Split (1)

train · 3.66k rows

doc_id int64	doc string	target string	arguments string	resps string	filtered_resps string	doc_hash string	prompt_hash string	target_hash string	extracted_answers string	source_file string	generation string	info string	evaluation_api_cost string
0	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 15 \\\\div 19 \\\\) step by step, follow these steps:\\n\\n1. Write the numbers vertically:\\n \\\\[\\n \\\\begin{array}{c@{}c}\\n & 15 \\\\\\\\\\n \\\\times & 19 \\\\\\\\\\n \\\\end{array}\\n \\\\]\\n\\n2. **Multiply the ones digit of the di...	["{'generation': \"To solve the long division equation \\\\( 15 \\\\div 19 \\\\) step by step, follow these steps:\\n\\n1. Write the numbers vertically:\\n \\\\[\\n \\\\begin{array}{c@{}c}\\n & 15 \\\\\\\\\\n \\\\times & 19 \\\\\\\\\\n \\\\end{array}\\n \\\\]\\n\\n2. **Multiply the ones digit of the div...	1fe4a3a3bdceb99acba3870b8820fb7d71d2b128097a35de13101519c94b2714	6adf7f5ba7f8982f91ce5cd729a078032176cbdfc8ebc8d4eaebb7f44a3a1fb4	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 15 \\div 19 \\) step by step, follow these steps:\n\n1. Write the numbers vertically:\n \\[\n \\begin{array}{c@{}c}\n & 15 \\\\\n \\times & 19 \\\\\n \\end{array}\n \\]\n\n2. Multiply the ones digit of the dividee with 15:\n \\[\n 5 \\times 15 = 75\n \...	[{"budget_forced_chunks": ["To solve the long division equation \\( 15 \\div 19 \\) step by step, follow these steps:\n\n1. Write the numbers vertically:\n \\[\n \\begin{array}{c@{}c}\n & 15 \\\\\n \\times & 19 \\\\\n \\end{array}\n \\]\n\n2. Multiply the ones digit of the dividee with 15:\n \\[\n...	null
1	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	10	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 9 \\\\) step by step, follow these steps:\\n\\n1. Break down the multiplication into smaller parts:\\n - First, multiply \\\\( 20 \\\\) by \\\\( 9 \\\\) directly.\\n - Next, break down \\\\( 9 \\\\) into \\\\( 10 - 1 \\\\) and try to make t...	["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 9 \\\\) step by step, follow these steps:\\n\\n1. Break down the multiplication into smaller parts:\\n - First, multiply \\\\( 20 \\\\) by \\\\( 9 \\\\) directly.\\n - Next, break down \\\\( 9 \\\\) into \\\\( 10 - 1 \\\\) and try to make th...	4e7925e9464d9cd3f15b66d7f0d396c2d208e935db23218e8e12a143a69fdcf5	bd97db98bf338537ff6865ad3edb32a5afd84e1c203f33f3a520ad9350cff93a	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 20 \\div 9 \\) step by step, follow these steps:\n\n1. Break down the multiplication into smaller parts:\n - First, multiply \\( 20 \\) by \\( 9 \\) directly.\n - Next, break down \\( 9 \\) into \\( 10 - 1 \\) and try to make the multiplication simpler.\n\n2. **Perform ...	[{"budget_forced_chunks": ["To solve the long division equation \\( 20 \\div 9 \\) step by step, follow these steps:\n\n1. Break down the multiplication into smaller parts:\n - First, multiply \\( 20 \\) by \\( 9 \\) directly.\n - Next, break down \\( 9 \\) into \\( 10 - 1 \\) and try to make the multiplication...	null
2	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division problem \\\\(13 \\\\div 3 = 4\\\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\\\(130\\\\). We add the carried over 1 t...	["{'generation': 'To solve the long division problem \\\\(13 \\\\div 3 = 4\\\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\\\(130\\\\). We add the carried over 1 to...	21d37d7882ca656e9c61892eb0e92eb17e6ccb0b44acbf990becc8d10939c8ba	01fe40f4315157fd51d595d12678270a8d4a97c88098425b3b2c89768f826ed6	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division problem \\(13 \\div 3 = 4\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\(130\\). We add the carried over 1 to 130, which gives us 131.\...	[{"budget_forced_chunks": ["To solve the long division problem \\(13 \\div 3 = 4\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\(130\\). We add the carried over 1 to...	null
3	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	21	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long multiplication equation \\\\(23 \\\\times 315\\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\\n\\n1. Break down 315 into 300 and 15.\\n \\\\[\\n 23 \\\\times 315 = 23 \\\\times (300 + 15)\\n...	["{'generation': \"To solve the long multiplication equation \\\\(23 \\\\times 315\\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\\n\\n1. Break down 315 into 300 and 15.\\n \\\\[\\n 23 \\\\times 315 = 23 \\\\times (300 + 15)\\n ...	95ef82ecb05d93a4ee380d4641abaeadd43e6bc9d99c871ce170758b6f305b44	b74d9dce0967059bc7deb16d7c3ce9ddb7cfb27d70d2987dea642c679674d513	6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long multiplication equation \\(23 \\times 315\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Break down 315 into 300 and 15.\n \\[\n 23 \\times 315 = 23 \\times (300 + 15)\n \\]\n\n2. Apply the distributive...	[{"budget_forced_chunks": ["To solve the long multiplication equation \\(23 \\times 315\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Break down 315 into 300 and 15.\n \\[\n 23 \\times 315 = 23 \\times (300 + 15)\n \\]\n\...	null
4	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(32 \\\\div 4\\\\), we'll follow these steps:\\n\\n1. Multiply the units digits: \\n \\\\[\\n 2 \\\\times 4 = 8\\n \\\\]\\n Write down 8.\\n\\n2. Multiply the tens digit of the first number with the units digit of the second number:\\n \\\\[\...	["{'generation': \"To solve the long division equation \\\\(32 \\\\div 4\\\\), we'll follow these steps:\\n\\n1. Multiply the units digits: \\n \\\\[\\n 2 \\\\times 4 = 8\\n \\\\]\\n Write down 8.\\n\\n2. Multiply the tens digit of the first number with the units digit of the second number:\\n \\\\[\\...	37e0958fcc9b1045189fb65b03cc9e071033593787e2f5171ceea9f86e8ebcf4	ec571e8688c75a5736ce86b7195b61373aaf0be543ff8182bc2cf3a6429e9eab	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(32 \\div 4\\), we'll follow these steps:\n\n1. Multiply the units digits: \n \\[\n 2 \\times 4 = 8\n \\]\n Write down 8.\n\n2. Multiply the tens digit of the first number with the units digit of the second number:\n \\[\n 3 \\times 4 = 12\n \\]\n Since we...	[{"budget_forced_chunks": ["To solve the long division equation \\(32 \\div 4\\), we'll follow these steps:\n\n1. Multiply the units digits: \n \\[\n 2 \\times 4 = 8\n \\]\n Write down 8.\n\n2. Multiply the tens digit of the first number with the units digit of the second number:\n \\[\n 3 \\times 4...	null
5	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\\n\\nStep 1: Multiply the first two numbers (12 and 6).\\n12 * 6 = 72\\n\\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are act...	["{'generation': 'To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\\n\\nStep 1: Multiply the first two numbers (12 and 6).\\n12 * 6 = 72\\n\\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are actu...	a4b2daca5c54b55b15980110f282e22f14fac0971c9652711d3a679e8bd89a3d	7cfb8ba4d40ba72deb7d7f9cb5b33545b9f643be9e6bb394acaf180179e28cd4	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\n\nStep 1: Multiply the first two numbers (12 and 6).\n12 * 6 = 72\n\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are actually multiplying by 1...	[{"budget_forced_chunks": ["To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\n\nStep 1: Multiply the first two numbers (12 and 6).\n12 * 6 = 72\n\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are...	null
6	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	21	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the problem \\\\( 6 \\\\times 15 \\\\times 13 \\\\times 9 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\\\( 10 + 5 \\\\), which allows us to break the multiplication into two parts:\\n\\...	["{'generation': 'To solve the problem \\\\( 6 \\\\times 15 \\\\times 13 \\\\times 9 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\\\( 10 + 5 \\\\), which allows us to break the multiplication into two parts:\\n\\n...	a7f237e6a8b37389748df0baa5ea27734734e3277f163e579d92165e4afed893	ab00774c40567d2e767072fc5936db116736f40a30593069488d7cfe010b27b9	6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem \\( 6 \\times 15 \\times 13 \\times 9 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\( 10 + 5 \\), which allows us to break the multiplication into two parts:\n\n\\[ 6 \\times 15 = 6 \\times (10...	[{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 15 \\times 13 \\times 9 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\( 10 + 5 \\), which allows us to break the multiplication into two parts:\n\n\\[ 6 ...	null
7	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 2 \\\\times 8 = 16 \\\\), add the zero from the intermediate step (16) to get \\\\( 160 \\\\).\\n\\nNext, add the result of the next multiplication step, \\\\( 2 \\\\times 2 = 4 \\\\), to \\\\( 160 \\\\) to get \\\\( 164 \\\\).\\n\\nFinally, add the result o...	["{'generation': \"To solve the long division equation \\\\( 2 \\\\times 8 = 16 \\\\), add the zero from the intermediate step (16) to get \\\\( 160 \\\\).\\n\\nNext, add the result of the next multiplication step, \\\\( 2 \\\\times 2 = 4 \\\\), to \\\\( 160 \\\\) to get \\\\( 164 \\\\).\\n\\nFinally, add the result of...	45c1e59b5a1a576b7ae49ac9ab5ee519341b3ff5d15693635b6c69819b16325f	0e76d7adfecf1d484230f45f4d7e233e3860bce62d005024a9c931e6fe2a8c02	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 2 \\times 8 = 16 \\), add the zero from the intermediate step (16) to get \\( 160 \\).\n\nNext, add the result of the next multiplication step, \\( 2 \\times 2 = 4 \\), to \\( 160 \\) to get \\( 164 \\).\n\nFinally, add the result of the final multiplication step, \\( 2 \\times...	[{"budget_forced_chunks": ["To solve the long division equation \\( 2 \\times 8 = 16 \\), add the zero from the intermediate step (16) to get \\( 160 \\).\n\nNext, add the result of the next multiplication step, \\( 2 \\times 2 = 4 \\), to \\( 160 \\) to get \\( 164 \\).\n\nFinally, add the result of the final multipli...	null
8	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	22	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\\n\\nFirst, we can break down the problem into simpler steps:\\n\\n1. Multiply the numbers in pairs:\\n - 21 * 15 = 315\\n - 21 * 9 = 189\\n\\n2. Add the result...	["{'generation': \"To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\\n\\nFirst, we can break down the problem into simpler steps:\\n\\n1. Multiply the numbers in pairs:\\n - 21 * 15 = 315\\n - 21 * 9 = 189\\n\\n2. Add the results...	167220307e1ef076a95de3ecc155ceac76542c67d9bfe7f28083afac878049e0	15b1e41847c3fd678b61f9e016eda0d418836829766dc3d9e8d8e1b5133c1d3a	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\n\nFirst, we can break down the problem into simpler steps:\n\n1. Multiply the numbers in pairs:\n - 21 * 15 = 315\n - 21 * 9 = 189\n\n2. Add the results of these multiplications...	[{"budget_forced_chunks": ["To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\n\nFirst, we can break down the problem into simpler steps:\n\n1. Multiply the numbers in pairs:\n - 21 * 15 = 315\n - 21 * 9 = 189\n\n2. Add the result...	null
9	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	14	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem \\\\( 6 \\\\times 22 \\\\) using step-by-step reasoning, we can break it down into simpler steps:\\n\\n1. Break down the multiplication:\\n \\\\[\\n 6 \\\\times 22 = 6 \\\\times (20 + 2)\\n \\\\]\\n\\n2. Apply the distributive property:\\n \\\\[\\n 6 \\\\times ...	["{'generation': \"To solve the problem \\\\( 6 \\\\times 22 \\\\) using step-by-step reasoning, we can break it down into simpler steps:\\n\\n1. Break down the multiplication:\\n \\\\[\\n 6 \\\\times 22 = 6 \\\\times (20 + 2)\\n \\\\]\\n\\n2. Apply the distributive property:\\n \\\\[\\n 6 \\\\times (...	9177efbdceb2c6d3585fa1de81c78225fbf88132fb0ae87fe539a216301a3389	a3d20e36b20880d64b880d4378e3aea9de8a3687a302888a392e88997a29b20f	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem \\( 6 \\times 22 \\) using step-by-step reasoning, we can break it down into simpler steps:\n\n1. Break down the multiplication:\n \\[\n 6 \\times 22 = 6 \\times (20 + 2)\n \\]\n\n2. Apply the distributive property:\n \\[\n 6 \\times (20 + 2) = 6 \\times 20 + 6 \\times 2\n \\]...	[{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 22 \\) using step-by-step reasoning, we can break it down into simpler steps:\n\n1. Break down the multiplication:\n \\[\n 6 \\times 22 = 6 \\times (20 + 2)\n \\]\n\n2. Apply the distributive property:\n \\[\n 6 \\times (20 + 2) = 6 \\time...	null
10	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	12	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation using the numbers[20, 15, 17] that equals 12, we can use basic arithmetic operations. Let's break it down:\\n\\nStep 1: Can we subtract 15 from 20? Yes, and the result is 5.\\nStep 2: Now, can we subtract 17 from 5? yes, and the result is 8.\\nStep 3: Now...	["{'generation': \"To solve the problem of creating an equation using the numbers[20, 15, 17] that equals 12, we can use basic arithmetic operations. Let's break it down:\\n\\nStep 1: Can we subtract 15 from 20? Yes, and the result is 5.\\nStep 2: Now, can we subtract 17 from 5? yes, and the result is 8.\\nStep 3: Now,...	fa4cb9ed4e55cbe2ea009410b3c7dcdfb08848fdb2331821ffa94d8b437f7ed2	484114ad1c6eb12bf2e842b3e234616a60cc354ec1f3bada427e5e83ddb21194	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation using the numbers[20, 15, 17] that equals 12, we can use basic arithmetic operations. Let's break it down:\n\nStep 1: Can we subtract 15 from 20? Yes, and the result is 5.\nStep 2: Now, can we subtract 17 from 5? yes, and the result is 8.\nStep 3: Now, can we add 17 to 15?...	[{"budget_forced_chunks": ["To solve the problem of creating an equation using the numbers[20, 15, 17] that equals 12, we can use basic arithmetic operations. Let's break it down:\n\nStep 1: Can we subtract 15 from 20? Yes, and the result is 5.\nStep 2: Now, can we subtract 17 from 5? yes, and the result is 8.\nStep 3:...	null
11	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem 18 x 9 x 21 x 11, we can break it down into simpler steps:\\n\\n1. First, let's multiply 18 by 9:\\n 18 x 9 = 162\\n\\n2. Now, let's multiply 18 by 21:\\n 18 x 21 = 378\\n\\n3. Finally, let's multiply 18 by 11:\\n 18 x 11 = 198\\n\\nNow, we need to multiply ...	["{'generation': \"To solve the multiplication problem 18 x 9 x 21 x 11, we can break it down into simpler steps:\\n\\n1. First, let's multiply 18 by 9:\\n 18 x 9 = 162\\n\\n2. Now, let's multiply 18 by 21:\\n 18 x 21 = 378\\n\\n3. Finally, let's multiply 18 by 11:\\n 18 x 11 = 198\\n\\nNow, we need to multiply t...	aeab403787979ca2e59c5279813784a23284ef1d2d9e6cce4c2f457d9a376fa5	7b22993c7049eb435ab1c64d209542f9d5b0889583f68f7daa920a8fdd4d143a	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem 18 x 9 x 21 x 11, we can break it down into simpler steps:\n\n1. First, let's multiply 18 by 9:\n 18 x 9 = 162\n\n2. Now, let's multiply 18 by 21:\n 18 x 21 = 378\n\n3. Finally, let's multiply 18 by 11:\n 18 x 11 = 198\n\nNow, we need to multiply the results of these three mu...	[{"budget_forced_chunks": ["To solve the multiplication problem 18 x 9 x 21 x 11, we can break it down into simpler steps:\n\n1. First, let's multiply 18 by 9:\n 18 x 9 = 162\n\n2. Now, let's multiply 18 by 21:\n 18 x 21 = 378\n\n3. Finally, let's multiply 18 by 11:\n 18 x 11 = 198\n\nNow, we need to multiply the...	null
12	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 24 \\\\div 9 \\\\), we'll follow these steps:\\n\\nStep 1:\\nWe need to multiply 24 by 9. \\n- \\\\( 24 \\\\times 9 \\\\) can be broken down as \\\\( (20 + 4) \\\\times 9 \\\\).\\n- First, multiply 20 by 9: \\\\( 20 \\\\times 9 = 180 \\\\).\\n- Then, mul...	["{'generation': \"To solve the long division equation \\\\( 24 \\\\div 9 \\\\), we'll follow these steps:\\n\\nStep 1:\\nWe need to multiply 24 by 9. \\n- \\\\( 24 \\\\times 9 \\\\) can be broken down as \\\\( (20 + 4) \\\\times 9 \\\\).\\n- First, multiply 20 by 9: \\\\( 20 \\\\times 9 = 180 \\\\).\\n- Then, mult...	94cc4d46a251029a832d451e9841ef5724b174c7b59c6c76e1127a5ee0081cab	7a5b85f69b00da4f91c788b8cf04b98ce70fb22eb4c3489edad15c24280dac29	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 24 \\div 9 \\), we'll follow these steps:\n\nStep 1:\nWe need to multiply 24 by 9. \n- \\( 24 \\times 9 \\) can be broken down as \\( (20 + 4) \\times 9 \\).\n- First, multiply 20 by 9: \\( 20 \\times 9 = 180 \\).\n- Then, multiply 4 by 9: \\( 4 \\times 9 = 36 \\).\n- Add t...	[{"budget_forced_chunks": ["To solve the long division equation \\( 24 \\div 9 \\), we'll follow these steps:\n\nStep 1:\nWe need to multiply 24 by 9. \n- \\( 24 \\times 9 \\) can be broken down as \\( (20 + 4) \\times 9 \\).\n- First, multiply 20 by 9: \\( 20 \\times 9 = 180 \\).\n- Then, multiply 4 by 9: \\( 4 \\...	null
13	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(10 \\\\div 21 \\\\div 17 \\\\div 20\\\\), we will follow the standard long division method.\\n\\n1. Divide 10 by 21:\\n \\\\[\\n 10 \\\\div 21 = 0 \\\\quad \\\\text{(10 is less than 21)}\\n \\\\]\\n So, we get 0 in the ones place of the answer.\\n...	["{'generation': \"To solve the long division equation \\\\(10 \\\\div 21 \\\\div 17 \\\\div 20\\\\), we will follow the standard long division method.\\n\\n1. Divide 10 by 21:\\n \\\\[\\n 10 \\\\div 21 = 0 \\\\quad \\\\text{(10 is less than 21)}\\n \\\\]\\n So, we get 0 in the ones place of the answer.\\n\...	1100061fa8b2c459d70a76ef486ae8bad9ac3ddfb304ee3c982e7dc2c573a770	d068197d7d7b5cec6b7b9f6025420f133708054938f2ab0eba12d3306994440a	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(10 \\div 21 \\div 17 \\div 20\\), we will follow the standard long division method.\n\n1. Divide 10 by 21:\n \\[\n 10 \\div 21 = 0 \\quad \\text{(10 is less than 21)}\n \\]\n So, we get 0 in the ones place of the answer.\n\n2. Divide 10 by 17:\n \\[\n 10 \\di...	[{"budget_forced_chunks": ["To solve the long division equation \\(10 \\div 21 \\div 17 \\div 20\\), we will follow the standard long division method.\n\n1. Divide 10 by 21:\n \\[\n 10 \\div 21 = 0 \\quad \\text{(10 is less than 21)}\n \\]\n So, we get 0 in the ones place of the answer.\n\n2. **Divide 10 by...	null
14	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 20 \\\\div 11 \\\\), we'll follow these steps:\\n\\n1. Break down the multiplication:\\n \\\\[\\n 20 \\\\times 11\\n \\\\]\\n\\n2. Multiply 20 by each digit of 11 separately:\\n - First, multiply 20 by 1:\\n \\\\[\\n 20 \\\\times 1 = ...	["{'generation': \"To solve the long division equation \\\\( 20 \\\\div 11 \\\\), we'll follow these steps:\\n\\n1. Break down the multiplication:\\n \\\\[\\n 20 \\\\times 11\\n \\\\]\\n\\n2. Multiply 20 by each digit of 11 separately:\\n - First, multiply 20 by 1:\\n \\\\[\\n 20 \\\\times 1 = 2...	02fd4efda14193a5a878824c080d69604c3ea776d1bc6cf3bc6bc40ea401d5a6	bdb69ef7d0d7581d293cc62945c5493161826c3dbb4a101a65138f34bc2cedcd	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 20 \\div 11 \\), we'll follow these steps:\n\n1. Break down the multiplication:\n \\[\n 20 \\times 11\n \\]\n\n2. Multiply 20 by each digit of 11 separately:\n - First, multiply 20 by 1:\n \\[\n 20 \\times 1 = 20\n \\]\n - Next, multiply 20 by 10:\...	[{"budget_forced_chunks": ["To solve the long division equation \\( 20 \\div 11 \\), we'll follow these steps:\n\n1. Break down the multiplication:\n \\[\n 20 \\times 11\n \\]\n\n2. Multiply 20 by each digit of 11 separately:\n - First, multiply 20 by 1:\n \\[\n 20 \\times 1 = 20\n \\]\n -...	null
15	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(10 \\\\div 8 = 2.5\\\\), we can break it down into simpler steps:\\n\\n1. Break down the multiplication: \\n - We're multiplying 10 by 8, and then by 2, and then adding those two results together.\\n\\n2. First multiplication:\\n - \\\\(10 \\\\tim...	["{'generation': \"To solve the long division equation \\\\(10 \\\\div 8 = 2.5\\\\), we can break it down into simpler steps:\\n\\n1. Break down the multiplication: \\n - We're multiplying 10 by 8, and then by 2, and then adding those two results together.\\n\\n2. First multiplication:\\n - \\\\(10 \\\\time...	e8f9d6da576987a0f9ad4e735715a675cb636b1e6359c3737005d2f84e0e931e	e47f6ad2fb6e83931a5c6e780c6c9c44cb122930e07b0fc80073a360594ffa5f	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(10 \\div 8 = 2.5\\), we can break it down into simpler steps:\n\n1. Break down the multiplication: \n - We're multiplying 10 by 8, and then by 2, and then adding those two results together.\n\n2. First multiplication:\n - \\(10 \\times 8 = 80\\). But we have to be ca...	[{"budget_forced_chunks": ["To solve the long division equation \\(10 \\div 8 = 2.5\\), we can break it down into simpler steps:\n\n1. Break down the multiplication: \n - We're multiplying 10 by 8, and then by 2, and then adding those two results together.\n\n2. First multiplication:\n - \\(10 \\times 8 = 8...	null
16	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	12	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the division problem \\\\( 18 \\\\div 6 \\\\) step by step:\\n\\n1. Break down the multiplication:\\n \\\\[\\n 18 \\\\times 6 = (18 \\\\times 2) \\\\times 3\\n \\\\]\\n\\n2. Calculate \\\\( 18 \\\\times 2 \\\\):\\n \\\\[\\n 18 \\\\times 2 = 36\\n \\\\]\\n\\n3. Multiply the result...	["{'generation': 'To solve the division problem \\\\( 18 \\\\div 6 \\\\) step by step:\\n\\n1. Break down the multiplication:\\n \\\\[\\n 18 \\\\times 6 = (18 \\\\times 2) \\\\times 3\\n \\\\]\\n\\n2. Calculate \\\\( 18 \\\\times 2 \\\\):\\n \\\\[\\n 18 \\\\times 2 = 36\\n \\\\]\\n\\n3. Multiply the result ...	d9866959919cc04a8c5fdc04301ce1d8f7a08914d45734f9db2a90cd577f5729	deb0fba45a8cb601a95fc271d175d8ba01be733fcd684e11ff3d617fd59cf7cb	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the division problem \\( 18 \\div 6 \\) step by step:\n\n1. Break down the multiplication:\n \\[\n 18 \\times 6 = (18 \\times 2) \\times 3\n \\]\n\n2. Calculate \\( 18 \\times 2 \\):\n \\[\n 18 \\times 2 = 36\n \\]\n\n3. Multiply the result by 3:\n \\[\n 36 \\times 3 = 108\n \\]\n\nThus, th...	[{"budget_forced_chunks": ["To solve the division problem \\( 18 \\div 6 \\) step by step:\n\n1. Break down the multiplication:\n \\[\n 18 \\times 6 = (18 \\times 2) \\times 3\n \\]\n\n2. Calculate \\( 18 \\times 2 \\):\n \\[\n 18 \\times 2 = 36\n \\]\n\n3. Multiply the result by 3:\n \\[\n 36 \\times 3...	null
17	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\( 18 \\\\times 24 \\\\) using step-by-step reasoning, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 18 \\\\) can be written as \\\\( 10 + 8 \\\\).\\n - \\\\( 24 \\\\) can be written as \\\\( 20 + 4 \\\\).\\n\\n2. **Apply the distributi...	["{'generation': \"To solve the multiplication problem \\\\( 18 \\\\times 24 \\\\) using step-by-step reasoning, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 18 \\\\) can be written as \\\\( 10 + 8 \\\\).\\n - \\\\( 24 \\\\) can be written as \\\\( 20 + 4 \\\\).\\n\\n2. **Apply the distributiv...	25ddf3f8a07e523e1d9a482834dcac9fcaaebbac9dc38427e65a040a73467cd9	660761dff690d0d86c98fbbb63a3514001fc3380534e701bd7dbfc911373b943	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 18 \\times 24 \\) using step-by-step reasoning, follow these steps:\n\n1. Break down the numbers:\n - \\( 18 \\) can be written as \\( 10 + 8 \\).\n - \\( 24 \\) can be written as \\( 20 + 4 \\).\n\n2. Apply the distributive property:\n \\[\n 18 \\times 24 = (10...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 18 \\times 24 \\) using step-by-step reasoning, follow these steps:\n\n1. Break down the numbers:\n - \\( 18 \\) can be written as \\( 10 + 8 \\).\n - \\( 24 \\) can be written as \\( 20 + 4 \\).\n\n2. Apply the distributive property:\n \...	null
18	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication equation \\\\(8 \\\\times 19 + 19 \\\\times 8\\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the first multiplication:\\n \\\\[\\n 8 \\\\times 19 + 19 \\\\times 8 = 8 \\\\times (10 ...	["{'generation': \"To solve the multiplication equation \\\\(8 \\\\times 19 + 19 \\\\times 8\\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the first multiplication:\\n \\\\[\\n 8 \\\\times 19 + 19 \\\\times 8 = 8 \\\\times (10 +...	1cd1ac367b8094381769d347eecffee28ecb19caa550d2df703e5cde7cd4becf	6bfcb228fc7047fd6a48a7db20c9b22405f716d78e11232a2351199c622a496b	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication equation \\(8 \\times 19 + 19 \\times 8\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the first multiplication:\n \\[\n 8 \\times 19 + 19 \\times 8 = 8 \\times (10 + 9) + 19 \\times 8\n \\]\n\n2. **Ap...	[{"budget_forced_chunks": ["To solve the multiplication equation \\(8 \\times 19 + 19 \\times 8\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the first multiplication:\n \\[\n 8 \\times 19 + 19 \\times 8 = 8 \\times (10 + 9) + 19 \\...	null
19	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	12	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\( 2 \\\\times 8 \\\\times 3 \\\\times 2 \\\\), we can break it down step by step.\\n\\n### Step 1: Break down the multiplication\\nWe can rewrite the multiplication as:\\n\\\\[ (2 \\\\times 8) \\\\times (3 \\\\times 2) \\\\]\\n\\n### Step 2: Multiply 2 by 8\\n...	["{'generation': \"To solve the multiplication problem \\\\( 2 \\\\times 8 \\\\times 3 \\\\times 2 \\\\), we can break it down step by step.\\n\\n### Step 1: Break down the multiplication\\nWe can rewrite the multiplication as:\\n\\\\[ (2 \\\\times 8) \\\\times (3 \\\\times 2) \\\\]\\n\\n### Step 2: Multiply 2 by 8\\n\...	60dc4901c356bcb56bba8d524e1d45208b1b9d878f2ef89d3af8dfd467b2a7df	1321f842cb74d6de4fc8454a45b42fec7481a7e861fdb5b5ca907b30d14ffda3	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 2 \\times 8 \\times 3 \\times 2 \\), we can break it down step by step.\n\n### Step 1: Break down the multiplication\nWe can rewrite the multiplication as:\n\\[ (2 \\times 8) \\times (3 \\times 2) \\]\n\n### Step 2: Multiply 2 by 8\n\\[ 2 \\times 8 = 16 \\]\n\n### Step 3: Multi...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 2 \\times 8 \\times 3 \\times 2 \\), we can break it down step by step.\n\n### Step 1: Break down the multiplication\nWe can rewrite the multiplication as:\n\\[ (2 \\times 8) \\times (3 \\times 2) \\]\n\n### Step 2: Multiply 2 by 8\n\\[ 2 \\times 8 = 1...	null
20	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	20	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(7 \\\\times 18 \\\\times 5 \\\\times 24\\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 7 by 5:\\n \\\\[\\n 7 \\\\times 5 = 35\\n \\\\]\\n Write down 5 and carry over 3.\\n\\n2. **Multiply 7 by 2 (and add the carry-o...	["{'generation': \"To solve the long division equation \\\\(7 \\\\times 18 \\\\times 5 \\\\times 24\\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 7 by 5:\\n \\\\[\\n 7 \\\\times 5 = 35\\n \\\\]\\n Write down 5 and carry over 3.\\n\\n2. **Multiply 7 by 2 (and add the carry-ov...	06cca78287b0d4bbe85792545a31e52e50410de869f5164f38c7f45cfaec36c0	29d339d1a73cab0b263042199e1b89def0f3593d74ca75cb8f89346bce8efeca	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(7 \\times 18 \\times 5 \\times 24\\), we will follow the standard long multiplication method.\n\n1. Multiply 7 by 5:\n \\[\n 7 \\times 5 = 35\n \\]\n Write down 5 and carry over 3.\n\n2. Multiply 7 by 2 (and add the carry-over 3):\n \\[\n (7 \\times 2) + 3 = ...	[{"budget_forced_chunks": ["To solve the long division equation \\(7 \\times 18 \\times 5 \\times 24\\), we will follow the standard long multiplication method.\n\n1. Multiply 7 by 5:\n \\[\n 7 \\times 5 = 35\n \\]\n Write down 5 and carry over 3.\n\n2. Multiply 7 by 2 (and add the carry-over 3):\n \\...	null
21	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	25	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 14 \\\\times 15 \\\\), we'll follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 14 \\\\) can be seen as \\\\( 10 + 4 \\\\).\\n - \\\\( 15 \\\\) can be seen as \\\\( 10 + 5 \\\\).\\n\\n2. Multiply each part:\\n - First, multiply \\\\...	["{'generation': \"To solve the long division equation \\\\( 14 \\\\times 15 \\\\), we'll follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 14 \\\\) can be seen as \\\\( 10 + 4 \\\\).\\n - \\\\( 15 \\\\) can be seen as \\\\( 10 + 5 \\\\).\\n\\n2. Multiply each part:\\n - First, multiply \\\\(...	1955abb6fb8a09c76c5348e083bbebb0a33332ecf20a36bb471cd1d8f35b73a1	b8a8b41d18a1eb8b0faef834e0879fe35579560714765ba93d86fd34739a4fc7	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 14 \\times 15 \\), we'll follow these steps:\n\n1. Break down the numbers:\n - \\( 14 \\) can be seen as \\( 10 + 4 \\).\n - \\( 15 \\) can be seen as \\( 10 + 5 \\).\n\n2. Multiply each part:\n - First, multiply \\( 10 \\) by \\( 15 \\):\n \\[\n 10 \\time...	[{"budget_forced_chunks": ["To solve the long division equation \\( 14 \\times 15 \\), we'll follow these steps:\n\n1. Break down the numbers:\n - \\( 14 \\) can be seen as \\( 10 + 4 \\).\n - \\( 15 \\) can be seen as \\( 10 + 5 \\).\n\n2. Multiply each part:\n - First, multiply \\( 10 \\) by \\( 15 \\):...	null
22	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	11	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 5 \\\\div 14 \\\\), we'll break it down step by step:\\n\\nStep 1: Break down the numbers into tens and ones\\n- 14 can be written as 10 + 4\\n- 9 can be written as 9\\n\\nStep 2: Multiply 10 by 5\\n\\\\[ 10 \\\\times 5 = 50 \\\\]\\n\\n**Step 3: Mult...	["{'generation': \"To solve the long division equation \\\\( 5 \\\\div 14 \\\\), we'll break it down step by step:\\n\\nStep 1: Break down the numbers into tens and ones\\n- 14 can be written as 10 + 4\\n- 9 can be written as 9\\n\\nStep 2: Multiply 10 by 5\\n\\\\[ 10 \\\\times 5 = 50 \\\\]\\n\\n**Step 3: Multi...	082771250b668f5226cf3648d240e6c619be27b661df71e8f29ac9c0df5488f9	37185b44b5e1a9df65f24f8419874e6140b44c63509ae6a7873eb6b60f0cf67e	4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 5 \\div 14 \\), we'll break it down step by step:\n\nStep 1: Break down the numbers into tens and ones\n- 14 can be written as 10 + 4\n- 9 can be written as 9\n\nStep 2: Multiply 10 by 5\n\\[ 10 \\times 5 = 50 \\]\n\nStep 3: Multiply 4 by 5\n\\[ 4 \\times 5 = 20 \\]...	[{"budget_forced_chunks": ["To solve the long division equation \\( 5 \\div 14 \\), we'll break it down step by step:\n\nStep 1: Break down the numbers into tens and ones\n- 14 can be written as 10 + 4\n- 9 can be written as 9\n\nStep 2: Multiply 10 by 5\n\\[ 10 \\times 5 = 50 \\]\n\nStep 3: Multiply 4 by 5...	null
23	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 385 \\\\div 14 \\\\), we'll break it down step by step:\\n\\n1. Break down the numbers:\\n - \\\\( 385 \\\\) can be seen as \\\\( 30 + 85 \\\\).\\n - \\\\( 14 \\\\) can be seen as \\\\( 10 + 4 \\\\).\\n\\n2. **Multiply each part of the first number b...	["{'generation': \"To solve the long division equation \\\\( 385 \\\\div 14 \\\\), we'll break it down step by step:\\n\\n1. Break down the numbers:\\n - \\\\( 385 \\\\) can be seen as \\\\( 30 + 85 \\\\).\\n - \\\\( 14 \\\\) can be seen as \\\\( 10 + 4 \\\\).\\n\\n2. **Multiply each part of the first number by...	8b9702914657f73013262b009fc3552edf08395b0dbe2e572bbc5cd37ecd3387	b75ad6172d90b6085ea5c6a2c9338e58019c6a42f9b71f4bd33140b7b0ca72d2	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 385 \\div 14 \\), we'll break it down step by step:\n\n1. Break down the numbers:\n - \\( 385 \\) can be seen as \\( 30 + 85 \\).\n - \\( 14 \\) can be seen as \\( 10 + 4 \\).\n\n2. Multiply each part of the first number by each part of the second number:\n - \\( ...	[{"budget_forced_chunks": ["To solve the long division equation \\( 385 \\div 14 \\), we'll break it down step by step:\n\n1. Break down the numbers:\n - \\( 385 \\) can be seen as \\( 30 + 85 \\).\n - \\( 14 \\) can be seen as \\( 10 + 4 \\).\n\n2. **Multiply each part of the first number by each part of the s...	null
24	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	25	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(13 \\\\times 25\\\\), we can break it down into simpler steps using the distributive property.\\n\\nFirst, we can express 25 as a sum of 20 and 5:\\n\\\\[ 13 \\\\times 25 = 13 \\\\times (20 + 5) \\\\]\\n\\nNext, we use the distributive property to distribute ...	["{'generation': \"To solve the long division equation \\\\(13 \\\\times 25\\\\), we can break it down into simpler steps using the distributive property.\\n\\nFirst, we can express 25 as a sum of 20 and 5:\\n\\\\[ 13 \\\\times 25 = 13 \\\\times (20 + 5) \\\\]\\n\\nNext, we use the distributive property to distribute t...	cf4237b8a4d528b6996957344229c797765e97e4d292bb00152890f0273bfe5d	510813f610ad2885b641030188a8c8d20ca83a50ca2a36b5355b3d8af2089c8b	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(13 \\times 25\\), we can break it down into simpler steps using the distributive property.\n\nFirst, we can express 25 as a sum of 20 and 5:\n\\[ 13 \\times 25 = 13 \\times (20 + 5) \\]\n\nNext, we use the distributive property to distribute the multiplication:\n\\[ 13 \\times (...	[{"budget_forced_chunks": ["To solve the long division equation \\(13 \\times 25\\), we can break it down into simpler steps using the distributive property.\n\nFirst, we can express 25 as a sum of 20 and 5:\n\\[ 13 \\times 25 = 13 \\times (20 + 5) \\]\n\nNext, we use the distributive property to distribute the multipl...	null
25	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	22	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of 13 x 9 = ?, we can use the standard long multiplication method.\\n\\nFirst, we multiply 13 by 9:\\n\\n13 x 9 = 117\\n\\nSo the answer is 117. Hold on, let me verify this answer. 13 x 9 should equal 117, not 22. I apologize, you are correct. Let's solve the problem again with ...	["{'generation': \"To solve the problem of 13 x 9 = ?, we can use the standard long multiplication method.\\n\\nFirst, we multiply 13 by 9:\\n\\n13 x 9 = 117\\n\\nSo the answer is 117. Hold on, let me verify this answer. 13 x 9 should equal 117, not 22. I apologize, you are correct. Let's solve the problem again with t...	f69cf0b77fe42a0d324ddf1ad2281a565cd8fe5a16a7ae869ce3b5af3648068e	da83e0c754606dd8653769cc1a82cbaae8fe676572547d75c872cdf58d56fc8f	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of 13 x 9 = ?, we can use the standard long multiplication method.\n\nFirst, we multiply 13 by 9:\n\n13 x 9 = 117\n\nSo the answer is 117. Hold on, let me verify this answer. 13 x 9 should equal 117, not 22. I apologize, you are correct. Let's solve the problem again with the correct equation. Wa...	[{"budget_forced_chunks": ["To solve the problem of 13 x 9 = ?, we can use the standard long multiplication method.\n\nFirst, we multiply 13 by 9:\n\n13 x 9 = 117\n\nSo the answer is 117.", " Hold on, let me verify this answer. 13 x 9 should equal 117, not 22. I apologize, you are correct. Let's solve the problem again...	null
26	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\( 16 \\\\times 5 \\\\times 7 \\\\times 10 \\\\), we can break it down into simpler steps using the associative property of multiplication.\\n\\nFirst, let's write the numbers in a more manageable order:\\n\\\\[\\n16 \\\\times 5 \\\\times 7 \\\\times 10\\n\\\\]...	["{'generation': \"To solve the multiplication problem \\\\( 16 \\\\times 5 \\\\times 7 \\\\times 10 \\\\), we can break it down into simpler steps using the associative property of multiplication.\\n\\nFirst, let's write the numbers in a more manageable order:\\n\\\\[\\n16 \\\\times 5 \\\\times 7 \\\\times 10\\n\\\\]\...	88082144b6bbe5af4c5b843fb0153a69cb4ffa01356400441326b9aeb27e7341	799ad6928102e3f10f3aba9eecfd691709262a50e7812cb4adcfcdd97353a464	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 16 \\times 5 \\times 7 \\times 10 \\), we can break it down into simpler steps using the associative property of multiplication.\n\nFirst, let's write the numbers in a more manageable order:\n\\[\n16 \\times 5 \\times 7 \\times 10\n\\]\n\nWe can shift the multiplication a bit t...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 16 \\times 5 \\times 7 \\times 10 \\), we can break it down into simpler steps using the associative property of multiplication.\n\nFirst, let's write the numbers in a more manageable order:\n\\[\n16 \\times 5 \\times 7 \\times 10\n\\]\n\nWe can shift ...	null
27	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division equation \\\\(19 \\\\times 24 \\\\times 18 \\\\times 2\\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 19 by 24:\\n - \\\\(19 \\\\times 24 = 446\\\\)\\n\\n2. Multiply 19 by 18:\\n - \\\\(19 \\\\times 18 = 342\\\\)\\n\\n3. **Multipl...	["{'generation': 'To solve the long division equation \\\\(19 \\\\times 24 \\\\times 18 \\\\times 2\\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 19 by 24:\\n - \\\\(19 \\\\times 24 = 446\\\\)\\n\\n2. Multiply 19 by 18:\\n - \\\\(19 \\\\times 18 = 342\\\\)\\n\\n3. **Multiply...	63792ff69af699c4a79245246a3a0ca868fd10c8a39aac99e71d88802ba4d89e	c8b96c17d1cc42d3cdd0a3944a65fc5cdc3ce1607a49e7659cba77c65bc2a3a2	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(19 \\times 24 \\times 18 \\times 2\\), we will follow the standard long multiplication method.\n\n1. Multiply 19 by 24:\n - \\(19 \\times 24 = 446\\)\n\n2. Multiply 19 by 18:\n - \\(19 \\times 18 = 342\\)\n\n3. Multiply 19 by 2:\n - \\(19 \\times 2 = 38\\)\n\nN...	[{"budget_forced_chunks": ["To solve the long division equation \\(19 \\times 24 \\times 18 \\times 2\\), we will follow the standard long multiplication method.\n\n1. Multiply 19 by 24:\n - \\(19 \\times 24 = 446\\)\n\n2. Multiply 19 by 18:\n - \\(19 \\times 18 = 342\\)\n\n3. Multiply 19 by 2:\n - \\...	null
28	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	20	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation using the numbers[17, 6, 2, 17] that equals 20, you can use basic arithmetic operations. \\nStep 1: 17 * 6 = 102\\nStep 2: 17 * 2 = 34\\nStep 3: Add the results from step 1 and step 2. \\n102 + 34 = 136\\n\\nSo, the equation that equals 20 is 17 * 6 + 17 ...	["{'generation': \"To solve the problem of creating an equation using the numbers[17, 6, 2, 17] that equals 20, you can use basic arithmetic operations. \\nStep 1: 17 * 6 = 102\\nStep 2: 17 * 2 = 34\\nStep 3: Add the results from step 1 and step 2. \\n102 + 34 = 136\\n\\nSo, the equation that equals 20 is 17 * 6 + 17 *...	3ebf9c654d2c23444bb49b95d6ffae3543f7edd3c874005aacb5efe0e8c72831	79627955b99d396c075d0879ad7a818d3b21c5d6a9f427e1405e67e23ac8e56e	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation using the numbers[17, 6, 2, 17] that equals 20, you can use basic arithmetic operations. \nStep 1: 17 * 6 = 102\nStep 2: 17 * 2 = 34\nStep 3: Add the results from step 1 and step 2. \n102 + 34 = 136\n\nSo, the equation that equals 20 is 17 * 6 + 17 * 2 = 136. Wait, how? 13...	[{"budget_forced_chunks": ["To solve the problem of creating an equation using the numbers[17, 6, 2, 17] that equals 20, you can use basic arithmetic operations. \nStep 1: 17 * 6 = 102\nStep 2: 17 * 2 = 34\nStep 3: Add the results from step 1 and step 2. \n102 + 34 = 136\n\nSo, the equation that equals 20 is 17 * 6 + 1...	null
29	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	12	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the equation \\\\( 3 \\\\times 20 + 3 \\\\times 22 \\\\), we can break it down into simpler steps:\\n\\n1. Break it into parts:\\n - First, multiply 3 by 20.\\n - Then, multiply 3 by 22.\\n - Finally, add the results of these two multiplications.\\n\\n2. Calculate each part:\\n...	["{'generation': 'To solve the equation \\\\( 3 \\\\times 20 + 3 \\\\times 22 \\\\), we can break it down into simpler steps:\\n\\n1. Break it into parts:\\n - First, multiply 3 by 20.\\n - Then, multiply 3 by 22.\\n - Finally, add the results of these two multiplications.\\n\\n2. Calculate each part:\\n ...	27faf0638979afa1b175846661e17479d01ceedaf0bf10d7dbb70aeb3521ef97	3f6f94c431163cd8cc49822757d645f85470473d307da501df3e89c4e031cae9	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the equation \\( 3 \\times 20 + 3 \\times 22 \\), we can break it down into simpler steps:\n\n1. Break it into parts:\n - First, multiply 3 by 20.\n - Then, multiply 3 by 22.\n - Finally, add the results of these two multiplications.\n\n2. Calculate each part:\n - Multiply 3 by 20: \n \\[...	[{"budget_forced_chunks": ["To solve the equation \\( 3 \\times 20 + 3 \\times 22 \\), we can break it down into simpler steps:\n\n1. Break it into parts:\n - First, multiply 3 by 20.\n - Then, multiply 3 by 22.\n - Finally, add the results of these two multiplications.\n\n2. Calculate each part:\n - Mu...	null
30	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the problem of creating an equation using the numbers[11, 8, 9, 13] that equals 17, we can use basic arithmetic operations.\\n\\nFirst, we can break down the addition as follows:\\nStep 1: 11 + 8 = 19\\nStep 2: 13 + 9 = 22\\nStep 3: Now, add the results from step 1 and step 2:\\n 19\\n+ 2...	["{'generation': 'To solve the problem of creating an equation using the numbers[11, 8, 9, 13] that equals 17, we can use basic arithmetic operations.\\n\\nFirst, we can break down the addition as follows:\\nStep 1: 11 + 8 = 19\\nStep 2: 13 + 9 = 22\\nStep 3: Now, add the results from step 1 and step 2:\\n 19\\n+ 22...	0cc1376e685c64555564eb12e63d0398e53a881d7ddd1ee152d5e5ae43fa7702	21a660424e8cbb50098eb005a75591915839535032517b245dd5062f33d5ac1b	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation using the numbers[11, 8, 9, 13] that equals 17, we can use basic arithmetic operations.\n\nFirst, we can break down the addition as follows:\nStep 1: 11 + 8 = 19\nStep 2: 13 + 9 = 22\nStep 3: Now, add the results from step 1 and step 2:\n 19\n+ 22\n-----\n 319\n\nThe...	[{"budget_forced_chunks": ["To solve the problem of creating an equation using the numbers[11, 8, 9, 13] that equals 17, we can use basic arithmetic operations.\n\nFirst, we can break down the addition as follows:\nStep 1: 11 + 8 = 19\nStep 2: 13 + 9 = 22\nStep 3: Now, add the results from step 1 and step 2:\n 19\n+...	null
31	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	14	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 36 \\\\div 18 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply the units digits: 6 x 8 = 48\\n2. Multiply the tens digit by the units digit: 3 x 8 = 24\\n - Now add the units result from the previous step to the tens result: 24 + 48...	["{'generation': \"To solve the long division equation \\\\( 36 \\\\div 18 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply the units digits: 6 x 8 = 48\\n2. Multiply the tens digit by the units digit: 3 x 8 = 24\\n - Now add the units result from the previous step to the tens result: 24 + 48 ...	0bff8a88f392bdea9bf78037fd9345e9a360c73183f41fac27009acbfcf45a45	284464ca2a666cb6ff9513a61057ef6b38f08efea9d5d1e57272daf5b514b30d	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 36 \\div 18 \\), we can break it down into simpler steps:\n\n1. Multiply the units digits: 6 x 8 = 48\n2. Multiply the tens digit by the units digit: 3 x 8 = 24\n - Now add the units result from the previous step to the tens result: 24 + 48 = 72\n\n3. **Multiply the t...	[{"budget_forced_chunks": ["To solve the long division equation \\( 36 \\div 18 \\), we can break it down into simpler steps:\n\n1. Multiply the units digits: 6 x 8 = 48\n2. Multiply the tens digit by the units digit: 3 x 8 = 24\n - Now add the units result from the previous step to the tens result: 24 + 48 =...	null
32	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the multiplication problem \\\\(6 \\\\times 15 \\\\times 18\\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n - \\\\(18\\\\) can be expressed as \\\\(10 + 8\\\\).\\n - The other numbers...	["{'generation': 'To solve the multiplication problem \\\\(6 \\\\times 15 \\\\times 18\\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n - \\\\(18\\\\) can be expressed as \\\\(10 + 8\\\\).\\n - The other numbers ...	dd4b144645f3044ade5370b84d2c8ffc297f7221b9b007340f14cfbc65e21d08	66bdbb1dbf3161fa4bd295ada53f214a78964d34cbac8721fc230f654dd84eb9	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\(6 \\times 15 \\times 18\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n - \\(18\\) can be expressed as \\(10 + 8\\).\n - The other numbers are \\(6\\) and \\(15\\).\n\n2. **Di...	[{"budget_forced_chunks": ["To solve the multiplication problem \\(6 \\times 15 \\times 18\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n - \\(18\\) can be expressed as \\(10 + 8\\).\n - The other numbers are \\(6\\...	null
33	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem \\\\( 21 \\\\times 17 \\\\times 1 \\\\times 22 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\n1. Break down the multiplication:\\n \\\\[\\n 21 \\\\times 17 \\\\times 1 \\\\times 22 = (21 \\\\times 17) \...	["{'generation': \"To solve the problem \\\\( 21 \\\\times 17 \\\\times 1 \\\\times 22 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\n1. Break down the multiplication:\\n \\\\[\\n 21 \\\\times 17 \\\\times 1 \\\\times 22 = (21 \\\\times 17) \\...	386f2658d165d4865e961a1c33162044ca2347736a789c08f0ef045ee45694e2	b67f903481c0c503505a89ffb5d2efc0440dab837c0f5b94fc16cd0f93e5e719	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem \\( 21 \\times 17 \\times 1 \\times 22 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Break down the multiplication:\n \\[\n 21 \\times 17 \\times 1 \\times 22 = (21 \\times 17) \\times 1 \\times 22\n \\]\n\n2. Multiply...	[{"budget_forced_chunks": ["To solve the problem \\( 21 \\times 17 \\times 1 \\times 22 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Break down the multiplication:\n \\[\n 21 \\times 17 \\times 1 \\times 22 = (21 \\times 17) \\times 1 \\times...	null
34	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long multiplication equation \\\\(7 \\\\times 23 \\\\times 11\\\\), we will break it down into simpler steps using the distributive property.\\n\\n1. Break down 23 into 20 and 3:\\n \\\\[\\n 7 \\\\times 23 = 7 \\\\times (20 + 3)\\n \\\\]\\n\\n2. **Apply the distributive proper...	["{'generation': \"To solve the long multiplication equation \\\\(7 \\\\times 23 \\\\times 11\\\\), we will break it down into simpler steps using the distributive property.\\n\\n1. Break down 23 into 20 and 3:\\n \\\\[\\n 7 \\\\times 23 = 7 \\\\times (20 + 3)\\n \\\\]\\n\\n2. **Apply the distributive propert...	11d4963569c689aaad5d7281b004c6802e6924ca6310338820f9a7a845258c03	cd94a9feffddb511cf4bb21a2989fbef048bfdac8f9ca47a4ddea52ecdff72f0	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long multiplication equation \\(7 \\times 23 \\times 11\\), we will break it down into simpler steps using the distributive property.\n\n1. Break down 23 into 20 and 3:\n \\[\n 7 \\times 23 = 7 \\times (20 + 3)\n \\]\n\n2. Apply the distributive property:\n \\[\n 7 \\times (20 + 3) = 7 ...	[{"budget_forced_chunks": ["To solve the long multiplication equation \\(7 \\times 23 \\times 11\\), we will break it down into simpler steps using the distributive property.\n\n1. Break down 23 into 20 and 3:\n \\[\n 7 \\times 23 = 7 \\times (20 + 3)\n \\]\n\n2. Apply the distributive property:\n \\[\n...	null
35	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 9 \\\\div 17 \\\\), follow these steps:\\n\\n1. Set up the problem:\\n\\n \\\\[\\n \\\\begin{array}{r}\\n 9 \\\\\\\\\\n \\\\times 17 \\\\\\\\\\n \\\\hline\\n \\\\end{array}\\n \\\\]\\n\\n2. **Multiply 17 by the ones digit of 9 (which is 9):...	["{'generation': \"To solve the long division equation \\\\( 9 \\\\div 17 \\\\), follow these steps:\\n\\n1. Set up the problem:\\n\\n \\\\[\\n \\\\begin{array}{r}\\n 9 \\\\\\\\\\n \\\\times 17 \\\\\\\\\\n \\\\hline\\n \\\\end{array}\\n \\\\]\\n\\n2. *Multiply 17 by the ones digit of 9 (which is 9):...	e2307676ba5945f3e2c373ae638ce1fbf09fef1f24485b95b0b9dae44c1099fb	1b4da6d5e75ebf799898cd96ebd7861935499bc7b18b914f13cc209f4ed6b549	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 9 \\div 17 \\), follow these steps:\n\n1. Set up the problem:\n\n \\[\n \\begin{array}{r}\n 9 \\\\\n \\times 17 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. Multiply 17 by the ones digit of 9 (which is 9):\n \\[\n 17 \\times 9 = 153\n \\]\n\n3. **Write ...	[{"budget_forced_chunks": ["To solve the long division equation \\( 9 \\div 17 \\), follow these steps:\n\n1. Set up the problem:\n\n \\[\n \\begin{array}{r}\n 9 \\\\\n \\times 17 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. Multiply 17 by the ones digit of 9 (which is 9):\n \\[\n 17 \\times 9 = ...	null
36	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	11	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 9 \\\\div 6 \\\\), we'll follow these steps:\\n\\n1. Break down the multiplication: \\n - \\\\( 9 \\\\times 6 \\\\) can be broken down into \\\\( 9 \\\\times (6 \\\\times 10) = 9 \\\\times 60 \\\\).\\n\\n2. Multiply \\\\( 9 \\\\) by \\\\( 6 \\\\):\...	["{'generation': \"To solve the long division equation \\\\( 9 \\\\div 6 \\\\), we'll follow these steps:\\n\\n1. Break down the multiplication: \\n - \\\\( 9 \\\\times 6 \\\\) can be broken down into \\\\( 9 \\\\times (6 \\\\times 10) = 9 \\\\times 60 \\\\).\\n\\n2. Multiply \\\\( 9 \\\\) by \\\\( 6 \\\\):\\...	055f38773f98fc1fe93514b433eb50b05677ceaa346ad81e22d44389b2c69218	d557d1a3780d56b3ad6c44c18a367bdb95da8e17c3271d31bd3c4625235d047c	4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 9 \\div 6 \\), we'll follow these steps:\n\n1. Break down the multiplication: \n - \\( 9 \\times 6 \\) can be broken down into \\( 9 \\times (6 \\times 10) = 9 \\times 60 \\).\n\n2. Multiply \\( 9 \\) by \\( 6 \\):\n - \\( 9 \\times 6 = 54 \\).\n\n3. **Multiply the ...	[{"budget_forced_chunks": ["To solve the long division equation \\( 9 \\div 6 \\), we'll follow these steps:\n\n1. Break down the multiplication: \n - \\( 9 \\times 6 \\) can be broken down into \\( 9 \\times (6 \\times 10) = 9 \\times 60 \\).\n\n2. Multiply \\( 9 \\) by \\( 6 \\):\n - \\( 9 \\times 6 = 54 ...	null
37	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of 12 x 19 x 18 x 5, we will follow the standard long multiplication method.\\n\\nStep 1: Multiply 12 by 5.\\n12 x 5 = 60\\nWrite down 0 and carry over 6.\\n\\nStep 2: Multiply 12 by 19 and add the carry-over.\\n12 x 19 = 228, then add the carried-over 6.\\n228 + 6 = 234\\nWrite...	["{'generation': \"To solve the problem of 12 x 19 x 18 x 5, we will follow the standard long multiplication method.\\n\\nStep 1: Multiply 12 by 5.\\n12 x 5 = 60\\nWrite down 0 and carry over 6.\\n\\nStep 2: Multiply 12 by 19 and add the carry-over.\\n12 x 19 = 228, then add the carried-over 6.\\n228 + 6 = 234\\nWrite ...	1e02d758f3506e31de59f006d92bf7c85dab20b9e23beaf41677a15949d9d257	f793bdad9ecf5e858a215f47764758b771996046772c2ab09c13997ff97fb08f	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of 12 x 19 x 18 x 5, we will follow the standard long multiplication method.\n\nStep 1: Multiply 12 by 5.\n12 x 5 = 60\nWrite down 0 and carry over 6.\n\nStep 2: Multiply 12 by 19 and add the carry-over.\n12 x 19 = 228, then add the carried-over 6.\n228 + 6 = 234\nWrite down 4 and carry over 2.\n...	[{"budget_forced_chunks": ["To solve the problem of 12 x 19 x 18 x 5, we will follow the standard long multiplication method.\n\nStep 1: Multiply 12 by 5.\n12 x 5 = 60\nWrite down 0 and carry over 6.\n\nStep 2: Multiply 12 by 19 and add the carry-over.\n12 x 19 = 228, then add the carried-over 6.\n228 + 6 = 234\nWrite ...	null
38	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 867 \\\\div 65 \\\\), we'll break it down step by step:\\n\\n1. Break down the numbers:\\n - \\\\( 867 \\\\) can be split into \\\\( 800 \\\\) and \\\\( 67 \\\\).\\n - \\\\( 65 \\\\) can be split into \\\\( 60 \\\\) and \\\\( 5 \\\\).\\n\\n2. **First...	["{'generation': \"To solve the long division equation \\\\( 867 \\\\div 65 \\\\), we'll break it down step by step:\\n\\n1. Break down the numbers:\\n - \\\\( 867 \\\\) can be split into \\\\( 800 \\\\) and \\\\( 67 \\\\).\\n - \\\\( 65 \\\\) can be split into \\\\( 60 \\\\) and \\\\( 5 \\\\).\\n\\n2. **First ...	2282af28b6f6534d090ed13558649edf72ec5e7d388ee194c9d515d532857337	ad151f6b94c236a705e099c3417b7c3decac063fdfea02b5158df46c0a2579bc	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 867 \\div 65 \\), we'll break it down step by step:\n\n1. Break down the numbers:\n - \\( 867 \\) can be split into \\( 800 \\) and \\( 67 \\).\n - \\( 65 \\) can be split into \\( 60 \\) and \\( 5 \\).\n\n2. First multiplication:\n - Multiply \\( 800 \\) by \\( 6...	[{"budget_forced_chunks": ["To solve the long division equation \\( 867 \\div 65 \\), we'll break it down step by step:\n\n1. Break down the numbers:\n - \\( 867 \\) can be split into \\( 800 \\) and \\( 67 \\).\n - \\( 65 \\) can be split into \\( 60 \\) and \\( 5 \\).\n\n2. First multiplication:\n - Mul...	null
39	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	10	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(8 \\\\times 9 = 72\\\\), we'll break it down step by step:\\n\\nStep 1: Multiply 8 by 9.\\nTo do this, start by multiplying 8 by the units digit of 9, which is 9. \\n\\n8 x 9 = 72\\n\\nStep 2: Now, multiply 8 by the tens digit of 9, which is 6.\\nTo do this, ...	["{'generation': \"To solve the long division equation \\\\(8 \\\\times 9 = 72\\\\), we'll break it down step by step:\\n\\nStep 1: Multiply 8 by 9.\\nTo do this, start by multiplying 8 by the units digit of 9, which is 9. \\n\\n8 x 9 = 72\\n\\nStep 2: Now, multiply 8 by the tens digit of 9, which is 6.\\nTo do this, t...	42ba5c03d722b5c353664340bb3fdd03fef285a1d746be67dc6080b64f3ed1f2	6010e5495bfc0eb1aaa69f8d33dafba7002318874f2f8993a899f6c2175341be	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(8 \\times 9 = 72\\), we'll break it down step by step:\n\nStep 1: Multiply 8 by 9.\nTo do this, start by multiplying 8 by the units digit of 9, which is 9. \n\n8 x 9 = 72\n\nStep 2: Now, multiply 8 by the tens digit of 9, which is 6.\nTo do this, take again the 8 we're multiplyi...	[{"budget_forced_chunks": ["To solve the long division equation \\(8 \\times 9 = 72\\), we'll break it down step by step:\n\nStep 1: Multiply 8 by 9.\nTo do this, start by multiplying 8 by the units digit of 9, which is 9. \n\n8 x 9 = 72\n\nStep 2: Now, multiply 8 by the tens digit of 9, which is 6.\nTo do this, take a...	null
40	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of 15 + 12 + 10, we can use the standard addition algorithm.\\n\\n1. First, we add 15 and 10:\\n 15 + 10 = 25\\n We write down 5 and carry over 2.\\n\\n2. Next, we add 15 and 2:\\n 15 + 2 = 17\\n We write down 7 and carry over 1.\\n\\n3. Finally, we add 12 and 1:\\n 12...	["{'generation': \"To solve the problem of 15 + 12 + 10, we can use the standard addition algorithm.\\n\\n1. First, we add 15 and 10:\\n 15 + 10 = 25\\n We write down 5 and carry over 2.\\n\\n2. Next, we add 15 and 2:\\n 15 + 2 = 17\\n We write down 7 and carry over 1.\\n\\n3. Finally, we add 12 and 1:\\n 12 ...	05f0d33714099cc656acf8c8eb68719411b73df92d0a070b3dc097d1897fa282	9182372ee604d8332a7f3e9623e2461b466d8b780a7500a2dd61955e54796104	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of 15 + 12 + 10, we can use the standard addition algorithm.\n\n1. First, we add 15 and 10:\n 15 + 10 = 25\n We write down 5 and carry over 2.\n\n2. Next, we add 15 and 2:\n 15 + 2 = 17\n We write down 7 and carry over 1.\n\n3. Finally, we add 12 and 1:\n 12 + 1 = 13\n We write down 3...	[{"budget_forced_chunks": ["To solve the problem of 15 + 12 + 10, we can use the standard addition algorithm.\n\n1. First, we add 15 and 10:\n 15 + 10 = 25\n We write down 5 and carry over 2.\n\n2. Next, we add 15 and 2:\n 15 + 2 = 17\n We write down 7 and carry over 1.\n\n3. Finally, we add 12 and 1:\n 12 + ...	null
41	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem (9 * 2) + (4 * 20), let's break it down step by step:\\n\\n1. First, we solve the multiplication inside the parentheses:\\n - 9 * 2 = 18\\n - 4 * 20 = 80\\n\\n2. Next, we add the results together:\\n - 18 + 80 = 98\\n\\nTherefore, the solution to the equation 9 * 2 + 4 * 2...	["{'generation': \"To solve the problem (9 * 2) + (4 * 20), let's break it down step by step:\\n\\n1. First, we solve the multiplication inside the parentheses:\\n - 9 * 2 = 18\\n - 4 * 20 = 80\\n\\n2. Next, we add the results together:\\n - 18 + 80 = 98\\n\\nTherefore, the solution to the equation 9 * 2 + 4 * 20...	0315f9a1c2b6e1bfbf8a8edbef44189839e111a96f251ea8c1e4116c60fd5cee	e9cafd581fb89d08a111dd7726405d183419160dd52f6dd12be72064f6226e87	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem (9 * 2) + (4 * 20), let's break it down step by step:\n\n1. First, we solve the multiplication inside the parentheses:\n - 9 * 2 = 18\n - 4 * 20 = 80\n\n2. Next, we add the results together:\n - 18 + 80 = 98\n\nTherefore, the solution to the equation 9 * 2 + 4 * 20 is 98. Wait! I can double...	[{"budget_forced_chunks": ["To solve the problem (9 * 2) + (4 * 20), let's break it down step by step:\n\n1. First, we solve the multiplication inside the parentheses:\n - 9 * 2 = 18\n - 4 * 20 = 80\n\n2. Next, we add the results together:\n - 18 + 80 = 98\n\nTherefore, the solution to the equation 9 * 2 + 4 * 20...	null
42	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(11 \\\\times 14 \\\\times 20\\\\), we can break it down into simpler steps based on place value.\\n\\n1. Multiply by the ones place of the second number (4):\\n \\\\[\\n 11 \\\\times 4 = 44\\n \\\\]\\n Write down 44 as the first part.\\n\\n2. **Mu...	["{'generation': \"To solve the long division equation \\\\(11 \\\\times 14 \\\\times 20\\\\), we can break it down into simpler steps based on place value.\\n\\n1. Multiply by the ones place of the second number (4):\\n \\\\[\\n 11 \\\\times 4 = 44\\n \\\\]\\n Write down 44 as the first part.\\n\\n2. **Mul...	e7235818189cee9d7974085c723f8c0c6789bf34cec743ad9090eeb5a74018c5	2a9d2117ec015b63c5be448e3dbe6c88b99d39f86ca94ccadf2e18578a6d5348	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(11 \\times 14 \\times 20\\), we can break it down into simpler steps based on place value.\n\n1. Multiply by the ones place of the second number (4):\n \\[\n 11 \\times 4 = 44\n \\]\n Write down 44 as the first part.\n\n2. **Multiply by the tens place of the second n...	[{"budget_forced_chunks": ["To solve the long division equation \\(11 \\times 14 \\times 20\\), we can break it down into simpler steps based on place value.\n\n1. Multiply by the ones place of the second number (4):\n \\[\n 11 \\times 4 = 44\n \\]\n Write down 44 as the first part.\n\n2. **Multiply by the ...	null
43	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem \\\\( 14 \\\\times 1 \\\\), we can break it down into simpler steps.\\n\\n1. Multiply 14 by 1:\\n \\\\[\\n 14 \\\\times 1 = 14\\n \\\\]\\n\\n2. Add the result to 14 again:\\n \\\\[\\n 14 \\\\times 1 = 14\\n \\\\]\\n \\\\[\\n 14 + 14 = 28\\n \\\\]\\n\\nS...	["{'generation': \"To solve the problem \\\\( 14 \\\\times 1 \\\\), we can break it down into simpler steps.\\n\\n1. Multiply 14 by 1:\\n \\\\[\\n 14 \\\\times 1 = 14\\n \\\\]\\n\\n2. Add the result to 14 again:\\n \\\\[\\n 14 \\\\times 1 = 14\\n \\\\]\\n \\\\[\\n 14 + 14 = 28\\n \\\\]\\n\\nSo...	28e1ffdd0700740151dde731e2bc7f7be8ed38e3f23333aa4e32bdaf61e5c613	690588146313ddc71ac5b6291a01a87d0b2a32176a8c9a537f84786c08a82d55	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem \\( 14 \\times 1 \\), we can break it down into simpler steps.\n\n1. Multiply 14 by 1:\n \\[\n 14 \\times 1 = 14\n \\]\n\n2. Add the result to 14 again:\n \\[\n 14 \\times 1 = 14\n \\]\n \\[\n 14 + 14 = 28\n \\]\n\nSo, the final answer is:\n\\[\n\\boxed{28}\n\\] But to c...	[{"budget_forced_chunks": ["To solve the problem \\( 14 \\times 1 \\), we can break it down into simpler steps.\n\n1. Multiply 14 by 1:\n \\[\n 14 \\times 1 = 14\n \\]\n\n2. Add the result to 14 again:\n \\[\n 14 \\times 1 = 14\n \\]\n \\[\n 14 + 14 = 28\n \\]\n\nSo, the final answer is:\n\\[\...	null
44	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 22 \\\\div 4 \\\\), let's break it down step by step:\\n\\n1. First Step: Multiply 4 by the ones digit of 22, which is 2. \\n \\\\[ 4 \\\\times 2 = 8 \\\\]\\n\\n2. Second Step: Multiply 4 by the tens digit of 22, which is 2, and remember to shift t...	["{'generation': \"To solve the long division equation \\\\( 22 \\\\div 4 \\\\), let's break it down step by step:\\n\\n1. First Step: Multiply 4 by the ones digit of 22, which is 2. \\n \\\\[ 4 \\\\times 2 = 8 \\\\]\\n\\n2. Second Step: Multiply 4 by the tens digit of 22, which is 2, and remember to shift th...	f3ddb34578e5f09132211961a1dd13853a41d2af86f1ac3cd4b520c9ccb55208	57ea06bd045d0c6c2eabfc9b26bc35cee2eb052a39546f25cd77f7c587a22742	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 22 \\div 4 \\), let's break it down step by step:\n\n1. First Step: Multiply 4 by the ones digit of 22, which is 2. \n \\[ 4 \\times 2 = 8 \\]\n\n2. Second Step: Multiply 4 by the tens digit of 22, which is 2, and remember to shift the result one place to the left (be...	[{"budget_forced_chunks": ["To solve the long division equation \\( 22 \\div 4 \\), let's break it down step by step:\n\n1. First Step: Multiply 4 by the ones digit of 22, which is 2. \n \\[ 4 \\times 2 = 8 \\]\n\n2. Second Step: Multiply 4 by the tens digit of 22, which is 2, and remember to shift the result...	null
45	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(7 \\\\times 14 = 98\\\\), we'll follow these steps:\\n\\n1. Break down the multiplication: We need to multiply 7 by 14. This can be broken down as \\\\(7 \\\\times 10 + 7 \\\\times 4\\\\).\\n\\n2. Multiply 7 by 10:\\n \\\\[\\n 7 \\\\times 10 = 70\...	["{'generation': \"To solve the long division equation \\\\(7 \\\\times 14 = 98\\\\), we'll follow these steps:\\n\\n1. Break down the multiplication: We need to multiply 7 by 14. This can be broken down as \\\\(7 \\\\times 10 + 7 \\\\times 4\\\\).\\n\\n2. Multiply 7 by 10:\\n \\\\[\\n 7 \\\\times 10 = 70\\...	d4148b73faad89dbbacfe944ac9870b26bc7780bfe26b5b6cc5809cc5575df84	ef8dc21e0133a2b6e6a1e76ca7547457a5f356117bdb5c02d1d1b0f3e2d30c9a	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(7 \\times 14 = 98\\), we'll follow these steps:\n\n1. Break down the multiplication: We need to multiply 7 by 14. This can be broken down as \\(7 \\times 10 + 7 \\times 4\\).\n\n2. Multiply 7 by 10:\n \\[\n 7 \\times 10 = 70\n \\]\n\n3. Multiply 7 by 4:\n \\[...	[{"budget_forced_chunks": ["To solve the long division equation \\(7 \\times 14 = 98\\), we'll follow these steps:\n\n1. Break down the multiplication: We need to multiply 7 by 14. This can be broken down as \\(7 \\times 10 + 7 \\times 4\\).\n\n2. Multiply 7 by 10:\n \\[\n 7 \\times 10 = 70\n \\]\n\n3. **...	null
46	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	15	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(10 \\\\div 13\\\\) step by step, we'll follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\(10\\\\) can be seen as \\\\(1 \\\\times 10\\\\).\\n - \\\\(13\\\\) can be seen as \\\\(1 \\\\times 13\\\\).\\n\\n2. **Multiply \\\\(1 \\\\times 10\\\\...	["{'generation': \"To solve the long division equation \\\\(10 \\\\div 13\\\\) step by step, we'll follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\(10\\\\) can be seen as \\\\(1 \\\\times 10\\\\).\\n - \\\\(13\\\\) can be seen as \\\\(1 \\\\times 13\\\\).\\n\\n2. **Multiply \\\\(1 \\\\times 10\\\\)...	f31d25479cb0879c1e473db5654734110af6012c3dec6787a432841c1e9f5e14	c56e96674fbf187c3876e536b5237e294f4469f36773c316a0e604a3e5091630	e629fa6598d732768f7c726b4b621285f9c3b85303900aa912017db7617d8bdb	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(10 \\div 13\\) step by step, we'll follow these steps:\n\n1. Break down the numbers:\n - \\(10\\) can be seen as \\(1 \\times 10\\).\n - \\(13\\) can be seen as \\(1 \\times 13\\).\n\n2. Multiply \\(1 \\times 10\\) by \\(1 \\times 13\\):\n - \\(1 \\times 10 \\times...	[{"budget_forced_chunks": ["To solve the long division equation \\(10 \\div 13\\) step by step, we'll follow these steps:\n\n1. Break down the numbers:\n - \\(10\\) can be seen as \\(1 \\times 10\\).\n - \\(13\\) can be seen as \\(1 \\times 13\\).\n\n2. Multiply \\(1 \\times 10\\) by \\(1 \\times 13\\):\n ...	null
47	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem \\\\( 10 + 17 - 22 + 21 \\\\), we can break it down into simpler steps using the distributive property of addition over subtraction.\\n\\n1. Break down the numbers:\\n - \\\\( 10 \\\\) can be thought of as \\\\( 1 \\\\times 10 \\\\).\\n - \\\\( 17 \\\\) can be thought of...	["{'generation': \"To solve the problem \\\\( 10 + 17 - 22 + 21 \\\\), we can break it down into simpler steps using the distributive property of addition over subtraction.\\n\\n1. Break down the numbers:\\n - \\\\( 10 \\\\) can be thought of as \\\\( 1 \\\\times 10 \\\\).\\n - \\\\( 17 \\\\) can be thought of ...	ec4723d791e04df97fc68140b01e5c04f54ca9d2222922ec78e3489918e89a8d	9e01c4026ea50c024f81b0b26b4133645ef725dd9cc13cf176c1e650623b1007	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem \\( 10 + 17 - 22 + 21 \\), we can break it down into simpler steps using the distributive property of addition over subtraction.\n\n1. Break down the numbers:\n - \\( 10 \\) can be thought of as \\( 1 \\times 10 \\).\n - \\( 17 \\) can be thought of as \\( 1 \\times 17 \\).\n - \\( 22 \...	[{"budget_forced_chunks": ["To solve the problem \\( 10 + 17 - 22 + 21 \\), we can break it down into simpler steps using the distributive property of addition over subtraction.\n\n1. Break down the numbers:\n - \\( 10 \\) can be thought of as \\( 1 \\times 10 \\).\n - \\( 17 \\) can be thought of as \\( 1 \\ti...	null
48	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	20	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\(23 \\\\times 23 - 13 \\\\times 16\\\\) step by step, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\(23\\\\) can be written as \\\\(20 + 3\\\\).\\n - \\\\(16\\\\) can be written as \\\\(10 + 6\\\\).\\n\\n2. **Apply the distributive prope...	["{'generation': \"To solve the multiplication problem \\\\(23 \\\\times 23 - 13 \\\\times 16\\\\) step by step, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\(23\\\\) can be written as \\\\(20 + 3\\\\).\\n - \\\\(16\\\\) can be written as \\\\(10 + 6\\\\).\\n\\n2. **Apply the distributive proper...	8e5566982343c0690d90c6bac61b52d7dfb907ee9c94df525e5757c4c97c4262	db237d201578701780659ed1aef2b60d06c349d2cd605d35b9c43e344346a198	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\(23 \\times 23 - 13 \\times 16\\) step by step, follow these steps:\n\n1. Break down the numbers:\n - \\(23\\) can be written as \\(20 + 3\\).\n - \\(16\\) can be written as \\(10 + 6\\).\n\n2. Apply the distributive property:\n \\[\n 23 \\times 23 - 13 \\times 16...	[{"budget_forced_chunks": ["To solve the multiplication problem \\(23 \\times 23 - 13 \\times 16\\) step by step, follow these steps:\n\n1. Break down the numbers:\n - \\(23\\) can be written as \\(20 + 3\\).\n - \\(16\\) can be written as \\(10 + 6\\).\n\n2. Apply the distributive property:\n \\[\n 23 ...	null
49	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	22	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the problem ofcreating an equation using the numbers 4, 14, 8, and 6 that equals 22, we can break it down into simpler steps.\\n\\n### Step 1: Break down the numbers\\nWe can think of the numbers as:\\n- 4 ones\\n- 14 tens\\n- 8 tens\\n- 6 units\\n\\n### Step 2: Combine the numbers\\nWe can ...	["{'generation': 'To solve the problem ofcreating an equation using the numbers 4, 14, 8, and 6 that equals 22, we can break it down into simpler steps.\\n\\n### Step 1: Break down the numbers\\nWe can think of the numbers as:\\n- 4 ones\\n- 14 tens\\n- 8 tens\\n- 6 units\\n\\n### Step 2: Combine the numbers\\nWe can c...	7aca7383c6015b2caa3691a0ea9a88ce61a224cc7fa4480f98bb178f67b3699a	abf814c17e6c9998a882dedeb9fefd5d9744207da8310ec3fe141485c9b0cece	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem ofcreating an equation using the numbers 4, 14, 8, and 6 that equals 22, we can break it down into simpler steps.\n\n### Step 1: Break down the numbers\nWe can think of the numbers as:\n- 4 ones\n- 14 tens\n- 8 tens\n- 6 units\n\n### Step 2: Combine the numbers\nWe can combine them by adding up a...	[{"budget_forced_chunks": ["To solve the problem ofcreating an equation using the numbers 4, 14, 8, and 6 that equals 22, we can break it down into simpler steps.\n\n### Step 1: Break down the numbers\nWe can think of the numbers as:\n- 4 ones\n- 14 tens\n- 8 tens\n- 6 units\n\n### Step 2: Combine the numbers\nWe can c...	null
50	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(15 \\\\times 22\\\\), we will break it down into simpler steps using the distributive property. Here are the steps:\\n\\n1. Break down 22 into 20 and 2:\\n \\\\[\\n 15 \\\\times 22 = 15 \\\\times (20 + 2)\\n \\\\]\\n\\n2. **Apply the distributive pr...	["{'generation': \"To solve the long division equation \\\\(15 \\\\times 22\\\\), we will break it down into simpler steps using the distributive property. Here are the steps:\\n\\n1. Break down 22 into 20 and 2:\\n \\\\[\\n 15 \\\\times 22 = 15 \\\\times (20 + 2)\\n \\\\]\\n\\n2. **Apply the distributive pro...	47bac1a2342eda30692108659694e008e612521cbc54ffec54c8d5678789649a	370dcedf0dfcaeedd84655684cc6bd37cdacaa0a8e5c4038cfa6e6c882e61060	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(15 \\times 22\\), we will break it down into simpler steps using the distributive property. Here are the steps:\n\n1. Break down 22 into 20 and 2:\n \\[\n 15 \\times 22 = 15 \\times (20 + 2)\n \\]\n\n2. Apply the distributive property:\n \\[\n 15 \\times (20 + ...	[{"budget_forced_chunks": ["To solve the long division equation \\(15 \\times 22\\), we will break it down into simpler steps using the distributive property. Here are the steps:\n\n1. Break down 22 into 20 and 2:\n \\[\n 15 \\times 22 = 15 \\times (20 + 2)\n \\]\n\n2. Apply the distributive property:\n ...	null
51	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	20	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(15 \\\\times 20\\\\), we will follow these steps:\\n\\n1. Multiply the units digits: \\n - Multiply the units digit of 15 (which is 5) by the units digit of 20 (which is 0).\\n - \\\\(5 \\\\times 0 = 0\\\\)\\n\\n2. **Multiply the tens digit of the fir...	["{'generation': \"To solve the long division equation \\\\(15 \\\\times 20\\\\), we will follow these steps:\\n\\n1. Multiply the units digits: \\n - Multiply the units digit of 15 (which is 5) by the units digit of 20 (which is 0).\\n - \\\\(5 \\\\times 0 = 0\\\\)\\n\\n2. **Multiply the tens digit of the firs...	e4cb65e43bd8799efe66b31342b571b532d5932afb20b4d16854be908cddc019	d4c729d6184e5dc678411950de66cc83e11b46733769289afddd5ec13f2cf251	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(15 \\times 20\\), we will follow these steps:\n\n1. Multiply the units digits: \n - Multiply the units digit of 15 (which is 5) by the units digit of 20 (which is 0).\n - \\(5 \\times 0 = 0\\)\n\n2. Multiply the tens digit of the first number by the first number: \n ...	[{"budget_forced_chunks": ["To solve the long division equation \\(15 \\times 20\\), we will follow these steps:\n\n1. Multiply the units digits: \n - Multiply the units digit of 15 (which is 5) by the units digit of 20 (which is 0).\n - \\(5 \\times 0 = 0\\)\n\n2. **Multiply the tens digit of the first number ...	null
52	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation with the numbers[18, 15, 6, 24] that equals 23, you can use basic arithmetic operations. \\nStep 1: Start with (18 * 15)\\n18 * 15 = 270\\n\\nStep 2: Next, do (270 - 6 * 18)\\n270 - 6 * 18 = 270 - 108 = 162\\n\\nStep 3: Finally, do (162 + 24 * 6)\\n162 + ...	["{'generation': \"To solve the problem of creating an equation with the numbers[18, 15, 6, 24] that equals 23, you can use basic arithmetic operations. \\nStep 1: Start with (18 * 15)\\n18 * 15 = 270\\n\\nStep 2: Next, do (270 - 6 * 18)\\n270 - 6 * 18 = 270 - 108 = 162\\n\\nStep 3: Finally, do (162 + 24 * 6)\\n162 + 2...	0dfd5c9b6911ee38ebcccfadea25fddef45481b0c639fa3795b35370f5d06ab6	10ed909db1dc7a655b9955cfebb2c5726d50b43576625d7b2e9e724c8580d160	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation with the numbers[18, 15, 6, 24] that equals 23, you can use basic arithmetic operations. \nStep 1: Start with (18 * 15)\n18 * 15 = 270\n\nStep 2: Next, do (270 - 6 * 18)\n270 - 6 * 18 = 270 - 108 = 162\n\nStep 3: Finally, do (162 + 24 * 6)\n162 + 24 * 6 = 162 + 144 = 306\n...	[{"budget_forced_chunks": ["To solve the problem of creating an equation with the numbers[18, 15, 6, 24] that equals 23, you can use basic arithmetic operations. \nStep 1: Start with (18 * 15)\n18 * 15 = 270\n\nStep 2: Next, do (270 - 6 * 18)\n270 - 6 * 18 = 270 - 108 = 162\n\nStep 3: Finally, do (162 + 24 * 6)\n162 + ...	null
53	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	25	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(17 \\\\times 16\\\\), let's break it down step by step:\\n\\n1. Write the numbers in a column format where the tens place is on top:\\n\\n\\\\[\\n\\\\begin{array}{c@{}c@{}c@{}c}\\n& 1 & 7 & \\\\\\\\\\n\\\\times & 1 & 6 & \\\\\\\\\\n\\\\end{array}\\n\\\\]\...	["{'generation': \"To solve the long division equation \\\\(17 \\\\times 16\\\\), let's break it down step by step:\\n\\n1. Write the numbers in a column format where the tens place is on top:\\n\\n\\\\[\\n\\\\begin{array}{c@{}c@{}c@{}c}\\n& 1 & 7 & \\\\\\\\\\n\\\\times & 1 & 6 & \\\\\\\\\\n\\\\end{array}\\n\\\\]\\...	a0bbf926e8f85501032b4b6c203376301dda401daa39981885d3c09c4387a5cd	1f6cc0a799203fca5c7ad993c753db7ebcc9bed4af86c541129c9788b48602c0	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(17 \\times 16\\), let's break it down step by step:\n\n1. Write the numbers in a column format where the tens place is on top:\n\n\\[\n\\begin{array}{c@{}c@{}c@{}c}\n& 1 & 7 & \\\\\n\\times & 1 & 6 & \\\\\n\\end{array}\n\\]\n\n2. Multiply 17 by 6:\n\n\\[\n17 \\times 6 = ...	[{"budget_forced_chunks": ["To solve the long division equation \\(17 \\times 16\\), let's break it down step by step:\n\n1. Write the numbers in a column format where the tens place is on top:\n\n\\[\n\\begin{array}{c@{}c@{}c@{}c}\n& 1 & 7 & \\\\\n\\times & 1 & 6 & \\\\\n\\end{array}\n\\]\n\n2. **Multiply 17 by 6:...	null
54	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(8 \\\\times 13 \\\\times 23\\\\), we'll follow the standard long division method.\\n\\n1. Multiply 8 by 3:\\n \\\\[\\n 8 \\\\times 3 = 24\\n \\\\]\\n Write down 4 and carry over 2.\\n\\n2. Multiply 8 by 2, and add the carry-over:\\n \\\\[\\n...	["{'generation': \"To solve the long division equation \\\\(8 \\\\times 13 \\\\times 23\\\\), we'll follow the standard long division method.\\n\\n1. Multiply 8 by 3:\\n \\\\[\\n 8 \\\\times 3 = 24\\n \\\\]\\n Write down 4 and carry over 2.\\n\\n2. Multiply 8 by 2, and add the carry-over:\\n \\\\[\\n ...	c5077f8f4a57d4767d513fa0140bb28369b0d97abe9081405ec1ce4977de6977	e089014c0c72e03c6f566a420ec27695fdf2cf37476b848f24bcd9cd7b103b2c	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(8 \\times 13 \\times 23\\), we'll follow the standard long division method.\n\n1. Multiply 8 by 3:\n \\[\n 8 \\times 3 = 24\n \\]\n Write down 4 and carry over 2.\n\n2. Multiply 8 by 2, and add the carry-over:\n \\[\n (8 \\times 2) + 2 = 16 + 2 = 18\n \\]\n...	[{"budget_forced_chunks": ["To solve the long division equation \\(8 \\times 13 \\times 23\\), we'll follow the standard long division method.\n\n1. Multiply 8 by 3:\n \\[\n 8 \\times 3 = 24\n \\]\n Write down 4 and carry over 2.\n\n2. Multiply 8 by 2, and add the carry-over:\n \\[\n (8 \\times 2) +...	null
55	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	14	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the equation \\\\( 3 + 14 \\\\times 14 + 11 \\\\), we will follow the order of operations, which is typically remembered by the acronym PEMDAS (Parentheses,exponents, multiplication, division, addition, subtraction).\\n\\n1. PEN: Perform the multiplication \\\\( 14 \\\\times 14 \\\\).\\...	["{'generation': \"To solve the equation \\\\( 3 + 14 \\\\times 14 + 11 \\\\), we will follow the order of operations, which is typically remembered by the acronym PEMDAS (Parentheses,exponents, multiplication, division, addition, subtraction).\\n\\n1. PEN: Perform the multiplication \\\\( 14 \\\\times 14 \\\\).\\n...	d52f1030f65184c430fb7423fea9454bcefcbc2dd8a80a98709d4fd82e33ff99	1ef05c7aaa7694efc259416e25c7e5610f7a9467e8c47827e59eb90e80c7ced2	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the equation \\( 3 + 14 \\times 14 + 11 \\), we will follow the order of operations, which is typically remembered by the acronym PEMDAS (Parentheses,exponents, multiplication, division, addition, subtraction).\n\n1. PEN: Perform the multiplication \\( 14 \\times 14 \\).\n \\[\n 14 \\times 14 = 196\n...	[{"budget_forced_chunks": ["To solve the equation \\( 3 + 14 \\times 14 + 11 \\), we will follow the order of operations, which is typically remembered by the acronym PEMDAS (Parentheses,exponents, multiplication, division, addition, subtraction).\n\n1. PEN: Perform the multiplication \\( 14 \\times 14 \\).\n \\[...	null
56	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication equation \\\\(19 \\\\times 23\\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\nFirst, break down the multiplication:\\n\\\\[ 19 \\\\times 23 = 19 \\\\times (20 + 3) \\\\]\\n\\nApply the distributive proper...	["{'generation': \"To solve the multiplication equation \\\\(19 \\\\times 23\\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\nFirst, break down the multiplication:\\n\\\\[ 19 \\\\times 23 = 19 \\\\times (20 + 3) \\\\]\\n\\nApply the distributive propert...	4adbd29da982f2d2d00599ad14573dc4c8eb945e3de91b443e8b27003bd52042	9eed663edc29ed6d7f3f24e24519ddadb989ae3ec75476c63f62b5bf8f4a57e5	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication equation \\(19 \\times 23\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, break down the multiplication:\n\\[ 19 \\times 23 = 19 \\times (20 + 3) \\]\n\nApply the distributive property:\n\\[ 19 \\times (20 + 3) = 19 \\t...	[{"budget_forced_chunks": ["To solve the multiplication equation \\(19 \\times 23\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, break down the multiplication:\n\\[ 19 \\times 23 = 19 \\times (20 + 3) \\]\n\nApply the distributive property:\n\\[ 19...	null
57	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	22	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the problem of creating an equation using the numbers[20, 8, 16, 8] that equals 22, we can use basic arithmetic operations.\\n\\nStep 1: Start by multiplying the first two numbers together, in this case, 20 and 8.\\n\\n20 x 8 = 160\\n\\nStep 2: Now, multiply the next two numbers together, wh...	["{'generation': 'To solve the problem of creating an equation using the numbers[20, 8, 16, 8] that equals 22, we can use basic arithmetic operations.\\n\\nStep 1: Start by multiplying the first two numbers together, in this case, 20 and 8.\\n\\n20 x 8 = 160\\n\\nStep 2: Now, multiply the next two numbers together, whi...	ebbe613099da63d1b55291f4b798ae73a232d8c4af2d918301eff2a8d08b9f58	76eaccefd1c4e5886e4057d7b18e969a4a9600226f4b26e60d6ef61df962b611	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation using the numbers[20, 8, 16, 8] that equals 22, we can use basic arithmetic operations.\n\nStep 1: Start by multiplying the first two numbers together, in this case, 20 and 8.\n\n20 x 8 = 160\n\nStep 2: Now, multiply the next two numbers together, which is 16 and 8.\n\n16 ...	[{"budget_forced_chunks": ["To solve the problem of creating an equation using the numbers[20, 8, 16, 8] that equals 22, we can use basic arithmetic operations.\n\nStep 1: Start by multiplying the first two numbers together, in this case, 20 and 8.\n\n20 x 8 = 160\n\nStep 2: Now, multiply the next two numbers together,...	null
58	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division equation \\\\(13 \\\\times 24 \\\\times 6 \\\\times 15\\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 13 by 4 (the units digit of 15):\\n \\\\[\\n 13 \\\\times 4 = 52\\n \\\\]\\n Write down 2 and carry over 5.\\n\\n2. **Multiply 1...	["{'generation': 'To solve the long division equation \\\\(13 \\\\times 24 \\\\times 6 \\\\times 15\\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 13 by 4 (the units digit of 15):\\n \\\\[\\n 13 \\\\times 4 = 52\\n \\\\]\\n Write down 2 and carry over 5.\\n\\n2. **Multiply 13...	4b8548a181e3a8daf0e5e5ef30f90b7996f6638d2697da69aefcccd58369ccc7	0f18306e93c6b30451422876db152449239137bebb974cc06ae779d1c0cc45a4	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(13 \\times 24 \\times 6 \\times 15\\), we will follow the standard long multiplication method.\n\n1. Multiply 13 by 4 (the units digit of 15):\n \\[\n 13 \\times 4 = 52\n \\]\n Write down 2 and carry over 5.\n\n2. **Multiply 13 by 6 (the tens digit of 15), and add th...	[{"budget_forced_chunks": ["To solve the long division equation \\(13 \\times 24 \\times 6 \\times 15\\), we will follow the standard long multiplication method.\n\n1. Multiply 13 by 4 (the units digit of 15):\n \\[\n 13 \\times 4 = 52\n \\]\n Write down 2 and carry over 5.\n\n2. **Multiply 13 by 6 (the ten...	null
59	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	14	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(18 \\\\div 13\\\\), we'll follow the standard long division method.\\n\\n1. Break down the numbers:\\n - \\\\(18\\\\) can be broken down into \\\\(10 + 8\\\\).\\n - \\\\(13\\\\) can be broken down into \\\\(10 + 3\\\\).\\n\\n2. **Divide each part of t...	["{'generation': \"To solve the long division equation \\\\(18 \\\\div 13\\\\), we'll follow the standard long division method.\\n\\n1. Break down the numbers:\\n - \\\\(18\\\\) can be broken down into \\\\(10 + 8\\\\).\\n - \\\\(13\\\\) can be broken down into \\\\(10 + 3\\\\).\\n\\n2. **Divide each part of th...	82ea3a7e9d54b8c6427e04636e9e192f8eb8392c2bc9348c8bd169df6d6bab64	d614d87b12fd03757ecddaaea21bceeba9aa9f77bb48c213e2338a8722b4f0fb	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(18 \\div 13\\), we'll follow the standard long division method.\n\n1. Break down the numbers:\n - \\(18\\) can be broken down into \\(10 + 8\\).\n - \\(13\\) can be broken down into \\(10 + 3\\).\n\n2. **Divide each part of the multi-digit number by the single-digit numb...	[{"budget_forced_chunks": ["To solve the long division equation \\(18 \\div 13\\), we'll follow the standard long division method.\n\n1. Break down the numbers:\n - \\(18\\) can be broken down into \\(10 + 8\\).\n - \\(13\\) can be broken down into \\(10 + 3\\).\n\n2. **Divide each part of the multi-digit numbe...	null
60	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	10	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(627 \\\\div 13\\\\), we'll follow these steps:\\n\\n1. Multiply the units digit of the dividend by the units digit of the multiplier:\\n - The units digit of 627 is 7.\\n - The units digit of 13 is 3.\\n - \\\\(7 \\\\times 3 = 21\\\\).\\n - Write ...	["{'generation': \"To solve the long division equation \\\\(627 \\\\div 13\\\\), we'll follow these steps:\\n\\n1. Multiply the units digit of the dividend by the units digit of the multiplier:\\n - The units digit of 627 is 7.\\n - The units digit of 13 is 3.\\n - \\\\(7 \\\\times 3 = 21\\\\).\\n - Write d...	04ec0523052570eab42f5d4df2df12752b6040a530a17ab530c1a34b68932cc3	a07b20493b2474140724f67ad0df567fa239ed4d890a1d12451e43c0282a8060	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(627 \\div 13\\), we'll follow these steps:\n\n1. Multiply the units digit of the dividend by the units digit of the multiplier:\n - The units digit of 627 is 7.\n - The units digit of 13 is 3.\n - \\(7 \\times 3 = 21\\).\n - Write down 1 and carry over 2.\n\n2. **Mul...	[{"budget_forced_chunks": ["To solve the long division equation \\(627 \\div 13\\), we'll follow these steps:\n\n1. Multiply the units digit of the dividend by the units digit of the multiplier:\n - The units digit of 627 is 7.\n - The units digit of 13 is 3.\n - \\(7 \\times 3 = 21\\).\n - Write down 1 and...	null
61	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	20	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of 14 x 9 x 3, we can break it down into simpler steps:\\n\\nStep 1: Multiply 14 by 3\\n14 x 3 = 42\\nStep 2: Multiply 14 by 9, but remember to shift the result one place to the left (since you're multiplying by a ten)\\n14 x 9 = 126, then shift left by one place gives 1260\\nSt...	["{'generation': \"To solve the problem of 14 x 9 x 3, we can break it down into simpler steps:\\n\\nStep 1: Multiply 14 by 3\\n14 x 3 = 42\\nStep 2: Multiply 14 by 9, but remember to shift the result one place to the left (since you're multiplying by a ten)\\n14 x 9 = 126, then shift left by one place gives 1260\\nSte...	886ed5f2b6b1ec35a422c1358478609a118536357450e8ce400e8f59fb3d572e	b2487dd970bb8721f302d46b97240e180f65fa3b6e19ad7c2ebf5771d607f653	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of 14 x 9 x 3, we can break it down into simpler steps:\n\nStep 1: Multiply 14 by 3\n14 x 3 = 42\nStep 2: Multiply 14 by 9, but remember to shift the result one place to the left (since you're multiplying by a ten)\n14 x 9 = 126, then shift left by one place gives 1260\nStep 3: Add the results fr...	[{"budget_forced_chunks": ["To solve the problem of 14 x 9 x 3, we can break it down into simpler steps:\n\nStep 1: Multiply 14 by 3\n14 x 3 = 42\nStep 2: Multiply 14 by 9, but remember to shift the result one place to the left (since you're multiplying by a ten)\n14 x 9 = 126, then shift left by one place gives 1260\n...	null
62	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	25	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 12 \\\\div 8 \\\\), follow these steps:\\n\\n1. Write the numbers one under the other: \\n \\\\[\\n \\\\begin{array}{c@{}c}\\n & 12 \\\\\\\\\\n & 8 \\\\\\\\\\n \\\\end{array}\\n \\\\]\\n\\n2. Multiply 8 by 12:\\n - Step 1: Multiply the ...	["{'generation': \"To solve the long division equation \\\\( 12 \\\\div 8 \\\\), follow these steps:\\n\\n1. Write the numbers one under the other: \\n \\\\[\\n \\\\begin{array}{c@{}c}\\n & 12 \\\\\\\\\\n & 8 \\\\\\\\\\n \\\\end{array}\\n \\\\]\\n\\n2. Multiply 8 by 12:\\n - Step 1: Multiply the u...	14bf1806f088e8b1c20121adc93dbe473a7bbc73cf92a5fec9a74e104fa45d4b	99a22a74fff81f8c48fa2dafb4921d6437452b79c4215850b3b783316fe6ca3c	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 12 \\div 8 \\), follow these steps:\n\n1. Write the numbers one under the other: \n \\[\n \\begin{array}{c@{}c}\n & 12 \\\\\n & 8 \\\\\n \\end{array}\n \\]\n\n2. Multiply 8 by 12:\n - Step 1: Multiply the units digit (2) by 8:\n \\[\n 2 \\times 8 =...	[{"budget_forced_chunks": ["To solve the long division equation \\( 12 \\div 8 \\), follow these steps:\n\n1. Write the numbers one under the other: \n \\[\n \\begin{array}{c@{}c}\n & 12 \\\\\n & 8 \\\\\n \\end{array}\n \\]\n\n2. Multiply 8 by 12:\n - Step 1: Multiply the units digit (2) by 8:\n ...	null
63	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	11	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 121 \\\\), we will perform the multiplication and division step by step.\\n\\n### Step 1: Multiply the ones place\\nMultiply 20 by 1:\\n\\\\[ 20 \\\\times 1 = 20 \\\\]\\n\\n### Step 2: Multiply the tens place\\nMultiply 20 by 2:\\n\\\\[ 20 \\\\time...	["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 121 \\\\), we will perform the multiplication and division step by step.\\n\\n### Step 1: Multiply the ones place\\nMultiply 20 by 1:\\n\\\\[ 20 \\\\times 1 = 20 \\\\]\\n\\n### Step 2: Multiply the tens place\\nMultiply 20 by 2:\\n\\\\[ 20 \\\\times...	05f8a72d36e87d7a5c71b839f12b84d258f67ed7ae386e28611b3519219b525e	c674bf199104dc45f397037060b82bed9ca09d088e60a8318b2aa7f82f573d61	4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 20 \\div 121 \\), we will perform the multiplication and division step by step.\n\n### Step 1: Multiply the ones place\nMultiply 20 by 1:\n\\[ 20 \\times 1 = 20 \\]\n\n### Step 2: Multiply the tens place\nMultiply 20 by 2:\n\\[ 20 \\times 2 = 40 \\]\nNow add the result from Ste...	[{"budget_forced_chunks": ["To solve the long division equation \\( 20 \\div 121 \\), we will perform the multiplication and division step by step.\n\n### Step 1: Multiply the ones place\nMultiply 20 by 1:\n\\[ 20 \\times 1 = 20 \\]\n\n### Step 2: Multiply the tens place\nMultiply 20 by 2:\n\\[ 20 \\times 2 = 40 \\]\nN...	null
64	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	14	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(6 \\\\times 10 + 19 - 4 \\\\times 10\\\\) step by step, we will perform the multiplication and follow the order of operations (multiplication before addition/subtraction).\\n\\n\\\\( \\\\begin{array}{r}\\n 6 \\\\times 10 \\\\\\\\\\n+ 19 \\\\\\\\\\n- 4 \\\\ti...	["{'generation': \"To solve the long division equation \\\\(6 \\\\times 10 + 19 - 4 \\\\times 10\\\\) step by step, we will perform the multiplication and follow the order of operations (multiplication before addition/subtraction).\\n\\n\\\\( \\\\begin{array}{r}\\n 6 \\\\times 10 \\\\\\\\\\n+ 19 \\\\\\\\\\n- 4 \\\\tim...	32c7d6edf9a791a9576fef36ee42924d15008a1a3cbcc17f728f099b122d86af	20e1f5327c8fb5ca8e924289cde96faf6c2e60df0573b7c58720d6df34666d96	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(6 \\times 10 + 19 - 4 \\times 10\\) step by step, we will perform the multiplication and follow the order of operations (multiplication before addition/subtraction).\n\n\\( \\begin{array}{r}\n 6 \\times 10 \\\\\n+ 19 \\\\\n- 4 \\times 10 \\\\\n\\hline\n \\end{array}\\)\n\n1. Ca...	[{"budget_forced_chunks": ["To solve the long division equation \\(6 \\times 10 + 19 - 4 \\times 10\\) step by step, we will perform the multiplication and follow the order of operations (multiplication before addition/subtraction).\n\n\\( \\begin{array}{r}\n 6 \\times 10 \\\\\n+ 19 \\\\\n- 4 \\times 10 \\\\\n\\hline\...	null
65	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	10	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(8 \\\\times 4 = 32\\\\), we'll follow these steps:\\n\\n1. Multiply the units digits: \\n - The units digit of 8 is 8, and the units digit of 4 is 4.\\n - Multiply these: \\\\(8 \\\\times 4 = 32\\\\).\\n\\n2. Write down the result:\\n - Set up t...	["{'generation': \"To solve the long division equation \\\\(8 \\\\times 4 = 32\\\\), we'll follow these steps:\\n\\n1. Multiply the units digits: \\n - The units digit of 8 is 8, and the units digit of 4 is 4.\\n - Multiply these: \\\\(8 \\\\times 4 = 32\\\\).\\n\\n2. Write down the result:\\n - Set up th...	37b100781adc7aea5bd0958ae572fe10470b8db410fd9723eb5360d5452d767d	27abc602b799c6c8ed4fa7f36db773c12da966e4d4118b130a622520943a48d5	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(8 \\times 4 = 32\\), we'll follow these steps:\n\n1. Multiply the units digits: \n - The units digit of 8 is 8, and the units digit of 4 is 4.\n - Multiply these: \\(8 \\times 4 = 32\\).\n\n2. Write down the result:\n - Set up the multiplication vertically:\n `...	[{"budget_forced_chunks": ["To solve the long division equation \\(8 \\times 4 = 32\\), we'll follow these steps:\n\n1. Multiply the units digits: \n - The units digit of 8 is 8, and the units digit of 4 is 4.\n - Multiply these: \\(8 \\times 4 = 32\\).\n\n2. Write down the result:\n - Set up the multipli...	null
66	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem \\\\(19 \\\\times 2 \\\\times 12 \\\\times 18\\\\), we can break it down into simpler steps:\\n\\n1. First, let's multiply 19 by 2:\\n \\\\[\\n 19 \\\\times 2 = 38\\n \\\\]\\n\\n2. Now, we need to multiply the result by 12:\\n \\\\[\\n 38 \\\\times 12 = 456\\n \\\\]\...	["{'generation': \"To solve the problem \\\\(19 \\\\times 2 \\\\times 12 \\\\times 18\\\\), we can break it down into simpler steps:\\n\\n1. First, let's multiply 19 by 2:\\n \\\\[\\n 19 \\\\times 2 = 38\\n \\\\]\\n\\n2. Now, we need to multiply the result by 12:\\n \\\\[\\n 38 \\\\times 12 = 456\\n \\\\]\\...	c98d820c226336c2035fa0efaa4d9aa2becdcb27feac1bbf9082d6efe4f5069f	1436914e7b70497d0e69375d7b70fd47527ca9e2cae49b0daf6cca5dd20d25a7	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem \\(19 \\times 2 \\times 12 \\times 18\\), we can break it down into simpler steps:\n\n1. First, let's multiply 19 by 2:\n \\[\n 19 \\times 2 = 38\n \\]\n\n2. Now, we need to multiply the result by 12:\n \\[\n 38 \\times 12 = 456\n \\]\n\n3. Finally, we need to multiply the result by 1...	[{"budget_forced_chunks": ["To solve the problem \\(19 \\times 2 \\times 12 \\times 18\\), we can break it down into simpler steps:\n\n1. First, let's multiply 19 by 2:\n \\[\n 19 \\times 2 = 38\n \\]\n\n2. Now, we need to multiply the result by 12:\n \\[\n 38 \\times 12 = 456\n \\]\n\n3. Finally, we need t...	null
67	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of multiplying the numbers 3, 17, 21, and 11, we can use the standard multiplication algorithm. Let's break it down step by step:\\n\\n1. Multiply 11 by 7 (the units digit of 17):\\n \\\\[\\n 11 \\\\times 7 = 77\\n \\\\]\\n Write down 77.\\n\\n2. **Multiply 11 by 1 (...	["{'generation': \"To solve the problem of multiplying the numbers 3, 17, 21, and 11, we can use the standard multiplication algorithm. Let's break it down step by step:\\n\\n1. Multiply 11 by 7 (the units digit of 17):\\n \\\\[\\n 11 \\\\times 7 = 77\\n \\\\]\\n Write down 77.\\n\\n2. **Multiply 11 by 1 (t...	3dee87e91e430e7f86936ddeb295f7a9006fcdac4e05ff39b8eb95e05789cda6	ff841f243937fbac16fcd7bbd6cf6794fc7f246070b234a925b75877ce633207	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of multiplying the numbers 3, 17, 21, and 11, we can use the standard multiplication algorithm. Let's break it down step by step:\n\n1. Multiply 11 by 7 (the units digit of 17):\n \\[\n 11 \\times 7 = 77\n \\]\n Write down 77.\n\n2. Multiply 11 by 1 (the tens digit of 17):\n \\[...	[{"budget_forced_chunks": ["To solve the problem of multiplying the numbers 3, 17, 21, and 11, we can use the standard multiplication algorithm. Let's break it down step by step:\n\n1. Multiply 11 by 7 (the units digit of 17):\n \\[\n 11 \\times 7 = 77\n \\]\n Write down 77.\n\n2. **Multiply 11 by 1 (the te...	null
68	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	10	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 16 \\\\div 4 \\\\), let's break it down step by step:\\n\\n1. Break down the numbers:\\n - \\\\( 16 \\\\) can be seen as \\\\( 10 + 6 \\\\).\\n - \\\\( 4 \\\\) can be seen as \\\\( 4 \\\\).\\n\\n2. Multiply the numbers:\\n - Multiply \\\\( 10 \...	["{'generation': \"To solve the long division equation \\\\( 16 \\\\div 4 \\\\), let's break it down step by step:\\n\\n1. Break down the numbers:\\n - \\\\( 16 \\\\) can be seen as \\\\( 10 + 6 \\\\).\\n - \\\\( 4 \\\\) can be seen as \\\\( 4 \\\\).\\n\\n2. Multiply the numbers:\\n - Multiply \\\\( 10 \\...	98ab1b38356ecf7abfc8d59f6051f122d58b27c2757f86694bf71568c3f579e6	cbe34bb42aa6666852658fa52a4884248cbbf63194ac9b9bcc86b2c69c103c04	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 16 \\div 4 \\), let's break it down step by step:\n\n1. Break down the numbers:\n - \\( 16 \\) can be seen as \\( 10 + 6 \\).\n - \\( 4 \\) can be seen as \\( 4 \\).\n\n2. Multiply the numbers:\n - Multiply \\( 10 \\) by \\( 4 \\): \\( 10 \\times 4 = 40 \\).\n -...	[{"budget_forced_chunks": ["To solve the long division equation \\( 16 \\div 4 \\), let's break it down step by step:\n\n1. Break down the numbers:\n - \\( 16 \\) can be seen as \\( 10 + 6 \\).\n - \\( 4 \\) can be seen as \\( 4 \\).\n\n2. Multiply the numbers:\n - Multiply \\( 10 \\) by \\( 4 \\): \\( 10...	null
69	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\( 9 \\\\times 20 \\\\times 18 \\\\times 16 \\\\), we will follow the standard algorithm for multiplication. We'll multiply each digit of the multiplicand (9) by each digit of the multiplier (20), then add the results together.\\n\\n1. Multiply 9 by 0: \\n...	["{'generation': \"To solve the multiplication problem \\\\( 9 \\\\times 20 \\\\times 18 \\\\times 16 \\\\), we will follow the standard algorithm for multiplication. We'll multiply each digit of the multiplicand (9) by each digit of the multiplier (20), then add the results together.\\n\\n1. Multiply 9 by 0: \\n ...	3ebb28261cbe5e14b7315a28166cc1db81b47ba4e9d15a19a7de1ca91ac3fc11	2636ec08d0fb37b2cf450273bfe2824cdd0f5cb1b0331db5775239f4dba1e73f	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 9 \\times 20 \\times 18 \\times 16 \\), we will follow the standard algorithm for multiplication. We'll multiply each digit of the multiplicand (9) by each digit of the multiplier (20), then add the results together.\n\n1. Multiply 9 by 0: \n \\[\n 9 \\times 0 = 0\n ...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 9 \\times 20 \\times 18 \\times 16 \\), we will follow the standard algorithm for multiplication. We'll multiply each digit of the multiplicand (9) by each digit of the multiplier (20), then add the results together.\n\n1. Multiply 9 by 0: \n \\...	null
70	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\( 8 \\\\times 3 \\\\times 9 \\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 8 by 9:\\n \\\\[\\n 8 \\\\times 9 = 72\\n \\\\]\\n Write down 72.\\n\\n2. Multiply 8 by 3, but shift the result one place to the left:\\...	["{'generation': \"To solve the multiplication problem \\\\( 8 \\\\times 3 \\\\times 9 \\\\), we will follow the standard long multiplication method.\\n\\n1. Multiply 8 by 9:\\n \\\\[\\n 8 \\\\times 9 = 72\\n \\\\]\\n Write down 72.\\n\\n2. Multiply 8 by 3, but shift the result one place to the left:\\n...	7a7930e021ceeb46d974fa00bbee28c1f4e7422d48a9c96427a545e4eed0fbdf	fd72a63df0361a86a94acd60ae8292cd8ac4221f55ee795b17a95ad2540b0988	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 8 \\times 3 \\times 9 \\), we will follow the standard long multiplication method.\n\n1. Multiply 8 by 9:\n \\[\n 8 \\times 9 = 72\n \\]\n Write down 72.\n\n2. Multiply 8 by 3, but shift the result one place to the left:\n \\[\n 8 \\times 3 = 24\n \\]\n ...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 8 \\times 3 \\times 9 \\), we will follow the standard long multiplication method.\n\n1. Multiply 8 by 9:\n \\[\n 8 \\times 9 = 72\n \\]\n Write down 72.\n\n2. Multiply 8 by 3, but shift the result one place to the left:\n \\[\n 8 \...	null
71	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\(15 \\\\times 19 \\\\times 20\\\\), we can break it down into simpler steps.\\n\\nFirst, let's break the multiplication into smaller parts:\\n\\\\[ 15 \\\\times 19 \\\\times 20 = 15 \\\\times (10 + 9) \\\\times 20 \\\\]\\n\\nNow, we can use the distributive pr...	["{'generation': \"To solve the multiplication problem \\\\(15 \\\\times 19 \\\\times 20\\\\), we can break it down into simpler steps.\\n\\nFirst, let's break the multiplication into smaller parts:\\n\\\\[ 15 \\\\times 19 \\\\times 20 = 15 \\\\times (10 + 9) \\\\times 20 \\\\]\\n\\nNow, we can use the distributive pro...	6233391fa323f1ae8f0498bde4e183b36b9bab90b39c8d544a67220125b83287	08ad970139b0652c99d841197987b916b8a1ef91494da8c899ab506134af2eb8	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\(15 \\times 19 \\times 20\\), we can break it down into simpler steps.\n\nFirst, let's break the multiplication into smaller parts:\n\\[ 15 \\times 19 \\times 20 = 15 \\times (10 + 9) \\times 20 \\]\n\nNow, we can use the distributive property of multiplication over addition:\n\\...	[{"budget_forced_chunks": ["To solve the multiplication problem \\(15 \\times 19 \\times 20\\), we can break it down into simpler steps.\n\nFirst, let's break the multiplication into smaller parts:\n\\[ 15 \\times 19 \\times 20 = 15 \\times (10 + 9) \\times 20 \\]\n\nNow, we can use the distributive property of multipl...	null
72	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	22	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation using the numbers[17, 7, 3, 8] that equals 22, you can use basic arithmetic operations. \\nStep 1: Start with (17 + 7)\\n17 + 7 = 24\\nStep 2: Now, (24 * 3)\\n24 * 3 = 72\\nStep 3: Finally, (72 + 8)\\n72 + 8 = 80\\n\\nSo, the equation is: \\n\\\\boxed{80}...	["{'generation': \"To solve the problem of creating an equation using the numbers[17, 7, 3, 8] that equals 22, you can use basic arithmetic operations. \\nStep 1: Start with (17 + 7)\\n17 + 7 = 24\\nStep 2: Now, (24 * 3)\\n24 * 3 = 72\\nStep 3: Finally, (72 + 8)\\n72 + 8 = 80\\n\\nSo, the equation is: \\n\\\\boxed{80} ...	d451de9faeade7c0b043fd49fe6172d6084cd97ff6acbb5e55fd09b604e52764	2020d77f8edf80ce2b99f12ded817ddb52c377b349252b70b0b2618f0961c036	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation using the numbers[17, 7, 3, 8] that equals 22, you can use basic arithmetic operations. \nStep 1: Start with (17 + 7)\n17 + 7 = 24\nStep 2: Now, (24 * 3)\n24 * 3 = 72\nStep 3: Finally, (72 + 8)\n72 + 8 = 80\n\nSo, the equation is: \n\\boxed{80} Wait, let me try 17*3 first ...	[{"budget_forced_chunks": ["To solve the problem of creating an equation using the numbers[17, 7, 3, 8] that equals 22, you can use basic arithmetic operations. \nStep 1: Start with (17 + 7)\n17 + 7 = 24\nStep 2: Now, (24 * 3)\n24 * 3 = 72\nStep 3: Finally, (72 + 8)\n72 + 8 = 80\n\nSo, the equation is: \n\\boxed{80}", ...	null
73	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 16 \\\\div 15 \\\\) and then add the result of \\\\( 15 \\\\div 1 \\\\), we can break it down into simpler steps.\\n\\n1. Multiply 16 by 5:\\n \\\\[\\n 16 \\\\times 5 = 80\\n \\\\]\\n\\n2. Multiply 16 by 10 (which is the same as 15 times 2):\\n...	["{'generation': \"To solve the long division equation \\\\( 16 \\\\div 15 \\\\) and then add the result of \\\\( 15 \\\\div 1 \\\\), we can break it down into simpler steps.\\n\\n1. Multiply 16 by 5:\\n \\\\[\\n 16 \\\\times 5 = 80\\n \\\\]\\n\\n2. Multiply 16 by 10 (which is the same as 15 times 2):\\n ...	d1910265333c2aec98a24231bd582fc8e6d688f4c3a08e889f54e26f260f6ff6	debf4e355f7604ffeeb5f3404d87d62b825d6527dc43fb065206a123921ce584	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 16 \\div 15 \\) and then add the result of \\( 15 \\div 1 \\), we can break it down into simpler steps.\n\n1. Multiply 16 by 5:\n \\[\n 16 \\times 5 = 80\n \\]\n\n2. Multiply 16 by 10 (which is the same as 15 times 2):\n \\[\n 16 \\times 10 = 160\n \\]\n\n3....	[{"budget_forced_chunks": ["To solve the long division equation \\( 16 \\div 15 \\) and then add the result of \\( 15 \\div 1 \\), we can break it down into simpler steps.\n\n1. Multiply 16 by 5:\n \\[\n 16 \\times 5 = 80\n \\]\n\n2. Multiply 16 by 10 (which is the same as 15 times 2):\n \\[\n 16 \\ti...	null
74	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\(24 \\\\times 18\\\\), let's break it down step by step:\\n\\n1. Break down the numbers: \\n - The first number, 24, can be written as \\\\(20 + 4\\\\).\\n - The second number, 18, can be written as \\\\(10 + 8\\\\).\\n\\n2. **Multiply the numbers in t...	["{'generation': \"To solve the long division equation \\\\(24 \\\\times 18\\\\), let's break it down step by step:\\n\\n1. Break down the numbers: \\n - The first number, 24, can be written as \\\\(20 + 4\\\\).\\n - The second number, 18, can be written as \\\\(10 + 8\\\\).\\n\\n2. **Multiply the numbers in th...	ef1eb782cf001ce26a20ed44e1b588a2148b04dffc4bdeb09208c9415768088f	802a5426bbc14fc70091630daf5ba791cfd4353339d08eb4744e729541630a94	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\(24 \\times 18\\), let's break it down step by step:\n\n1. Break down the numbers: \n - The first number, 24, can be written as \\(20 + 4\\).\n - The second number, 18, can be written as \\(10 + 8\\).\n\n2. **Multiply the numbers in the unit position (rightmost positions)...	[{"budget_forced_chunks": ["To solve the long division equation \\(24 \\times 18\\), let's break it down step by step:\n\n1. Break down the numbers: \n - The first number, 24, can be written as \\(20 + 4\\).\n - The second number, 18, can be written as \\(10 + 8\\).\n\n2. **Multiply the numbers in the unit posi...	null
75	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	15	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division equation \\\\( 17 \\\\div 20 \\\\), we can break it down into simpler steps.\\n\\n1. Break down the numbers:\\n - \\\\( 17 \\\\) can be written as \\\\( 10 + 7 \\\\).\\n - \\\\( 20 \\\\) is already a single-digit number.\\n\\n2. Multiply the digits:\\n - First...	["{'generation': 'To solve the long division equation \\\\( 17 \\\\div 20 \\\\), we can break it down into simpler steps.\\n\\n1. Break down the numbers:\\n - \\\\( 17 \\\\) can be written as \\\\( 10 + 7 \\\\).\\n - \\\\( 20 \\\\) is already a single-digit number.\\n\\n2. Multiply the digits:\\n - First,...	6db3fbd49b81d0debd08a217bb92f3efa1f6831c4999048dd50260c4a2a8e8c0	3bc056dfd0233c3b03fb4c3539e85fcd8989a7fad15a268f596aa2dfc3a7bce3	e629fa6598d732768f7c726b4b621285f9c3b85303900aa912017db7617d8bdb	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 17 \\div 20 \\), we can break it down into simpler steps.\n\n1. Break down the numbers:\n - \\( 17 \\) can be written as \\( 10 + 7 \\).\n - \\( 20 \\) is already a single-digit number.\n\n2. Multiply the digits:\n - First, multiply \\( 10 \\) by \\( 20 \\):\n ...	[{"budget_forced_chunks": ["To solve the long division equation \\( 17 \\div 20 \\), we can break it down into simpler steps.\n\n1. Break down the numbers:\n - \\( 17 \\) can be written as \\( 10 + 7 \\).\n - \\( 20 \\) is already a single-digit number.\n\n2. Multiply the digits:\n - First, multiply \\( 1...	null
76	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the target number 16 using the given numbers 12, 6, and 10, we can break it down into simpler steps:\\n\\nStep 1: Break down the multiplication\\n(10 * 6) + (10 * 1) + (6 * 1) = 60 + 10 + 6 = 76\\n\\nStep 2: Add the results\\n76 + 120 = 196\\n\\nSo, the final answer is 196. But according to...	["{'generation': \"To solve the target number 16 using the given numbers 12, 6, and 10, we can break it down into simpler steps:\\n\\nStep 1: Break down the multiplication\\n(10 * 6) + (10 * 1) + (6 * 1) = 60 + 10 + 6 = 76\\n\\nStep 2: Add the results\\n76 + 120 = 196\\n\\nSo, the final answer is 196. But according to ...	35b1c2b18fee46db7d7d486eb513d6e14310ea4dce3e14fc7920f45913c73d48	82a5b9ead972f062769857dd7132e626f4b355aaba3fb500fe19fd767cae5fe9	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the target number 16 using the given numbers 12, 6, and 10, we can break it down into simpler steps:\n\nStep 1: Break down the multiplication\n(10 * 6) + (10 * 1) + (6 * 1) = 60 + 10 + 6 = 76\n\nStep 2: Add the results\n76 + 120 = 196\n\nSo, the final answer is 196. But according to 12, 6, and 10, the correc...	[{"budget_forced_chunks": ["To solve the target number 16 using the given numbers 12, 6, and 10, we can break it down into simpler steps:\n\nStep 1: Break down the multiplication\n(10 * 6) + (10 * 1) + (6 * 1) = 60 + 10 + 6 = 76\n\nStep 2: Add the results\n76 + 120 = 196\n\nSo, the final answer is 196.", " But accordin...	null
77	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	10	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the equation \\\\(5 \\\\times 9 + 2 \\\\times 2\\\\), let's break it down step by step:\\n\\n1. Multiply 5 by 9:\\n \\\\[\\n 5 \\\\times 9 = 45\\n \\\\]\\n\\n2. Multiply 5 by 2:\\n \\\\[\\n 5 \\\\times 2 = 10\\n \\\\]\\n\\n3. **Add the results from the two multiplication...	["{'generation': \"To solve the equation \\\\(5 \\\\times 9 + 2 \\\\times 2\\\\), let's break it down step by step:\\n\\n1. Multiply 5 by 9:\\n \\\\[\\n 5 \\\\times 9 = 45\\n \\\\]\\n\\n2. Multiply 5 by 2:\\n \\\\[\\n 5 \\\\times 2 = 10\\n \\\\]\\n\\n3. **Add the results from the two multiplications...	b793b535bd0b3280ad4a8bc7d71b5cf4f234571620473d65acae50acc825ec57	e8cbd5ee01dec1857224acb722f9c821b946597da44f1d2b0e054dcb5fbfde53	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the equation \\(5 \\times 9 + 2 \\times 2\\), let's break it down step by step:\n\n1. Multiply 5 by 9:\n \\[\n 5 \\times 9 = 45\n \\]\n\n2. Multiply 5 by 2:\n \\[\n 5 \\times 2 = 10\n \\]\n\n3. Add the results from the two multiplications:\n \\[\n 45 + 10 = 55\n \\]\n\nSo, the e...	[{"budget_forced_chunks": ["To solve the equation \\(5 \\times 9 + 2 \\times 2\\), let's break it down step by step:\n\n1. Multiply 5 by 9:\n \\[\n 5 \\times 9 = 45\n \\]\n\n2. Multiply 5 by 2:\n \\[\n 5 \\times 2 = 10\n \\]\n\n3. Add the results from the two multiplications:\n \\[\n 45 + 10...	null
78	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem using the numbers 19, 10, 16, and 16, we can create the equation:\\n\\n19 * 10 + 16 * 16 = 19 * 10 + 256 = 190 + 256 = 446\\n\\nSo the solution is: \\\\boxed{446} But I need to verify this. Let's break it down:\\n\\n1. Multiply 19 by 6 (the first digit of 16): 19 * 6 = 114\\n2....	["{'generation': \"To solve the problem using the numbers 19, 10, 16, and 16, we can create the equation:\\n\\n19 * 10 + 16 * 16 = 19 * 10 + 256 = 190 + 256 = 446\\n\\nSo the solution is: \\\\boxed{446} But I need to verify this. Let's break it down:\\n\\n1. Multiply 19 by 6 (the first digit of 16): 19 * 6 = 114\\n2. ...	9d80570a7343e6d2d68246a0e09ce47e1a6a96dc24feecbb35ad65e514cb2939	78b473de32b43d7c002173d5378657ba52a42625ce5708900ecdbf5b9789453f	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem using the numbers 19, 10, 16, and 16, we can create the equation:\n\n19 * 10 + 16 * 16 = 19 * 10 + 256 = 190 + 256 = 446\n\nSo the solution is: \\boxed{446} But I need to verify this. Let's break it down:\n\n1. Multiply 19 by 6 (the first digit of 16): 19 * 6 = 114\n2. Multiply 19 by 1 (the seco...	[{"budget_forced_chunks": ["To solve the problem using the numbers 19, 10, 16, and 16, we can create the equation:\n\n19 * 10 + 16 * 16 = 19 * 10 + 256 = 190 + 256 = 446\n\nSo the solution is: \\boxed{446}", " But I need to verify this. Let's break it down:\n\n1. Multiply 19 by 6 (the first digit of 16): 19 * 6 = 114\...	null
79	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem 5 x 19 using long multiplication, follow these steps:\\n\\n1. Write the numbers one below the other:\\n\\n 5\\n x 19\\n -----\\n\\n2. Multiply 5 by 9, which gives 45. Write this down below the line, shifted one place to the left because we're multiplying by t...	["{'generation': \"To solve the multiplication problem 5 x 19 using long multiplication, follow these steps:\\n\\n1. Write the numbers one below the other:\\n\\n 5\\n x 19\\n -----\\n\\n2. Multiply 5 by 9, which gives 45. Write this down below the line, shifted one place to the left because we're multiplying by th...	99d6fbffa160a424f45d4b78de11360cd4b97354c1dce2e3ae62d5f2f03d5b38	8f74b7e3c369679f1e12c6c9ec9b3b85d51f5d6e89c2181cc67e3ed90f706203	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem 5 x 19 using long multiplication, follow these steps:\n\n1. Write the numbers one below the other:\n\n 5\n x 19\n -----\n\n2. Multiply 5 by 9, which gives 45. Write this down below the line, shifted one place to the left because we're multiplying by the ones place of 19.\n\n ...	[{"budget_forced_chunks": ["To solve the multiplication problem 5 x 19 using long multiplication, follow these steps:\n\n1. Write the numbers one below the other:\n\n 5\n x 19\n -----\n\n2. Multiply 5 by 9, which gives 45. Write this down below the line, shifted one place to the left because we're multiplying by t...	null
80	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the multiplication problem \\\\( 17 \\\\times 13 \\\\) step by step, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 17 \\\\) can be broken down into \\\\( 10 + 7 \\\\).\\n - \\\\( 13 \\\\) can be broken down into \\\\( 10 + 3 \\\\).\\n\\n2. **Apply the distributive pr...	["{'generation': 'To solve the multiplication problem \\\\( 17 \\\\times 13 \\\\) step by step, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 17 \\\\) can be broken down into \\\\( 10 + 7 \\\\).\\n - \\\\( 13 \\\\) can be broken down into \\\\( 10 + 3 \\\\).\\n\\n2. **Apply the distributive pro...	1fd81e2df0bd7f0dd3fc40b5f6617fc216f2550b4fbc63bb64c3d55a28fe4268	0b4c367a3bb495638c386032c2d90db43eae78f510b2126270bb3052fff05c8a	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 17 \\times 13 \\) step by step, follow these steps:\n\n1. Break down the numbers:\n - \\( 17 \\) can be broken down into \\( 10 + 7 \\).\n - \\( 13 \\) can be broken down into \\( 10 + 3 \\).\n\n2. Apply the distributive property:\n \\[\n 17 \\times 13 = (10 + 7...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 17 \\times 13 \\) step by step, follow these steps:\n\n1. Break down the numbers:\n - \\( 17 \\) can be broken down into \\( 10 + 7 \\).\n - \\( 13 \\) can be broken down into \\( 10 + 3 \\).\n\n2. Apply the distributive property:\n \\[\n...	null
81	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division problem \\\\( 24 \\\\div 4 \\\\), we'll follow these steps:\\n\\n1. Break down the multiplication: \\n - First, multiply \\\\( 24 \\\\) by \\\\( 4 \\\\).\\n - Then, multiply \\\\( 24 \\\\) by \\\\( 20 \\\\) (which is \\\\( 2 \\\\) multiplied by \\\\( 10 \\\\)).\\n ...	["{'generation': \"To solve the long division problem \\\\( 24 \\\\div 4 \\\\), we'll follow these steps:\\n\\n1. Break down the multiplication: \\n - First, multiply \\\\( 24 \\\\) by \\\\( 4 \\\\).\\n - Then, multiply \\\\( 24 \\\\) by \\\\( 20 \\\\) (which is \\\\( 2 \\\\) multiplied by \\\\( 10 \\\\)).\\n ...	997f99b3e946a10a23c993819c4b0e619ddc9a6fa3027b29726c423e97f82ed3	234784e30f512a638cd6dec8311f44a87e65a74d04d0e2478165e83a9d0ecb75	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division problem \\( 24 \\div 4 \\), we'll follow these steps:\n\n1. Break down the multiplication: \n - First, multiply \\( 24 \\) by \\( 4 \\).\n - Then, multiply \\( 24 \\) by \\( 20 \\) (which is \\( 2 \\) multiplied by \\( 10 \\)).\n \n2. Calculate \\( 24 \\times 4 \\):\n - \\( ...	[{"budget_forced_chunks": ["To solve the long division problem \\( 24 \\div 4 \\), we'll follow these steps:\n\n1. Break down the multiplication: \n - First, multiply \\( 24 \\) by \\( 4 \\).\n - Then, multiply \\( 24 \\) by \\( 20 \\) (which is \\( 2 \\) multiplied by \\( 10 \\)).\n \n2. **Calculate \\( 24 \...	null
82	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 9 \\\\div 22 \\\\), we'll follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 9 \\\\) can be seen as \\\\( 9 \\\\times 1 \\\\).\\n - \\\\( 22 \\\\) can be seen as \\\\( 20 \\\\) plus \\\\( 2 \\\\).\\n\\n2. First multiplication:\\n - ...	["{'generation': \"To solve the long division equation \\\\( 9 \\\\div 22 \\\\), we'll follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 9 \\\\) can be seen as \\\\( 9 \\\\times 1 \\\\).\\n - \\\\( 22 \\\\) can be seen as \\\\( 20 \\\\) plus \\\\( 2 \\\\).\\n\\n2. First multiplication:\\n - M...	03ce236c2139b2502530b7d1a7b9f04b0a228c5b913baf576c61ea4f747ed6d7	dda06b36cd550be53e6e802ae533a72a54ee914cd5531f6e91af805bc15e3093	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 9 \\div 22 \\), we'll follow these steps:\n\n1. Break down the numbers:\n - \\( 9 \\) can be seen as \\( 9 \\times 1 \\).\n - \\( 22 \\) can be seen as \\( 20 \\) plus \\( 2 \\).\n\n2. First multiplication:\n - Multiply \\( 9 \\) by \\( 20 \\):\n \\[\n 9 \...	[{"budget_forced_chunks": ["To solve the long division equation \\( 9 \\div 22 \\), we'll follow these steps:\n\n1. Break down the numbers:\n - \\( 9 \\) can be seen as \\( 9 \\times 1 \\).\n - \\( 22 \\) can be seen as \\( 20 \\) plus \\( 2 \\).\n\n2. First multiplication:\n - Multiply \\( 9 \\) by \\( 2...	null
83	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the equation \\\\(3 \\\\times 6 + 1 = 17\\\\), we can break it down into simpler steps:\\n\\n1. First Step: Multiply 3 by 6.\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n Write down 18.\\n\\n2. Second Step: Multiply 3 by 1 (which is essentially 3 times 10 because there are 10 o...	["{'generation': \"To solve the equation \\\\(3 \\\\times 6 + 1 = 17\\\\), we can break it down into simpler steps:\\n\\n1. First Step: Multiply 3 by 6.\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n Write down 18.\\n\\n2. Second Step: Multiply 3 by 1 (which is essentially 3 times 10 because there are 10 on...	7212f88580197608ee45310d3946ace5165c460930b98ffcf2efbf62fbb9fd78	100530f6b8ebe121df0720a72d5b462f72fe2f623c2939e4925f50602d8c1ac8	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the equation \\(3 \\times 6 + 1 = 17\\), we can break it down into simpler steps:\n\n1. First Step: Multiply 3 by 6.\n \\[\n 3 \\times 6 = 18\n \\]\n Write down 18.\n\n2. Second Step: Multiply 3 by 1 (which is essentially 3 times 10 because there are 10 ones in 18).\n \\[\n 3 \\times 10 =...	[{"budget_forced_chunks": ["To solve the equation \\(3 \\times 6 + 1 = 17\\), we can break it down into simpler steps:\n\n1. First Step: Multiply 3 by 6.\n \\[\n 3 \\times 6 = 18\n \\]\n Write down 18.\n\n2. Second Step: Multiply 3 by 1 (which is essentially 3 times 10 because there are 10 ones in 18).\...	null
84	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem step by step, we can use the standard algorithm for long multiplication. \\n\\nHere are the steps:\\n\\n1. Multiply the ones digit of the bottom number (3) by the top number (15). \\n\\n \\\\(3 \\\\times 5 = 15\\\\)\\n\\n Write down 5 and carry over 1.\\n\\n2. Next, multiply...	["{'generation': \"To solve the problem step by step, we can use the standard algorithm for long multiplication. \\n\\nHere are the steps:\\n\\n1. Multiply the ones digit of the bottom number (3) by the top number (15). \\n\\n \\\\(3 \\\\times 5 = 15\\\\)\\n\\n Write down 5 and carry over 1.\\n\\n2. Next, multiply ...	4cc81a73edb3c70a7f9a4e66405067bdd3cd557192e4ccc5363b1c3ffd066337	a521bb80ce8b527bb25590df9a522d4cf8e9b94627649d903e1c6902c0f1408e	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem step by step, we can use the standard algorithm for long multiplication. \n\nHere are the steps:\n\n1. Multiply the ones digit of the bottom number (3) by the top number (15). \n\n \\(3 \\times 5 = 15\\)\n\n Write down 5 and carry over 1.\n\n2. Next, multiply the ones digit of the bottom numb...	[{"budget_forced_chunks": ["To solve the problem step by step, we can use the standard algorithm for long multiplication. \n\nHere are the steps:\n\n1. Multiply the ones digit of the bottom number (3) by the top number (15). \n\n \\(3 \\times 5 = 15\\)\n\n Write down 5 and carry over 1.\n\n2. Next, multiply the one...	null
85	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\( 21 \\\\times 19 \\\\) step by step, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 21 \\\\) can be written as \\\\( 20 + 1 \\\\).\\n - \\\\( 19 \\\\) can be written as \\\\( 10 + 9 \\\\).\\n\\n2. Apply the distributive property:\\...	["{'generation': \"To solve the multiplication problem \\\\( 21 \\\\times 19 \\\\) step by step, follow these steps:\\n\\n1. Break down the numbers:\\n - \\\\( 21 \\\\) can be written as \\\\( 20 + 1 \\\\).\\n - \\\\( 19 \\\\) can be written as \\\\( 10 + 9 \\\\).\\n\\n2. Apply the distributive property:\\n...	0ae865d4dbc5cfaea27c1a97d5dd26fd6cfc693d41b25c8bb22dfbab6e87b839	d70ed273c01a94ba8bc2003830f89de9ad22d231a38e797ec80738614d894fa3	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\( 21 \\times 19 \\) step by step, follow these steps:\n\n1. Break down the numbers:\n - \\( 21 \\) can be written as \\( 20 + 1 \\).\n - \\( 19 \\) can be written as \\( 10 + 9 \\).\n\n2. Apply the distributive property:\n \\[\n 21 \\times 19 = (20 + 1) \\times (1...	[{"budget_forced_chunks": ["To solve the multiplication problem \\( 21 \\times 19 \\) step by step, follow these steps:\n\n1. Break down the numbers:\n - \\( 21 \\) can be written as \\( 20 + 1 \\).\n - \\( 19 \\) can be written as \\( 10 + 9 \\).\n\n2. Apply the distributive property:\n \\[\n 21 \\time...	null
86	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long multiplication equation \\\\(5 \\\\times 3 + 2 \\\\times 6\\\\), let's break it down step by step:\\n\\n1. Multiply 5 by 6: \\n \\\\[\\n 5 \\\\times 6 = 30\\n \\\\]\\n Write down 0 and carry over 3.\\n\\n2. Multiply 5 by 3, and add the carry-over value:\\n \\\\[\\...	["{'generation': \"To solve the long multiplication equation \\\\(5 \\\\times 3 + 2 \\\\times 6\\\\), let's break it down step by step:\\n\\n1. Multiply 5 by 6: \\n \\\\[\\n 5 \\\\times 6 = 30\\n \\\\]\\n Write down 0 and carry over 3.\\n\\n2. Multiply 5 by 3, and add the carry-over value:\\n \\\\[\\n...	e78c916c002984bf26b644862b714de89c9d41e56e57ccb2d0f7a65240145933	286866cc7d3d0e46a70d9a216c094be68ed8b30cb640270203c4a394f86b9e49	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long multiplication equation \\(5 \\times 3 + 2 \\times 6\\), let's break it down step by step:\n\n1. Multiply 5 by 6: \n \\[\n 5 \\times 6 = 30\n \\]\n Write down 0 and carry over 3.\n\n2. Multiply 5 by 3, and add the carry-over value:\n \\[\n 5 \\times 3 = 15, \\quad \\text{and} \\q...	[{"budget_forced_chunks": ["To solve the long multiplication equation \\(5 \\times 3 + 2 \\times 6\\), let's break it down step by step:\n\n1. Multiply 5 by 6: \n \\[\n 5 \\times 6 = 30\n \\]\n Write down 0 and carry over 3.\n\n2. Multiply 5 by 3, and add the carry-over value:\n \\[\n 5 \\times 3 = ...	null
87	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	19	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation with the numbers[19, 10, 15, 4] that equals 19, we can use basic arithmetic operations.\\n\\nStep 1: Start by multiplying the first two numbers together, in this case, 19 * 10 = 190.\\n\\nStep 2: Now take the third number, 15, and multiply it by 19. To do...	["{'generation': \"To solve the problem of creating an equation with the numbers[19, 10, 15, 4] that equals 19, we can use basic arithmetic operations.\\n\\nStep 1: Start by multiplying the first two numbers together, in this case, 19 * 10 = 190.\\n\\nStep 2: Now take the third number, 15, and multiply it by 19. To do ...	8a18d4ad61f45669c35df9a8a11b091e5c9e57abb679b3d8d308f8c349b25e5f	fad17fb3a3ee78823eb8e4ca95379f63edd21a5e12798b1e0789047beff91fd7	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation with the numbers[19, 10, 15, 4] that equals 19, we can use basic arithmetic operations.\n\nStep 1: Start by multiplying the first two numbers together, in this case, 19 * 10 = 190.\n\nStep 2: Now take the third number, 15, and multiply it by 19. To do this, split 15 into 1...	[{"budget_forced_chunks": ["To solve the problem of creating an equation with the numbers[19, 10, 15, 4] that equals 19, we can use basic arithmetic operations.\n\nStep 1: Start by multiplying the first two numbers together, in this case, 19 * 10 = 190.\n\nStep 2: Now take the third number, 15, and multiply it by 19. T...	null
88	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem using the numbers 23, 13, 9, and 17, we can use the standard multiplication algorithm.\\n\\nStep 1: Multiply 17 by 23:\\n17 x 23 = 341\\n\\nStep 2: Multiply 17 by 13:\\n17 x 13 = 221\\n\\nStep 3: Add the results from steps 1 and 2:\\n341 + 221 = 562\\n\\nSo, the solution to the ...	["{'generation': \"To solve the problem using the numbers 23, 13, 9, and 17, we can use the standard multiplication algorithm.\\n\\nStep 1: Multiply 17 by 23:\\n17 x 23 = 341\\n\\nStep 2: Multiply 17 by 13:\\n17 x 13 = 221\\n\\nStep 3: Add the results from steps 1 and 2:\\n341 + 221 = 562\\n\\nSo, the solution to the m...	a939fd76dd91760abb7e4ac6dd9cdd69c16832cb3afe806f723809d6674d9183	3af93761d572522bee5fffcdc85aac9c40d522a4f5704eb204a2145e90ca8e13	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem using the numbers 23, 13, 9, and 17, we can use the standard multiplication algorithm.\n\nStep 1: Multiply 17 by 23:\n17 x 23 = 341\n\nStep 2: Multiply 17 by 13:\n17 x 13 = 221\n\nStep 3: Add the results from steps 1 and 2:\n341 + 221 = 562\n\nSo, the solution to the multiplication problem 23 x 1...	[{"budget_forced_chunks": ["To solve the problem using the numbers 23, 13, 9, and 17, we can use the standard multiplication algorithm.\n\nStep 1: Multiply 17 by 23:\n17 x 23 = 341\n\nStep 2: Multiply 17 by 13:\n17 x 13 = 221\n\nStep 3: Add the results from steps 1 and 2:\n341 + 221 = 562\n\nSo, the solution to the mul...	null
89	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	25	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 9 \\\\) using the numbers 20, 9, 1, and 3, we will follow these steps:\\n\\n1. Multiply the numbers:\\n - First, multiply 20 by 9:\\n \\\\[\\n 20 \\\\times 9 = 180\\n \\\\]\\n\\n2. Divide the result:\\n - Now, divide 180 by ...	["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 9 \\\\) using the numbers 20, 9, 1, and 3, we will follow these steps:\\n\\n1. Multiply the numbers:\\n - First, multiply 20 by 9:\\n \\\\[\\n 20 \\\\times 9 = 180\\n \\\\]\\n\\n2. Divide the result:\\n - Now, divide 180 by 3...	54074718fc33cde0d1ffb866e238f9ee9e73e4eb30deff57612ecfcabb7c0aa8	09a3501b533aecd2d38214aab61d6e005bf47b6c36df8a3cb6cc750794728110	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 20 \\div 9 \\) using the numbers 20, 9, 1, and 3, we will follow these steps:\n\n1. Multiply the numbers:\n - First, multiply 20 by 9:\n \\[\n 20 \\times 9 = 180\n \\]\n\n2. Divide the result:\n - Now, divide 180 by 3:\n \\[\n 180 \\div 3 = 54\n ...	[{"budget_forced_chunks": ["To solve the long division equation \\( 20 \\div 9 \\) using the numbers 20, 9, 1, and 3, we will follow these steps:\n\n1. Multiply the numbers:\n - First, multiply 20 by 9:\n \\[\n 20 \\times 9 = 180\n \\]\n\n2. Divide the result:\n - Now, divide 180 by 3:\n \\[...	null
90	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication equation \\\\(19 \\\\times 19 = 361\\\\), we can break it down into simpler steps.\\n\\n1. Break down the multiplication: \\n - Write down the numbers: \\\\(19 \\\\times 19\\\\).\\n - Break it into two separate multiplications: \\\\(19 \\\\times 10 + 19 \\\\times ...	["{'generation': \"To solve the multiplication equation \\\\(19 \\\\times 19 = 361\\\\), we can break it down into simpler steps.\\n\\n1. Break down the multiplication: \\n - Write down the numbers: \\\\(19 \\\\times 19\\\\).\\n - Break it into two separate multiplications: \\\\(19 \\\\times 10 + 19 \\\\times 9...	5e9a09fdc605b12c61135540e930f653f86cd4d1572d9149cb281ff1e69004e0	4a1eb49f78824faa8128953d30b3c4be9bcc3515c1d66b954e7165e50b92606f	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication equation \\(19 \\times 19 = 361\\), we can break it down into simpler steps.\n\n1. Break down the multiplication: \n - Write down the numbers: \\(19 \\times 19\\).\n - Break it into two separate multiplications: \\(19 \\times 10 + 19 \\times 9\\).\n\n2. Calculate the first part...	[{"budget_forced_chunks": ["To solve the multiplication equation \\(19 \\times 19 = 361\\), we can break it down into simpler steps.\n\n1. Break down the multiplication: \n - Write down the numbers: \\(19 \\times 19\\).\n - Break it into two separate multiplications: \\(19 \\times 10 + 19 \\times 9\\).\n\n2. **...	null
91	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation that equals 18 using the numbers 6, 16, 17, and 21, we can break it down into simpler steps:\\n\\n1. First, let's multiply the numbers into two parts: 6 and 17, which equals 102. Then, we will multiply the remaining numbers: 16 and 21, which equals 376.\\...	["{'generation': \"To solve the problem of creating an equation that equals 18 using the numbers 6, 16, 17, and 21, we can break it down into simpler steps:\\n\\n1. First, let's multiply the numbers into two parts: 6 and 17, which equals 102. Then, we will multiply the remaining numbers: 16 and 21, which equals 376.\\n...	5d6946d5bae41ad89ef8b142890fcccb941af44fcb19a052c920cc994415c022	656e0436e2d4c37f42635c0cc65e38bc1a4c562af47a499516eb06749fdba456	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation that equals 18 using the numbers 6, 16, 17, and 21, we can break it down into simpler steps:\n\n1. First, let's multiply the numbers into two parts: 6 and 17, which equals 102. Then, we will multiply the remaining numbers: 16 and 21, which equals 376.\n2. Now, let's add th...	[{"budget_forced_chunks": ["To solve the problem of creating an equation that equals 18 using the numbers 6, 16, 17, and 21, we can break it down into simpler steps:\n\n1. First, let's multiply the numbers into two parts: 6 and 17, which equals 102. Then, we will multiply the remaining numbers: 16 and 21, which equals ...	null
92	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	24	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of multiplying the numbers 3, 16, 12, and 14 using the basic arithmetic operations, we can break it down into simpler steps:\\n\\n1. First, let's multiply the numbers into two parts: 3 + 12 and 16 + 14.\\n - 3 + 12 = 15\\n - 16 + 14 = 30\\n\\n2. Now, we need to multiply thes...	["{'generation': \"To solve the problem of multiplying the numbers 3, 16, 12, and 14 using the basic arithmetic operations, we can break it down into simpler steps:\\n\\n1. First, let's multiply the numbers into two parts: 3 + 12 and 16 + 14.\\n - 3 + 12 = 15\\n - 16 + 14 = 30\\n\\n2. Now, we need to multiply these...	d8bbffa5e5aafaa81683a064a1e22217380d39e326b48c7a3892f8be8bd55e73	ec25b954d4c64b681f6a629e1bebf6d529c421771c4d7ef6b38b109b278a8b99	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of multiplying the numbers 3, 16, 12, and 14 using the basic arithmetic operations, we can break it down into simpler steps:\n\n1. First, let's multiply the numbers into two parts: 3 + 12 and 16 + 14.\n - 3 + 12 = 15\n - 16 + 14 = 30\n\n2. Now, we need to multiply these two results together: ...	[{"budget_forced_chunks": ["To solve the problem of multiplying the numbers 3, 16, 12, and 14 using the basic arithmetic operations, we can break it down into simpler steps:\n\n1. First, let's multiply the numbers into two parts: 3 + 12 and 16 + 14.\n - 3 + 12 = 15\n - 16 + 14 = 30\n\n2. Now, we need to multiply th...	null
93	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	20	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 462 \\\\div 32 \\\\), we can break it down into simpler steps:\\n\\n1. First, let's multiply the units digit of the numbers:\\n - The units digit of 462 is 2.\\n - The units digit of 32 is 2.\\n - \\\\( 2 \\\\times 2 = 4 \\\\).\\n\\n2. **Second, le...	["{'generation': \"To solve the long division equation \\\\( 462 \\\\div 32 \\\\), we can break it down into simpler steps:\\n\\n1. First, let's multiply the units digit of the numbers:\\n - The units digit of 462 is 2.\\n - The units digit of 32 is 2.\\n - \\\\( 2 \\\\times 2 = 4 \\\\).\\n\\n2. **Second, let...	e1fd07ae613d4433c60203d498668d3115bfa1c141ec77d811980d28281a64ce	97371084dfc8c3d3a11b264c62dd52e390799a6af505406ad31e1b2b54b56055	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 462 \\div 32 \\), we can break it down into simpler steps:\n\n1. First, let's multiply the units digit of the numbers:\n - The units digit of 462 is 2.\n - The units digit of 32 is 2.\n - \\( 2 \\times 2 = 4 \\).\n\n2. **Second, let's multiply the tens digit of the fi...	[{"budget_forced_chunks": ["To solve the long division equation \\( 462 \\div 32 \\), we can break it down into simpler steps:\n\n1. First, let's multiply the units digit of the numbers:\n - The units digit of 462 is 2.\n - The units digit of 32 is 2.\n - \\( 2 \\times 2 = 4 \\).\n\n2. **Second, let's multipl...	null
94	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	23	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problemStated, we need to develop a step-by-step method to solve it. \\n\\none such method could be to break the numbers into parts and then use the distributive property of multiplication over addition.\\n\\nFor example, we can break down 23 as:\\n\\n23 = 20 + 3\\n\\nThen we can rewrit...	["{'generation': \"To solve the problemStated, we need to develop a step-by-step method to solve it. \\n\\none such method could be to break the numbers into parts and then use the distributive property of multiplication over addition.\\n\\nFor example, we can break down 23 as:\\n\\n23 = 20 + 3\\n\\nThen we can rewrite...	3a1b25f4d472756ebdf562f6119b65b746b767ea84a4dd799bd070e16ecfe97b	d458798ae840986384fb19120fb9fb1a5e41c093e8037f36a443be3fcc0dcaf9	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problemStated, we need to develop a step-by-step method to solve it. \n\none such method could be to break the numbers into parts and then use the distributive property of multiplication over addition.\n\nFor example, we can break down 23 as:\n\n23 = 20 + 3\n\nThen we can rewrite the multiplication as:\n...	[{"budget_forced_chunks": ["To solve the problemStated, we need to develop a step-by-step method to solve it. \n\none such method could be to break the numbers into parts and then use the distributive property of multiplication over addition.\n\nFor example, we can break down 23 as:\n\n23 = 20 + 3\n\nThen we can rewrit...	null
95	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	16	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the multiplication problem \\\\(16 \\\\times 4 \\\\times 1 \\\\times 21\\\\) step by step, we can break it down into simpler parts.\\n\\n1. Break down the multiplication:\\n - First, multiply 16 by 4:\\n \\\\[\\n 16 \\\\times 4 = 64\\n \\\\]\\n\\n2. **Multiply the result b...	["{'generation': \"To solve the multiplication problem \\\\(16 \\\\times 4 \\\\times 1 \\\\times 21\\\\) step by step, we can break it down into simpler parts.\\n\\n1. Break down the multiplication:\\n - First, multiply 16 by 4:\\n \\\\[\\n 16 \\\\times 4 = 64\\n \\\\]\\n\\n2. **Multiply the result by...	d072894f0ec9b0cfbfa2cc48b6771ecc2c365ef18772bb99cdcc43a7540ee46f	7bde26e5b3b1575939cd70cea46432c285a6285297650ad797a14d239b460762	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the multiplication problem \\(16 \\times 4 \\times 1 \\times 21\\) step by step, we can break it down into simpler parts.\n\n1. Break down the multiplication:\n - First, multiply 16 by 4:\n \\[\n 16 \\times 4 = 64\n \\]\n\n2. Multiply the result by the next number:\n - Now, multiply 6...	[{"budget_forced_chunks": ["To solve the multiplication problem \\(16 \\times 4 \\times 1 \\times 21\\) step by step, we can break it down into simpler parts.\n\n1. Break down the multiplication:\n - First, multiply 16 by 4:\n \\[\n 16 \\times 4 = 64\n \\]\n\n2. **Multiply the result by the next numbe...	null
96	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	17	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem (8 - 4) x 15 using the given numbers, we can break it down into simpler steps:\\n\\nStep 1: Break down the multiplication into parts.\\n(8 x 10) - (4 x 10) = 80 - 40\\nThis gives us 40 as a base to multiply by 15.\\n\\nStep 2: Multiply the base (40) by 15.\\n40 x 15 = 600\\n\\nS...	["{'generation': \"To solve the problem (8 - 4) x 15 using the given numbers, we can break it down into simpler steps:\\n\\nStep 1: Break down the multiplication into parts.\\n(8 x 10) - (4 x 10) = 80 - 40\\nThis gives us 40 as a base to multiply by 15.\\n\\nStep 2: Multiply the base (40) by 15.\\n40 x 15 = 600\\n\\nSo...	efcaf1a72cc1c5524e2e8c8faf13eb037aad0cfaeda5e5f50a2a2902dde53333	23aa6021a0c062a9b897ef9afa175819a2757915f30ab230bbb56d2e9f0d4379	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem (8 - 4) x 15 using the given numbers, we can break it down into simpler steps:\n\nStep 1: Break down the multiplication into parts.\n(8 x 10) - (4 x 10) = 80 - 40\nThis gives us 40 as a base to multiply by 15.\n\nStep 2: Multiply the base (40) by 15.\n40 x 15 = 600\n\nSo, the final answer is 600....	[{"budget_forced_chunks": ["To solve the problem (8 - 4) x 15 using the given numbers, we can break it down into simpler steps:\n\nStep 1: Break down the multiplication into parts.\n(8 x 10) - (4 x 10) = 80 - 40\nThis gives us 40 as a base to multiply by 15.\n\nStep 2: Multiply the base (40) by 15.\n40 x 15 = 600\n\nSo...	null
97	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	13	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 20 \\\\times 17 \\\\times 24 \\\\), we will multiply the numbers according to the standard multiplication algorithm. Let's break it down:\\n\\n1. Multiply 20 by 4 (the units digit of 24):\\n \\\\[\\n 20 \\\\times 4 = 80\\n \\\\]\\n\\n2. **Multiply ...	["{'generation': \"To solve the long division equation \\\\( 20 \\\\times 17 \\\\times 24 \\\\), we will multiply the numbers according to the standard multiplication algorithm. Let's break it down:\\n\\n1. Multiply 20 by 4 (the units digit of 24):\\n \\\\[\\n 20 \\\\times 4 = 80\\n \\\\]\\n\\n2. **Multiply 2...	06649405689279406a3c70aecf0a5a85d6c4f8da6b95412e61bf2dca98890c04	55ba249ea0e0bd5cabb609e0cc089c7f40c89a4d809e27c8712b899ba78b1571	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 20 \\times 17 \\times 24 \\), we will multiply the numbers according to the standard multiplication algorithm. Let's break it down:\n\n1. Multiply 20 by 4 (the units digit of 24):\n \\[\n 20 \\times 4 = 80\n \\]\n\n2. **Multiply 20 by 2 (the tens digit of 24, which is...	[{"budget_forced_chunks": ["To solve the long division equation \\( 20 \\times 17 \\times 24 \\), we will multiply the numbers according to the standard multiplication algorithm. Let's break it down:\n\n1. Multiply 20 by 4 (the units digit of 24):\n \\[\n 20 \\times 4 = 80\n \\]\n\n2. **Multiply 20 by 2 (the ...	null
98	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	14	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the problem of creating an equation that equals 14 using the numbers 9, 14, 11, and 17, we can break it down into simpler steps.\\n\\nStep 1: Break the multiplication into smaller parts.\\n(9 * 10) + (9 * 4) = (90 + 36) = 126\\n\\nSo far, we have 126 from the multiplication. Now, we need to...	["{'generation': \"To solve the problem of creating an equation that equals 14 using the numbers 9, 14, 11, and 17, we can break it down into simpler steps.\\n\\nStep 1: Break the multiplication into smaller parts.\\n(9 * 10) + (9 * 4) = (90 + 36) = 126\\n\\nSo far, we have 126 from the multiplication. Now, we need to ...	0e937e0893608a7dccea4dc5ebe2f18c3d7a0f90b5cea4b17f34fb5a0fddcb7e	4367a333b8fbb8824e45aa74045b82d4909a70148afc968b397a44152d78cf2d	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the problem of creating an equation that equals 14 using the numbers 9, 14, 11, and 17, we can break it down into simpler steps.\n\nStep 1: Break the multiplication into smaller parts.\n(9 * 10) + (9 * 4) = (90 + 36) = 126\n\nSo far, we have 126 from the multiplication. Now, we need to add the remaining numb...	[{"budget_forced_chunks": ["To solve the problem of creating an equation that equals 14 using the numbers 9, 14, 11, and 17, we can break it down into simpler steps.\n\nStep 1: Break the multiplication into smaller parts.\n(9 * 10) + (9 * 4) = (90 + 36) = 126\n\nSo far, we have 126 from the multiplication. Now, we need...	null
99	{"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that...	18	{"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\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha...	[["{'generation': \"To solve the long division equation \\\\( 22 \\\\div 16 \\\\), we'll follow these steps:\\n\\n1. Break it down into simpler parts: \\n - First, break it into smaller division problems: \\\\( 22 \\\\div 10 \\\\) and \\\\( 22 \\\\div 6 \\\\).\\n - Calculate these separately to understand the s...	["{'generation': \"To solve the long division equation \\\\( 22 \\\\div 16 \\\\), we'll follow these steps:\\n\\n1. Break it down into simpler parts: \\n - First, break it into smaller division problems: \\\\( 22 \\\\div 10 \\\\) and \\\\( 22 \\\\div 6 \\\\).\\n - Calculate these separately to understand the st...	c05b04ca7ae2cc4348826abbfbaf15c8c666eac685b4eac2862b07de889f7024	a3e4733b904b745aded4db23f1be09a0a5ea7593a933cb6bee0e85f6aba4d55f	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-06T02-10-35.135228.jsonl	["To solve the long division equation \\( 22 \\div 16 \\), we'll follow these steps:\n\n1. Break it down into simpler parts: \n - First, break it into smaller division problems: \\( 22 \\div 10 \\) and \\( 22 \\div 6 \\).\n - Calculate these separately to understand the structure of the answer.\n\n2. **Calculat...	[{"budget_forced_chunks": ["To solve the long division equation \\( 22 \\div 16 \\), we'll follow these steps:\n\n1. Break it down into simpler parts: \n - First, break it into smaller division problems: \\( 22 \\div 10 \\) and \\( 22 \\div 6 \\).\n - Calculate these separately to understand the structure of th...	null

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