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 problem \\\\( 15 + 19 - 9 \\\\), we can break it down into simpler steps:\\n\\n1. Combine 15 and 19:\\n \\\\[\\n 15 + 19 = 34\\n \\\\]\\n\\n2. Subtract 9 from the result:\\n \\\\[\\n 34 - 9 = 25\\n \\\\]\\n\\nSo, the final result is \\\\( 25 \\\\).\\n\\n\\\\[\\n\\\\b...	["{'generation': \"To solve the problem \\\\( 15 + 19 - 9 \\\\), we can break it down into simpler steps:\\n\\n1. Combine 15 and 19:\\n \\\\[\\n 15 + 19 = 34\\n \\\\]\\n\\n2. Subtract 9 from the result:\\n \\\\[\\n 34 - 9 = 25\\n \\\\]\\n\\nSo, the final result is \\\\( 25 \\\\).\\n\\n\\\\[\\n\\\\bo...	1fe4a3a3bdceb99acba3870b8820fb7d71d2b128097a35de13101519c94b2714	6adf7f5ba7f8982f91ce5cd729a078032176cbdfc8ebc8d4eaebb7f44a3a1fb4	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 15 + 19 - 9 \\), we can break it down into simpler steps:\n\n1. Combine 15 and 19:\n \\[\n 15 + 19 = 34\n \\]\n\n2. Subtract 9 from the result:\n \\[\n 34 - 9 = 25\n \\]\n\nSo, the final result is \\( 25 \\).\n\n\\[\n\\boxed{25}\n\\] Wait, let me try 15, 19, 9 = (15 + 19) ...	[{"budget_forced_chunks": ["To solve the problem \\( 15 + 19 - 9 \\), we can break it down into simpler steps:\n\n1. Combine 15 and 19:\n \\[\n 15 + 19 = 34\n \\]\n\n2. Subtract 9 from the result:\n \\[\n 34 - 9 = 25\n \\]\n\nSo, the final result is \\( 25 \\).\n\n\\[\n\\boxed{25}\n\\]", " Wait, let...	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 problem \\\\( 20 + 9 - 2 + 24 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the numbers step by step:\\n - First, add 20 and 9.\\n \\\\[\\n 20 + 9 = 29\\n \\\\]\\n - Next, subtract 2 from the result.\\n \\\\[\\n 29 - 2 = 27\\n \\\\]\\n ...	["{'generation': \"To solve the problem \\\\( 20 + 9 - 2 + 24 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the numbers step by step:\\n - First, add 20 and 9.\\n \\\\[\\n 20 + 9 = 29\\n \\\\]\\n - Next, subtract 2 from the result.\\n \\\\[\\n 29 - 2 = 27\\n \\\\]\\n ...	4e7925e9464d9cd3f15b66d7f0d396c2d208e935db23218e8e12a143a69fdcf5	bd97db98bf338537ff6865ad3edb32a5afd84e1c203f33f3a520ad9350cff93a	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 20 + 9 - 2 + 24 \\), we can break it down into simpler steps:\n\n1. Combine the numbers step by step:\n - First, add 20 and 9.\n \\[\n 20 + 9 = 29\n \\]\n - Next, subtract 2 from the result.\n \\[\n 29 - 2 = 27\n \\]\n - Finally, add 24 to the result.\n \...	[{"budget_forced_chunks": ["To solve the problem \\( 20 + 9 - 2 + 24 \\), we can break it down into simpler steps:\n\n1. Combine the numbers step by step:\n - First, add 20 and 9.\n \\[\n 20 + 9 = 29\n \\]\n - Next, subtract 2 from the result.\n \\[\n 29 - 2 = 27\n \\]\n - Finally, add...	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 problem \\\\(13 + 3 \\\\times 18 + 10\\\\), we can break it down into simpler steps:\\n\\n1. First Step: Add 13 and 3:\\n \\\\[\\n 13 + 3 = 16\\n \\\\]\\n\\n2. Second Step: Multiply the result by 18:\\n \\\\[\\n 16 \\\\times 18 = 288\\n \\\\]\\n\\n3. Third Step: A...	["{'generation': 'To solve the problem \\\\(13 + 3 \\\\times 18 + 10\\\\), we can break it down into simpler steps:\\n\\n1. First Step: Add 13 and 3:\\n \\\\[\\n 13 + 3 = 16\\n \\\\]\\n\\n2. Second Step: Multiply the result by 18:\\n \\\\[\\n 16 \\\\times 18 = 288\\n \\\\]\\n\\n3. Third Step: Ad...	21d37d7882ca656e9c61892eb0e92eb17e6ccb0b44acbf990becc8d10939c8ba	01fe40f4315157fd51d595d12678270a8d4a97c88098425b3b2c89768f826ed6	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\(13 + 3 \\times 18 + 10\\), we can break it down into simpler steps:\n\n1. First Step: Add 13 and 3:\n \\[\n 13 + 3 = 16\n \\]\n\n2. Second Step: Multiply the result by 18:\n \\[\n 16 \\times 18 = 288\n \\]\n\n3. Third Step: Add the result to 10:\n \\[\n 288 + 10 = 2...	[{"budget_forced_chunks": ["To solve the problem \\(13 + 3 \\times 18 + 10\\), we can break it down into simpler steps:\n\n1. First Step: Add 13 and 3:\n \\[\n 13 + 3 = 16\n \\]\n\n2. Second Step: Multiply the result by 18:\n \\[\n 16 \\times 18 = 288\n \\]\n\n3. Third Step: Add the result to 10...	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 problem \\\\( 23 \\\\times 3 \\\\times 2 \\\\times 22 \\\\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the result by the remaining number.\\n\\n### Step 1: Multiply 23 by 3\\n\\\\[\\n23 \\\\times 3 = 69\\n\\\\]\\n\\n### Step 2: Multipl...	["{'generation': \"To solve the problem \\\\( 23 \\\\times 3 \\\\times 2 \\\\times 22 \\\\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the result by the remaining number.\\n\\n### Step 1: Multiply 23 by 3\\n\\\\[\\n23 \\\\times 3 = 69\\n\\\\]\\n\\n### Step 2: Multiply...	95ef82ecb05d93a4ee380d4641abaeadd43e6bc9d99c871ce170758b6f305b44	b74d9dce0967059bc7deb16d7c3ce9ddb7cfb27d70d2987dea642c679674d513	6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 23 \\times 3 \\times 2 \\times 22 \\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the result by the remaining number.\n\n### Step 1: Multiply 23 by 3\n\\[\n23 \\times 3 = 69\n\\]\n\n### Step 2: Multiply the result by 2\n\\[\n69 \\times 2 = 13...	[{"budget_forced_chunks": ["To solve the problem \\( 23 \\times 3 \\times 2 \\times 22 \\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the result by the remaining number.\n\n### Step 1: Multiply 23 by 3\n\\[\n23 \\times 3 = 69\n\\]\n\n### Step 2: Multiply the result by...	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 problem \\\\( 3 \\\\times 8 \\\\times 4 \\\\times 13 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n - \\\\( 3 \\\\) can be written as \\\\( 10 - 7 \\\\).\\n - \\\\( 8 \\\\) can...	["{'generation': \"To solve the problem \\\\( 3 \\\\times 8 \\\\times 4 \\\\times 13 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n - \\\\( 3 \\\\) can be written as \\\\( 10 - 7 \\\\).\\n - \\\\( 8 \\\\) can ...	37e0958fcc9b1045189fb65b03cc9e071033593787e2f5171ceea9f86e8ebcf4	ec571e8688c75a5736ce86b7195b61373aaf0be543ff8182bc2cf3a6429e9eab	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 3 \\times 8 \\times 4 \\times 13 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n - \\( 3 \\) can be written as \\( 10 - 7 \\).\n - \\( 8 \\) can be written as \\( 10 + 8 \\).\n - \\( 4 \...	[{"budget_forced_chunks": ["To solve the problem \\( 3 \\times 8 \\times 4 \\times 13 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n - \\( 3 \\) can be written as \\( 10 - 7 \\).\n - \\( 8 \\) can be written as \\(...	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 problem \\\\( 12 \\\\times 6 \\\\times 12 \\\\), we can break it down into simpler steps:\\n\\n1. First, multiply 12 and 6:\\n \\\\[\\n 12 \\\\times 6 = 72\\n \\\\]\\n\\n2. Next, multiply the result by 10 (since there are two zeros in 12):\\n \\\\[\\n 72 \\\\times 10 = 720\\n ...	["{'generation': \"To solve the problem \\\\( 12 \\\\times 6 \\\\times 12 \\\\), we can break it down into simpler steps:\\n\\n1. First, multiply 12 and 6:\\n \\\\[\\n 12 \\\\times 6 = 72\\n \\\\]\\n\\n2. Next, multiply the result by 10 (since there are two zeros in 12):\\n \\\\[\\n 72 \\\\times 10 = 720\\n ...	a4b2daca5c54b55b15980110f282e22f14fac0971c9652711d3a679e8bd89a3d	7cfb8ba4d40ba72deb7d7f9cb5b33545b9f643be9e6bb394acaf180179e28cd4	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 12 \\times 6 \\times 12 \\), we can break it down into simpler steps:\n\n1. First, multiply 12 and 6:\n \\[\n 12 \\times 6 = 72\n \\]\n\n2. Next, multiply the result by 10 (since there are two zeros in 12):\n \\[\n 72 \\times 10 = 720\n \\]\n\n3. Finally, add 12 to the previous re...	[{"budget_forced_chunks": ["To solve the problem \\( 12 \\times 6 \\times 12 \\), we can break it down into simpler steps:\n\n1. First, multiply 12 and 6:\n \\[\n 12 \\times 6 = 72\n \\]\n\n2. Next, multiply the result by 10 (since there are two zeros in 12):\n \\[\n 72 \\times 10 = 720\n \\]\n\n3. Finally,...	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 using the numbers 6, 15, 13, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 13 and 9:\\n 13 * 9 = 117\\n\\n2. Next, multiply 6 and 15:\\n 6 * 15 = 90\\n\\n3. Now, add the two results together:\\n 117 + 90 = 207\\n\\nSo, the equation that equals 21 ...	["{'generation': \"To solve the problem using the numbers 6, 15, 13, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 13 and 9:\\n 13 * 9 = 117\\n\\n2. Next, multiply 6 and 15:\\n 6 * 15 = 90\\n\\n3. Now, add the two results together:\\n 117 + 90 = 207\\n\\nSo, the equation that equals 21 i...	a7f237e6a8b37389748df0baa5ea27734734e3277f163e579d92165e4afed893	ab00774c40567d2e767072fc5936db116736f40a30593069488d7cfe010b27b9	6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 6, 15, 13, and 9, we can break it down into simpler steps:\n\n1. First, multiply 13 and 9:\n 13 * 9 = 117\n\n2. Next, multiply 6 and 15:\n 6 * 15 = 90\n\n3. Now, add the two results together:\n 117 + 90 = 207\n\nSo, the equation that equals 21 is:\n(1 + 2) * 3 + 4 = 207\n\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 6, 15, 13, and 9, we can break it down into simpler steps:\n\n1. First, multiply 13 and 9:\n 13 * 9 = 117\n\n2. Next, multiply 6 and 15:\n 6 * 15 = 90\n\n3. Now, add the two results together:\n 117 + 90 = 207\n\nSo, the equation that equals 21 is:...	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 problem \\\\(2 \\\\times 8 \\\\times 2 \\\\times 11\\\\) step by step, we can break it down into simpler multiplications and then add the results.\\n\\n1. First Step: Multiply 2 and 8.\\n \\\\[\\n 2 \\\\times 8 = 16\\n \\\\]\\n\\n2. **Second Step: Multiply the result from the ...	["{'generation': \"To solve the problem \\\\(2 \\\\times 8 \\\\times 2 \\\\times 11\\\\) step by step, we can break it down into simpler multiplications and then add the results.\\n\\n1. First Step: Multiply 2 and 8.\\n \\\\[\\n 2 \\\\times 8 = 16\\n \\\\]\\n\\n2. **Second Step: Multiply the result from the f...	45c1e59b5a1a576b7ae49ac9ab5ee519341b3ff5d15693635b6c69819b16325f	0e76d7adfecf1d484230f45f4d7e233e3860bce62d005024a9c931e6fe2a8c02	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\(2 \\times 8 \\times 2 \\times 11\\) step by step, we can break it down into simpler multiplications and then add the results.\n\n1. First Step: Multiply 2 and 8.\n \\[\n 2 \\times 8 = 16\n \\]\n\n2. Second Step: Multiply the result from the first step by 2.\n \\[\n 16 \\times...	[{"budget_forced_chunks": ["To solve the problem \\(2 \\times 8 \\times 2 \\times 11\\) step by step, we can break it down into simpler multiplications and then add the results.\n\n1. First Step: Multiply 2 and 8.\n \\[\n 2 \\times 8 = 16\n \\]\n\n2. **Second Step: Multiply the result from the first step by 2...	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 using the numbers 21, 15, 5, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 21 by 5:\\n \\\\[ 21 * 5 = 105 \\\\]\\n\\n2. Next, multiply 21 by 15:\\n \\\\[ 21 * 15 = 315 \\\\]\\n\\n3. Now, add the two results together:\\n \\\\[ 105 + 315 = 420 \\\\]...	["{'generation': \"To solve the problem using the numbers 21, 15, 5, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 21 by 5:\\n \\\\[ 21 * 5 = 105 \\\\]\\n\\n2. Next, multiply 21 by 15:\\n \\\\[ 21 * 15 = 315 \\\\]\\n\\n3. Now, add the two results together:\\n \\\\[ 105 + 315 = 420 \\\\]\...	167220307e1ef076a95de3ecc155ceac76542c67d9bfe7f28083afac878049e0	15b1e41847c3fd678b61f9e016eda0d418836829766dc3d9e8d8e1b5133c1d3a	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 21, 15, 5, and 9, we can break it down into simpler steps:\n\n1. First, multiply 21 by 5:\n \\[ 21 * 5 = 105 \\]\n\n2. Next, multiply 21 by 15:\n \\[ 21 * 15 = 315 \\]\n\n3. Now, add the two results together:\n \\[ 105 + 315 = 420 \\]\n\nSo, the equation that equals 22 is:...	[{"budget_forced_chunks": ["To solve the problem using the numbers 21, 15, 5, and 9, we can break it down into simpler steps:\n\n1. First, multiply 21 by 5:\n \\[ 21 * 5 = 105 \\]\n\n2. Next, multiply 21 by 15:\n \\[ 21 * 15 = 315 \\]\n\n3. Now, add the two results together:\n \\[ 105 + 315 = 420 \\]\n\nSo, the e...	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 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the multiplication:\\n \\\\[\\n 6 \\\\times 22 = 6 \\\\times (20 + 2)\\n \\\\]\\n\\n2. **Apply the distributive prope...	["{'generation': \"To solve the problem \\\\( 6 \\\\times 22 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the multiplication:\\n \\\\[\\n 6 \\\\times 22 = 6 \\\\times (20 + 2)\\n \\\\]\\n\\n2. **Apply the distributive proper...	9177efbdceb2c6d3585fa1de81c78225fbf88132fb0ae87fe539a216301a3389	a3d20e36b20880d64b880d4378e3aea9de8a3687a302888a392e88997a29b20f	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 6 \\times 22 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the multiplication:\n \\[\n 6 \\times 22 = 6 \\times (20 + 2)\n \\]\n\n2. Apply the distributive property:\n \\[\n 6 \\times (20 + 2) =...	[{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 22 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the multiplication:\n \\[\n 6 \\times 22 = 6 \\times (20 + 2)\n \\]\n\n2. Apply the distributive property:\n \\...	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 \\\\( 20 + 15 + 17 \\\\), we can break it down into simpler steps:\\n\\n1. Add the first two numbers:\\n \\\\[\\n 20 + 15 = 35\\n \\\\]\\n\\n2. Add the result to the third number:\\n \\\\[\\n 35 + 17 = 52\\n \\\\]\\n\\nSo, the final step would be to write:\\n...	["{'generation': \"To solve the problem \\\\( 20 + 15 + 17 \\\\), we can break it down into simpler steps:\\n\\n1. Add the first two numbers:\\n \\\\[\\n 20 + 15 = 35\\n \\\\]\\n\\n2. Add the result to the third number:\\n \\\\[\\n 35 + 17 = 52\\n \\\\]\\n\\nSo, the final step would be to write:\\n\...	fa4cb9ed4e55cbe2ea009410b3c7dcdfb08848fdb2331821ffa94d8b437f7ed2	484114ad1c6eb12bf2e842b3e234616a60cc354ec1f3bada427e5e83ddb21194	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 20 + 15 + 17 \\), we can break it down into simpler steps:\n\n1. Add the first two numbers:\n \\[\n 20 + 15 = 35\n \\]\n\n2. Add the result to the third number:\n \\[\n 35 + 17 = 52\n \\]\n\nSo, the final step would be to write:\n\\[\n52 + 0 = 52\n\\]\n\nTherefore, the ans...	[{"budget_forced_chunks": ["To solve the problem \\( 20 + 15 + 17 \\), we can break it down into simpler steps:\n\n1. Add the first two numbers:\n \\[\n 20 + 15 = 35\n \\]\n\n2. Add the result to the third number:\n \\[\n 35 + 17 = 52\n \\]\n\nSo, the final step would be to write:\n\\[\n52 + 0 = 52\...	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 problem using the numbers 18, 9, 21, and 11, we can break it down into simpler steps:\\n\\n1. First, let's multiply 11 by 9:\\n 11 * 9 = 99\\n\\n2. Now, we need to multiply 11 by 21. To do this more easily, we can think of 21 as 20 + 1:\\n 11 * (20 + 1) = 11 * 20 + 11 * 1\\n 11 * ...	["{'generation': \"To solve the problem using the numbers 18, 9, 21, and 11, we can break it down into simpler steps:\\n\\n1. First, let's multiply 11 by 9:\\n 11 * 9 = 99\\n\\n2. Now, we need to multiply 11 by 21. To do this more easily, we can think of 21 as 20 + 1:\\n 11 * (20 + 1) = 11 * 20 + 11 * 1\\n 11 * 2...	aeab403787979ca2e59c5279813784a23284ef1d2d9e6cce4c2f457d9a376fa5	7b22993c7049eb435ab1c64d209542f9d5b0889583f68f7daa920a8fdd4d143a	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 18, 9, 21, and 11, we can break it down into simpler steps:\n\n1. First, let's multiply 11 by 9:\n 11 * 9 = 99\n\n2. Now, we need to multiply 11 by 21. To do this more easily, we can think of 21 as 20 + 1:\n 11 * (20 + 1) = 11 * 20 + 11 * 1\n 11 * 20 = 220\n 11 * 1 = 11\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 18, 9, 21, and 11, we can break it down into simpler steps:\n\n1. First, let's multiply 11 by 9:\n 11 * 9 = 99\n\n2. Now, we need to multiply 11 by 21. To do this more easily, we can think of 21 as 20 + 1:\n 11 * (20 + 1) = 11 * 20 + 11 * 1\n 11 *...	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 problem \\\\( 13 \\\\) using the numbers \\\\( 24, 9, 17, 6 \\\\) with each number used once, we can follow these steps:\\n\\n1. Break down the problem into smaller parts:\\n - Find a way to combine the numbers that equals \\\\( 10 \\\\) because \\\\( 13 = 10 + 3 \\\\).\\n - Fin...	["{'generation': \"To solve the problem \\\\( 13 \\\\) using the numbers \\\\( 24, 9, 17, 6 \\\\) with each number used once, we can follow these steps:\\n\\n1. Break down the problem into smaller parts:\\n - Find a way to combine the numbers that equals \\\\( 10 \\\\) because \\\\( 13 = 10 + 3 \\\\).\\n - Find...	94cc4d46a251029a832d451e9841ef5724b174c7b59c6c76e1127a5ee0081cab	7a5b85f69b00da4f91c788b8cf04b98ce70fb22eb4c3489edad15c24280dac29	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 13 \\) using the numbers \\( 24, 9, 17, 6 \\) with each number used once, we can follow these steps:\n\n1. Break down the problem into smaller parts:\n - Find a way to combine the numbers that equals \\( 10 \\) because \\( 13 = 10 + 3 \\).\n - Find another way to combine the numbers t...	[{"budget_forced_chunks": ["To solve the problem \\( 13 \\) using the numbers \\( 24, 9, 17, 6 \\) with each number used once, we can follow these steps:\n\n1. Break down the problem into smaller parts:\n - Find a way to combine the numbers that equals \\( 10 \\) because \\( 13 = 10 + 3 \\).\n - Find another wa...	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 problem \\\\( 10 + 21 - 17 + 20 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Combine the numbers:\\n \\\\[\\n 10 + 21 = 31\\n \\\\]\\n\\n2. Step 2: Subtract 17 from the result:\\n \\\\[\\n 31 - 17 = 14\\n \\\\]\\n\\n3. Step 3: Add the remaining...	["{'generation': \"To solve the problem \\\\( 10 + 21 - 17 + 20 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Combine the numbers:\\n \\\\[\\n 10 + 21 = 31\\n \\\\]\\n\\n2. Step 2: Subtract 17 from the result:\\n \\\\[\\n 31 - 17 = 14\\n \\\\]\\n\\n3. Step 3: Add the remaining ...	1100061fa8b2c459d70a76ef486ae8bad9ac3ddfb304ee3c982e7dc2c573a770	d068197d7d7b5cec6b7b9f6025420f133708054938f2ab0eba12d3306994440a	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 10 + 21 - 17 + 20 \\), we can break it down into simpler steps:\n\n1. Step 1: Combine the numbers:\n \\[\n 10 + 21 = 31\n \\]\n\n2. Step 2: Subtract 17 from the result:\n \\[\n 31 - 17 = 14\n \\]\n\n3. Step 3: Add the remaining 20 to the result:\n \\[\n 14 + 20 = 3...	[{"budget_forced_chunks": ["To solve the problem \\( 10 + 21 - 17 + 20 \\), we can break it down into simpler steps:\n\n1. Step 1: Combine the numbers:\n \\[\n 10 + 21 = 31\n \\]\n\n2. Step 2: Subtract 17 from the result:\n \\[\n 31 - 17 = 14\n \\]\n\n3. Step 3: Add the remaining 20 to the resul...	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 problem using the numbers 20, 11, 16, and 1, we can break it down into simpler steps:\\n\\n1. First, let's multiply 16 by 1: \\n \\\\[ 16 \\\\times 1 = 16 \\\\]\\n\\n2. Now, we need to multiply 16 by 11. To do this step-by-step:\\n - Multiply 16 by 1 (which we already know is 16).\\...	["{'generation': \"To solve the problem using the numbers 20, 11, 16, and 1, we can break it down into simpler steps:\\n\\n1. First, let's multiply 16 by 1: \\n \\\\[ 16 \\\\times 1 = 16 \\\\]\\n\\n2. Now, we need to multiply 16 by 11. To do this step-by-step:\\n - Multiply 16 by 1 (which we already know is 16).\\n...	02fd4efda14193a5a878824c080d69604c3ea776d1bc6cf3bc6bc40ea401d5a6	bdb69ef7d0d7581d293cc62945c5493161826c3dbb4a101a65138f34bc2cedcd	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 20, 11, 16, and 1, we can break it down into simpler steps:\n\n1. First, let's multiply 16 by 1: \n \\[ 16 \\times 1 = 16 \\]\n\n2. Now, we need to multiply 16 by 11. To do this step-by-step:\n - Multiply 16 by 1 (which we already know is 16).\n - Then, multiply 16 by 10 (...	[{"budget_forced_chunks": ["To solve the problem using the numbers 20, 11, 16, and 1, we can break it down into simpler steps:\n\n1. First, let's multiply 16 by 1: \n \\[ 16 \\times 1 = 16 \\]\n\n2. Now, we need to multiply 16 by 11. To do this step-by-step:\n - Multiply 16 by 1 (which we already know is 16).\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 problem \\\\( 10 + 8 - 2 + 8 \\\\), we can break it down into simpler steps:\\n\\n1. First, add 10 and 8:\\n \\\\[\\n 10 + 8 = 18\\n \\\\]\\n\\n2. Next, subtract 2 from the result:\\n \\\\[\\n 18 - 2 = 16\\n \\\\]\\n\\n3. Finally, add the remaining 8 to the result:\\n \\\\...	["{'generation': \"To solve the problem \\\\( 10 + 8 - 2 + 8 \\\\), we can break it down into simpler steps:\\n\\n1. First, add 10 and 8:\\n \\\\[\\n 10 + 8 = 18\\n \\\\]\\n\\n2. Next, subtract 2 from the result:\\n \\\\[\\n 18 - 2 = 16\\n \\\\]\\n\\n3. Finally, add the remaining 8 to the result:\\n \\\\[...	e8f9d6da576987a0f9ad4e735715a675cb636b1e6359c3737005d2f84e0e931e	e47f6ad2fb6e83931a5c6e780c6c9c44cb122930e07b0fc80073a360594ffa5f	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 10 + 8 - 2 + 8 \\), we can break it down into simpler steps:\n\n1. First, add 10 and 8:\n \\[\n 10 + 8 = 18\n \\]\n\n2. Next, subtract 2 from the result:\n \\[\n 18 - 2 = 16\n \\]\n\n3. Finally, add the remaining 8 to the result:\n \\[\n 16 + 8 = 24\n \\]\n\nSo, the final an...	[{"budget_forced_chunks": ["To solve the problem \\( 10 + 8 - 2 + 8 \\), we can break it down into simpler steps:\n\n1. First, add 10 and 8:\n \\[\n 10 + 8 = 18\n \\]\n\n2. Next, subtract 2 from the result:\n \\[\n 18 - 2 = 16\n \\]\n\n3. Finally, add the remaining 8 to the result:\n \\[\n 16 + 8 = 24\n...	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 problem \\\\( 18 \\\\times 6 \\\\times 9 \\\\), we can break it down into simpler steps by first multiplying 18 by 6 and then multiplying the result by 9.\\n\\n1. Step 1: Multiply 18 by 6.\\n \\\\[\\n 18 \\\\times 6 = 108\\n \\\\]\\n\\n2. Step 2: Multiply the result by 9.\...	["{'generation': \"To solve the problem \\\\( 18 \\\\times 6 \\\\times 9 \\\\), we can break it down into simpler steps by first multiplying 18 by 6 and then multiplying the result by 9.\\n\\n1. Step 1: Multiply 18 by 6.\\n \\\\[\\n 18 \\\\times 6 = 108\\n \\\\]\\n\\n2. Step 2: Multiply the result by 9.\\...	d9866959919cc04a8c5fdc04301ce1d8f7a08914d45734f9db2a90cd577f5729	deb0fba45a8cb601a95fc271d175d8ba01be733fcd684e11ff3d617fd59cf7cb	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 18 \\times 6 \\times 9 \\), we can break it down into simpler steps by first multiplying 18 by 6 and then multiplying the result by 9.\n\n1. Step 1: Multiply 18 by 6.\n \\[\n 18 \\times 6 = 108\n \\]\n\n2. Step 2: Multiply the result by 9.\n \\[\n 108 \\times 9 = 972\n \\]...	[{"budget_forced_chunks": ["To solve the problem \\( 18 \\times 6 \\times 9 \\), we can break it down into simpler steps by first multiplying 18 by 6 and then multiplying the result by 9.\n\n1. Step 1: Multiply 18 by 6.\n \\[\n 18 \\times 6 = 108\n \\]\n\n2. Step 2: Multiply the result by 9.\n \\[\n 1...	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 problem using the numbers 18, 24, 23, and 7, we can break it down into simpler steps:\\n\\n1. First, let's multiply 24 by 23:\\n [24 * 23 = 552]\\n\\n2. Now, we need to multiply 7 by the result from step 1:\\n [7 * 552]\\n\\n3. Let's do the multiplication:\\n [7 * 552 = 3864]\\n\\...	["{'generation': \"To solve the problem using the numbers 18, 24, 23, and 7, we can break it down into simpler steps:\\n\\n1. First, let's multiply 24 by 23:\\n [24 * 23 = 552]\\n\\n2. Now, we need to multiply 7 by the result from step 1:\\n [7 * 552]\\n\\n3. Let's do the multiplication:\\n [7 * 552 = 3864]\\n\\n...	25ddf3f8a07e523e1d9a482834dcac9fcaaebbac9dc38427e65a040a73467cd9	660761dff690d0d86c98fbbb63a3514001fc3380534e701bd7dbfc911373b943	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 18, 24, 23, and 7, we can break it down into simpler steps:\n\n1. First, let's multiply 24 by 23:\n [24 * 23 = 552]\n\n2. Now, we need to multiply 7 by the result from step 1:\n [7 * 552]\n\n3. Let's do the multiplication:\n [7 * 552 = 3864]\n\nSo, the final step is to mul...	[{"budget_forced_chunks": ["To solve the problem using the numbers 18, 24, 23, and 7, we can break it down into simpler steps:\n\n1. First, let's multiply 24 by 23:\n [24 * 23 = 552]\n\n2. Now, we need to multiply 7 by the result from step 1:\n [7 * 552]\n\n3. Let's do the multiplication:\n [7 * 552 = 3864]\n\nSo...	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 problem using the numbers 8, 19, 8, and 1, we can break it down into simpler steps:\\n\\n1. First, multiply 19 by 8:\\n \\\\[ 19 \\\\times 8 = 152 \\\\]\\n\\n2. Then, multiply the result by 1:\\n \\\\[ 152 \\\\times 1 = 152 \\\\]\\n\\n3. Finally, add the two results together:\\n \\...	["{'generation': 'To solve the problem using the numbers 8, 19, 8, and 1, we can break it down into simpler steps:\\n\\n1. First, multiply 19 by 8:\\n \\\\[ 19 \\\\times 8 = 152 \\\\]\\n\\n2. Then, multiply the result by 1:\\n \\\\[ 152 \\\\times 1 = 152 \\\\]\\n\\n3. Finally, add the two results together:\\n \\\...	1cd1ac367b8094381769d347eecffee28ecb19caa550d2df703e5cde7cd4becf	6bfcb228fc7047fd6a48a7db20c9b22405f716d78e11232a2351199c622a496b	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 8, 19, 8, and 1, we can break it down into simpler steps:\n\n1. First, multiply 19 by 8:\n \\[ 19 \\times 8 = 152 \\]\n\n2. Then, multiply the result by 1:\n \\[ 152 \\times 1 = 152 \\]\n\n3. Finally, add the two results together:\n \\[ 152 + 152 = 304 \\]\n\nSo, the equat...	[{"budget_forced_chunks": ["To solve the problem using the numbers 8, 19, 8, and 1, we can break it down into simpler steps:\n\n1. First, multiply 19 by 8:\n \\[ 19 \\times 8 = 152 \\]\n\n2. Then, multiply the result by 1:\n \\[ 152 \\times 1 = 152 \\]\n\n3. Finally, add the two results together:\n \\[ 152 + 152 ...	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 problem using the numbers 2, 8, 3, and 2, we can break it down into simpler steps:\\n\\n1. First, let's multiply 2 and 3: \\n \\\\[ 2 \\\\times 3 = 6 \\\\]\\n\\n2. Next, we'll add 2 to the result:\\n \\\\[ 6 + 2 = 8 \\\\]\\n\\n3. Finally, we'll multiply the two results together:\\n ...	["{'generation': \"To solve the problem using the numbers 2, 8, 3, and 2, we can break it down into simpler steps:\\n\\n1. First, let's multiply 2 and 3: \\n \\\\[ 2 \\\\times 3 = 6 \\\\]\\n\\n2. Next, we'll add 2 to the result:\\n \\\\[ 6 + 2 = 8 \\\\]\\n\\n3. Finally, we'll multiply the two results together:\\n ...	60dc4901c356bcb56bba8d524e1d45208b1b9d878f2ef89d3af8dfd467b2a7df	1321f842cb74d6de4fc8454a45b42fec7481a7e861fdb5b5ca907b30d14ffda3	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 2, 8, 3, and 2, we can break it down into simpler steps:\n\n1. First, let's multiply 2 and 3: \n \\[ 2 \\times 3 = 6 \\]\n\n2. Next, we'll add 2 to the result:\n \\[ 6 + 2 = 8 \\]\n\n3. Finally, we'll multiply the two results together:\n \\[ 8 \\times 8 = 64 \\]\n\nSo, the...	[{"budget_forced_chunks": ["To solve the problem using the numbers 2, 8, 3, and 2, we can break it down into simpler steps:\n\n1. First, let's multiply 2 and 3: \n \\[ 2 \\times 3 = 6 \\]\n\n2. Next, we'll add 2 to the result:\n \\[ 6 + 2 = 8 \\]\n\n3. Finally, we'll multiply the two results together:\n \\[ 8 \\t...	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 problem using the numbers 7, 18, 5, and 24, we can break it down into simpler steps:\\n\\n1. First, multiply 18 by 5:\\n \\\\[ 18 * 5 = 90 \\\\]\\n\\n2. Next, multiply the result by 2 (as given in the problem)):\\n \\\\[ 90 * 2 = 180 \\\\]\\n\\n3. Finally, add the two results togeth...	["{'generation': \"To solve the problem using the numbers 7, 18, 5, and 24, we can break it down into simpler steps:\\n\\n1. First, multiply 18 by 5:\\n \\\\[ 18 * 5 = 90 \\\\]\\n\\n2. Next, multiply the result by 2 (as given in the problem)):\\n \\\\[ 90 * 2 = 180 \\\\]\\n\\n3. Finally, add the two results togethe...	06cca78287b0d4bbe85792545a31e52e50410de869f5164f38c7f45cfaec36c0	29d339d1a73cab0b263042199e1b89def0f3593d74ca75cb8f89346bce8efeca	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 7, 18, 5, and 24, we can break it down into simpler steps:\n\n1. First, multiply 18 by 5:\n \\[ 18 * 5 = 90 \\]\n\n2. Next, multiply the result by 2 (as given in the problem)):\n \\[ 90 * 2 = 180 \\]\n\n3. Finally, add the two results together:\n \\[ 360 + 180 = 540 \\]\n\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 7, 18, 5, and 24, we can break it down into simpler steps:\n\n1. First, multiply 18 by 5:\n \\[ 18 * 5 = 90 \\]\n\n2. Next, multiply the result by 2 (as given in the problem)):\n \\[ 90 * 2 = 180 \\]\n\n3. Finally, add the two results together:\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 problem \\\\( 14 + 15 + 24 = 25 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Break down the numbers\\n - 14 can be written as 10 + 4\\n - 15 can be written as 10 + 5\\n - 24 can be written as 20 + 4\\n\\n2. Step 2: Add the numbers\\n - First, add the h...	["{'generation': \"To solve the problem \\\\( 14 + 15 + 24 = 25 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Break down the numbers\\n - 14 can be written as 10 + 4\\n - 15 can be written as 10 + 5\\n - 24 can be written as 20 + 4\\n\\n2. Step 2: Add the numbers\\n - First, add the ho...	1955abb6fb8a09c76c5348e083bbebb0a33332ecf20a36bb471cd1d8f35b73a1	b8a8b41d18a1eb8b0faef834e0879fe35579560714765ba93d86fd34739a4fc7	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 14 + 15 + 24 = 25 \\), we can break it down into simpler steps:\n\n1. Step 1: Break down the numbers\n - 14 can be written as 10 + 4\n - 15 can be written as 10 + 5\n - 24 can be written as 20 + 4\n\n2. Step 2: Add the numbers\n - First, add the hourglass shapes: \\( 10 + 5 = ...	[{"budget_forced_chunks": ["To solve the problem \\( 14 + 15 + 24 = 25 \\), we can break it down into simpler steps:\n\n1. Step 1: Break down the numbers\n - 14 can be written as 10 + 4\n - 15 can be written as 10 + 5\n - 24 can be written as 20 + 4\n\n2. Step 2: Add the numbers\n - First, add the hourg...	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 problem using the numbers 5, 14, 6, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 14 by 6:\\n \\\\[ 14 \\\\times 6 = 84 \\\\]\\n\\n2. Next, multiply the result by 5:\\n \\\\[ 84 \\\\times 5 = 420 \\\\]\\n\\nSo, the final step to\u8fbe\u523011 is to multiply ...	["{'generation': 'To solve the problem using the numbers 5, 14, 6, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 14 by 6:\\n \\\\[ 14 \\\\times 6 = 84 \\\\]\\n\\n2. Next, multiply the result by 5:\\n \\\\[ 84 \\\\times 5 = 420 \\\\]\\n\\nSo, the final step to\u8fbe\u523011 is to multiply t...	082771250b668f5226cf3648d240e6c619be27b661df71e8f29ac9c0df5488f9	37185b44b5e1a9df65f24f8419874e6140b44c63509ae6a7873eb6b60f0cf67e	4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 5, 14, 6, and 9, we can break it down into simpler steps:\n\n1. First, multiply 14 by 6:\n \\[ 14 \\times 6 = 84 \\]\n\n2. Next, multiply the result by 5:\n \\[ 84 \\times 5 = 420 \\]\n\nSo, the final step to\u8fbe\u523011 is to multiply the second number (6) by the first nu...	[{"budget_forced_chunks": ["To solve the problem using the numbers 5, 14, 6, and 9, we can break it down into simpler steps:\n\n1. First, multiply 14 by 6:\n \\[ 14 \\times 6 = 84 \\]\n\n2. Next, multiply the result by 5:\n \\[ 84 \\times 5 = 420 \\]\n\nSo, the final step to\u8fbe\u523011 is to multiply the second ...	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 problem using the numbers 3, 8, 6, and 14, we can break it down into simpler steps:\\n\\n1. First, multiply 8 and 6:\\n \\\\[ 8 \\\\times 6 = 48 \\\\]\\n\\n2. Next, add the result to 14:\\n \\\\[ 48 + 14 = 62 \\\\]\\n\\n3. Finally, add the result to 3:\\n \\\\[ 62 + 3 = 65 \\\\]\\...	["{'generation': \"To solve the problem using the numbers 3, 8, 6, and 14, we can break it down into simpler steps:\\n\\n1. First, multiply 8 and 6:\\n \\\\[ 8 \\\\times 6 = 48 \\\\]\\n\\n2. Next, add the result to 14:\\n \\\\[ 48 + 14 = 62 \\\\]\\n\\n3. Finally, add the result to 3:\\n \\\\[ 62 + 3 = 65 \\\\]\\n...	8b9702914657f73013262b009fc3552edf08395b0dbe2e572bbc5cd37ecd3387	b75ad6172d90b6085ea5c6a2c9338e58019c6a42f9b71f4bd33140b7b0ca72d2	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 3, 8, 6, and 14, we can break it down into simpler steps:\n\n1. First, multiply 8 and 6:\n \\[ 8 \\times 6 = 48 \\]\n\n2. Next, add the result to 14:\n \\[ 48 + 14 = 62 \\]\n\n3. Finally, add the result to 3:\n \\[ 62 + 3 = 65 \\]\n\nSo, the equation that equals 24 is:\n\\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 3, 8, 6, and 14, we can break it down into simpler steps:\n\n1. First, multiply 8 and 6:\n \\[ 8 \\times 6 = 48 \\]\n\n2. Next, add the result to 14:\n \\[ 48 + 14 = 62 \\]\n\n3. Finally, add the result to 3:\n \\[ 62 + 3 = 65 \\]\n\nSo, the equat...	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 problem \\\\( 13 + 2 \\\\times 6 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 2 by 6: \\n \\\\[ 2 \\\\times 6 = 12 \\\\]\\n\\n2. Add the result to 13: \\n \\\\[ 13 + 12 = 25 \\\\]\\n\\nSo, the equation \\\\( 13 + 2 \\\\times 6 \\\\) equals 25.\\n\\n\\\\...	["{'generation': \"To solve the problem \\\\( 13 + 2 \\\\times 6 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 2 by 6: \\n \\\\[ 2 \\\\times 6 = 12 \\\\]\\n\\n2. Add the result to 13: \\n \\\\[ 13 + 12 = 25 \\\\]\\n\\nSo, the equation \\\\( 13 + 2 \\\\times 6 \\\\) equals 25.\\n\\n\\\\[...	cf4237b8a4d528b6996957344229c797765e97e4d292bb00152890f0273bfe5d	510813f610ad2885b641030188a8c8d20ca83a50ca2a36b5355b3d8af2089c8b	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 13 + 2 \\times 6 \\), we can break it down into simpler steps:\n\n1. Multiply 2 by 6: \n \\[ 2 \\times 6 = 12 \\]\n\n2. Add the result to 13: \n \\[ 13 + 12 = 25 \\]\n\nSo, the equation \\( 13 + 2 \\times 6 \\) equals 25.\n\n\\[\n\\boxed{25}\n\\] Wait, how? 2 times 6 is 12, and ...	[{"budget_forced_chunks": ["To solve the problem \\( 13 + 2 \\times 6 \\), we can break it down into simpler steps:\n\n1. Multiply 2 by 6: \n \\[ 2 \\times 6 = 12 \\]\n\n2. Add the result to 13: \n \\[ 13 + 12 = 25 \\]\n\nSo, the equation \\( 13 + 2 \\times 6 \\) equals 25.\n\n\\[\n\\boxed{25}\n\\]", " Wa...	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 \\\\( 13 \\\\times 9 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the numbers:\\n \\\\[\\n 13 \\\\times 9 = 13 \\\\times (10 - 1)\\n \\\\]\\n\\n2. Apply the distributive property:...	["{'generation': \"To solve the problem \\\\( 13 \\\\times 9 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the numbers:\\n \\\\[\\n 13 \\\\times 9 = 13 \\\\times (10 - 1)\\n \\\\]\\n\\n2. Apply the distributive property:\...	f69cf0b77fe42a0d324ddf1ad2281a565cd8fe5a16a7ae869ce3b5af3648068e	da83e0c754606dd8653769cc1a82cbaae8fe676572547d75c872cdf58d56fc8f	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 13 \\times 9 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the numbers:\n \\[\n 13 \\times 9 = 13 \\times (10 - 1)\n \\]\n\n2. Apply the distributive property:\n \\[\n 13 \\times (10 - 1) = 13 \...	[{"budget_forced_chunks": ["To solve the problem \\( 13 \\times 9 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the numbers:\n \\[\n 13 \\times 9 = 13 \\times (10 - 1)\n \\]\n\n2. Apply the distributive property:\n \\[\n ...	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 problem \\\\( 16 \\\\times 5 + 7 - 10 \\\\), we can break it down into simpler steps:\\n\\n1. First Step: Multiply 16 by 5.\\n \\\\[\\n 16 \\\\times 5 = 80\\n \\\\]\\n\\n2. Second Step: Add 7 to the result from the first step.\\n \\\\[\\n 80 + 7 = 87\\n \\\\]\\n\\n3....	["{'generation': \"To solve the problem \\\\( 16 \\\\times 5 + 7 - 10 \\\\), we can break it down into simpler steps:\\n\\n1. First Step: Multiply 16 by 5.\\n \\\\[\\n 16 \\\\times 5 = 80\\n \\\\]\\n\\n2. Second Step: Add 7 to the result from the first step.\\n \\\\[\\n 80 + 7 = 87\\n \\\\]\\n\\n3. ...	88082144b6bbe5af4c5b843fb0153a69cb4ffa01356400441326b9aeb27e7341	799ad6928102e3f10f3aba9eecfd691709262a50e7812cb4adcfcdd97353a464	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 16 \\times 5 + 7 - 10 \\), we can break it down into simpler steps:\n\n1. First Step: Multiply 16 by 5.\n \\[\n 16 \\times 5 = 80\n \\]\n\n2. Second Step: Add 7 to the result from the first step.\n \\[\n 80 + 7 = 87\n \\]\n\n3. Third Step: Subtract 10 from the result o...	[{"budget_forced_chunks": ["To solve the problem \\( 16 \\times 5 + 7 - 10 \\), we can break it down into simpler steps:\n\n1. First Step: Multiply 16 by 5.\n \\[\n 16 \\times 5 = 80\n \\]\n\n2. Second Step: Add 7 to the result from the first step.\n \\[\n 80 + 7 = 87\n \\]\n\n3. Third Step: Sub...	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 problem \\\\( 19 + 24 - 18 + 2 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 19 + 24 = 43\\n \\\\]\\n\\n2. Subtract the third number from the result:\\n \\\\[\\n 43 - 18 = 25\\n \\\\]\\n\\n3. **Add the last number ...	["{'generation': \"To solve the problem \\\\( 19 + 24 - 18 + 2 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 19 + 24 = 43\\n \\\\]\\n\\n2. Subtract the third number from the result:\\n \\\\[\\n 43 - 18 = 25\\n \\\\]\\n\\n3. **Add the last number t...	63792ff69af699c4a79245246a3a0ca868fd10c8a39aac99e71d88802ba4d89e	c8b96c17d1cc42d3cdd0a3944a65fc5cdc3ce1607a49e7659cba77c65bc2a3a2	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 19 + 24 - 18 + 2 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 19 + 24 = 43\n \\]\n\n2. Subtract the third number from the result:\n \\[\n 43 - 18 = 25\n \\]\n\n3. Add the last number to the result:\n \\[\n 25 + 2 = 27\n...	[{"budget_forced_chunks": ["To solve the problem \\( 19 + 24 - 18 + 2 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 19 + 24 = 43\n \\]\n\n2. Subtract the third number from the result:\n \\[\n 43 - 18 = 25\n \\]\n\n3. Add the last number to the result:...	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 using the numbers 17, 6, 2, and 17, we can break it down into simpler steps:\\n\\n1. First, multiply 17 by 2:\\n \\\\[ 17 \\\\times 2 = 34 \\\\]\\n\\n2. Next, multiply the result by 6:\\n \\\\[ 34 \\\\times 6 = 204 \\\\]\\n\\n3. Finally, add the two results together:\\n \\...	["{'generation': \"To solve the problem using the numbers 17, 6, 2, and 17, we can break it down into simpler steps:\\n\\n1. First, multiply 17 by 2:\\n \\\\[ 17 \\\\times 2 = 34 \\\\]\\n\\n2. Next, multiply the result by 6:\\n \\\\[ 34 \\\\times 6 = 204 \\\\]\\n\\n3. Finally, add the two results together:\\n \\\...	3ebf9c654d2c23444bb49b95d6ffae3543f7edd3c874005aacb5efe0e8c72831	79627955b99d396c075d0879ad7a818d3b21c5d6a9f427e1405e67e23ac8e56e	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 17, 6, 2, and 17, we can break it down into simpler steps:\n\n1. First, multiply 17 by 2:\n \\[ 17 \\times 2 = 34 \\]\n\n2. Next, multiply the result by 6:\n \\[ 34 \\times 6 = 204 \\]\n\n3. Finally, add the two results together:\n \\[ 204 + 34 = 238 \\]\n\nSo, the equatio...	[{"budget_forced_chunks": ["To solve the problem using the numbers 17, 6, 2, and 17, we can break it down into simpler steps:\n\n1. First, multiply 17 by 2:\n \\[ 17 \\times 2 = 34 \\]\n\n2. Next, multiply the result by 6:\n \\[ 34 \\times 6 = 204 \\]\n\n3. Finally, add the two results together:\n \\[ 204 + 34 = ...	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 problem using the numbers 3, 20, 3, and 22, we can break it down into simpler steps:\\n\\n1. First, multiply 20 by 3:\\n \\\\[ 20 * 3 = 60 \\\\]\\n\\n2. Next, multiply the result by 3 again:\\n \\\\[ 60 * 3 = 180 \\\\]\\n\\n3. Finally, add the two results together:\\n \\\\[ 180 + ...	["{'generation': \"To solve the problem using the numbers 3, 20, 3, and 22, we can break it down into simpler steps:\\n\\n1. First, multiply 20 by 3:\\n \\\\[ 20 * 3 = 60 \\\\]\\n\\n2. Next, multiply the result by 3 again:\\n \\\\[ 60 * 3 = 180 \\\\]\\n\\n3. Finally, add the two results together:\\n \\\\[ 180 + 6...	27faf0638979afa1b175846661e17479d01ceedaf0bf10d7dbb70aeb3521ef97	3f6f94c431163cd8cc49822757d645f85470473d307da501df3e89c4e031cae9	6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 3, 20, 3, and 22, we can break it down into simpler steps:\n\n1. First, multiply 20 by 3:\n \\[ 20 * 3 = 60 \\]\n\n2. Next, multiply the result by 3 again:\n \\[ 60 * 3 = 180 \\]\n\n3. Finally, add the two results together:\n \\[ 180 + 60 = 240 \\]\n\nSo, the equation that...	[{"budget_forced_chunks": ["To solve the problem using the numbers 3, 20, 3, and 22, we can break it down into simpler steps:\n\n1. First, multiply 20 by 3:\n \\[ 20 * 3 = 60 \\]\n\n2. Next, multiply the result by 3 again:\n \\[ 60 * 3 = 180 \\]\n\n3. Finally, add the two results together:\n \\[ 180 + 60 = 240 \\...	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 \\\\( 11 + 8 - 9 + 13 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 11 + 8 = 19\\n \\\\]\\n\\n2. Subtract the second number from the result:\\n \\\\[\\n 19 - 9 = 10\\n \\\\]\\n\\n3. **Add the final number t...	["{'generation': \"To solve the problem \\\\( 11 + 8 - 9 + 13 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 11 + 8 = 19\\n \\\\]\\n\\n2. Subtract the second number from the result:\\n \\\\[\\n 19 - 9 = 10\\n \\\\]\\n\\n3. **Add the final number to...	0cc1376e685c64555564eb12e63d0398e53a881d7ddd1ee152d5e5ae43fa7702	21a660424e8cbb50098eb005a75591915839535032517b245dd5062f33d5ac1b	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 11 + 8 - 9 + 13 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 11 + 8 = 19\n \\]\n\n2. Subtract the second number from the result:\n \\[\n 19 - 9 = 10\n \\]\n\n3. Add the final number to the result:\n \\[\n 10 + 13 = 23\n...	[{"budget_forced_chunks": ["To solve the problem \\( 11 + 8 - 9 + 13 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 11 + 8 = 19\n \\]\n\n2. Subtract the second number from the result:\n \\[\n 19 - 9 = 10\n \\]\n\n3. Add the final number to the result:\...	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 problem \\\\( 14 \\\\) using the numbers \\\\( 3, 18, 7, 17 \\\\) and basic arithmetic operations, we can break it down into simpler steps.\\n\\n1. Break down the numbers:\\n - \\\\( 18 \\\\) can be written as \\\\( 10 + 8 \\\\).\\n - \\\\( 7 \\\\) can be written as \\\\( 7 \\\\...	["{'generation': \"To solve the problem \\\\( 14 \\\\) using the numbers \\\\( 3, 18, 7, 17 \\\\) and basic arithmetic operations, we can break it down into simpler steps.\\n\\n1. Break down the numbers:\\n - \\\\( 18 \\\\) can be written as \\\\( 10 + 8 \\\\).\\n - \\\\( 7 \\\\) can be written as \\\\( 7 \\\\t...	0bff8a88f392bdea9bf78037fd9345e9a360c73183f41fac27009acbfcf45a45	284464ca2a666cb6ff9513a61057ef6b38f08efea9d5d1e57272daf5b514b30d	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 14 \\) using the numbers \\( 3, 18, 7, 17 \\) and basic arithmetic operations, we can break it down into simpler steps.\n\n1. Break down the numbers:\n - \\( 18 \\) can be written as \\( 10 + 8 \\).\n - \\( 7 \\) can be written as \\( 7 \\times 1 \\).\n - \\( 17 \\) can be written a...	[{"budget_forced_chunks": ["To solve the problem \\( 14 \\) using the numbers \\( 3, 18, 7, 17 \\) and basic arithmetic operations, we can break it down into simpler steps.\n\n1. Break down the numbers:\n - \\( 18 \\) can be written as \\( 10 + 8 \\).\n - \\( 7 \\) can be written as \\( 7 \\times 1 \\).\n - \...	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 problem using the numbers 6, 15, and 18, we can follow these steps:\\n\\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 18 in this case.\\n\\n2. **Construct the equation...	["{'generation': \"To solve the problem using the numbers 6, 15, and 18, we can follow these steps:\\n\\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 18 in this case.\\n\\n2. *Construct the equation...	dd4b144645f3044ade5370b84d2c8ffc297f7221b9b007340f14cfbc65e21d08	66bdbb1dbf3161fa4bd295ada53f214a78964d34cbac8721fc230f654dd84eb9	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 6, 15, and 18, we can follow these steps:\n\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 18 in this case.\n\n2. Construct the equation:\n - First, multi...	[{"budget_forced_chunks": ["To solve the problem using the numbers 6, 15, and 18, we can follow these steps:\n\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 18 in this case.\n\n2. **Construct the equa...	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 + 17 - 1 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the addition and subtraction:\\n \\\\[\\n 21 + 17 = 38\\n \\\\]\\n \\\\[\\n 38 - 1 = 37\\n \\\\]\\n \\\\[\\n 37 + 22 = 59\\n \\\\]\\n\\n2. **Verify the calculation by usi...	["{'generation': \"To solve the problem \\\\( 21 + 17 - 1 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the addition and subtraction:\\n \\\\[\\n 21 + 17 = 38\\n \\\\]\\n \\\\[\\n 38 - 1 = 37\\n \\\\]\\n \\\\[\\n 37 + 22 = 59\\n \\\\]\\n\\n2. **Verify the calculation by usin...	386f2658d165d4865e961a1c33162044ca2347736a789c08f0ef045ee45694e2	b67f903481c0c503505a89ffb5d2efc0440dab837c0f5b94fc16cd0f93e5e719	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 21 + 17 - 1 + 22 \\), we can break it down into simpler steps:\n\n1. Combine the addition and subtraction:\n \\[\n 21 + 17 = 38\n \\]\n \\[\n 38 - 1 = 37\n \\]\n \\[\n 37 + 22 = 59\n \\]\n\n2. Verify the calculation by using the\u9006\u6ce2\u5170\u5f0f (postfix):\n ...	[{"budget_forced_chunks": ["To solve the problem \\( 21 + 17 - 1 + 22 \\), we can break it down into simpler steps:\n\n1. Combine the addition and subtraction:\n \\[\n 21 + 17 = 38\n \\]\n \\[\n 38 - 1 = 37\n \\]\n \\[\n 37 + 22 = 59\n \\]\n\n2. **Verify the calculation by using the\u9006\u6ce2\u5...	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 problem \\\\( 7 \\\\times 23 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n We can express 23 as \\\\( 20 + 3 \\\\).\\n\\n2. Multiply step-by-step:\\n - First, multiply 7 by 3...	["{'generation': \"To solve the problem \\\\( 7 \\\\times 23 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n We can express 23 as \\\\( 20 + 3 \\\\).\\n\\n2. Multiply step-by-step:\\n - First, multiply 7 by 3:...	11d4963569c689aaad5d7281b004c6802e6924ca6310338820f9a7a845258c03	cd94a9feffddb511cf4bb21a2989fbef048bfdac8f9ca47a4ddea52ecdff72f0	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 7 \\times 23 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n We can express 23 as \\( 20 + 3 \\).\n\n2. Multiply step-by-step:\n - First, multiply 7 by 3:\n \\[\n 7 \\times 3 = 21...	[{"budget_forced_chunks": ["To solve the problem \\( 7 \\times 23 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n We can express 23 as \\( 20 + 3 \\).\n\n2. Multiply step-by-step:\n - First, multiply 7 by 3:\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 problem using the numbers 9, 17, 16, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 9:\\n \\\\[ 16 \\\\times 9 = 144 \\\\]\\n\\n2. Next, multiply 17 by 9:\\n \\\\[ 17 \\\\times 9 = 153 \\\\]\\n\\n3. Now, add the results from the two multiplications:\\n...	["{'generation': \"To solve the problem using the numbers 9, 17, 16, and 9, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 9:\\n \\\\[ 16 \\\\times 9 = 144 \\\\]\\n\\n2. Next, multiply 17 by 9:\\n \\\\[ 17 \\\\times 9 = 153 \\\\]\\n\\n3. Now, add the results from the two multiplications:\\n ...	e2307676ba5945f3e2c373ae638ce1fbf09fef1f24485b95b0b9dae44c1099fb	1b4da6d5e75ebf799898cd96ebd7861935499bc7b18b914f13cc209f4ed6b549	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 9, 17, 16, and 9, we can break it down into simpler steps:\n\n1. First, multiply 16 by 9:\n \\[ 16 \\times 9 = 144 \\]\n\n2. Next, multiply 17 by 9:\n \\[ 17 \\times 9 = 153 \\]\n\n3. Now, add the results from the two multiplications:\n \\[ 144 + 153 = 297 \\]\n\nSo, the e...	[{"budget_forced_chunks": ["To solve the problem using the numbers 9, 17, 16, and 9, we can break it down into simpler steps:\n\n1. First, multiply 16 by 9:\n \\[ 16 \\times 9 = 144 \\]\n\n2. Next, multiply 17 by 9:\n \\[ 17 \\times 9 = 153 \\]\n\n3. Now, add the results from the two multiplications:\n \\[ 144 + ...	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 problem \\\\( 9 + 6 - 24 + 15 \\\\), we can break it down into simpler steps by first performing the multiplication and then the addition and subtraction.\\n\\n1. Multiply 24 by 15:\\n \\\\[\\n 24 \\\\times 15 = 360\\n \\\\]\\n\\n2. Multiply 9 by 15:\\n \\\\[\\n 9 \\\\...	["{'generation': \"To solve the problem \\\\( 9 + 6 - 24 + 15 \\\\), we can break it down into simpler steps by first performing the multiplication and then the addition and subtraction.\\n\\n1. Multiply 24 by 15:\\n \\\\[\\n 24 \\\\times 15 = 360\\n \\\\]\\n\\n2. Multiply 9 by 15:\\n \\\\[\\n 9 \\\\t...	055f38773f98fc1fe93514b433eb50b05677ceaa346ad81e22d44389b2c69218	d557d1a3780d56b3ad6c44c18a367bdb95da8e17c3271d31bd3c4625235d047c	4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 9 + 6 - 24 + 15 \\), we can break it down into simpler steps by first performing the multiplication and then the addition and subtraction.\n\n1. Multiply 24 by 15:\n \\[\n 24 \\times 15 = 360\n \\]\n\n2. Multiply 9 by 15:\n \\[\n 9 \\times 15 = 135\n \\]\n\n3. **Multiply 9...	[{"budget_forced_chunks": ["To solve the problem \\( 9 + 6 - 24 + 15 \\), we can break it down into simpler steps by first performing the multiplication and then the addition and subtraction.\n\n1. Multiply 24 by 15:\n \\[\n 24 \\times 15 = 360\n \\]\n\n2. Multiply 9 by 15:\n \\[\n 9 \\times 15 = 135\...	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 \\\\( 12 + 19 - 18 + 5 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 12 + 19 = 31\\n \\\\]\\n\\n2. Subtract the third number from the result:\\n \\\\[\\n 31 - 18 = 13\\n \\\\]\\n\\n3. **Add the final number...	["{'generation': \"To solve the problem \\\\( 12 + 19 - 18 + 5 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 12 + 19 = 31\\n \\\\]\\n\\n2. Subtract the third number from the result:\\n \\\\[\\n 31 - 18 = 13\\n \\\\]\\n\\n3. **Add the final number ...	1e02d758f3506e31de59f006d92bf7c85dab20b9e23beaf41677a15949d9d257	f793bdad9ecf5e858a215f47764758b771996046772c2ab09c13997ff97fb08f	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 12 + 19 - 18 + 5 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 12 + 19 = 31\n \\]\n\n2. Subtract the third number from the result:\n \\[\n 31 - 18 = 13\n \\]\n\n3. Add the final number to the result:\n \\[\n 13 + 5 = 18\...	[{"budget_forced_chunks": ["To solve the problem \\( 12 + 19 - 18 + 5 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 12 + 19 = 31\n \\]\n\n2. Subtract the third number from the result:\n \\[\n 31 - 18 = 13\n \\]\n\n3. *Add the final number to the result:...	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 problem using the numbers 8, 6, 6, and 14, we can break it down into simpler steps:\\n\\n1. First, multiply 6 and 6:\\n [6 * 6 = 36]\\n\\n2. Now, multiply the result by 14:\\n [36 * 14 = 504]\\n\\n3. Finally, add the two results together:\\n [504 + 36 = 540]\\n\\nSo, the equation ...	["{'generation': \"To solve the problem using the numbers 8, 6, 6, and 14, we can break it down into simpler steps:\\n\\n1. First, multiply 6 and 6:\\n [6 * 6 = 36]\\n\\n2. Now, multiply the result by 14:\\n [36 * 14 = 504]\\n\\n3. Finally, add the two results together:\\n [504 + 36 = 540]\\n\\nSo, the equation t...	2282af28b6f6534d090ed13558649edf72ec5e7d388ee194c9d515d532857337	ad151f6b94c236a705e099c3417b7c3decac063fdfea02b5158df46c0a2579bc	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 8, 6, 6, and 14, we can break it down into simpler steps:\n\n1. First, multiply 6 and 6:\n [6 * 6 = 36]\n\n2. Now, multiply the result by 14:\n [36 * 14 = 504]\n\n3. Finally, add the two results together:\n [504 + 36 = 540]\n\nSo, the equation that equals 23 is:\n[14 * 6 *...	[{"budget_forced_chunks": ["To solve the problem using the numbers 8, 6, 6, and 14, we can break it down into simpler steps:\n\n1. First, multiply 6 and 6:\n [6 * 6 = 36]\n\n2. Now, multiply the result by 14:\n [36 * 14 = 504]\n\n3. Finally, add the two results together:\n [504 + 36 = 540]\n\nSo, the equation tha...	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 problem \\\\( 8 \\\\times 9 \\\\times 6 \\\\times 23 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition:\\n\\n1. Break it into simpler multiplications:\\n \\\\[\\n 8 \\\\times 9 = 72\\n \\\\]\\n \\\\[\\n 6 \\\\t...	["{'generation': 'To solve the problem \\\\( 8 \\\\times 9 \\\\times 6 \\\\times 23 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition:\\n\\n1. Break it into simpler multiplications:\\n \\\\[\\n 8 \\\\times 9 = 72\\n \\\\]\\n \\\\[\\n 6 \\\\ti...	42ba5c03d722b5c353664340bb3fdd03fef285a1d746be67dc6080b64f3ed1f2	6010e5495bfc0eb1aaa69f8d33dafba7002318874f2f8993a899f6c2175341be	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 8 \\times 9 \\times 6 \\times 23 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition:\n\n1. Break it into simpler multiplications:\n \\[\n 8 \\times 9 = 72\n \\]\n \\[\n 6 \\times 23 = 138\n \\]\n\n2. **Add the result...	[{"budget_forced_chunks": ["To solve the problem \\( 8 \\times 9 \\times 6 \\times 23 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition:\n\n1. Break it into simpler multiplications:\n \\[\n 8 \\times 9 = 72\n \\]\n \\[\n 6 \\times 23 = 138\n ...	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 \\\\( 15 + 12 + 10 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. First, add 15 and 10:\\n \\\\[\\n 15 + 10 = 25\\n \\\\]\\n\\n2. Next, add the result to 12:\\n \\\\[\\n 25 + 12 = 37\\n \\\\]\\n\\n3. Finally, simplify the expression \\\\( 25 + 10 \\\\) ...	["{'generation': \"To solve the problem \\\\( 15 + 12 + 10 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. First, add 15 and 10:\\n \\\\[\\n 15 + 10 = 25\\n \\\\]\\n\\n2. Next, add the result to 12:\\n \\\\[\\n 25 + 12 = 37\\n \\\\]\\n\\n3. Finally, simplify the expression \\\\( 25 + 10 \\\\) t...	05f0d33714099cc656acf8c8eb68719411b73df92d0a070b3dc097d1897fa282	9182372ee604d8332a7f3e9623e2461b466d8b780a7500a2dd61955e54796104	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 15 + 12 + 10 = 13 \\), we can break it down into simpler steps:\n\n1. First, add 15 and 10:\n \\[\n 15 + 10 = 25\n \\]\n\n2. Next, add the result to 12:\n \\[\n 25 + 12 = 37\n \\]\n\n3. Finally, simplify the expression \\( 25 + 10 \\) to get:\n \\[\n 25 + 10 = 37\n \\]\n\nSo...	[{"budget_forced_chunks": ["To solve the problem \\( 15 + 12 + 10 = 13 \\), we can break it down into simpler steps:\n\n1. First, add 15 and 10:\n \\[\n 15 + 10 = 25\n \\]\n\n2. Next, add the result to 12:\n \\[\n 25 + 12 = 37\n \\]\n\n3. Finally, simplify the expression \\( 25 + 10 \\) to get:\n \\[\n ...	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 \\\\times 4 \\\\times 20 \\\\), we can break it down into simpler steps:\\n\\n1. First Step: Multiply 2 by 4:\\n \\\\[\\n 2 \\\\times 4 = 8\\n \\\\]\\n\\n2. Second Step: Multiply the result by 20:\\n \\\\[\\n 8 \\\\times 20 = 160\\n \\\\]\\n\\n3. ...	["{'generation': \"To solve the problem \\\\( 9 + 2 \\\\times 4 \\\\times 20 \\\\), we can break it down into simpler steps:\\n\\n1. First Step: Multiply 2 by 4:\\n \\\\[\\n 2 \\\\times 4 = 8\\n \\\\]\\n\\n2. Second Step: Multiply the result by 20:\\n \\\\[\\n 8 \\\\times 20 = 160\\n \\\\]\\n\\n3. *...	0315f9a1c2b6e1bfbf8a8edbef44189839e111a96f251ea8c1e4116c60fd5cee	e9cafd581fb89d08a111dd7726405d183419160dd52f6dd12be72064f6226e87	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 9 + 2 \\times 4 \\times 20 \\), we can break it down into simpler steps:\n\n1. First Step: Multiply 2 by 4:\n \\[\n 2 \\times 4 = 8\n \\]\n\n2. Second Step: Multiply the result by 20:\n \\[\n 8 \\times 20 = 160\n \\]\n\n3. Third Step: Add the result from the second ste...	[{"budget_forced_chunks": ["To solve the problem \\( 9 + 2 \\times 4 \\times 20 \\), we can break it down into simpler steps:\n\n1. First Step: Multiply 2 by 4:\n \\[\n 2 \\times 4 = 8\n \\]\n\n2. Second Step: Multiply the result by 20:\n \\[\n 8 \\times 20 = 160\n \\]\n\n3. Third Step: Add the ...	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 problem \\\\( 11 + 14 + 20 = 23 \\\\), we can break it down into simpler steps:\\n\\n1. Add 11 and 14:\\n \\\\[\\n 11 + 14 = 25\\n \\\\]\\n\\n2. Add the result to 20:\\n \\\\[\\n 25 + 20 = 45\\n \\\\]\\n\\nSo, the final step is to add 11 and 14, which equals 25, and t...	["{'generation': 'To solve the problem \\\\( 11 + 14 + 20 = 23 \\\\), we can break it down into simpler steps:\\n\\n1. Add 11 and 14:\\n \\\\[\\n 11 + 14 = 25\\n \\\\]\\n\\n2. Add the result to 20:\\n \\\\[\\n 25 + 20 = 45\\n \\\\]\\n\\nSo, the final step is to add 11 and 14, which equals 25, and th...	e7235818189cee9d7974085c723f8c0c6789bf34cec743ad9090eeb5a74018c5	2a9d2117ec015b63c5be448e3dbe6c88b99d39f86ca94ccadf2e18578a6d5348	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 11 + 14 + 20 = 23 \\), we can break it down into simpler steps:\n\n1. Add 11 and 14:\n \\[\n 11 + 14 = 25\n \\]\n\n2. Add the result to 20:\n \\[\n 25 + 20 = 45\n \\]\n\nSo, the final step is to add 11 and 14, which equals 25, and then add 20 to the result, which equals 45...	[{"budget_forced_chunks": ["To solve the problem \\( 11 + 14 + 20 = 23 \\), we can break it down into simpler steps:\n\n1. Add 11 and 14:\n \\[\n 11 + 14 = 25\n \\]\n\n2. Add the result to 20:\n \\[\n 25 + 20 = 45\n \\]\n\nSo, the final step is to add 11 and 14, which equals 25, and then add 20 to t...	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 + 1 \\\\), we can break it down into simpler steps:\\n\\n1. Add 14 and 1:\\n \\\\[\\n 14 + 1 = 15\\n \\\\]\\n\\n2. Identify the operations:\\n The primary operation here is addition.\\n\\n3. present the solution:\\n \\\\[\\n 14 + 1 = 15\\n \\\...	["{'generation': \"To solve the problem \\\\( 14 + 1 \\\\), we can break it down into simpler steps:\\n\\n1. Add 14 and 1:\\n \\\\[\\n 14 + 1 = 15\\n \\\\]\\n\\n2. Identify the operations:\\n The primary operation here is addition.\\n\\n3. present the solution:\\n \\\\[\\n 14 + 1 = 15\\n \\\\...	28e1ffdd0700740151dde731e2bc7f7be8ed38e3f23333aa4e32bdaf61e5c613	690588146313ddc71ac5b6291a01a87d0b2a32176a8c9a537f84786c08a82d55	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 14 + 1 \\), we can break it down into simpler steps:\n\n1. Add 14 and 1:\n \\[\n 14 + 1 = 15\n \\]\n\n2. Identify the operations:\n The primary operation here is addition.\n\n3. present the solution:\n \\[\n 14 + 1 = 15\n \\]\n\nThus, the final answer is \\boxed{15}...	[{"budget_forced_chunks": ["To solve the problem \\( 14 + 1 \\), we can break it down into simpler steps:\n\n1. Add 14 and 1:\n \\[\n 14 + 1 = 15\n \\]\n\n2. Identify the operations:\n The primary operation here is addition.\n\n3. present the solution:\n \\[\n 14 + 1 = 15\n \\]\n\nThus, the f...	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 problem \\\\( 22 \\\\times 4 \\\\times 24 \\\\times 10 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the result by the third number.\\n\\n### Step 1: Multiply 22 and 4\\n\\\\[ 22 \\\\times 4 \\\\]\\n\\nWe can simplify this mul...	["{'generation': 'To solve the problem \\\\( 22 \\\\times 4 \\\\times 24 \\\\times 10 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the result by the third number.\\n\\n### Step 1: Multiply 22 and 4\\n\\\\[ 22 \\\\times 4 \\\\]\\n\\nWe can simplify this mult...	f3ddb34578e5f09132211961a1dd13853a41d2af86f1ac3cd4b520c9ccb55208	57ea06bd045d0c6c2eabfc9b26bc35cee2eb052a39546f25cd77f7c587a22742	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 22 \\times 4 \\times 24 \\times 10 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the result by the third number.\n\n### Step 1: Multiply 22 and 4\n\\[ 22 \\times 4 \\]\n\nWe can simplify this multiplication:\n\\[ 22 \\times 4 = (20 +...	[{"budget_forced_chunks": ["To solve the problem \\( 22 \\times 4 \\times 24 \\times 10 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the result by the third number.\n\n### Step 1: Multiply 22 and 4\n\\[ 22 \\times 4 \\]\n\nWe can simplify this multiplication:...	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 problem \\\\( 7 \\\\times 14 \\\\times 22 \\\\times 13 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\nFirst, let's group the numbers in a way that makes sense:\\n\\\\[ 7 \\\\times 14 \\\\times 22 \\\\times 13 = (7 ...	["{'generation': \"To solve the problem \\\\( 7 \\\\times 14 \\\\times 22 \\\\times 13 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\nFirst, let's group the numbers in a way that makes sense:\\n\\\\[ 7 \\\\times 14 \\\\times 22 \\\\times 13 = (7 \...	d4148b73faad89dbbacfe944ac9870b26bc7780bfe26b5b6cc5809cc5575df84	ef8dc21e0133a2b6e6a1e76ca7547457a5f356117bdb5c02d1d1b0f3e2d30c9a	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 7 \\times 14 \\times 22 \\times 13 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's group the numbers in a way that makes sense:\n\\[ 7 \\times 14 \\times 22 \\times 13 = (7 \\times 14) \\times (22 \\times 13) \\]...	[{"budget_forced_chunks": ["To solve the problem \\( 7 \\times 14 \\times 22 \\times 13 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's group the numbers in a way that makes sense:\n\\[ 7 \\times 14 \\times 22 \\times 13 = (7 \\times 14) \...	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 problem \\\\( 10 + 13 - 18 + 1 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 10 + 13 = 23\\n \\\\]\\n\\n2. Subtract the next number from the result:\\n \\\\[\\n 23 - 18 = 5\\n \\\\]\\n\\n3. **Add the final number t...	["{'generation': \"To solve the problem \\\\( 10 + 13 - 18 + 1 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 10 + 13 = 23\\n \\\\]\\n\\n2. Subtract the next number from the result:\\n \\\\[\\n 23 - 18 = 5\\n \\\\]\\n\\n3. **Add the final number to...	f31d25479cb0879c1e473db5654734110af6012c3dec6787a432841c1e9f5e14	c56e96674fbf187c3876e536b5237e294f4469f36773c316a0e604a3e5091630	e629fa6598d732768f7c726b4b621285f9c3b85303900aa912017db7617d8bdb	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 10 + 13 - 18 + 1 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 10 + 13 = 23\n \\]\n\n2. Subtract the next number from the result:\n \\[\n 23 - 18 = 5\n \\]\n\n3. Add the final number to the result:\n \\[\n 5 + 1 = 6\n ...	[{"budget_forced_chunks": ["To solve the problem \\( 10 + 13 - 18 + 1 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 10 + 13 = 23\n \\]\n\n2. Subtract the next number from the result:\n \\[\n 23 - 18 = 5\n \\]\n\n3. Add the final number to the result:\...	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:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 10 + 17 = 27\\n \\\\]\\n\\n2. Subtract the next number from the result:\\n \\\\[\\n 27 - 22 = 5\\n \\\\]\\n\\n3. **Add the final number t...	["{'generation': 'To solve the problem \\\\( 10 + 17 - 22 + 21 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 10 + 17 = 27\\n \\\\]\\n\\n2. Subtract the next number from the result:\\n \\\\[\\n 27 - 22 = 5\\n \\\\]\\n\\n3. **Add the final number to...	ec4723d791e04df97fc68140b01e5c04f54ca9d2222922ec78e3489918e89a8d	9e01c4026ea50c024f81b0b26b4133645ef725dd9cc13cf176c1e650623b1007	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 10 + 17 - 22 + 21 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 10 + 17 = 27\n \\]\n\n2. Subtract the next number from the result:\n \\[\n 27 - 22 = 5\n \\]\n\n3. Add the final number to the result:\n \\[\n 5 + 21 = 26\n...	[{"budget_forced_chunks": ["To solve the problem \\( 10 + 17 - 22 + 21 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 10 + 17 = 27\n \\]\n\n2. Subtract the next number from the result:\n \\[\n 27 - 22 = 5\n \\]\n\n3. Add the final number to the result:...	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 problem using the numbers 23, 23, 13, and 16, we can break it down into simpler steps:\\n\\n1. First, multiply 13 and 16:\\n 13 * 16 = 208\\n\\n2. Now, we need to add 23 to the result of the previous step:\\n 208 + 23 = 231\\n\\nSo, the final answer is 231. But I need to verify this...	["{'generation': \"To solve the problem using the numbers 23, 23, 13, and 16, we can break it down into simpler steps:\\n\\n1. First, multiply 13 and 16:\\n 13 * 16 = 208\\n\\n2. Now, we need to add 23 to the result of the previous step:\\n 208 + 23 = 231\\n\\nSo, the final answer is 231. But I need to verify this....	8e5566982343c0690d90c6bac61b52d7dfb907ee9c94df525e5757c4c97c4262	db237d201578701780659ed1aef2b60d06c349d2cd605d35b9c43e344346a198	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 23, 23, 13, and 16, we can break it down into simpler steps:\n\n1. First, multiply 13 and 16:\n 13 * 16 = 208\n\n2. Now, we need to add 23 to the result of the previous step:\n 208 + 23 = 231\n\nSo, the final answer is 231. But I need to verify this. 231 - 23 * 2 = 231 - 46 ...	[{"budget_forced_chunks": ["To solve the problem using the numbers 23, 23, 13, and 16, we can break it down into simpler steps:\n\n1. First, multiply 13 and 16:\n 13 * 16 = 208\n\n2. Now, we need to add 23 to the result of the previous step:\n 208 + 23 = 231\n\nSo, the final answer is 231.", " But I need to verify ...	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 using the numbers 4, 14, 8, and 6, we can break it down into simpler steps:\\n\\n1. First, multiply 14 and 8:\\n \\\\[ 14 \\\\times 8 = 112 \\\\]\\n\\n2. Now, we need to multiply 6 by the result of the first step. Since 6 is less than 10, it's safest to add a zero at the end t...	["{'generation': \"To solve the problem using the numbers 4, 14, 8, and 6, we can break it down into simpler steps:\\n\\n1. First, multiply 14 and 8:\\n \\\\[ 14 \\\\times 8 = 112 \\\\]\\n\\n2. Now, we need to multiply 6 by the result of the first step. Since 6 is less than 10, it's safest to add a zero at the end to...	7aca7383c6015b2caa3691a0ea9a88ce61a224cc7fa4480f98bb178f67b3699a	abf814c17e6c9998a882dedeb9fefd5d9744207da8310ec3fe141485c9b0cece	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 4, 14, 8, and 6, we can break it down into simpler steps:\n\n1. First, multiply 14 and 8:\n \\[ 14 \\times 8 = 112 \\]\n\n2. Now, we need to multiply 6 by the result of the first step. Since 6 is less than 10, it's safest to add a zero at the end to ensure accurate multiplicat...	[{"budget_forced_chunks": ["To solve the problem using the numbers 4, 14, 8, and 6, we can break it down into simpler steps:\n\n1. First, multiply 14 and 8:\n \\[ 14 \\times 8 = 112 \\]\n\n2. Now, we need to multiply 6 by the result of the first step. Since 6 is less than 10, it's safest to add a zero at the end to e...	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 problem using the numbers 15, 22, and 17, we can follow these steps:\\n\\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 24 in this case.\\n\\n2. **Construct the equatio...	["{'generation': \"To solve the problem using the numbers 15, 22, and 17, we can follow these steps:\\n\\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 24 in this case.\\n\\n2. **Construct the equation...	47bac1a2342eda30692108659694e008e612521cbc54ffec54c8d5678789649a	370dcedf0dfcaeedd84655684cc6bd37cdacaa0a8e5c4038cfa6e6c882e61060	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 15, 22, and 17, we can follow these steps:\n\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 24 in this case.\n\n2. Construct the equation:\n - First, mult...	[{"budget_forced_chunks": ["To solve the problem using the numbers 15, 22, and 17, we can follow these steps:\n\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 24 in this case.\n\n2. **Construct the equ...	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 problem using the numbers 15, 20, 24, and 17, we can break it down into simpler steps:\\n\\n1. First, multiply 17 by 20:\\n [17 * 20 = 340]\\n\\n2. Next, multiply 15 by 24:\\n [15 * 24 = 360]\\n\\n3. Now, add the two results together:\\n [340 + 360 = 700]\\n\\nSo, the final answer ...	["{'generation': 'To solve the problem using the numbers 15, 20, 24, and 17, we can break it down into simpler steps:\\n\\n1. First, multiply 17 by 20:\\n [17 * 20 = 340]\\n\\n2. Next, multiply 15 by 24:\\n [15 * 24 = 360]\\n\\n3. Now, add the two results together:\\n [340 + 360 = 700]\\n\\nSo, the final answer i...	e4cb65e43bd8799efe66b31342b571b532d5932afb20b4d16854be908cddc019	d4c729d6184e5dc678411950de66cc83e11b46733769289afddd5ec13f2cf251	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 15, 20, 24, and 17, we can break it down into simpler steps:\n\n1. First, multiply 17 by 20:\n [17 * 20 = 340]\n\n2. Next, multiply 15 by 24:\n [15 * 24 = 360]\n\n3. Now, add the two results together:\n [340 + 360 = 700]\n\nSo, the final answer is 700.\n\n<final_answer> 70...	[{"budget_forced_chunks": ["To solve the problem using the numbers 15, 20, 24, and 17, we can break it down into simpler steps:\n\n1. First, multiply 17 by 20:\n [17 * 20 = 340]\n\n2. Next, multiply 15 by 24:\n [15 * 24 = 360]\n\n3. Now, add the two results together:\n [340 + 360 = 700]\n\nSo, the final answer is...	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 \\\\( 18 \\\\times 15 \\\\times 6 \\\\times 24 \\\\), we can break it down into simpler steps by first multiplying the numbers that are easier to handle:\\n\\n1. Multiply 18 and 6:\\n \\\\[\\n 18 \\\\times 6 = 108\\n \\\\]\\n\\n2. Multiply 18 and 24:\\n \\\\[\\n 18 \\\\...	["{'generation': 'To solve the problem \\\\( 18 \\\\times 15 \\\\times 6 \\\\times 24 \\\\), we can break it down into simpler steps by first multiplying the numbers that are easier to handle:\\n\\n1. Multiply 18 and 6:\\n \\\\[\\n 18 \\\\times 6 = 108\\n \\\\]\\n\\n2. Multiply 18 and 24:\\n \\\\[\\n 18 \\\\t...	0dfd5c9b6911ee38ebcccfadea25fddef45481b0c639fa3795b35370f5d06ab6	10ed909db1dc7a655b9955cfebb2c5726d50b43576625d7b2e9e724c8580d160	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 18 \\times 15 \\times 6 \\times 24 \\), we can break it down into simpler steps by first multiplying the numbers that are easier to handle:\n\n1. Multiply 18 and 6:\n \\[\n 18 \\times 6 = 108\n \\]\n\n2. Multiply 18 and 24:\n \\[\n 18 \\times 24 = 18 \\times (20 + 4) = (18 \\times 2...	[{"budget_forced_chunks": ["To solve the problem \\( 18 \\times 15 \\times 6 \\times 24 \\), we can break it down into simpler steps by first multiplying the numbers that are easier to handle:\n\n1. Multiply 18 and 6:\n \\[\n 18 \\times 6 = 108\n \\]\n\n2. Multiply 18 and 24:\n \\[\n 18 \\times 24 = 18 \\time...	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 problem \\\\( 17 \\\\times 16 \\\\times 21 \\\\times 8 \\\\) step by step, we can break it down into simpler multiplications, recognizing that some numbers can be factored or broken down further.\\n\\n### Step 1: Break down the numbers\\nWe can break down the numbers 17, 16, 21, and 8 i...	["{'generation': \"To solve the problem \\\\( 17 \\\\times 16 \\\\times 21 \\\\times 8 \\\\) step by step, we can break it down into simpler multiplications, recognizing that some numbers can be factored or broken down further.\\n\\n### Step 1: Break down the numbers\\nWe can break down the numbers 17, 16, 21, and 8 in...	a0bbf926e8f85501032b4b6c203376301dda401daa39981885d3c09c4387a5cd	1f6cc0a799203fca5c7ad993c753db7ebcc9bed4af86c541129c9788b48602c0	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 17 \\times 16 \\times 21 \\times 8 \\) step by step, we can break it down into simpler multiplications, recognizing that some numbers can be factored or broken down further.\n\n### Step 1: Break down the numbers\nWe can break down the numbers 17, 16, 21, and 8 into more manageable parts:\n- \...	[{"budget_forced_chunks": ["To solve the problem \\( 17 \\times 16 \\times 21 \\times 8 \\) step by step, we can break it down into simpler multiplications, recognizing that some numbers can be factored or broken down further.\n\n### Step 1: Break down the numbers\nWe can break down the numbers 17, 16, 21, and 8 into m...	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 problem \\\\( 8 \\\\times 13 \\\\times 23 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n \\\\[\\n 8 = 10 - 2\\n \\\\]\\n \\\\[\\n 13 = 10 + 3\\n \\\\]\\n \\\\[\\n 23 =...	["{'generation': \"To solve the problem \\\\( 8 \\\\times 13 \\\\times 23 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Break down the numbers:\\n \\\\[\\n 8 = 10 - 2\\n \\\\]\\n \\\\[\\n 13 = 10 + 3\\n \\\\]\\n \\\\[\\n 23 = ...	c5077f8f4a57d4767d513fa0140bb28369b0d97abe9081405ec1ce4977de6977	e089014c0c72e03c6f566a420ec27695fdf2cf37476b848f24bcd9cd7b103b2c	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 8 \\times 13 \\times 23 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n \\[\n 8 = 10 - 2\n \\]\n \\[\n 13 = 10 + 3\n \\]\n \\[\n 23 = 20 + 3\n \\]\n\n2. **Apply the distributive...	[{"budget_forced_chunks": ["To solve the problem \\( 8 \\times 13 \\times 23 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Break down the numbers:\n \\[\n 8 = 10 - 2\n \\]\n \\[\n 13 = 10 + 3\n \\]\n \\[\n 23 = 20 + 3\n \\]\n\n2...	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 problem using the numbers 3, 14, 14, and 11, we can break it down into simpler steps:\\n\\n1. First, let's multiply 14 by 11:\\n - 14 * 11 = 154\\n\\n2. Now we have 3 and 14 left. Let's multiply 14 by 3:\\n - 14 * 3 = 42\\n\\n3. We have two results now: 154 and 42. We add them toget...	["{'generation': \"To solve the problem using the numbers 3, 14, 14, and 11, we can break it down into simpler steps:\\n\\n1. First, let's multiply 14 by 11:\\n - 14 * 11 = 154\\n\\n2. Now we have 3 and 14 left. Let's multiply 14 by 3:\\n - 14 * 3 = 42\\n\\n3. We have two results now: 154 and 42. We add them togeth...	d52f1030f65184c430fb7423fea9454bcefcbc2dd8a80a98709d4fd82e33ff99	1ef05c7aaa7694efc259416e25c7e5610f7a9467e8c47827e59eb90e80c7ced2	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 3, 14, 14, and 11, we can break it down into simpler steps:\n\n1. First, let's multiply 14 by 11:\n - 14 * 11 = 154\n\n2. Now we have 3 and 14 left. Let's multiply 14 by 3:\n - 14 * 3 = 42\n\n3. We have two results now: 154 and 42. We add them together:\n - 154 + 42 = 196\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 3, 14, 14, and 11, we can break it down into simpler steps:\n\n1. First, let's multiply 14 by 11:\n - 14 * 11 = 154\n\n2. Now we have 3 and 14 left. Let's multiply 14 by 3:\n - 14 * 3 = 42\n\n3. We have two results now: 154 and 42. We add them toget...	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 problem \\\\( 19 + 23 - 1 + 19 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the numbers:\\n \\\\[\\n 19 + 23 = 42\\n \\\\]\\n \\\\[\\n 42 - 1 = 41\\n \\\\]\\n \\\\[\\n 41 + 19 = 60\\n \\\\]\\n\\nSo the equation \\\\( 19 + 23 - 1 + 19 \\\\) simplifies...	["{'generation': \"To solve the problem \\\\( 19 + 23 - 1 + 19 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the numbers:\\n \\\\[\\n 19 + 23 = 42\\n \\\\]\\n \\\\[\\n 42 - 1 = 41\\n \\\\]\\n \\\\[\\n 41 + 19 = 60\\n \\\\]\\n\\nSo the equation \\\\( 19 + 23 - 1 + 19 \\\\) simplifies ...	4adbd29da982f2d2d00599ad14573dc4c8eb945e3de91b443e8b27003bd52042	9eed663edc29ed6d7f3f24e24519ddadb989ae3ec75476c63f62b5bf8f4a57e5	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 19 + 23 - 1 + 19 \\), we can break it down into simpler steps:\n\n1. Combine the numbers:\n \\[\n 19 + 23 = 42\n \\]\n \\[\n 42 - 1 = 41\n \\]\n \\[\n 41 + 19 = 60\n \\]\n\nSo the equation \\( 19 + 23 - 1 + 19 \\) simplifies to \\( 60 \\).\n\nNow, let's put this into the req...	[{"budget_forced_chunks": ["To solve the problem \\( 19 + 23 - 1 + 19 \\), we can break it down into simpler steps:\n\n1. Combine the numbers:\n \\[\n 19 + 23 = 42\n \\]\n \\[\n 42 - 1 = 41\n \\]\n \\[\n 41 + 19 = 60\n \\]\n\nSo the equation \\( 19 + 23 - 1 + 19 \\) simplifies to \\( 60 \\).\n\nNow, l...	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 step by step, we can break it down as follows:\\n\\n1. Combine the numbers using addition and subtraction:\\n - We start with the numbers 20, 8, 16, and 8.\\n - First, combine 20 and 8: \\\\( 20 + 8 = 28 \\\\).\\n - Next, combine 16 and 8: \\\\( 16 + 8 = 24 \\\\).\\n\\...	["{'generation': \"To solve the problem step by step, we can break it down as follows:\\n\\n1. Combine the numbers using addition and subtraction:\\n - We start with the numbers 20, 8, 16, and 8.\\n - First, combine 20 and 8: \\\\( 20 + 8 = 28 \\\\).\\n - Next, combine 16 and 8: \\\\( 16 + 8 = 24 \\\\).\\n\\n...	ebbe613099da63d1b55291f4b798ae73a232d8c4af2d918301eff2a8d08b9f58	76eaccefd1c4e5886e4057d7b18e969a4a9600226f4b26e60d6ef61df962b611	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem step by step, we can break it down as follows:\n\n1. Combine the numbers using addition and subtraction:\n - We start with the numbers 20, 8, 16, and 8.\n - First, combine 20 and 8: \\( 20 + 8 = 28 \\).\n - Next, combine 16 and 8: \\( 16 + 8 = 24 \\).\n\n So far, we have \\( 28 \\) an...	[{"budget_forced_chunks": ["To solve the problem step by step, we can break it down as follows:\n\n1. Combine the numbers using addition and subtraction:\n - We start with the numbers 20, 8, 16, and 8.\n - First, combine 20 and 8: \\( 20 + 8 = 28 \\).\n - Next, combine 16 and 8: \\( 16 + 8 = 24 \\).\n\n So ...	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 problem \\\\( 13 + 24 - 6 + 15 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Add 13 and 24.\\n \\\\[\\n 13 + 24 = 37\\n \\\\]\\n\\n2. Step 2: Subtract 6 from the result.\\n \\\\[\\n 37 - 6 = 31\\n \\\\]\\n\\n3. Step 3: Add the result from Step 2 ...	["{'generation': 'To solve the problem \\\\( 13 + 24 - 6 + 15 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Add 13 and 24.\\n \\\\[\\n 13 + 24 = 37\\n \\\\]\\n\\n2. Step 2: Subtract 6 from the result.\\n \\\\[\\n 37 - 6 = 31\\n \\\\]\\n\\n3. Step 3: Add the result from Step 2 t...	4b8548a181e3a8daf0e5e5ef30f90b7996f6638d2697da69aefcccd58369ccc7	0f18306e93c6b30451422876db152449239137bebb974cc06ae779d1c0cc45a4	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 13 + 24 - 6 + 15 \\), we can break it down into simpler steps:\n\n1. Step 1: Add 13 and 24.\n \\[\n 13 + 24 = 37\n \\]\n\n2. Step 2: Subtract 6 from the result.\n \\[\n 37 - 6 = 31\n \\]\n\n3. Step 3: Add the result from Step 2 to 15.\n \\[\n 31 + 15 = 46\n \\]\n...	[{"budget_forced_chunks": ["To solve the problem \\( 13 + 24 - 6 + 15 \\), we can break it down into simpler steps:\n\n1. Step 1: Add 13 and 24.\n \\[\n 13 + 24 = 37\n \\]\n\n2. Step 2: Subtract 6 from the result.\n \\[\n 37 - 6 = 31\n \\]\n\n3. Step 3: Add the result from Step 2 to 15.\n \\[\...	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 problem \\\\( 18 \\\\times 13 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the numbers:\\n \\\\[\\n 18 \\\\times 13 = 18 \\\\times (10 + 3)\\n \\\\]\\n\\n2. **Apply the distributive property:...	["{'generation': \"To solve the problem \\\\( 18 \\\\times 13 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the numbers:\\n \\\\[\\n 18 \\\\times 13 = 18 \\\\times (10 + 3)\\n \\\\]\\n\\n2. *Apply the distributive property:...	82ea3a7e9d54b8c6427e04636e9e192f8eb8392c2bc9348c8bd169df6d6bab64	d614d87b12fd03757ecddaaea21bceeba9aa9f77bb48c213e2338a8722b4f0fb	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 18 \\times 13 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the numbers:\n \\[\n 18 \\times 13 = 18 \\times (10 + 3)\n \\]\n\n2. Apply the distributive property:\n \\[\n 18 \\times (10 + 3) = (1...	[{"budget_forced_chunks": ["To solve the problem \\( 18 \\times 13 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the numbers:\n \\[\n 18 \\times 13 = 18 \\times (10 + 3)\n \\]\n\n2. Apply the distributive property:\n \\[\n ...	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 problem using the numbers 6, 2, 9, and 13, we can break it down into simpler steps:\\n\\n1. First, multiply 9 by 13:\\n \\\\[ 9 \\\\times 13 = 117 \\\\]\\n\\n2. Next, multiply 6 by 9:\\n \\\\[ 6 \\\\times 9 = 54 \\\\]\\n\\n3. Now, add the results from the two multiplications:\\n \...	["{'generation': \"To solve the problem using the numbers 6, 2, 9, and 13, we can break it down into simpler steps:\\n\\n1. First, multiply 9 by 13:\\n \\\\[ 9 \\\\times 13 = 117 \\\\]\\n\\n2. Next, multiply 6 by 9:\\n \\\\[ 6 \\\\times 9 = 54 \\\\]\\n\\n3. Now, add the results from the two multiplications:\\n \\...	04ec0523052570eab42f5d4df2df12752b6040a530a17ab530c1a34b68932cc3	a07b20493b2474140724f67ad0df567fa239ed4d890a1d12451e43c0282a8060	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 6, 2, 9, and 13, we can break it down into simpler steps:\n\n1. First, multiply 9 by 13:\n \\[ 9 \\times 13 = 117 \\]\n\n2. Next, multiply 6 by 9:\n \\[ 6 \\times 9 = 54 \\]\n\n3. Now, add the results from the two multiplications:\n \\[ 117 + 54 = 171 \\]\n\nSo, the equati...	[{"budget_forced_chunks": ["To solve the problem using the numbers 6, 2, 9, and 13, we can break it down into simpler steps:\n\n1. First, multiply 9 by 13:\n \\[ 9 \\times 13 = 117 \\]\n\n2. Next, multiply 6 by 9:\n \\[ 6 \\times 9 = 54 \\]\n\n3. Now, add the results from the two multiplications:\n \\[ 117 + 54 =...	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 \\\\( 14 + 9 - 3 \\\\), we can break it down into simpler steps:\\n\\n1. Add the numbers without the minus sign:\\n \\\\[\\n 14 + 9 = 23\\n \\\\]\\n\\n2. Subtract 3 from the result:\\n \\\\[\\n 23 - 3 = 20\\n \\\\]\\n\\nSo, the final result is \\\\( 20 \\\\).\...	["{'generation': 'To solve the problem \\\\( 14 + 9 - 3 \\\\), we can break it down into simpler steps:\\n\\n1. Add the numbers without the minus sign:\\n \\\\[\\n 14 + 9 = 23\\n \\\\]\\n\\n2. Subtract 3 from the result:\\n \\\\[\\n 23 - 3 = 20\\n \\\\]\\n\\nSo, the final result is \\\\( 20 \\\\).\\...	886ed5f2b6b1ec35a422c1358478609a118536357450e8ce400e8f59fb3d572e	b2487dd970bb8721f302d46b97240e180f65fa3b6e19ad7c2ebf5771d607f653	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 14 + 9 - 3 \\), we can break it down into simpler steps:\n\n1. Add the numbers without the minus sign:\n \\[\n 14 + 9 = 23\n \\]\n\n2. Subtract 3 from the result:\n \\[\n 23 - 3 = 20\n \\]\n\nSo, the final result is \\( 20 \\).\n\nTherefore, the answer in the required form...	[{"budget_forced_chunks": ["To solve the problem \\( 14 + 9 - 3 \\), we can break it down into simpler steps:\n\n1. Add the numbers without the minus sign:\n \\[\n 14 + 9 = 23\n \\]\n\n2. Subtract 3 from the result:\n \\[\n 23 - 3 = 20\n \\]\n\nSo, the final result is \\( 20 \\).\n\nTherefore, the a...	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 problem \\\\( 12 + 8 - 21 + 3 \\\\), we will follow the standard order of operations in mathematics, often remembered by the acronym PEMDAS, which stands for:\\n\\n- P: Parentheses\\n- E: Exponents\\n- M: Multiplication\\n- D: Division\\n- A: Addition\\n- S: Subt...	["{'generation': \"To solve the problem \\\\( 12 + 8 - 21 + 3 \\\\), we will follow the standard order of operations in mathematics, often remembered by the acronym PEMDAS, which stands for:\\n\\n- P: Parentheses\\n- E: Exponents\\n- M: Multiplication\\n- D: Division\\n- A: Addition\\n- S: Subtr...	14bf1806f088e8b1c20121adc93dbe473a7bbc73cf92a5fec9a74e104fa45d4b	99a22a74fff81f8c48fa2dafb4921d6437452b79c4215850b3b783316fe6ca3c	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 12 + 8 - 21 + 3 \\), we will follow the standard order of operations in mathematics, often remembered by the acronym PEMDAS, which stands for:\n\n- P: Parentheses\n- E: Exponents\n- M: Multiplication\n- D: Division\n- A: Addition\n- S: Subtraction\n\nThe order states t...	[{"budget_forced_chunks": ["To solve the problem \\( 12 + 8 - 21 + 3 \\), we will follow the standard order of operations in mathematics, often remembered by the acronym PEMDAS, which stands for:\n\n- P: Parentheses\n- E: Exponents\n- M: Multiplication\n- D: Division\n- A: Addition\n- S: Subtrac...	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 problem \\\\( 8 \\\\times 7 \\\\times 1 \\\\times 20 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 8 by 7:\\n \\\\[\\n 8 \\\\times 7 = 56\\n \\\\]\\n\\n2. Multiply the result by 1:\\n \\\\[\\n 56 \\\\times 1 = 56\\n \\\\]\\n\\n3. **Multiply the fin...	["{'generation': \"To solve the problem \\\\( 8 \\\\times 7 \\\\times 1 \\\\times 20 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 8 by 7:\\n \\\\[\\n 8 \\\\times 7 = 56\\n \\\\]\\n\\n2. Multiply the result by 1:\\n \\\\[\\n 56 \\\\times 1 = 56\\n \\\\]\\n\\n3. **Multiply the fina...	05f8a72d36e87d7a5c71b839f12b84d258f67ed7ae386e28611b3519219b525e	c674bf199104dc45f397037060b82bed9ca09d088e60a8318b2aa7f82f573d61	4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 8 \\times 7 \\times 1 \\times 20 \\), we can break it down into simpler steps:\n\n1. Multiply 8 by 7:\n \\[\n 8 \\times 7 = 56\n \\]\n\n2. Multiply the result by 1:\n \\[\n 56 \\times 1 = 56\n \\]\n\n3. Multiply the final result by 20:\n \\[\n 56 \\times 20 = 1120\...	[{"budget_forced_chunks": ["To solve the problem \\( 8 \\times 7 \\times 1 \\times 20 \\), we can break it down into simpler steps:\n\n1. Multiply 8 by 7:\n \\[\n 8 \\times 7 = 56\n \\]\n\n2. Multiply the result by 1:\n \\[\n 56 \\times 1 = 56\n \\]\n\n3. Multiply the final result by 20:\n \\[...	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 problem \\\\( 6 + 10 - 4 + 19 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 6 + 10 = 16\\n \\\\]\\n\\n2. Add the result to the next number:\\n \\\\[\\n 16 - 4 = 12\\n \\\\]\\n\\n3. **Add the final number to the res...	["{'generation': \"To solve the problem \\\\( 6 + 10 - 4 + 19 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 6 + 10 = 16\\n \\\\]\\n\\n2. Add the result to the next number:\\n \\\\[\\n 16 - 4 = 12\\n \\\\]\\n\\n3. **Add the final number to the resu...	32c7d6edf9a791a9576fef36ee42924d15008a1a3cbcc17f728f099b122d86af	20e1f5327c8fb5ca8e924289cde96faf6c2e60df0573b7c58720d6df34666d96	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 6 + 10 - 4 + 19 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 6 + 10 = 16\n \\]\n\n2. Add the result to the next number:\n \\[\n 16 - 4 = 12\n \\]\n\n3. Add the final number to the result:\n \\[\n 12 + 19 = 31\n \\]\n\...	[{"budget_forced_chunks": ["To solve the problem \\( 6 + 10 - 4 + 19 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 6 + 10 = 16\n \\]\n\n2. Add the result to the next number:\n \\[\n 16 - 4 = 12\n \\]\n\n3. Add the final number to the result:\n \\[\n...	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 problem using the numbers 8, 4, 23, and 10, we can break it down into simpler steps:\\n\\n1. First, multiply 23 by 10:\\n [23 x 10 = 230]\\n\\n2. Now, we need to add 8 to the result:\\n [230 + 8 = 238]\\n\\nSo, the final answer is 238. However, 238 is not one of the given options. I...	["{'generation': \"To solve the problem using the numbers 8, 4, 23, and 10, we can break it down into simpler steps:\\n\\n1. First, multiply 23 by 10:\\n [23 x 10 = 230]\\n\\n2. Now, we need to add 8 to the result:\\n [230 + 8 = 238]\\n\\nSo, the final answer is 238. However, 238 is not one of the given options. It...	37b100781adc7aea5bd0958ae572fe10470b8db410fd9723eb5360d5452d767d	27abc602b799c6c8ed4fa7f36db773c12da966e4d4118b130a622520943a48d5	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 8, 4, 23, and 10, we can break it down into simpler steps:\n\n1. First, multiply 23 by 10:\n [23 x 10 = 230]\n\n2. Now, we need to add 8 to the result:\n [230 + 8 = 238]\n\nSo, the final answer is 238. However, 238 is not one of the given options. It seems there might be a m...	[{"budget_forced_chunks": ["To solve the problem using the numbers 8, 4, 23, and 10, we can break it down into simpler steps:\n\n1. First, multiply 23 by 10:\n [23 x 10 = 230]\n\n2. Now, we need to add 8 to the result:\n [230 + 8 = 238]\n\nSo, the final answer is 238.", " However, 238 is not one of the given option...	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 + 2 - 12 + 18 \\\\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\\n\\n1. First, add 19 and 2:\\n \\\\[\\n 19 + 2 = 21\\n \\\\]\\n\\n2. Next, subtract 12 from the result:\\n \\\\[\...	["{'generation': \"To solve the problem \\\\( 19 + 2 - 12 + 18 \\\\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\\n\\n1. First, add 19 and 2:\\n \\\\[\\n 19 + 2 = 21\\n \\\\]\\n\\n2. Next, subtract 12 from the result:\\n \\\\[\\...	c98d820c226336c2035fa0efaa4d9aa2becdcb27feac1bbf9082d6efe4f5069f	1436914e7b70497d0e69375d7b70fd47527ca9e2cae49b0daf6cca5dd20d25a7	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 19 + 2 - 12 + 18 \\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\n\n1. First, add 19 and 2:\n \\[\n 19 + 2 = 21\n \\]\n\n2. Next, subtract 12 from the result:\n \\[\n 21 - 12 = 9\n \\]\n\n3. Finall...	[{"budget_forced_chunks": ["To solve the problem \\( 19 + 2 - 12 + 18 \\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\n\n1. First, add 19 and 2:\n \\[\n 19 + 2 = 21\n \\]\n\n2. Next, subtract 12 from the result:\n \\[\n 21 - 1...	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 using the numbers 3, 17, 21, and 11, we can break it down into simpler steps:\\n\\n1. First, multiply 11 and 21:\\n 11 * 21 = 231\\n\\n2. Now, we need to add 3 to the result:\\n 231 + 3 = 234\\n\\n3. Finally, we need to subtract 7 (which is 11 * 2 - 1) from the result:\\n 2...	["{'generation': 'To solve the problem using the numbers 3, 17, 21, and 11, we can break it down into simpler steps:\\n\\n1. First, multiply 11 and 21:\\n 11 * 21 = 231\\n\\n2. Now, we need to add 3 to the result:\\n 231 + 3 = 234\\n\\n3. Finally, we need to subtract 7 (which is 11 * 2 - 1) from the result:\\n 23...	3dee87e91e430e7f86936ddeb295f7a9006fcdac4e05ff39b8eb95e05789cda6	ff841f243937fbac16fcd7bbd6cf6794fc7f246070b234a925b75877ce633207	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 3, 17, 21, and 11, we can break it down into simpler steps:\n\n1. First, multiply 11 and 21:\n 11 * 21 = 231\n\n2. Now, we need to add 3 to the result:\n 231 + 3 = 234\n\n3. Finally, we need to subtract 7 (which is 11 * 2 - 1) from the result:\n 234 - 7 = 227\n\nSo, the fi...	[{"budget_forced_chunks": ["To solve the problem using the numbers 3, 17, 21, and 11, we can break it down into simpler steps:\n\n1. First, multiply 11 and 21:\n 11 * 21 = 231\n\n2. Now, we need to add 3 to the result:\n 231 + 3 = 234\n\n3. Finally, we need to subtract 7 (which is 11 * 2 - 1) from the result:\n 2...	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 problem \\\\( 16 \\\\times 4 \\\\times 14 \\\\times 12 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results. This is because \\\\( 16 \\\\times 4 \\\\) and \\\\( 14 \\\\times 12 \\\\) ar...	["{'generation': \"To solve the problem \\\\( 16 \\\\times 4 \\\\times 14 \\\\times 12 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results. This is because \\\\( 16 \\\\times 4 \\\\) and \\\\( 14 \\\\times 12 \\\\) are...	98ab1b38356ecf7abfc8d59f6051f122d58b27c2757f86694bf71568c3f579e6	cbe34bb42aa6666852658fa52a4884248cbbf63194ac9b9bcc86b2c69c103c04	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 16 \\times 4 \\times 14 \\times 12 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results. This is because \\( 16 \\times 4 \\) and \\( 14 \\times 12 \\) are easier to compute mentally.\n\n1. Calc...	[{"budget_forced_chunks": ["To solve the problem \\( 16 \\times 4 \\times 14 \\times 12 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results. This is because \\( 16 \\times 4 \\) and \\( 14 \\times 12 \\) are easier to co...	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 problem using the numbers 9, 20, 18, and 16, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 20:\\n \\\\[ 16 \\\\times 20 = 320 \\\\]\\n\\n2. Next, multiply 16 by 9:\\n \\\\[ 16 \\\\times 9 = 144 \\\\]\\n\\n3. Then, multiply 9 by 18:\\n \\\\[ 9 \\\\times 18 ...	["{'generation': \"To solve the problem using the numbers 9, 20, 18, and 16, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 20:\\n \\\\[ 16 \\\\times 20 = 320 \\\\]\\n\\n2. Next, multiply 16 by 9:\\n \\\\[ 16 \\\\times 9 = 144 \\\\]\\n\\n3. Then, multiply 9 by 18:\\n \\\\[ 9 \\\\times 18 =...	3ebb28261cbe5e14b7315a28166cc1db81b47ba4e9d15a19a7de1ca91ac3fc11	2636ec08d0fb37b2cf450273bfe2824cdd0f5cb1b0331db5775239f4dba1e73f	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 9, 20, 18, and 16, we can break it down into simpler steps:\n\n1. First, multiply 16 by 20:\n \\[ 16 \\times 20 = 320 \\]\n\n2. Next, multiply 16 by 9:\n \\[ 16 \\times 9 = 144 \\]\n\n3. Then, multiply 9 by 18:\n \\[ 9 \\times 18 = 162 \\]\n\n4. Finally, add the results fr...	[{"budget_forced_chunks": ["To solve the problem using the numbers 9, 20, 18, and 16, we can break it down into simpler steps:\n\n1. First, multiply 16 by 20:\n \\[ 16 \\times 20 = 320 \\]\n\n2. Next, multiply 16 by 9:\n \\[ 16 \\times 9 = 144 \\]\n\n3. Then, multiply 9 by 18:\n \\[ 9 \\times 18 = 162 \\]\n\n4. F...	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 problem \\\\( 8 \\\\times 3 \\\\times 9 \\\\) step by step, we can break it down into simpler multiplications and then add the results together.\\n\\n### Step 1: Break down the multiplication\\nWe can rewrite \\\\( 8 \\\\times 3 \\\\times 9 \\\\) as:\\n\\\\[ (8 \\\\times 3) \\\\times 9 ...	["{'generation': \"To solve the problem \\\\( 8 \\\\times 3 \\\\times 9 \\\\) step by step, we can break it down into simpler multiplications and then add the results together.\\n\\n### Step 1: Break down the multiplication\\nWe can rewrite \\\\( 8 \\\\times 3 \\\\times 9 \\\\) as:\\n\\\\[ (8 \\\\times 3) \\\\times 9 \...	7a7930e021ceeb46d974fa00bbee28c1f4e7422d48a9c96427a545e4eed0fbdf	fd72a63df0361a86a94acd60ae8292cd8ac4221f55ee795b17a95ad2540b0988	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 8 \\times 3 \\times 9 \\) step by step, we can break it down into simpler multiplications and then add the results together.\n\n### Step 1: Break down the multiplication\nWe can rewrite \\( 8 \\times 3 \\times 9 \\) as:\n\\[ (8 \\times 3) \\times 9 \\]\n\n### Step 2: Perform the first multipl...	[{"budget_forced_chunks": ["To solve the problem \\( 8 \\times 3 \\times 9 \\) step by step, we can break it down into simpler multiplications and then add the results together.\n\n### Step 1: Break down the multiplication\nWe can rewrite \\( 8 \\times 3 \\times 9 \\) as:\n\\[ (8 \\times 3) \\times 9 \\]\n\n### Step 2:...	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 problem \\\\( 15 \\\\times 19 \\\\times 20 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the second number (19) across the first number (15):\\n \\\\[\\n 15 \\\\times 19 = 15 \\\\times (10 + 9) ...	["{'generation': \"To solve the problem \\\\( 15 \\\\times 19 \\\\times 20 \\\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\\n\\n1. Distribute the second number (19) across the first number (15):\\n \\\\[\\n 15 \\\\times 19 = 15 \\\\times (10 + 9) =...	6233391fa323f1ae8f0498bde4e183b36b9bab90b39c8d544a67220125b83287	08ad970139b0652c99d841197987b916b8a1ef91494da8c899ab506134af2eb8	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 15 \\times 19 \\times 20 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the second number (19) across the first number (15):\n \\[\n 15 \\times 19 = 15 \\times (10 + 9) = 15 \\times 10 + 15 \\times 9\n \...	[{"budget_forced_chunks": ["To solve the problem \\( 15 \\times 19 \\times 20 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\n1. Distribute the second number (19) across the first number (15):\n \\[\n 15 \\times 19 = 15 \\times (10 + 9) = 15 \\tim...	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 \\\\( 17 \\\\times 7 \\\\times 3 \\\\times 8 \\\\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the other two numbers.\\n\\n### Step 1: Multiply 17 and 7\\n\\\\[ 17 \\\\times 7 \\\\]\\n\\n### Step 2: Multiply the results from Ste...	["{'generation': \"To solve the problem \\\\( 17 \\\\times 7 \\\\times 3 \\\\times 8 \\\\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the other two numbers.\\n\\n### Step 1: Multiply 17 and 7\\n\\\\[ 17 \\\\times 7 \\\\]\\n\\n### Step 2: Multiply the results from Step...	d451de9faeade7c0b043fd49fe6172d6084cd97ff6acbb5e55fd09b604e52764	2020d77f8edf80ce2b99f12ded817ddb52c377b349252b70b0b2618f0961c036	785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 17 \\times 7 \\times 3 \\times 8 \\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the other two numbers.\n\n### Step 1: Multiply 17 and 7\n\\[ 17 \\times 7 \\]\n\n### Step 2: Multiply the results from Step 1 by 3\n\\[ (17 \\times 7) \\times 3 ...	[{"budget_forced_chunks": ["To solve the problem \\( 17 \\times 7 \\times 3 \\times 8 \\), we can break it down into simpler steps by first multiplying two numbers and then multiplying the other two numbers.\n\n### Step 1: Multiply 17 and 7\n\\[ 17 \\times 7 \\]\n\n### Step 2: Multiply the results from Step 1 by 3\n\\[...	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 problem \\\\( 16 \\\\times 15 \\\\times 1 \\\\times 3 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 16 by 15:\\n \\\\[\\n 16 \\\\times 15 = 240\\n \\\\]\\n\\n2. Multiply 16 by 1:\\n \\\\[\\n 16 \\\\times 1 = 16\\n \\\\]\\n\\n3. *Multiply 16 by 3:...	["{'generation': \"To solve the problem \\\\( 16 \\\\times 15 \\\\times 1 \\\\times 3 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 16 by 15:\\n \\\\[\\n 16 \\\\times 15 = 240\\n \\\\]\\n\\n2. Multiply 16 by 1:\\n \\\\[\\n 16 \\\\times 1 = 16\\n \\\\]\\n\\n3. Multiply 16 by 3:...	d1910265333c2aec98a24231bd582fc8e6d688f4c3a08e889f54e26f260f6ff6	debf4e355f7604ffeeb5f3404d87d62b825d6527dc43fb065206a123921ce584	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 16 \\times 15 \\times 1 \\times 3 \\), we can break it down into simpler steps:\n\n1. Multiply 16 by 15:\n \\[\n 16 \\times 15 = 240\n \\]\n\n2. Multiply 16 by 1:\n \\[\n 16 \\times 1 = 16\n \\]\n\n3. Multiply 16 by 3:\n \\[\n 16 \\times 3 = 48\n \\]\n\n4. **Add ...	[{"budget_forced_chunks": ["To solve the problem \\( 16 \\times 15 \\times 1 \\times 3 \\), we can break it down into simpler steps:\n\n1. Multiply 16 by 15:\n \\[\n 16 \\times 15 = 240\n \\]\n\n2. Multiply 16 by 1:\n \\[\n 16 \\times 1 = 16\n \\]\n\n3. Multiply 16 by 3:\n \\[\n 16 \\times 3...	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 problem \\\\( 24 \\\\times 18 \\\\times 23 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\nFirst, let's expand the multiplication:\\n\\\\[ 24 \\\\times 18 \\\\times 23 = (24 \\\\times 10) \\\\times (24 \\\\times 1) ...	["{'generation': \"To solve the problem \\\\( 24 \\\\times 18 \\\\times 23 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\\n\\nFirst, let's expand the multiplication:\\n\\\\[ 24 \\\\times 18 \\\\times 23 = (24 \\\\times 10) \\\\times (24 \\\\times 1) \...	ef1eb782cf001ce26a20ed44e1b588a2148b04dffc4bdeb09208c9415768088f	802a5426bbc14fc70091630daf5ba791cfd4353339d08eb4744e729541630a94	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 24 \\times 18 \\times 23 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[ 24 \\times 18 \\times 23 = (24 \\times 10) \\times (24 \\times 1) \\times (24 \\times 3) \\]\n\nWe can simp...	[{"budget_forced_chunks": ["To solve the problem \\( 24 \\times 18 \\times 23 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[ 24 \\times 18 \\times 23 = (24 \\times 10) \\times (24 \\times 1) \\times (24 \\t...	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 problem \\\\( 17 + 20 - 10 + 4 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 17 + 20 = 37\\n \\\\]\\n\\n2. Add the result to the third number:\\n \\\\[\\n 37 + 4 = 41\\n \\\\]\\n\\nSo, the final step gives us:\\n\\...	["{'generation': \"To solve the problem \\\\( 17 + 20 - 10 + 4 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the first two numbers:\\n \\\\[\\n 17 + 20 = 37\\n \\\\]\\n\\n2. Add the result to the third number:\\n \\\\[\\n 37 + 4 = 41\\n \\\\]\\n\\nSo, the final step gives us:\\n\\n...	6db3fbd49b81d0debd08a217bb92f3efa1f6831c4999048dd50260c4a2a8e8c0	3bc056dfd0233c3b03fb4c3539e85fcd8989a7fad15a268f596aa2dfc3a7bce3	e629fa6598d732768f7c726b4b621285f9c3b85303900aa912017db7617d8bdb	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 17 + 20 - 10 + 4 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 17 + 20 = 37\n \\]\n\n2. Add the result to the third number:\n \\[\n 37 + 4 = 41\n \\]\n\nSo, the final step gives us:\n\n\\[\n41\n\\]\n\nTherefore, the answer is:\n...	[{"budget_forced_chunks": ["To solve the problem \\( 17 + 20 - 10 + 4 \\), we can break it down into simpler steps:\n\n1. Combine the first two numbers:\n \\[\n 17 + 20 = 37\n \\]\n\n2. Add the result to the third number:\n \\[\n 37 + 4 = 41\n \\]\n\nSo, the final step gives us:\n\n\\[\n41\n\\]\n\nT...	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 problem \\\\( 12 \\\\times 6 \\\\times 10 = 16 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 12 by 6:\\n \\\\[\\n 12 \\\\times 6 = 72\\n \\\\]\\n\\n2. Multiply the result by 10:\\n \\\\[\\n 72 \\\\times 10 = 720\\n \\\\]\\n\\nSo, the final step is ...	["{'generation': \"To solve the problem \\\\( 12 \\\\times 6 \\\\times 10 = 16 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 12 by 6:\\n \\\\[\\n 12 \\\\times 6 = 72\\n \\\\]\\n\\n2. Multiply the result by 10:\\n \\\\[\\n 72 \\\\times 10 = 720\\n \\\\]\\n\\nSo, the final step is t...	35b1c2b18fee46db7d7d486eb513d6e14310ea4dce3e14fc7920f45913c73d48	82a5b9ead972f062769857dd7132e626f4b355aaba3fb500fe19fd767cae5fe9	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 12 \\times 6 \\times 10 = 16 \\), we can break it down into simpler steps:\n\n1. Multiply 12 by 6:\n \\[\n 12 \\times 6 = 72\n \\]\n\n2. Multiply the result by 10:\n \\[\n 72 \\times 10 = 720\n \\]\n\nSo, the final step is to multiply the result by 10, which shifts the dec...	[{"budget_forced_chunks": ["To solve the problem \\( 12 \\times 6 \\times 10 = 16 \\), we can break it down into simpler steps:\n\n1. Multiply 12 by 6:\n \\[\n 12 \\times 6 = 72\n \\]\n\n2. Multiply the result by 10:\n \\[\n 72 \\times 10 = 720\n \\]\n\nSo, the final step is to multiply the result b...	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 problem using the numbers 5, 9, 2, and 2, we can follow these steps:\\n\\n1. Combine the numbers using arithmetic operations:\\n - First, add 5 and 9: \\\\( 5 + 9 = 14 \\\\)\\n - Next, multiply 14 by 2: \\\\( 14 \\\\times 2 = 28 \\\\)\\n - Finally, multiply the result by 2 aga...	["{'generation': \"To solve the problem using the numbers 5, 9, 2, and 2, we can follow these steps:\\n\\n1. Combine the numbers using arithmetic operations:\\n - First, add 5 and 9: \\\\( 5 + 9 = 14 \\\\)\\n - Next, multiply 14 by 2: \\\\( 14 \\\\times 2 = 28 \\\\)\\n - Finally, multiply the result by 2 agai...	b793b535bd0b3280ad4a8bc7d71b5cf4f234571620473d65acae50acc825ec57	e8cbd5ee01dec1857224acb722f9c821b946597da44f1d2b0e054dcb5fbfde53	4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 5, 9, 2, and 2, we can follow these steps:\n\n1. Combine the numbers using arithmetic operations:\n - First, add 5 and 9: \\( 5 + 9 = 14 \\)\n - Next, multiply 14 by 2: \\( 14 \\times 2 = 28 \\)\n - Finally, multiply the result by 2 again: \\( 28 \\times 2 = 56 \\)\n\n...	[{"budget_forced_chunks": ["To solve the problem using the numbers 5, 9, 2, and 2, we can follow these steps:\n\n1. Combine the numbers using arithmetic operations:\n - First, add 5 and 9: \\( 5 + 9 = 14 \\)\n - Next, multiply 14 by 2: \\( 14 \\times 2 = 28 \\)\n - Finally, multiply the result by 2 again: \\(...	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 break it down into simpler steps:\\n\\n1. First, let's multiply 16 and 10:\\n [16 * 10 = 160]\\n\\n2. Now, we need to multiply 16 and 19, but we can't do 16 * 19 directly. Instead, we can break it down further:\\n [16 * 19 = 16 * ...	["{'generation': \"To solve the problem using the numbers 19, 10, 16, and 16, we can break it down into simpler steps:\\n\\n1. First, let's multiply 16 and 10:\\n [16 * 10 = 160]\\n\\n2. Now, we need to multiply 16 and 19, but we can't do 16 * 19 directly. Instead, we can break it down further:\\n [16 * 19 = 16 * (...	9d80570a7343e6d2d68246a0e09ce47e1a6a96dc24feecbb35ad65e514cb2939	78b473de32b43d7c002173d5378657ba52a42625ce5708900ecdbf5b9789453f	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 19, 10, 16, and 16, we can break it down into simpler steps:\n\n1. First, let's multiply 16 and 10:\n [16 * 10 = 160]\n\n2. Now, we need to multiply 16 and 19, but we can't do 16 * 19 directly. Instead, we can break it down further:\n [16 * 19 = 16 * (10 + 9) = (16 * 10) + (...	[{"budget_forced_chunks": ["To solve the problem using the numbers 19, 10, 16, and 16, we can break it down into simpler steps:\n\n1. First, let's multiply 16 and 10:\n [16 * 10 = 160]\n\n2. Now, we need to multiply 16 and 19, but we can't do 16 * 19 directly. Instead, we can break it down further:\n [16 * 19 = 16 ...	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 problem \\\\(5 + 19 = 24\\\\) using the steps you provided, we would follow these steps:\\n\\n1. Identify the numbers and operations: The numbers are 5 and 19, and the operation is addition.\\n2. Verify the numbers are being used correctly: We are using each number only once.\\n...	["{'generation': \"To solve the problem \\\\(5 + 19 = 24\\\\) using the steps you provided, we would follow these steps:\\n\\n1. Identify the numbers and operations: The numbers are 5 and 19, and the operation is addition.\\n2. Verify the numbers are being used correctly: We are using each number only once.\\n3...	99d6fbffa160a424f45d4b78de11360cd4b97354c1dce2e3ae62d5f2f03d5b38	8f74b7e3c369679f1e12c6c9ec9b3b85d51f5d6e89c2181cc67e3ed90f706203	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\(5 + 19 = 24\\) using the steps you provided, we would follow these steps:\n\n1. Identify the numbers and operations: The numbers are 5 and 19, and the operation is addition.\n2. Verify the numbers are being used correctly: We are using each number only once.\n3. **Write the equation fo...	[{"budget_forced_chunks": ["To solve the problem \\(5 + 19 = 24\\) using the steps you provided, we would follow these steps:\n\n1. Identify the numbers and operations: The numbers are 5 and 19, and the operation is addition.\n2. Verify the numbers are being used correctly: We are using each number only once.\n...	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 problem \\\\( 17 + 13 + 15 = 19 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Break down the numbers into smaller groups that are easier to handle.\\n \\\\[\\n 17 = 10 + 7\\n \\\\]\\n \\\\[\\n 13 = 10 + 3\\n \\\\]\\n \\\\[\\n 15 = 10 + 5\\n \\\\]\...	["{'generation': \"To solve the problem \\\\( 17 + 13 + 15 = 19 \\\\), we can break it down into simpler steps:\\n\\n1. Step 1: Break down the numbers into smaller groups that are easier to handle.\\n \\\\[\\n 17 = 10 + 7\\n \\\\]\\n \\\\[\\n 13 = 10 + 3\\n \\\\]\\n \\\\[\\n 15 = 10 + 5\\n \\\\]\\...	1fd81e2df0bd7f0dd3fc40b5f6617fc216f2550b4fbc63bb64c3d55a28fe4268	0b4c367a3bb495638c386032c2d90db43eae78f510b2126270bb3052fff05c8a	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 17 + 13 + 15 = 19 \\), we can break it down into simpler steps:\n\n1. Step 1: Break down the numbers into smaller groups that are easier to handle.\n \\[\n 17 = 10 + 7\n \\]\n \\[\n 13 = 10 + 3\n \\]\n \\[\n 15 = 10 + 5\n \\]\n\n2. **Step 2: Add the numbers within each g...	[{"budget_forced_chunks": ["To solve the problem \\( 17 + 13 + 15 = 19 \\), we can break it down into simpler steps:\n\n1. Step 1: Break down the numbers into smaller groups that are easier to handle.\n \\[\n 17 = 10 + 7\n \\]\n \\[\n 13 = 10 + 3\n \\]\n \\[\n 15 = 10 + 5\n \\]\n\n2. **Step 2: Add...	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 problem using the numbers 2, 20, 24, and 4, we can break it down into simpler steps:\\n\\n1. First, let's multiply 24 by 4:\\n \\\\[ 24 \\\\times 4 = 96 \\\\]\\n\\n2. Now, let's multiply 20 by 4 and then add the result to the previous step's product:\\n \\\\[ 20 \\\\times 4 = 80 \\\...	["{'generation': \"To solve the problem using the numbers 2, 20, 24, and 4, we can break it down into simpler steps:\\n\\n1. First, let's multiply 24 by 4:\\n \\\\[ 24 \\\\times 4 = 96 \\\\]\\n\\n2. Now, let's multiply 20 by 4 and then add the result to the previous step's product:\\n \\\\[ 20 \\\\times 4 = 80 \\\\...	997f99b3e946a10a23c993819c4b0e619ddc9a6fa3027b29726c423e97f82ed3	234784e30f512a638cd6dec8311f44a87e65a74d04d0e2478165e83a9d0ecb75	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 2, 20, 24, and 4, we can break it down into simpler steps:\n\n1. First, let's multiply 24 by 4:\n \\[ 24 \\times 4 = 96 \\]\n\n2. Now, let's multiply 20 by 4 and then add the result to the previous step's product:\n \\[ 20 \\times 4 = 80 \\]\n And:\n \\[ 80 + 96 = 166 \\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 2, 20, 24, and 4, we can break it down into simpler steps:\n\n1. First, let's multiply 24 by 4:\n \\[ 24 \\times 4 = 96 \\]\n\n2. Now, let's multiply 20 by 4 and then add the result to the previous step's product:\n \\[ 20 \\times 4 = 80 \\]\n And...	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 problem \\\\( 9 + 22 - 3 \\\\times 6 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 3 by 6:\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n\\n2. Add the result of the multiplication to the result of the subtraction:\\n First, we need to determine the value of...	["{'generation': 'To solve the problem \\\\( 9 + 22 - 3 \\\\times 6 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 3 by 6:\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n\\n2. Add the result of the multiplication to the result of the subtraction:\\n First, we need to determine the value of ...	03ce236c2139b2502530b7d1a7b9f04b0a228c5b913baf576c61ea4f747ed6d7	dda06b36cd550be53e6e802ae533a72a54ee914cd5531f6e91af805bc15e3093	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 9 + 22 - 3 \\times 6 \\), we can break it down into simpler steps:\n\n1. Multiply 3 by 6:\n \\[\n 3 \\times 6 = 18\n \\]\n\n2. Add the result of the multiplication to the result of the subtraction:\n First, we need to determine the value of the subtraction \\( 22 - 3 \\):\n ...	[{"budget_forced_chunks": ["To solve the problem \\( 9 + 22 - 3 \\times 6 \\), we can break it down into simpler steps:\n\n1. Multiply 3 by 6:\n \\[\n 3 \\times 6 = 18\n \\]\n\n2. Add the result of the multiplication to the result of the subtraction:\n First, we need to determine the value of the subtra...	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 problem \\\\( 3 \\\\times 6 + 1 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 3 and 6:\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n\\n2. Add the result to 1:\\n \\\\[\\n 18 + 1 = 19\\n \\\\]\\n\\nSo, the final step is to add 1 to the product of 3 and...	["{'generation': \"To solve the problem \\\\( 3 \\\\times 6 + 1 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 3 and 6:\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n\\n2. Add the result to 1:\\n \\\\[\\n 18 + 1 = 19\\n \\\\]\\n\\nSo, the final step is to add 1 to the product of 3 and ...	7212f88580197608ee45310d3946ace5165c460930b98ffcf2efbf62fbb9fd78	100530f6b8ebe121df0720a72d5b462f72fe2f623c2939e4925f50602d8c1ac8	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 3 \\times 6 + 1 \\), we can break it down into simpler steps:\n\n1. Multiply 3 and 6:\n \\[\n 3 \\times 6 = 18\n \\]\n\n2. Add the result to 1:\n \\[\n 18 + 1 = 19\n \\]\n\nSo, the final step is to add 1 to the product of 3 and 6.\n\nTherefore, the solution to the equation...	[{"budget_forced_chunks": ["To solve the problem \\( 3 \\times 6 + 1 \\), we can break it down into simpler steps:\n\n1. Multiply 3 and 6:\n \\[\n 3 \\times 6 = 18\n \\]\n\n2. Add the result to 1:\n \\[\n 18 + 1 = 19\n \\]\n\nSo, the final step is to add 1 to the product of 3 and 6.\n\nTherefore, th...	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 \\\\( 15 + 3 \\\\times 22 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 3 by 20 (the last digit of 22):\\n \\\\[\\n 3 \\\\times 20 = 60\\n \\\\]\\n\\n2. Multiply 3 by 2 (the next digit of 22):\\n \\\\[\\n 3 \\\\times 2 = 6\\n \\\\]\\n\\n3. ...	["{'generation': \"To solve the problem \\\\( 15 + 3 \\\\times 22 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 3 by 20 (the last digit of 22):\\n \\\\[\\n 3 \\\\times 20 = 60\\n \\\\]\\n\\n2. Multiply 3 by 2 (the next digit of 22):\\n \\\\[\\n 3 \\\\times 2 = 6\\n \\\\]\\n\\n3. *...	4cc81a73edb3c70a7f9a4e66405067bdd3cd557192e4ccc5363b1c3ffd066337	a521bb80ce8b527bb25590df9a522d4cf8e9b94627649d903e1c6902c0f1408e	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 15 + 3 \\times 22 \\), we can break it down into simpler steps:\n\n1. Multiply 3 by 20 (the last digit of 22):\n \\[\n 3 \\times 20 = 60\n \\]\n\n2. Multiply 3 by 2 (the next digit of 22):\n \\[\n 3 \\times 2 = 6\n \\]\n\n3. *Add the results from the two multiplications:...	[{"budget_forced_chunks": ["To solve the problem \\( 15 + 3 \\times 22 \\), we can break it down into simpler steps:\n\n1. Multiply 3 by 20 (the last digit of 22):\n \\[\n 3 \\times 20 = 60\n \\]\n\n2. Multiply 3 by 2 (the next digit of 22):\n \\[\n 3 \\times 2 = 6\n \\]\n\n3. **Add the results from...	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 problem \\\\( 21 + 19 - 22 + 7 \\\\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\\n\\n1. First, add 21 and 19:\\n \\\\[\\n 21 + 19 = 40\\n \\\\]\\n\\n2. Next, subtract 22 from the result:\\n \\\\...	["{'generation': \"To solve the problem \\\\( 21 + 19 - 22 + 7 \\\\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\\n\\n1. First, add 21 and 19:\\n \\\\[\\n 21 + 19 = 40\\n \\\\]\\n\\n2. Next, subtract 22 from the result:\\n \\\\[...	0ae865d4dbc5cfaea27c1a97d5dd26fd6cfc693d41b25c8bb22dfbab6e87b839	d70ed273c01a94ba8bc2003830f89de9ad22d231a38e797ec80738614d894fa3	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 21 + 19 - 22 + 7 \\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\n\n1. First, add 21 and 19:\n \\[\n 21 + 19 = 40\n \\]\n\n2. Next, subtract 22 from the result:\n \\[\n 40 - 22 = 18\n \\]\n\n3. Fin...	[{"budget_forced_chunks": ["To solve the problem \\( 21 + 19 - 22 + 7 \\), we can break it down into simpler steps by grouping the numbers in a way that makes addition easier. Here's how you can do it:\n\n1. First, add 21 and 19:\n \\[\n 21 + 19 = 40\n \\]\n\n2. Next, subtract 22 from the result:\n \\[\n 40 -...	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 problem using the numbers 5, 3, 2, and 6, we can follow these steps:\\n\\n1. Step 1: Multiply 5 by 3.\\n - 5 x 3 = 15\\n - So, we write down 15.\\n\\n2. Step 2: Multiply 5 by 2.\\n - 5 x 2 = 10\\n - We then carry over the 10 to the next column.\\n\\n3. Step 3: Add the...	["{'generation': 'To solve the problem using the numbers 5, 3, 2, and 6, we can follow these steps:\\n\\n1. Step 1: Multiply 5 by 3.\\n - 5 x 3 = 15\\n - So, we write down 15.\\n\\n2. Step 2: Multiply 5 by 2.\\n - 5 x 2 = 10\\n - We then carry over the 10 to the next column.\\n\\n3. Step 3: Add the ...	e78c916c002984bf26b644862b714de89c9d41e56e57ccb2d0f7a65240145933	286866cc7d3d0e46a70d9a216c094be68ed8b30cb640270203c4a394f86b9e49	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 5, 3, 2, and 6, we can follow these steps:\n\n1. Step 1: Multiply 5 by 3.\n - 5 x 3 = 15\n - So, we write down 15.\n\n2. Step 2: Multiply 5 by 2.\n - 5 x 2 = 10\n - We then carry over the 10 to the next column.\n\n3. Step 3: Add the carried over 10 to the res...	[{"budget_forced_chunks": ["To solve the problem using the numbers 5, 3, 2, and 6, we can follow these steps:\n\n1. Step 1: Multiply 5 by 3.\n - 5 x 3 = 15\n - So, we write down 15.\n\n2. Step 2: Multiply 5 by 2.\n - 5 x 2 = 10\n - We then carry over the 10 to the next column.\n\n3. Step 3: Add the ...	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 using the numbers 19, 10, 15, and 4, we can break it down into simpler steps:\\n\\n1. First, let's multiply 15 by 4:\\n 15 * 4 = 60\\n Now we have 60.\\n\\n2. Next, let's multiply 19 by 10:\\n 19 * 10 = 190\\n Now we have 60 + 190 = 250.\\n\\n3. Finally, let's add the tw...	["{'generation': \"To solve the problem using the numbers 19, 10, 15, and 4, we can break it down into simpler steps:\\n\\n1. First, let's multiply 15 by 4:\\n 15 * 4 = 60\\n Now we have 60.\\n\\n2. Next, let's multiply 19 by 10:\\n 19 * 10 = 190\\n Now we have 60 + 190 = 250.\\n\\n3. Finally, let's add the two...	8a18d4ad61f45669c35df9a8a11b091e5c9e57abb679b3d8d308f8c349b25e5f	fad17fb3a3ee78823eb8e4ca95379f63edd21a5e12798b1e0789047beff91fd7	9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 19, 10, 15, and 4, we can break it down into simpler steps:\n\n1. First, let's multiply 15 by 4:\n 15 * 4 = 60\n Now we have 60.\n\n2. Next, let's multiply 19 by 10:\n 19 * 10 = 190\n Now we have 60 + 190 = 250.\n\n3. Finally, let's add the two results together:\n 60 +...	[{"budget_forced_chunks": ["To solve the problem using the numbers 19, 10, 15, and 4, we can break it down into simpler steps:\n\n1. First, let's multiply 15 by 4:\n 15 * 4 = 60\n Now we have 60.\n\n2. Next, let's multiply 19 by 10:\n 19 * 10 = 190\n Now we have 60 + 190 = 250.\n\n3. Finally, let's add the two ...	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 break it down into simpler steps:\\n\\n1. First, multiply 13 and 9:\\n 13 * 9 = 117\\n\\n2. Now, we need to add 23 to 117:\\n 117 + 23 = 140\\n\\nSo, the equation that equals 24 using the given numbers is:\\n\\n<final_answer> 140 <...	["{'generation': \"To solve the problem using the numbers 23, 13, 9, and 17, we can break it down into simpler steps:\\n\\n1. First, multiply 13 and 9:\\n 13 * 9 = 117\\n\\n2. Now, we need to add 23 to 117:\\n 117 + 23 = 140\\n\\nSo, the equation that equals 24 using the given numbers is:\\n\\n<final_answer> 140 </...	a939fd76dd91760abb7e4ac6dd9cdd69c16832cb3afe806f723809d6674d9183	3af93761d572522bee5fffcdc85aac9c40d522a4f5704eb204a2145e90ca8e13	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 23, 13, 9, and 17, we can break it down into simpler steps:\n\n1. First, multiply 13 and 9:\n 13 * 9 = 117\n\n2. Now, we need to add 23 to 117:\n 117 + 23 = 140\n\nSo, the equation that equals 24 using the given numbers is:\n\n<final_answer> 140 </final_answer>\n\nAnd step-b...	[{"budget_forced_chunks": ["To solve the problem using the numbers 23, 13, 9, and 17, we can break it down into simpler steps:\n\n1. First, multiply 13 and 9:\n 13 * 9 = 117\n\n2. Now, we need to add 23 to 117:\n 117 + 23 = 140\n\nSo, the equation that equals 24 using the given numbers is:\n\n<final_answer> 140 </f...	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 problem \\\\( 20 + 9 - 1 + 3 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the addition and subtraction: \\n \\\\[ 20 + 9 = 29 \\\\]\\n Then subtract 1:\\n \\\\[ 29 - 1 = 28 \\\\]\\n\\n2. Add the result to the remaining number:\\n \\\\[ 28 + 3 = 31 \\\\...	["{'generation': \"To solve the problem \\\\( 20 + 9 - 1 + 3 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the addition and subtraction: \\n \\\\[ 20 + 9 = 29 \\\\]\\n Then subtract 1:\\n \\\\[ 29 - 1 = 28 \\\\]\\n\\n2. Add the result to the remaining number:\\n \\\\[ 28 + 3 = 31 \\\\]...	54074718fc33cde0d1ffb866e238f9ee9e73e4eb30deff57612ecfcabb7c0aa8	09a3501b533aecd2d38214aab61d6e005bf47b6c36df8a3cb6cc750794728110	b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 20 + 9 - 1 + 3 \\), we can break it down into simpler steps:\n\n1. Combine the addition and subtraction: \n \\[ 20 + 9 = 29 \\]\n Then subtract 1:\n \\[ 29 - 1 = 28 \\]\n\n2. Add the result to the remaining number:\n \\[ 28 + 3 = 31 \\]\n\nSo, the final step is to add 31 to 1:...	[{"budget_forced_chunks": ["To solve the problem \\( 20 + 9 - 1 + 3 \\), we can break it down into simpler steps:\n\n1. Combine the addition and subtraction: \n \\[ 20 + 9 = 29 \\]\n Then subtract 1:\n \\[ 29 - 1 = 28 \\]\n\n2. Add the result to the remaining number:\n \\[ 28 + 3 = 31 \\]\n\nSo, the fin...	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 problem \\\\( 19 + 19 - 1 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the numbers:\\n \\\\[\\n 19 + 19 = 38\\n \\\\]\\n \\\\[\\n 38 - 1 = 37\\n \\\\]\\n \\\\[\\n 37 + 22 = 59\\n \\\\]\\n\\nSo, the final result is \\\\( 59 \\\\).\\n\\n\\\\[\\...	["{'generation': 'To solve the problem \\\\( 19 + 19 - 1 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. Combine the numbers:\\n \\\\[\\n 19 + 19 = 38\\n \\\\]\\n \\\\[\\n 38 - 1 = 37\\n \\\\]\\n \\\\[\\n 37 + 22 = 59\\n \\\\]\\n\\nSo, the final result is \\\\( 59 \\\\).\\n\\n\\\\[\\n...	5e9a09fdc605b12c61135540e930f653f86cd4d1572d9149cb281ff1e69004e0	4a1eb49f78824faa8128953d30b3c4be9bcc3515c1d66b954e7165e50b92606f	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 19 + 19 - 1 + 22 \\), we can break it down into simpler steps:\n\n1. Combine the numbers:\n \\[\n 19 + 19 = 38\n \\]\n \\[\n 38 - 1 = 37\n \\]\n \\[\n 37 + 22 = 59\n \\]\n\nSo, the final result is \\( 59 \\).\n\n\\[\n\\boxed{59}\n\\] Hold on, let me verify this answer. 1...	[{"budget_forced_chunks": ["To solve the problem \\( 19 + 19 - 1 + 22 \\), we can break it down into simpler steps:\n\n1. Combine the numbers:\n \\[\n 19 + 19 = 38\n \\]\n \\[\n 38 - 1 = 37\n \\]\n \\[\n 37 + 22 = 59\n \\]\n\nSo, the final result is \\( 59 \\).\n\n\\[\n\\boxed{59}\n\\]", " Hold on...	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 \\\\( 6 \\\\times 16 \\\\times 17 \\\\times 21 \\\\), we will follow the standard multiplication algorithm. We'll break it down step by step:\\n\\n1. Multiply 6 by 17:\\n \\\\[\\n 6 \\\\times 17 = 6 \\\\times (10 + 7) = 6 \\\\times 10 + 6 \\\\times 7 = 60 + 42 = 102\\n ...	["{'generation': \"To solve the problem \\\\( 6 \\\\times 16 \\\\times 17 \\\\times 21 \\\\), we will follow the standard multiplication algorithm. We'll break it down step by step:\\n\\n1. Multiply 6 by 17:\\n \\\\[\\n 6 \\\\times 17 = 6 \\\\times (10 + 7) = 6 \\\\times 10 + 6 \\\\times 7 = 60 + 42 = 102\\n ...	5d6946d5bae41ad89ef8b142890fcccb941af44fcb19a052c920cc994415c022	656e0436e2d4c37f42635c0cc65e38bc1a4c562af47a499516eb06749fdba456	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 6 \\times 16 \\times 17 \\times 21 \\), we will follow the standard multiplication algorithm. We'll break it down step by step:\n\n1. Multiply 6 by 17:\n \\[\n 6 \\times 17 = 6 \\times (10 + 7) = 6 \\times 10 + 6 \\times 7 = 60 + 42 = 102\n \\]\n\n2. **Multiply 6 by 2 (and use the c...	[{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 16 \\times 17 \\times 21 \\), we will follow the standard multiplication algorithm. We'll break it down step by step:\n\n1. Multiply 6 by 17:\n \\[\n 6 \\times 17 = 6 \\times (10 + 7) = 6 \\times 10 + 6 \\times 7 = 60 + 42 = 102\n \\]\n\n2. **Mult...	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 using the numbers 3, 16, 12, and 14, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 12:\\n \\\\[ 16 \\\\times 12 = 192 \\\\]\\n\\n2. Now, we need to multiply the result by 3:\\n \\\\[ 192 \\\\times 3 = 576 \\\\]\\n\\n3. Finally, we need to add 14 to t...	["{'generation': \"To solve the problem using the numbers 3, 16, 12, and 14, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 12:\\n \\\\[ 16 \\\\times 12 = 192 \\\\]\\n\\n2. Now, we need to multiply the result by 3:\\n \\\\[ 192 \\\\times 3 = 576 \\\\]\\n\\n3. Finally, we need to add 14 to th...	d8bbffa5e5aafaa81683a064a1e22217380d39e326b48c7a3892f8be8bd55e73	ec25b954d4c64b681f6a629e1bebf6d529c421771c4d7ef6b38b109b278a8b99	c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 3, 16, 12, and 14, we can break it down into simpler steps:\n\n1. First, multiply 16 by 12:\n \\[ 16 \\times 12 = 192 \\]\n\n2. Now, we need to multiply the result by 3:\n \\[ 192 \\times 3 = 576 \\]\n\n3. Finally, we need to add 14 to the result:\n \\[ 576 + 14 = 590 \\]\...	[{"budget_forced_chunks": ["To solve the problem using the numbers 3, 16, 12, and 14, we can break it down into simpler steps:\n\n1. First, multiply 16 by 12:\n \\[ 16 \\times 12 = 192 \\]\n\n2. Now, we need to multiply the result by 3:\n \\[ 192 \\times 3 = 576 \\]\n\n3. Finally, we need to add 14 to the result:\n...	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 problem \\\\( 4 + 6 + 11 \\\\), we can break it down into simpler steps:\\n\\n1. Add 4 and 6:\\n \\\\[\\n 4 + 6 = 10\\n \\\\]\\n\\n2. Multiply the result by 11:\\n \\\\[\\n 11 \\\\times 10 = 110\\n \\\\]\\n\\nSo, the final step is to multiply the sum of 4 and 6 by 11...	["{'generation': \"To solve the problem \\\\( 4 + 6 + 11 \\\\), we can break it down into simpler steps:\\n\\n1. Add 4 and 6:\\n \\\\[\\n 4 + 6 = 10\\n \\\\]\\n\\n2. Multiply the result by 11:\\n \\\\[\\n 11 \\\\times 10 = 110\\n \\\\]\\n\\nSo, the final step is to multiply the sum of 4 and 6 by 11....	e1fd07ae613d4433c60203d498668d3115bfa1c141ec77d811980d28281a64ce	97371084dfc8c3d3a11b264c62dd52e390799a6af505406ad31e1b2b54b56055	f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 4 + 6 + 11 \\), we can break it down into simpler steps:\n\n1. Add 4 and 6:\n \\[\n 4 + 6 = 10\n \\]\n\n2. Multiply the result by 11:\n \\[\n 11 \\times 10 = 110\n \\]\n\nSo, the final step is to multiply the sum of 4 and 6 by 11. Therefore, the solution is:\n\n\\[\n4 + 6 ...	[{"budget_forced_chunks": ["To solve the problem \\( 4 + 6 + 11 \\), we can break it down into simpler steps:\n\n1. Add 4 and 6:\n \\[\n 4 + 6 = 10\n \\]\n\n2. Multiply the result by 11:\n \\[\n 11 \\times 10 = 110\n \\]\n\nSo, the final step is to multiply the sum of 4 and 6 by 11. Therefore, the s...	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 problem \\\\( 16 \\\\times 21 \\\\times 15 \\\\times 2 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two:\\n\\n1. Multiply the first two numbers:\\n \\\\[\\n 16 \\\\times 21 = 336\\n \\\\]\\n\\n2. Multiply the...	["{'generation': \"To solve the problem \\\\( 16 \\\\times 21 \\\\times 15 \\\\times 2 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two:\\n\\n1. Multiply the first two numbers:\\n \\\\[\\n 16 \\\\times 21 = 336\\n \\\\]\\n\\n2. Multiply the ...	3a1b25f4d472756ebdf562f6119b65b746b767ea84a4dd799bd070e16ecfe97b	d458798ae840986384fb19120fb9fb1a5e41c093e8037f36a443be3fcc0dcaf9	535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 16 \\times 21 \\times 15 \\times 2 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two:\n\n1. Multiply the first two numbers:\n \\[\n 16 \\times 21 = 336\n \\]\n\n2. Multiply the next two numbers:\n \\[\n 15 \\times...	[{"budget_forced_chunks": ["To solve the problem \\( 16 \\times 21 \\times 15 \\times 2 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two:\n\n1. Multiply the first two numbers:\n \\[\n 16 \\times 21 = 336\n \\]\n\n2. Multiply the next two numbe...	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 problem using the numbers 16, 4, 1, and 21, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 4:\\n [16 * 4 = 64]\\n\\n2. Next, multiply the result by 1 (which is just 1, so it doesn't change the value):\\n [64 * 1 = 64]\\n\\n3. Finally, add the two results toge...	["{'generation': \"To solve the problem using the numbers 16, 4, 1, and 21, we can break it down into simpler steps:\\n\\n1. First, multiply 16 by 4:\\n [16 * 4 = 64]\\n\\n2. Next, multiply the result by 1 (which is just 1, so it doesn't change the value):\\n [64 * 1 = 64]\\n\\n3. Finally, add the two results toget...	d072894f0ec9b0cfbfa2cc48b6771ecc2c365ef18772bb99cdcc43a7540ee46f	7bde26e5b3b1575939cd70cea46432c285a6285297650ad797a14d239b460762	b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 16, 4, 1, and 21, we can break it down into simpler steps:\n\n1. First, multiply 16 by 4:\n [16 * 4 = 64]\n\n2. Next, multiply the result by 1 (which is just 1, so it doesn't change the value):\n [64 * 1 = 64]\n\n3. Finally, add the two results together to get the final prod...	[{"budget_forced_chunks": ["To solve the problem using the numbers 16, 4, 1, and 21, we can break it down into simpler steps:\n\n1. First, multiply 16 by 4:\n [16 * 4 = 64]\n\n2. Next, multiply the result by 1 (which is just 1, so it doesn't change the value):\n [64 * 1 = 64]\n\n3. Finally, add the two results toge...	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 \\\\times 4 \\\\times 15 = 17 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 8 by 4:\\n \\\\[\\n 8 \\\\times 4 = 32\\n \\\\]\\n\\n2. Multiply the result by 15:\\n \\\\[\\n 32 \\\\times 15 = 480\\n \\\\]\\n\\n3. **Verify the result by...	["{'generation': \"To solve the problem \\\\( 8 \\\\times 4 \\\\times 15 = 17 \\\\), we can break it down into simpler steps:\\n\\n1. Multiply 8 by 4:\\n \\\\[\\n 8 \\\\times 4 = 32\\n \\\\]\\n\\n2. Multiply the result by 15:\\n \\\\[\\n 32 \\\\times 15 = 480\\n \\\\]\\n\\n3. **Verify the result by ...	efcaf1a72cc1c5524e2e8c8faf13eb037aad0cfaeda5e5f50a2a2902dde53333	23aa6021a0c062a9b897ef9afa175819a2757915f30ab230bbb56d2e9f0d4379	4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 8 \\times 4 \\times 15 = 17 \\), we can break it down into simpler steps:\n\n1. Multiply 8 by 4:\n \\[\n 8 \\times 4 = 32\n \\]\n\n2. Multiply the result by 15:\n \\[\n 32 \\times 15 = 480\n \\]\n\n3. Verify the result by using the original multiplication order:\n \\...	[{"budget_forced_chunks": ["To solve the problem \\( 8 \\times 4 \\times 15 = 17 \\), we can break it down into simpler steps:\n\n1. Multiply 8 by 4:\n \\[\n 8 \\times 4 = 32\n \\]\n\n2. Multiply the result by 15:\n \\[\n 32 \\times 15 = 480\n \\]\n\n3. **Verify the result by using the original mult...	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 problem \\\\( 20 + 17 - 24 \\\\), we can break it down into simpler steps by using basic arithmetic operations.\\n\\n### Step 1: Break down the numbers\\nWe can rewrite 20, 17, and 24 using simpler numbers:\\n- 20 as \\\\( 10 + 10 \\\\)\\n- 17 as \\\\( 10 + 7 \\\\)\\n- 24 as \\\\( 20 + ...	["{'generation': \"To solve the problem \\\\( 20 + 17 - 24 \\\\), we can break it down into simpler steps by using basic arithmetic operations.\\n\\n### Step 1: Break down the numbers\\nWe can rewrite 20, 17, and 24 using simpler numbers:\\n- 20 as \\\\( 10 + 10 \\\\)\\n- 17 as \\\\( 10 + 7 \\\\)\\n- 24 as \\\\( 20 + 4...	06649405689279406a3c70aecf0a5a85d6c4f8da6b95412e61bf2dca98890c04	55ba249ea0e0bd5cabb609e0cc089c7f40c89a4d809e27c8712b899ba78b1571	3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 20 + 17 - 24 \\), we can break it down into simpler steps by using basic arithmetic operations.\n\n### Step 1: Break down the numbers\nWe can rewrite 20, 17, and 24 using simpler numbers:\n- 20 as \\( 10 + 10 \\)\n- 17 as \\( 10 + 7 \\)\n- 24 as \\( 20 + 4 \\)\n\n### Step 2: Test different co...	[{"budget_forced_chunks": ["To solve the problem \\( 20 + 17 - 24 \\), we can break it down into simpler steps by using basic arithmetic operations.\n\n### Step 1: Break down the numbers\nWe can rewrite 20, 17, and 24 using simpler numbers:\n- 20 as \\( 10 + 10 \\)\n- 17 as \\( 10 + 7 \\)\n- 24 as \\( 20 + 4 \\)\n\n###...	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 using the numbers 9, 14, 11, and 17, we can follow these steps:\\n\\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 14 in this case.\\n\\n2. **Construct the equa...	["{'generation': \"To solve the problem using the numbers 9, 14, 11, and 17, we can follow these steps:\\n\\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 14 in this case.\\n\\n2. **Construct the equat...	0e937e0893608a7dccea4dc5ebe2f18c3d7a0f90b5cea4b17f34fb5a0fddcb7e	4367a333b8fbb8824e45aa74045b82d4909a70148afc968b397a44152d78cf2d	8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem using the numbers 9, 14, 11, and 17, we can follow these steps:\n\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 14 in this case.\n\n2. Construct the equation:\n - Step 1: ...	[{"budget_forced_chunks": ["To solve the problem using the numbers 9, 14, 11, and 17, we can follow these steps:\n\n1. Identify the operations needed: We need to combine the numbers using addition, subtraction, multiplication, and division to reach the target number, which is 14 in this case.\n\n2. **Construct the ...	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 problem \\\\( 22 \\\\times 16 \\\\times 5 \\\\times 15 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results.\\n\\nStep 1: Multiply 22 by 15.\\n\\\\[ 22 \\\\times 15 = (20 + 2) \\\\times ...	["{'generation': \"To solve the problem \\\\( 22 \\\\times 16 \\\\times 5 \\\\times 15 \\\\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results.\\n\\nStep 1: Multiply 22 by 15.\\n\\\\[ 22 \\\\times 15 = (20 + 2) \\\\times 1...	c05b04ca7ae2cc4348826abbfbaf15c8c666eac685b4eac2862b07de889f7024	a3e4733b904b745aded4db23f1be09a0a5ea7593a933cb6bee0e85f6aba4d55f	4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a	[false]	samples_countdown_2025-06-05T15-54-45.609462.jsonl	["To solve the problem \\( 22 \\times 16 \\times 5 \\times 15 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results.\n\nStep 1: Multiply 22 by 15.\n\\[ 22 \\times 15 = (20 + 2) \\times 15 = (20 \\times 15) + (2 \\times 15)...	[{"budget_forced_chunks": ["To solve the problem \\( 22 \\times 16 \\times 5 \\times 15 \\), we can break it down into simpler steps by first multiplying two of the numbers and then multiplying the other two, and finally adding the results.\n\nStep 1: Multiply 22 by 15.\n\\[ 22 \\times 15 = (20 + 2) \\times 15 = (20 \\...	null

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