [
"To solve the long multiplication equation \\(4098 \\times 1982\\), 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 & 4098 \\\\\n \\times & 1982 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 4098 by 2 (the ones ... | 2bda6e069b3b7dfaa5fb9903dd50e880fba91bf478b2931f1270ad0dc8d4c2e1 | c7869162a3c6102a52b8d5d3e2aa9870ceec3a260b3a6abb17715c53d0394c7d | 054b3571eb9d73a52c39b2f322ffcc6d5d52a0a7a2f494c7eb36b50d41bc2208 | 0 | [
"37776"
] | 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 4098 x 1982 is \(\boxed{37776}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"37776"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 4098 and 1982 step by step. \n\n1. First, we can break down the multiplication: \n - 4098 x 1982 can be calculated as follows:\n - 4098 x 1982 = 4098 x (2000 - 18) = 4098 x 2000 - 4098... | |
90 | {
"answer": "68236670",
"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... | 68236670 | {
"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\n7655 x 8914\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 7655 \\times 8914 \\), 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 & 6 & 5 & 5 \\\\\n \\times & 8 & 9 & 1 & 4 \\\\\n \\end{array}\n \\]\n\n... | [
"To solve the long multiplication equation \\( 7655 \\times 8914 \\), 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 & 6 & 5 & 5 \\\\\n \\times & 8 & 9 & 1 & 4 \\\\\n \\end{array}\n \\]\n\n2. **M... | ef59a8900d35a71122cbc9acdfde2440b2dd1081a3461bf41f6f80be145f7088 | af948f2fa1912b2733cf26fe9d259e8e500fe23e88d83cff3f924c74fdde9c25 | c8d4d0fe0ac64b677a0b6ecf701b930d320602b1373a31a2f1146c0d0857a5c4 | 0 | [
"100510"
] | 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 7655 x 8914 is \(\boxed{100510}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"100510"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 7655 and 8914 step by step. \n\n1. First, we multiply 7655 by each digit of 8914, starting from the rightmost digit:\n - 7655 x 4 = 30620\n - 7655 x 1 = 7655 (shifted one position... | |
91 | {
"answer": "7973532",
"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 ... | 7973532 | {
"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\n1791 x 4452\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 1791 \\times 4452 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 1 & 7 & 9 \\\\\n \\times & 4 & 4 & 5 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 1791 by 5 (the units digit of 4... | [
"To solve the long multiplication equation \\( 1791 \\times 4452 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 1 & 7 & 9 \\\\\n \\times & 4 & 4 & 5 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 1791 by 5 (the units digit of 4452):*... | c77f6edf353d39a8ca42fde3da14f3bdd71df18815a0ca892e4473f2fab5e2b4 | 2c903c628137f50088bb3c2b9e539ce9dc0dc79de945bfc9846ee312d36939fd | d6d7f29613fd4431a5e7218c59c2890c92f7196483eec4e2e540c6a36394a7bc | 0 | [
"71655"
] | 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 answer is \(\boxed{71655}\)." This is a clear proposal of the final answer to the multiplication problem. | 1 | [
"71655"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 1791 and 4452 step by step:\n\n1. Multiply 1791 by 2 (the last digit of 4452):\n 1791 x 2 = 3582\n\n2. Multiply 1791 by 5 (the second digit of 4452, shifted one position to the left... | |
92 | {
"answer": "10219660",
"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... | 10219660 | {
"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\n2255 x 4532\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(2255 \\times 4532\\), 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 & 2 & 2 & 5 & 5 \\\\\n \\times & 4 & 5 & 3 & 2 \\\\\n \\end{array}\n \\]\n\n2.... | [
"To solve the long multiplication equation \\(2255 \\times 4532\\), 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 & 2 & 2 & 5 & 5 \\\\\n \\times & 4 & 5 & 3 & 2 \\\\\n \\end{array}\n \\]\n\n2. **Mul... | 42baba1dae56fdb6336245c8d8efd707c54957604c1381ab74ac060963e20ea1 | 947a07a2b60255841dbb28c6edd76e3fad187122379a55c4f65324cdc27abb5c | e3bfd31a14f74c0d6f247819191cae9de647edd18165480f5ed8f2abf09d79e8 | 0 | [
"13530"
] | 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 2255 x 4532 is \(\boxed{13530}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"13530"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 2255 by 4532, we can perform the calculation step by step:\n\n1. Multiply 2255 by 2 (the last digit of 4532): 2255 x 2 = 4510\n2. Multiply 2255 by 3 (the second digit of 4532): 2255 x 3 = 6765, but this is actually 6765 shifted one position... | |
93 | {
"answer": "31656604",
"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... | 31656604 | {
"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\n6503 x 4868\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 6503 \\times 4868 \\), 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 & 6503 \\\\\n \\times & 4868 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6503 by 8 (t... | [
"To solve the long multiplication equation \\( 6503 \\times 4868 \\), 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 & 6503 \\\\\n \\times & 4868 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 6503 by 8 (the uni... | d276285aaae2a9b79540e0ed36f80d1c65ceb3cae93d73c576eeb27a2f25c375 | 71ba49b1acc92f8331f0988bedd91e30f7b9e69b63c1b48c88c3cf4a7effcb98 | 32f888cfeec8e8dbde8e50461a0c07c6b2e37d513f47da71817e0f41e482c637 | 0 | [
"682524"
] | 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 6503 x 4868 is \(\boxed{682524}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"682524"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 6503 and 4868 step by step:\n\n1. Multiply 6503 by each digit of 4868, starting from the rightmost digit:\n - 6503 x 8 = 52024\n - 6503 x 6 = 39018 (shifted one position to the le... | |
94 | {
"answer": "22964864",
"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... | 22964864 | {
"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\n3848 x 5968\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3848 \\times 5968\\), 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 & 3848 \\\\\n \\times & 5968 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3848 by 8 (the... | [
"To solve the long multiplication equation \\(3848 \\times 5968\\), 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 & 3848 \\\\\n \\times & 5968 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3848 by 8 (the units... | 67e139c1ec46689ac2d4c0cf303c101772e239bf62ac3b9d0363df25ff364758 | dcb052e45c88ee84c058ff00b17e7565da4e9e87938bb147efde0590618fce05 | 42c84201700d810185282cff80ac555248b14235fdc8404de189e5e88650afac | 0 | [
"374688"
] | 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 3848 x 5968 is \(\boxed{374688}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"374688"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 3848 and 5968 step by step. \n\n1. First, we multiply 3848 by each digit of 5968, starting from the rightmost digit:\n - 3848 x 8 = 30784\n - 3848 x 6 = 23088 (shifted one positio... | |
95 | {
"answer": "18951400",
"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... | 18951400 | {
"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\n3848 x 4925\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(3848 \\times 4925\\), 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 & 3848 \\\\\n \\times & 4925 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3848 by 5 ... | [
"To solve the long multiplication equation \\(3848 \\times 4925\\), 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 & 3848 \\\\\n \\times & 4925 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 3848 by 5 (the u... | f84100cb6e26ff386de07fa5541984f5ffe619fd2b09f7e0b4f0bc4f3a0d207e | f187aa52c2ddab6f8d658c6f01189ae82f323aeec8a014ebd51a88a4578ec558 | 877f6fcbea6f1f02b6be6da4ef7a06ee99afa21123786d75a72ababcd35a7fc4 | 0 | [
"172360"
] | 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 3848 x 4925 is \(\boxed{172360}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"172360"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 3848 by 4925, we can perform the long multiplication step by step:\n\n1. Multiply 3848 by 5 (the units digit of 4925):\n 3848 x 5 = 19240\n\n2. Multiply 3848 by 2 (the tens digit of 4925), and shift one position to the left:\n 3848 x 2 ... | |
96 | {
"answer": "30500504",
"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... | 30500504 | {
"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\n5468 x 5578\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 5468 \\times 5578 \\), we will break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down the numbers into parts:\n\\[ 5468 = 5000 + 468 \\]\n\\[ 5578 = 5000 + 578 \\]\n\nStep 2: Apply the distributive ... | [
"To solve the long multiplication equation \\( 5468 \\times 5578 \\), we will break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down the numbers into parts:\n\\[ 5468 = 5000 + 468 \\]\n\\[ 5578 = 5000 + 578 \\]\n\nStep 2: Apply the distributive proper... | e88545ef91957b972367833f28be5f89494c8b375090e25d8ece79efd67204fe | 3d7e8af8468fb655109ba77a3d284f1461edf23249081cb13edc6713bd497c48 | 235f4fbd8262e12f698ced4a80b5c0352263da298f8e68d8421b13dcb6ed12ff | 0 | [
"To solve the long multiplication equation \\( 5468 \\times 5578 \\), we will break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep 1: Break down the numbers into parts:\n\\[ 5468 = 5000 + 468 \\]\n\\[ 5578 = 5000 + 578 \\]\n\nStep 2: Apply the distributive proper... | 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 5468 x 5578 is 288224." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"288224"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the multiplication of 5468 and 5578 step by step. \n\n1. **Break down the multiplication**: \n - 5468 can be broken down as 5000 + 400 + 60 + 8. \n - 5578 can be broken down as 5000 + 500 + 70 + 8. \n\n2. *... | |
97 | {
"answer": "21585825",
"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... | 21585825 | {
"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\n5085 x 4245\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(5085 \\times 4245\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 5085 \\\\\n \\times 4245 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5085 by 5 (the units digit of 4245):**\n \\[\n 5085 \\times 5 =... | [
"To solve the long multiplication equation \\(5085 \\times 4245\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 5085 \\\\\n \\times 4245 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 5085 by 5 (the units digit of 4245):**\n \\[\n 5085 \\times 5 = 25425... | d7e732b48173ff5714ec0d31805037ade0dff93ad6014768ec8596414cba9513 | 4a82a7eb9f445c64cccfa085b6908f2ed10d79882f974f7ee9e20b4a1e904514 | 4329490bbf93890682c108388448692bea2354f8b7cb5c168dc9975130e11f51 | 0 | [
"127125"
] | 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 5085 x 4245 is \(\boxed{127125}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"127125"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 5085 and 4245, we can perform the long multiplication step by step:\n\n1. Multiply 5085 by each digit of 4245, starting from the rightmost digit:\n - 5085 x 5 = 25425\n - 5085 x 4 = 20340 (shifted one position to the left, so it's 20340... | |
98 | {
"answer": "45787148",
"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... | 45787148 | {
"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\n9209 x 4972\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\( 9209 \\times 4972 \\), 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 & 9209 \\\\\n \\times & 4972 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 9209 by 2 (t... | [
"To solve the long multiplication equation \\( 9209 \\times 4972 \\), 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 & 9209 \\\\\n \\times & 4972 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 9209 by 2 (the one... | 0de620503e2bea5183b659cc6c0792508bb1932133471476c168a93f2dad907c | 224f9a334ae64f96b2062fdf3b852a5c8eb80cb2bac951ae19dd168b8f9d90ec | 9f3ce0e7936a2400e7171d73892f3d5a5a97bf418730c8faa07f54350cbd7402 | 0 | [
"847228"
] | 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 9209 x 4972 is \(\boxed{847228}\)'. This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"847228"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the correctness of the solution, we need to perform the long multiplication of 9209 and 4972 step by step:\n\n1. Multiply 9209 by 2 (the last digit of 4972):\n 9209 x 2 = 18418\n\n2. Multiply 9209 by 7 (the second digit of 4972):\n 9209 x 7 = 64463, but sinc... | |
99 | {
"answer": "33130300",
"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... | 33130300 | {
"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\n9275 x 3572\n\nThink step by step.<|im_end|>\n<|im_start|>assistant\n",
"arg_1": {
"do_samp... | [
[
"To solve the long multiplication equation \\(9275 \\times 3572\\), 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 & 2 & 7 & 5 \\\\\n \\times & & 3 & 5 & 7 & 2 \\\\\n \\hline\n \\end{arra... | [
"To solve the long multiplication equation \\(9275 \\times 3572\\), 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 & 2 & 7 & 5 \\\\\n \\times & & 3 & 5 & 7 & 2 \\\\\n \\hline\n \\end{array}\n ... | 3c81eef7624b254e40f20cf11ddb9ac6a3a843b79f2b65a31555f9e8992d07d0 | 5c8988a856dd951e684dd7756f10caccb99943d8bccbe129de1a00908dbb668d | ac960ec003b1eddcd90ebec8b1a4d7ac82a75c4d33eb398837cc2dc8cfdd6719 | 0 | [
"296800"
] | 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 9275 x 3572 is \(\boxed{296800}\)." This is a clear proposal of the final answer, which counts as one instance. | 1 | [
"296800"
] | [
false
] | [
{
"correct": false,
"reasoning": "To evaluate the multiplication of 9275 by 3572, we can perform the long multiplication step by step:\n\n1. Multiply 9275 by 2 (the last digit of 3572):\n 9275 x 2 = 18550\n\n2. Multiply 9275 by 7 (the second digit of 3572, shifted one position to the left):\n 9275 x 7 =... |
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