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What is the solution to the long multiplication equation below? 10 x 37 Think step by step.
370
"{\"arg1\": 10, \"arg2\": 37, \"solution\": 370}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n10 x 37\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the multiplication problem \\(10 \\times 37\\), we can follow these steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Break down the numbers into their place values.\n- The number 10 has one digit (1) in the tens place and zero digits in the ones place.\n- The number 37 has three digits (3 and 7).\n\n#...
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[ "To solve the problem of multiplying 10 by 37 using long multiplication, follow these steps:\n\nStep 1: Write down the numbers one below the other.\n```\n 37\n × 10\n _______\n```\n\nStep 2: Multiply each digit of the second number (37) by the first number (10).\n- First, multiply 37 by 0:\n ```\n 37...
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[ "To solve the problem \\(10 \\times 37\\), we can follow these steps:\n\nStep 1: Identify the numbers involved in the multiplication.\n- The first number is 10.\n- The second number is 37.\n\nStep 2: Multiply the digit of 10 (which is 1) by each digit of 37.\n - First, multiply 1 by 3:\n \\[\n 1 \\times 3...
{"continuation_phrases": ["Wait, this result is", "Wait, how?"], "continuations": [" incorrect. Let me correct it.\n\nWait, this result is incorrect. Let me correct it.\n\nStep 4: Add the intermediate results from Step 2:\n - Since there was no carry-over when multiplying 1 by either digit of 37, simply add them up:\...
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[ "To solve this problem using long multiplication, we follow these steps:\n\nStep 1: Multiply the ones digit of the second number (7) by the first number (10).\n\n10 × 7 = 70\n\nStep 2: Write down the result from Step 1.\n\nNow our problem looks like this:\n```\n 10\n× 37\n-----\n```\n\nStep 3: Next, multiply the ...
{"all_responses": ["To solve this problem using long multiplication, we follow these steps:\n\nStep 1: Multiply the ones digit of the second number (7) by the first number (10).\n\n10 \u00d7 7 = 70\n\nStep 2: Write down the result from Step 1.\n\nNow our problem looks like this:\n```\n 10\n\u00d7 37\n-----\n```\n\nSt...
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[ false ]
[ "3700" ]
{ "all_spans_summary": [ { "answer": "3700", "context": "So, the final answer is 3700.", "end_line": 39, "start_line": 39 } ], "empty_response": false, "extraction_method": "llm_judge", "final_span_info": { "answer": "3700", "context": "So, the final answer is 3700.", ...
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[ [ false ] ]
[ [ "3700" ] ]
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What is the solution to the long multiplication equation below? 66 x 91 Think step by step.
6006
"{\"arg1\": 66, \"arg2\": 91, \"solution\": 6006}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n66 x 91\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve this problem using long multiplication, we'll follow these steps:\n\n**Step 1:** Multiply the units digit of one number (6) by the other's units digit (1).\n - \\( 6 \\times 1 = 6 \\)\n\n**Step 2:** Next, multiply the tens digit of the first number (6) by the ones digit of the second number (1), then ad...
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[ "To solve the problem of multiplying 66 by 91 using long multiplication, follow these steps:\n\n### Step-by-Step Solution:\n\n**Step 1: Multiply 66 by 1 (the rightmost digit of 91).**\n\n\\[ \n\\begin{array}{r}\n 66 \\\\\n\\times 1 \\\\\n\\hline\n 66 \\\\\n\\end{array}\n\\]\n\n**Step 2: Multiply 66 by 9 (t...
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[ "To solve this problem using long multiplication, we'll follow these steps:\n\n### Step 1: Multiply the units digits.\n- Units digit of 66 = 6\n- Units digit of 91 = 1\n- Product of these two digits = \\( 6 \\times 1 = 6 \\)\n\n### Step 2: Multiply the tens digits and add any carry-over from the previous step.\n- T...
{"continuation_phrases": ["But I need to verify this.", "But to confirm,"], "continuations": [" Let me correct my approach since I made an error in understanding how to handle carries correctly.\n\nCorrected Steps:\n\n### Corrected Step 1: Multiply the units digits.\n- Units digit of 66 = 6\n- Units digit of 91 = 1\n- ...
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[ "To solve this problem using long multiplication, we'll break it down into steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 66 by 1 (units place)\n\\[ \n\\begin{array}{c@{}c}\n & 66 \\\\\n\\times & \\phantom{0}1 \\\\\n\\hline\n & 66 \\\\\n\\end{array}\n\\]\n\nHere, multiplying any number by 1 gives us ...
{"all_responses": ["To solve this problem using long multiplication, we'll break it down into steps:\n\n### Step-by-Step Solution:\n\n#### Step 1: Multiply 66 by 1 (units place)\n\\[ \n\\begin{array}{c@{}c}\n & 66 \\\\\n\\times & \\phantom{0}1 \\\\\n\\hline\n & 66 \\\\\n\\end{array}\n\\]\n\nHere, multiplying any number...
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[ false ]
[ "6004" ]
{ "all_spans_summary": [ { "answer": "6004", "context": "\\begin{array}{r}\n 66 \\\n\\times 91 \\\n\\hline\n 6004 \\\n\\end{array}", "end_line": 37, "start_line": 37 }, { "answer": "6004", "context": "Therefore, \\( 66 \\times 91 = 6004 \\).", "end_line": 4...
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[ [ false, false, false ] ]
[ [ "6004", "6004", "6004" ] ]
{ "empty_response": false, "extraction_method": "llm_judge", "internal_spans_detailed": [ { "answer": "6004", "context": "\\begin{array}{r}\n 66 \\\n\\times 91 \\\n\\hline\n 6004 \\\n\\end{array}", "end_line": 37, "end_pos": 617, "start_line": 37, "start_pos": 606 ...
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What is the solution to the long multiplication equation below? 36 x 67 Think step by step.
2412
"{\"arg1\": 36, \"arg2\": 67, \"solution\": 2412}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n36 x 67\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
null
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[ "To solve this problem using long multiplication, we'll follow these steps:\n\n1. **Multiply the units digit of both numbers:**\n - Multiply 3 (from 36) by 7 (from 67).\n \\[\n 3 \\times 7 = 21\n \\]\n - Write down 1 and carry over 2.\n\n2. **Multiply the tens digit of one number by the units digit ...
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[ "To solve the problem of multiplying 36 by 67 using long multiplication, follow these steps:\n\n1. **Set up the multiplication**: Write 36 above 67.\n\n ```\n 36\n × 67\n ```\n\n2. **Multiply 36 by 7**:\n - Multiply 36 by 7: \\( 36 \\times 7 = 252 \\)\n - Write 252 below 36.\n\n ```\n 36\n ...
{"api_url": "http://127.0.0.1:54835", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/SIE-mock_search_v2_first_attempt__nonmixed_rl-rl", "prompt": [{"content": "What is th...
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[ "To solve the problem \\( 36 \\times 67 \\), we can break it down into simpler steps.\n\n### Step-by-Step Solution:\n\n1. **Break Down the Multiplication:**\n - First, multiply 36 by 7 (the units digit of 67).\n \\[\n 36 \\times 7 = 252\n \\]\n \n2. **Multiply the Next Digit:**\n - Next, multiply ...
{"continuation_phrases": ["Wait! I can double check this answer.", "But I need to verify this."], "continuations": [" Let me verify it with another method.\n \n4. **Using Expanded Form:**\n - Another way to look at it is using expanded form:\n \\[\n 36 \\times 67 = (30 + 6) \\times (60 + 7)\n \\]\n ...
{"api_url": "http://127.0.0.1:54835", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "min_tokens": 10, "temperature": 0.7, "top_p": 0.8}, "model_name": "hosted_vllm/TAUR-dev/SIE-mock_search_v2_first_attempt__nonmixed_rl-rl", "prompt": [{"con...
[ "To solve the problem \\(36 \\times 67\\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 36 \\\\\n \\times 67 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 36 by 7 (the units digit of 67):**\n \\[\n 36 \\times 7 = 252\n \\]\n Write ...
{"all_responses": ["To solve the problem \\(36 \\times 67\\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 36 \\\\\n \\times 67 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 36 by 7 (the units digit of 67):**\n \\[\n 36 \\times 7 = 252\n ...
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[ true ]
[ "2412" ]
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[ [ "2412" ] ]
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What is the solution to the long multiplication equation below? 43 x 53 Think step by step.
2279
"{\"arg1\": 43, \"arg2\": 53, \"solution\": 2279}"
[ { "content": "What is the solution to the long multiplication equation below?\n\n43 x 53\n\nThink step by step.", "role": "user" } ]
longmult
longmult_2dig
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[ "To solve the problem \\( 43 \\times 53 \\), we can use the standard method of long multiplication.\n\nStep 1: Multiply 43 by 3.\n\\[ 43 \\times 3 = 129 \\]\n\nStep 2: Multiply 43 by 50 (which is the same as multiplying by 5 and then adding a zero at the end).\n\\[ 43 \\times 50 = 2150 \\]\n\nStep 3: Add the result...
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[ "To solve the problem of multiplying 43 and 53 using long multiplication, follow these steps:\n\n1. **Set up the multiplication**: Write down the numbers one above the other, aligning them by place value.\n\n ```\n 43\n × 53\n ```\n\n2. **Multiply each digit of the bottom number by the top number**:\n \...
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[ "To solve the long multiplication problem \\( 43 \\times 53 \\), we will follow these steps:\n\n### Step 1: Multiply 40 (the tens digit of 43) by 53.\n\\[ 40 \\times 53 = 2120 \\]\n\n### Step 2: Multiply 3 (the ones digit of 43) by 53.\n\\[ 3 \\times 53 = 159 \\]\n\n### Step 3: Add the results from Step 1 and Step ...
{"continuation_phrases": ["But I need to verify this.", "Hold on, let me verify this answer."], "continuations": [" Let's do it again carefully.\n\nFirst, let\u2019s break down the multiplication into smaller parts:\n- Multiply 43 by 50 (which is like taking away one zero from 53):\n \\[ 43 \\times 50 = 2150 \\]\n \n...
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[ "To solve the problem \\( 43 \\times 53 \\), we can follow these steps:\n\n### Step 1: Break down the numbers into parts.\nWe can break down 43 and 53 into more manageable parts.\n\n- \\( 43 = 40 + 3 \\)\n- \\( 53 = 50 + 3 \\)\n\n### Step 2: Use the distributive property of multiplication over addition.\nThe distri...
{"all_responses": ["To solve the problem \\( 43 \\times 53 \\), we can follow these steps:\n\n### Step 1: Break down the numbers into parts.\nWe can break down 43 and 53 into more manageable parts.\n\n- \\( 43 = 40 + 3 \\)\n- \\( 53 = 50 + 3 \\)\n\n### Step 2: Use the distributive property of multiplication over additi...
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[ false ]
[ "2171" ]
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[ [ false ] ]
[ [ "2171" ] ]
{ "empty_response": false, "extraction_method": "llm_judge", "internal_spans_detailed": [ { "answer": "2171", "context": "So, the final answer to \\( 43 \\times 53 \\) is **2171**.", "end_line": 53, "end_pos": 1120, "start_line": 53, "start_pos": 1065 } ], "is_final...
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What is the solution to the long multiplication equation below? 33 x 34 Think step by step.
1122
"{\"arg1\": 33, \"arg2\": 34, \"solution\": 1122}"
[{"content":"What is the solution to the long multiplication equation below?\n\n33 x 34\n\nThink ste(...TRUNCATED)
longmult
longmult_2dig
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["To solve the problem \\(33 \\times 34\\) using long multiplication, follow these steps:\n\n1. **Se(...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
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["To solve the problem of multiplying 33 by 34 using long multiplication, follow these steps:\n\n1. (...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
"{\"backend\": \"litellm\", \"model_name\": \"hosted_vllm/TAUR-dev/SIE-mock_search_v2_first_attempt_(...TRUNCATED)
["To solve the multiplication problem \\( 33 \\times 34 \\), we can follow these steps:\n\n### Step-(...TRUNCATED)
"{\"continuation_phrases\": [\"However,\", \"Wait, how?\"], \"continuations\": [\" since it's in the(...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
["To solve the problem of multiplying two numbers using long multiplication, let's break it down int(...TRUNCATED)
"{\"all_responses\": [\"To solve the problem of multiplying two numbers using long multiplication, l(...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
[ true ]
[ "33 \\times 34 = 1122" ]
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What is the solution to the long multiplication equation below? 88 x 45 Think step by step.
3960
"{\"arg1\": 88, \"arg2\": 45, \"solution\": 3960}"
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["To solve the problem of multiplying 88 by 45 using long multiplication, follow these steps:\n\n1. (...TRUNCATED)
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["To solve the multiplication problem \\( 88 \\times 45 \\), we can follow these steps:\n\n1. **Brea(...TRUNCATED)
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[ false ]
[ "6800" ]
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[ [ "792", "792", "3560", "6800" ] ]
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What is the solution to the long multiplication equation below? 53 x 13 Think step by step.
689
"{\"arg1\": 53, \"arg2\": 13, \"solution\": 689}"
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"{\"continuation_phrases\": [\"But to confirm,\", \"But I need to verify this.\"], \"continuations\"(...TRUNCATED)
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[ "53 \\times 13 = 689" ]
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[ [ "53 \\times 13 = 689", "689" ] ]
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What is the solution to the long multiplication equation below? 87 x 87 Think step by step.
7569
"{\"arg1\": 87, \"arg2\": 87, \"solution\": 7569}"
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["To solve the problem of multiplying two-digit numbers like \\(87 \\times 87\\), you can follow the(...TRUNCATED)
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["To solve the problem of multiplying two-digit numbers like 87 and 87 using long multiplication, fo(...TRUNCATED)
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["To solve the problem of multiplying two-digit numbers like \\(87 \\times 87\\), we can follow thes(...TRUNCATED)
"{\"continuation_phrases\": [\"Wait! I can double check this answer.\", \"Wait, this result is\"], \(...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
["To solve the problem of multiplying 87 by itself (i.e., \\( 87 \\times 87 \\)), we can follow thes(...TRUNCATED)
"{\"all_responses\": [\"To solve the problem of multiplying 87 by itself (i.e., \\\\( 87 \\\\times 8(...TRUNCATED)
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[ true ]
[ "7569" ]
{"all_spans_summary":[{"answer":"7569","context":"57: 7569 \\","end_line":57,"start_line":57},{"answ(...TRUNCATED)
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What is the solution to the long multiplication equation below? 89 x 80 Think step by step.
7120
"{\"arg1\": 89, \"arg2\": 80, \"solution\": 7120}"
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["To solve the problem \\( 89 \\times 80 \\), we can follow these steps:\n\n1. **Break down the numb(...TRUNCATED)
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["To solve the problem of multiplying 89 by 80 using long multiplication, follow these steps:\n\n1. (...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
"{\"backend\": \"litellm\", \"model_name\": \"hosted_vllm/TAUR-dev/SIE-mock_search_v2_first_attempt_(...TRUNCATED)
["To solve the problem \\( 89 \\times 80 \\), we can follow these steps:\n\n1. **Break down the numb(...TRUNCATED)
"{\"continuation_phrases\": [\"Wait, this result is\", \"Wait, this result is\"], \"continuations\":(...TRUNCATED)
"{\"api_url\": \"http://127.0.0.1:54835\", \"backend\": \"litellm\", \"chat_template_applied\": true(...TRUNCATED)
["To solve the long multiplication problem \\( 89 \\times 80 \\), follow these steps:\n\n1. **Set up(...TRUNCATED)
"{\"all_responses\": [\"To solve the long multiplication problem \\\\( 89 \\\\times 80 \\\\), follow(...TRUNCATED)
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What is the solution to the long multiplication equation below? 23 x 58 Think step by step.
1334
"{\"arg1\": 23, \"arg2\": 58, \"solution\": 1334}"
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longmult
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["To solve this problem using long multiplication, we'll follow these steps:\n\n1. **Multiply the un(...TRUNCATED)
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["To solve the problem of multiplying 23 by 58 using long multiplication, follow these steps:\n\n1. (...TRUNCATED)
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"{\"continuation_phrases\": [\"Wait, let me try\", \"Wait, this result is\"], \"continuations\": [\"(...TRUNCATED)
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[ "13640" ]
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