doc_id int64 | doc string | target string | arguments string | resps string | filtered_resps string | doc_hash string | prompt_hash string | target_hash string | exact_match int64 | 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': '<think>First, we need to use the numbers 15, 19, and 9 to create an equation that equals 13. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 15 + 19 = 34\\nStep 2: 34 - 9 = 25\\n</final_answer>\\n\\n<answer> (15 + 19) - 9 = 25 </answer> Wait, this result is 25, not 13. did i m... | ["{'generation': '<think>First, we need to use the numbers 15, 19, and 9 to create an equation that equals 13. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 15 + 19 = 34\\nStep 2: 34 - 9 = 25\\n</final_answer>\\n\\n<answer> (15 + 19) - 9 = 25 </answer> Wait, this result is 25, not 13. did i mi... | 1fe4a3a3bdceb99acba3870b8820fb7d71d2b128097a35de13101519c94b2714 | 6adf7f5ba7f8982f91ce5cd729a078032176cbdfc8ebc8d4eaebb7f44a3a1fb4 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 15, 19, and 9 to create an equation that equals 13. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 15 + 19 = 34\nStep 2: 34 - 9 = 25\n</final_answer>\n\n<answer> (15 + 19) - 9 = 25 </answer> Wait, this result is 25, not 13. did i miss something?</Assistan... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 15, 19, and 9 to create an equation that equals 13. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 15 + 19 = 34\nStep 2: 34 - 9 = 25\n</final_answer>\n\n<answer> (15 + 19) - 9 = 25 </answer>", " Wait, this result is 25, not 13. d... | 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 will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mu... | ["{'generation': \"To solve the problem \\\\( 20 + 9 - 2 + 24 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mul... | 4e7925e9464d9cd3f15b66d7f0d396c2d208e935db23218e8e12a143a69fdcf5 | bd97db98bf338537ff6865ad3edb32a5afd84e1c203f33f3a520ad9350cff93a | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 20 + 9 - 2 + 24 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Multiply next to the first n... | [{"budget_forced_chunks": ["To solve the problem \\( 20 + 9 - 2 + 24 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Mu... | 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': '<think>First, we can add or subtract the numbers at the first glance. In this case, 13 and 3 can be eliminated because they sum up to 16 which is not divisible by 3. So we are left with 18 and 10.</think>\\\\n<final_answer>\\\\nStep 1: 18 * 10 = 180\\\\n</final_answer>\\' Wait, let me try 13 + 3 firs... | ["{'generation': '<think>First, we can add or subtract the numbers at the first glance. In this case, 13 and 3 can be eliminated because they sum up to 16 which is not divisible by 3. So we are left with 18 and 10.</think>\\\\n<final_answer>\\\\nStep 1: 18 * 10 = 180\\\\n</final_answer>\\' Wait, let me try 13 + 3 first... | 21d37d7882ca656e9c61892eb0e92eb17e6ccb0b44acbf990becc8d10939c8ba | 01fe40f4315157fd51d595d12678270a8d4a97c88098425b3b2c89768f826ed6 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we can add or subtract the numbers at the first glance. In this case, 13 and 3 can be eliminated because they sum up to 16 which is not divisible by 3. So we are left with 18 and 10.</think>\\n<final_answer>\\nStep 1: 18 * 10 = 180\\n</final_answer>' Wait, let me try 13 + 3 first...</wait><think>13 * 3 ... | [{"budget_forced_chunks": ["<think>First, we can add or subtract the numbers at the first glance. In this case, 13 and 3 can be eliminated because they sum up to 16 which is not divisible by 3. So we are left with 18 and 10.</think>\\n<final_answer>\\nStep 1: 18 * 10 = 180\\n</final_answer>'", " Wait, let me try 13 + 3... | 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 + 3 \\\\times 2 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step**: Multiply 3 by 2.\\n \\\\[\\n 3 \\\\times 2 = 6\\n \\\\]\\n\\n2. **Second Step**: Add the result from the first step to 22.\\n \\\\[\\n 22 + 6 = 28\\n \\\\]\\n\\n3. **... | ["{'generation': 'To solve the problem \\\\( 23 + 3 \\\\times 2 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step**: Multiply 3 by 2.\\n \\\\[\\n 3 \\\\times 2 = 6\\n \\\\]\\n\\n2. **Second Step**: Add the result from the first step to 22.\\n \\\\[\\n 22 + 6 = 28\\n \\\\]\\n\\n3. **T... | 95ef82ecb05d93a4ee380d4641abaeadd43e6bc9d99c871ce170758b6f305b44 | b74d9dce0967059bc7deb16d7c3ce9ddb7cfb27d70d2987dea642c679674d513 | 6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 23 + 3 \\times 2 + 22 \\), we can break it down into simpler steps:\n\n1. **First Step**: Multiply 3 by 2.\n \\[\n 3 \\times 2 = 6\n \\]\n\n2. **Second Step**: Add the result from the first step to 22.\n \\[\n 22 + 6 = 28\n \\]\n\n3. **Third Step**: Add the result from the second ... | [{"budget_forced_chunks": ["To solve the problem \\( 23 + 3 \\times 2 + 22 \\), we can break it down into simpler steps:\n\n1. **First Step**: Multiply 3 by 2.\n \\[\n 3 \\times 2 = 6\n \\]\n\n2. **Second Step**: Add the result from the first step to 22.\n \\[\n 22 + 6 = 28\n \\]\n\n3. **Third Step**: Add t... | 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': \"<think>Step 1: We need to use the numbers 3, 8, 4, and 13 exactly once each. We can start by combining the larger numbers: 13 and 8.</think>\\n<final_answer>\\nStep 1: 13 * 8 = 104\\n</final_answer> Wait, this result is 104, not 17. did i misunderstand the question?</assistant> Wait, how? 13 * 8 is ... | ["{'generation': \"<think>Step 1: We need to use the numbers 3, 8, 4, and 13 exactly once each. We can start by combining the larger numbers: 13 and 8.</think>\\n<final_answer>\\nStep 1: 13 * 8 = 104\\n</final_answer> Wait, this result is 104, not 17. did i misunderstand the question?</assistant> Wait, how? 13 * 8 is n... | 37e0958fcc9b1045189fb65b03cc9e071033593787e2f5171ceea9f86e8ebcf4 | ec571e8688c75a5736ce86b7195b61373aaf0be543ff8182bc2cf3a6429e9eab | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: We need to use the numbers 3, 8, 4, and 13 exactly once each. We can start by combining the larger numbers: 13 and 8.</think>\n<final_answer>\nStep 1: 13 * 8 = 104\n</final_answer> Wait, this result is 104, not 17. did i misunderstand the question?</assistant> Wait, how? 13 * 8 is not enough, i need to... | [{"budget_forced_chunks": ["<think>Step 1: We need to use the numbers 3, 8, 4, and 13 exactly once each. We can start by combining the larger numbers: 13 and 8.</think>\n<final_answer>\nStep 1: 13 * 8 = 104\n</final_answer>", " Wait, this result is 104, not 17. did i misunderstand the question?</assistant>", " Wait, ho... | 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': \"<think>18 can be obtained by multiplying 12 by 6, and then adding 12 to the result. This is because 12 * 6 = 72, and 72 + 12 = 84. However, we need to use each number once, so we will rearrange the operations.</think>\\\\n<final_answer>\\\\\\nStep 1: 12 * 6 = 72\\nStep 2: 72 + 12 = 84\\n</final_answ... | ["{'generation': \"<think>18 can be obtained by multiplying 12 by 6, and then adding 12 to the result. This is because 12 * 6 = 72, and 72 + 12 = 84. However, we need to use each number once, so we will rearrange the operations.</think>\\\\n<final_answer>\\\\\\nStep 1: 12 * 6 = 72\\nStep 2: 72 + 12 = 84\\n</final_answe... | a4b2daca5c54b55b15980110f282e22f14fac0971c9652711d3a679e8bd89a3d | 7cfb8ba4d40ba72deb7d7f9cb5b33545b9f643be9e6bb394acaf180179e28cd4 | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>18 can be obtained by multiplying 12 by 6, and then adding 12 to the result. This is because 12 * 6 = 72, and 72 + 12 = 84. However, we need to use each number once, so we will rearrange the operations.</think>\\n<final_answer>\\\nStep 1: 12 * 6 = 72\nStep 2: 72 + 12 = 84\n</final_answer>' But to confirm, 12(1... | [{"budget_forced_chunks": ["<think>18 can be obtained by multiplying 12 by 6, and then adding 12 to the result. This is because 12 * 6 = 72, and 72 + 12 = 84. However, we need to use each number once, so we will rearrange the operations.</think>\\n<final_answer>\\\nStep 1: 12 * 6 = 72\nStep 2: 72 + 12 = 84\n</final_ans... | 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': \"<think>Step 1: We need to use the numbers 6, 15, 13, and 9 exactly once each in our equation.\\nStep 2: The target number is 21.\\nStep 3: We can start by multiplying the two largest numbers, 15 and 13.\\n</think>\\n\\n<final_answer>\\nStep 1: 15 * 13 = 195\\nStep 2: Now we need to multiply the next... | ["{'generation': \"<think>Step 1: We need to use the numbers 6, 15, 13, and 9 exactly once each in our equation.\\nStep 2: The target number is 21.\\nStep 3: We can start by multiplying the two largest numbers, 15 and 13.\\n</think>\\n\\n<final_answer>\\nStep 1: 15 * 13 = 195\\nStep 2: Now we need to multiply the next ... | a7f237e6a8b37389748df0baa5ea27734734e3277f163e579d92165e4afed893 | ab00774c40567d2e767072fc5936db116736f40a30593069488d7cfe010b27b9 | 6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: We need to use the numbers 6, 15, 13, and 9 exactly once each in our equation.\nStep 2: The target number is 21.\nStep 3: We can start by multiplying the two largest numbers, 15 and 13.\n</think>\n\n<final_answer>\nStep 1: 15 * 13 = 195\nStep 2: Now we need to multiply the next number, 9, by either 15 ... | [{"budget_forced_chunks": ["<think>Step 1: We need to use the numbers 6, 15, 13, and 9 exactly once each in our equation.\nStep 2: The target number is 21.\nStep 3: We can start by multiplying the two largest numbers, 15 and 13.\n</think>\n\n<final_answer>\nStep 1: 15 * 13 = 195\nStep 2: Now we need to multiply the nex... | 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 + 8 + 2 + 11 \\\\), we can break it down into simpler steps:\\n\\n1. **Add the first two numbers:**\\n \\\\[\\n 2 + 8 = 10\\n \\\\]\\n\\n2. **Add the next two numbers:**\\n \\\\[\\n 2 + 11 = 13\\n \\\\]\\n\\n3. **Combine the results from step 1 and step 2:**\... | ["{'generation': \"To solve the problem \\\\( 2 + 8 + 2 + 11 \\\\), we can break it down into simpler steps:\\n\\n1. **Add the first two numbers:**\\n \\\\[\\n 2 + 8 = 10\\n \\\\]\\n\\n2. **Add the next two numbers:**\\n \\\\[\\n 2 + 11 = 13\\n \\\\]\\n\\n3. **Combine the results from step 1 and step 2:**\\... | 45c1e59b5a1a576b7ae49ac9ab5ee519341b3ff5d15693635b6c69819b16325f | 0e76d7adfecf1d484230f45f4d7e233e3860bce62d005024a9c931e6fe2a8c02 | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 2 + 8 + 2 + 11 \\), we can break it down into simpler steps:\n\n1. **Add the first two numbers:**\n \\[\n 2 + 8 = 10\n \\]\n\n2. **Add the next two numbers:**\n \\[\n 2 + 11 = 13\n \\]\n\n3. **Combine the results from step 1 and step 2:**\n \\[\n 10 + 13 = 23\n \\]\n\nSo, th... | [{"budget_forced_chunks": ["To solve the problem \\( 2 + 8 + 2 + 11 \\), we can break it down into simpler steps:\n\n1. **Add the first two numbers:**\n \\[\n 2 + 8 = 10\n \\]\n\n2. **Add the next two numbers:**\n \\[\n 2 + 11 = 13\n \\]\n\n3. **Combine the results from step 1 and step 2:**\n \\[\n 10 +... | 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 \\\\( 21 + 15 + 5 + 9 \\\\), we will follow the standard method of adding multiple numbers together. Let's break it down step by step:\\n\\n1. **Add the first two numbers:**\\n \\\\[\\n 21 + 15 = 36\\n \\\\]\\n\\n2. **Add the next number to the result:**\\n \\\\[\\n 36... | ["{'generation': \"To solve the problem \\\\( 21 + 15 + 5 + 9 \\\\), we will follow the standard method of adding multiple numbers together. Let's break it down step by step:\\n\\n1. **Add the first two numbers:**\\n \\\\[\\n 21 + 15 = 36\\n \\\\]\\n\\n2. **Add the next number to the result:**\\n \\\\[\\n 36 ... | 167220307e1ef076a95de3ecc155ceac76542c67d9bfe7f28083afac878049e0 | 15b1e41847c3fd678b61f9e016eda0d418836829766dc3d9e8d8e1b5133c1d3a | 785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 21 + 15 + 5 + 9 \\), we will follow the standard method of adding multiple numbers together. Let's break it down step by step:\n\n1. **Add the first two numbers:**\n \\[\n 21 + 15 = 36\n \\]\n\n2. **Add the next number to the result:**\n \\[\n 36 + 5 = 41\n \\]\n\n3. **Add the fin... | [{"budget_forced_chunks": ["To solve the problem \\( 21 + 15 + 5 + 9 \\), we will follow the standard method of adding multiple numbers together. Let's break it down step by step:\n\n1. **Add the first two numbers:**\n \\[\n 21 + 15 = 36\n \\]\n\n2. **Add the next number to the result:**\n \\[\n 36 + 5 = 41\n... | 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': \"<think>Step 1: We need to use the numbers 6, 22, and 14 to create an equation that equals 14. We can only use each number once.</think>\\n<think>Step 2: Let's start by multiplying the two larger numbers, 22 and 14.</think>\\n<think>14 x 14 = 196</think>\\n<think>Now, we need to multiply the result b... | ["{'generation': \"<think>Step 1: We need to use the numbers 6, 22, and 14 to create an equation that equals 14. We can only use each number once.</think>\\n<think>Step 2: Let's start by multiplying the two larger numbers, 22 and 14.</think>\\n<think>14 x 14 = 196</think>\\n<think>Now, we need to multiply the result by... | 9177efbdceb2c6d3585fa1de81c78225fbf88132fb0ae87fe539a216301a3389 | a3d20e36b20880d64b880d4378e3aea9de8a3687a302888a392e88997a29b20f | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: We need to use the numbers 6, 22, and 14 to create an equation that equals 14. We can only use each number once.</think>\n<think>Step 2: Let's start by multiplying the two larger numbers, 22 and 14.</think>\n<think>14 x 14 = 196</think>\n<think>Now, we need to multiply the result by the remaining numbe... | [{"budget_forced_chunks": ["<think>Step 1: We need to use the numbers 6, 22, and 14 to create an equation that equals 14. We can only use each number once.</think>\n<think>Step 2: Let's start by multiplying the two larger numbers, 22 and 14.</think>\n<think>14 x 14 = 196</think>\n<think>Now, we need to multiply the res... | 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 = 12 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n - \\\\( 20 + 15 \\\\)\\n - \\\\( 15 + 17 \\\\)\\n\\n2. **Add the numbers within each group:**\\n - For \\\\( 20 + 15 \\\\):\\n \\\\[\\n 20 + 15 = 3... | ["{'generation': \"To solve the problem \\\\( 20 + 15 + 17 = 12 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n - \\\\( 20 + 15 \\\\)\\n - \\\\( 15 + 17 \\\\)\\n\\n2. **Add the numbers within each group:**\\n - For \\\\( 20 + 15 \\\\):\\n \\\\[\\n 20 + 15 = 35... | fa4cb9ed4e55cbe2ea009410b3c7dcdfb08848fdb2331821ffa94d8b437f7ed2 | 484114ad1c6eb12bf2e842b3e234616a60cc354ec1f3bada427e5e83ddb21194 | 6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 20 + 15 + 17 = 12 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n - \\( 20 + 15 \\)\n - \\( 15 + 17 \\)\n\n2. **Add the numbers within each group:**\n - For \\( 20 + 15 \\):\n \\[\n 20 + 15 = 35\n \\]\n - For \\( 15 + 17 \\):\n ... | [{"budget_forced_chunks": ["To solve the problem \\( 20 + 15 + 17 = 12 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n - \\( 20 + 15 \\)\n - \\( 15 + 17 \\)\n\n2. **Add the numbers within each group:**\n - For \\( 20 + 15 \\):\n \\[\n 20 + 15 = 35\n \\]\n - F... | 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': \"<think>Step 1: We need to use the numbers 18, 9, 21, and 11 in some order within the arithmetic operations (+, -, *, /). We'll start with the highest numbers and work our way down.</think>\\n<think>Step 2: Let's try subtracting the smaller numbers from the larger ones.</think>\\n<think> try1: 21 - 9... | ["{'generation': \"<think>Step 1: We need to use the numbers 18, 9, 21, and 11 in some order within the arithmetic operations (+, -, *, /). We'll start with the highest numbers and work our way down.</think>\\n<think>Step 2: Let's try subtracting the smaller numbers from the larger ones.</think>\\n<think> try1: 21 - 9 ... | aeab403787979ca2e59c5279813784a23284ef1d2d9e6cce4c2f457d9a376fa5 | 7b22993c7049eb435ab1c64d209542f9d5b0889583f68f7daa920a8fdd4d143a | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: We need to use the numbers 18, 9, 21, and 11 in some order within the arithmetic operations (+, -, *, /). We'll start with the highest numbers and work our way down.</think>\n<think>Step 2: Let's try subtracting the smaller numbers from the larger ones.</think>\n<think> try1: 21 - 9 = 12 </think>\n<thi... | [{"budget_forced_chunks": ["<think>Step 1: We need to use the numbers 18, 9, 21, and 11 in some order within the arithmetic operations (+, -, *, /). We'll start with the highest numbers and work our way down.</think>\n<think>Step 2: Let's try subtracting the smaller numbers from the larger ones.</think>\n<think> try1: ... | 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 \\\\( 24 + 9 - 17 + 6 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mu... | ["{'generation': \"To solve the problem \\\\( 24 + 9 - 17 + 6 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mul... | 94cc4d46a251029a832d451e9841ef5724b174c7b59c6c76e1127a5ee0081cab | 7a5b85f69b00da4f91c788b8cf04b98ce70fb22eb4c3489edad15c24280dac29 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 24 + 9 - 17 + 6 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Multiply next to the first n... | [{"budget_forced_chunks": ["To solve the problem \\( 24 + 9 - 17 + 6 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Mu... | 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. **First Step:** Calculate \\\\( 10 + 21 \\\\):\\n \\\\[\\n 10 + 21 = 31\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 17 \\\\) from the result:\\n \\\\[\\n 31 - 17 = 14\\n \\\\]\\n\\n3... | ["{'generation': \"To solve the problem \\\\( 10 + 21 - 17 + 20 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Calculate \\\\( 10 + 21 \\\\):\\n \\\\[\\n 10 + 21 = 31\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 17 \\\\) from the result:\\n \\\\[\\n 31 - 17 = 14\\n \\\\]\\n\\n3.... | 1100061fa8b2c459d70a76ef486ae8bad9ac3ddfb304ee3c982e7dc2c573a770 | d068197d7d7b5cec6b7b9f6025420f133708054938f2ab0eba12d3306994440a | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 10 + 21 - 17 + 20 \\), we can break it down into simpler steps:\n\n1. **First Step:** Calculate \\( 10 + 21 \\):\n \\[\n 10 + 21 = 31\n \\]\n\n2. **Second Step:** Subtract \\( 17 \\) from the result:\n \\[\n 31 - 17 = 14\n \\]\n\n3. **Third Step:** Add \\( 20 \\) to the result of ... | [{"budget_forced_chunks": ["To solve the problem \\( 10 + 21 - 17 + 20 \\), we can break it down into simpler steps:\n\n1. **First Step:** Calculate \\( 10 + 21 \\):\n \\[\n 10 + 21 = 31\n \\]\n\n2. **Second Step:** Subtract \\( 17 \\) from the result:\n \\[\n 31 - 17 = 14\n \\]\n\n3. **Third Step:** Add \\... | 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, we can use the numbers [20, 11, 16, 1] and apply the basic arithmetic operations (+, -, *, /). We need to use each number once.\\n\\n<think>Step 1: We can start by adding the two largest numbers, 20 and 16.</think>\\n<final_answer>\\nStep 1: 20 + 16 = 36\\n</final_answer> Wait,... | ["{'generation': \"To solve the problem, we can use the numbers [20, 11, 16, 1] and apply the basic arithmetic operations (+, -, *, /). We need to use each number once.\\n\\n<think>Step 1: We can start by adding the two largest numbers, 20 and 16.</think>\\n<final_answer>\\nStep 1: 20 + 16 = 36\\n</final_answer> Wait, ... | 02fd4efda14193a5a878824c080d69604c3ea776d1bc6cf3bc6bc40ea401d5a6 | bdb69ef7d0d7581d293cc62945c5493161826c3dbb4a101a65138f34bc2cedcd | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the numbers [20, 11, 16, 1] and apply the basic arithmetic operations (+, -, *, /). We need to use each number once.\n\n<think>Step 1: We can start by adding the two largest numbers, 20 and 16.</think>\n<final_answer>\nStep 1: 20 + 16 = 36\n</final_answer> Wait, this result is 36, not... | [{"budget_forced_chunks": ["To solve the problem, we can use the numbers [20, 11, 16, 1] and apply the basic arithmetic operations (+, -, *, /). We need to use each number once.\n\n<think>Step 1: We can start by adding the two largest numbers, 20 and 16.</think>\n<final_answer>\nStep 1: 20 + 16 = 36\n</final_answer>", ... | 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 8 to the result:\\n \\\\[\\n 16 + 8 ... | ["{'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 8 to the result:\\n \\\\[\\n 16 + 8 =... | e8f9d6da576987a0f9ad4e735715a675cb636b1e6359c3737005d2f84e0e931e | e47f6ad2fb6e83931a5c6e780c6c9c44cb122930e07b0fc80073a360594ffa5f | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.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 8 to the result:\n \\[\n 16 + 8 = 24\n \\]\n\nSo, the solution to the equati... | [{"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 8 to the result:\n \\[\n 16 + 8 = 24\n \\]\n\nSo, ... | 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': \"<think>First, we need to use the numbers 18, 6, and 9 to create an equation that equals 12. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 18 + 6 = 24\\nStep 2: 24 - 9 = 15\\n</final_answer>\\n\\n<answer> (18 + 6) - 9 </answer> However, 18 + 6 = 24, 24 - 9 = 15, so the corre... | ["{'generation': \"<think>First, we need to use the numbers 18, 6, and 9 to create an equation that equals 12. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 18 + 6 = 24\\nStep 2: 24 - 9 = 15\\n</final_answer>\\n\\n<answer> (18 + 6) - 9 </answer> However, 18 + 6 = 24, 24 - 9 = 15, so the correc... | d9866959919cc04a8c5fdc04301ce1d8f7a08914d45734f9db2a90cd577f5729 | deb0fba45a8cb601a95fc271d175d8ba01be733fcd684e11ff3d617fd59cf7cb | 6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 18, 6, and 9 to create an equation that equals 12. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 18 + 6 = 24\nStep 2: 24 - 9 = 15\n</final_answer>\n\n<answer> (18 + 6) - 9 </answer> However, 18 + 6 = 24, 24 - 9 = 15, so the correct answer is <final_answe... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 18, 6, and 9 to create an equation that equals 12. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 18 + 6 = 24\nStep 2: 24 - 9 = 15\n</final_answer>\n\n<answer> (18 + 6) - 9 </answer>", " However, 18 + 6 = 24, 24 - 9 = 15, so the ... | 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, we can use the given numbers [18, 24, 23, 7] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 23.\\n\\n<think>Let's break down the numbers and think about combining them in different ways:</think>\\n\\n<final_answer>\\nStep 1: 18 +... | ["{'generation': \"To solve the problem, we can use the given numbers [18, 24, 23, 7] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 23.\\n\\n<think>Let's break down the numbers and think about combining them in different ways:</think>\\n\\n<final_answer>\\nStep 1: 18 + ... | 25ddf3f8a07e523e1d9a482834dcac9fcaaebbac9dc38427e65a040a73467cd9 | 660761dff690d0d86c98fbbb63a3514001fc3380534e701bd7dbfc911373b943 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the given numbers [18, 24, 23, 7] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 23.\n\n<think>Let's break down the numbers and think about combining them in different ways:</think>\n\n<final_answer>\nStep 1: 18 + 24 = 42\nStep 2: 42 - ... | [{"budget_forced_chunks": ["To solve the problem, we can use the given numbers [18, 24, 23, 7] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 23.\n\n<think>Let's break down the numbers and think about combining them in different ways:</think>\n\n<final_answer>\nStep 1: 1... | 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 \\\\( 8 \\\\times 19 \\\\) using the given numbers and operations, we can break it down into simpler steps.\\n\\n1. **Break down the multiplication:**\\n \\\\[\\n 8 \\\\times 19 = 8 \\\\times (10 + 9)\\n \\\\]\\n This is based on the distributive property of multiplicati... | ["{'generation': \"To solve the problem \\\\( 8 \\\\times 19 \\\\) using the given numbers and operations, we can break it down into simpler steps.\\n\\n1. **Break down the multiplication:**\\n \\\\[\\n 8 \\\\times 19 = 8 \\\\times (10 + 9)\\n \\\\]\\n This is based on the distributive property of multiplicatio... | 1cd1ac367b8094381769d347eecffee28ecb19caa550d2df703e5cde7cd4becf | 6bfcb228fc7047fd6a48a7db20c9b22405f716d78e11232a2351199c622a496b | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 8 \\times 19 \\) using the given numbers and operations, we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 8 \\times 19 = 8 \\times (10 + 9)\n \\]\n This is based on the distributive property of multiplication over addition.\n\n2. **Apply the di... | [{"budget_forced_chunks": ["To solve the problem \\( 8 \\times 19 \\) using the given numbers and operations, we can break it down into simpler steps.\n\n1. **Break down the multiplication:**\n \\[\n 8 \\times 19 = 8 \\times (10 + 9)\n \\]\n This is based on the distributive property of multiplication over addi... | 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 8: \\n \\\\[\\n 2 \\\\times 8 = 16\\n \\\\]\\n\\n2. Next, multiply 3 and 2:\\n \\\\[\\n 3 \\\\times 2 = 6\\n \\\\]\\n\\n3. Now, add the results from the two... | ["{'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 8: \\n \\\\[\\n 2 \\\\times 8 = 16\\n \\\\]\\n\\n2. Next, multiply 3 and 2:\\n \\\\[\\n 3 \\\\times 2 = 6\\n \\\\]\\n\\n3. Now, add the results from the two ... | 60dc4901c356bcb56bba8d524e1d45208b1b9d878f2ef89d3af8dfd467b2a7df | 1321f842cb74d6de4fc8454a45b42fec7481a7e861fdb5b5ca907b30d14ffda3 | 6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.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 8: \n \\[\n 2 \\times 8 = 16\n \\]\n\n2. Next, multiply 3 and 2:\n \\[\n 3 \\times 2 = 6\n \\]\n\n3. Now, add the results from the two multiplications:\n \\[\n 16 + 6 = 22\... | [{"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 8: \n \\[\n 2 \\times 8 = 16\n \\]\n\n2. Next, multiply 3 and 2:\n \\[\n 3 \\times 2 = 6\n \\]\n\n3. Now, add the results from the two multiplications... | 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 \\\\( 7 + 18 - 5 + 24 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Calculate \\\\( 7 + 18 \\\\).\\n \\\\[\\n 7 + 18 = 25\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 5 \\\\) from the result.\\n \\\\[\\n 25 - 5 = 20\\n \\\\]\\n\\n3. **Th... | ["{'generation': \"To solve the problem \\\\( 7 + 18 - 5 + 24 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Calculate \\\\( 7 + 18 \\\\).\\n \\\\[\\n 7 + 18 = 25\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 5 \\\\) from the result.\\n \\\\[\\n 25 - 5 = 20\\n \\\\]\\n\\n3. **Thi... | 06cca78287b0d4bbe85792545a31e52e50410de869f5164f38c7f45cfaec36c0 | 29d339d1a73cab0b263042199e1b89def0f3593d74ca75cb8f89346bce8efeca | f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 7 + 18 - 5 + 24 \\), we can break it down into simpler steps:\n\n1. **First Step:** Calculate \\( 7 + 18 \\).\n \\[\n 7 + 18 = 25\n \\]\n\n2. **Second Step:** Subtract \\( 5 \\) from the result.\n \\[\n 25 - 5 = 20\n \\]\n\n3. **Third Step:** Add \\( 24 \\) to the result from the ... | [{"budget_forced_chunks": ["To solve the problem \\( 7 + 18 - 5 + 24 \\), we can break it down into simpler steps:\n\n1. **First Step:** Calculate \\( 7 + 18 \\).\n \\[\n 7 + 18 = 25\n \\]\n\n2. **Second Step:** Subtract \\( 5 \\) from the result.\n \\[\n 25 - 5 = 20\n \\]\n\n3. **Third Step:** Add \\( 24 \... | 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': \"<think>First, we can add 14 and 15 to get 29, and then subtract 24 from 29 to get 5. This uses four of the five numbers.</think>\\\\n<final_answer>\\\\nStep 1: 14 + 15 = 29\\nStep 2: 29 - 24 = 5\\n</final_answer>'Assistant: <answer> 5</answer> However, 15 was used twice, so the correct equation shou... | ["{'generation': \"<think>First, we can add 14 and 15 to get 29, and then subtract 24 from 29 to get 5. This uses four of the five numbers.</think>\\\\n<final_answer>\\\\nStep 1: 14 + 15 = 29\\nStep 2: 29 - 24 = 5\\n</final_answer>'Assistant: <answer> 5</answer> However, 15 was used twice, so the correct equation shoul... | 1955abb6fb8a09c76c5348e083bbebb0a33332ecf20a36bb471cd1d8f35b73a1 | b8a8b41d18a1eb8b0faef834e0879fe35579560714765ba93d86fd34739a4fc7 | b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we can add 14 and 15 to get 29, and then subtract 24 from 29 to get 5. This uses four of the five numbers.</think>\\n<final_answer>\\nStep 1: 14 + 15 = 29\nStep 2: 29 - 24 = 5\n</final_answer>'Assistant: <answer> 5</answer> However, 15 was used twice, so the correct equation should be:<think>Using 14, 1... | [{"budget_forced_chunks": ["<think>First, we can add 14 and 15 to get 29, and then subtract 24 from 29 to get 5. This uses four of the five numbers.</think>\\n<final_answer>\\nStep 1: 14 + 15 = 29\nStep 2: 29 - 24 = 5\n</final_answer>'Assistant: <answer> 5</answer>", " However, 15 was used twice, so the correct equatio... | 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, let's multiply 14 by 6:\\n - 14 * 6 = 84\\n\\n2. Now, we need to multiply 9 by the result from step 1 (84):\\n - 9 * 84 = 756\\n\\n3. Finally, we need to add 5 to the result from step ... | ["{'generation': \"To solve the problem using the numbers 5, 14, 6, and 9, we can break it down into simpler steps:\\n\\n1. First, let's multiply 14 by 6:\\n - 14 * 6 = 84\\n\\n2. Now, we need to multiply 9 by the result from step 1 (84):\\n - 9 * 84 = 756\\n\\n3. Finally, we need to add 5 to the result from step 2... | 082771250b668f5226cf3648d240e6c619be27b661df71e8f29ac9c0df5488f9 | 37185b44b5e1a9df65f24f8419874e6140b44c63509ae6a7873eb6b60f0cf67e | 4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem using the numbers 5, 14, 6, and 9, we can break it down into simpler steps:\n\n1. First, let's multiply 14 by 6:\n - 14 * 6 = 84\n\n2. Now, we need to multiply 9 by the result from step 1 (84):\n - 9 * 84 = 756\n\n3. Finally, we need to add 5 to the result from step 2 (756):\n - 756 + 5 = 7... | [{"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, let's multiply 14 by 6:\n - 14 * 6 = 84\n\n2. Now, we need to multiply 9 by the result from step 1 (84):\n - 9 * 84 = 756\n\n3. Finally, we need to add 5 to the result from step ... | 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': \"<think>First, let's try to combine the numbers in some way:</think>\\n<final_answer>\\nStep 1: 3 x 8 = 24 (we can't use 3 again, so we'll keep it as is)\\nStep 2: 6 x 14 = 84\\nAdding them together: 24 + 84 = 108\\n</final_answer>' Wait! I can double check this answer. 3*8 is 24, and 6*14 is 84. Com... | ["{'generation': \"<think>First, let's try to combine the numbers in some way:</think>\\n<final_answer>\\nStep 1: 3 x 8 = 24 (we can't use 3 again, so we'll keep it as is)\\nStep 2: 6 x 14 = 84\\nAdding them together: 24 + 84 = 108\\n</final_answer>' Wait! I can double check this answer. 3*8 is 24, and 6*14 is 84. Comb... | 8b9702914657f73013262b009fc3552edf08395b0dbe2e572bbc5cd37ecd3387 | b75ad6172d90b6085ea5c6a2c9338e58019c6a42f9b71f4bd33140b7b0ca72d2 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, let's try to combine the numbers in some way:</think>\n<final_answer>\nStep 1: 3 x 8 = 24 (we can't use 3 again, so we'll keep it as is)\nStep 2: 6 x 14 = 84\nAdding them together: 24 + 84 = 108\n</final_answer>' Wait! I can double check this answer. 3*8 is 24, and 6*14 is 84. Combine them and you'll ge... | [{"budget_forced_chunks": ["<think>First, let's try to combine the numbers in some way:</think>\n<final_answer>\nStep 1: 3 x 8 = 24 (we can't use 3 again, so we'll keep it as is)\nStep 2: 6 x 14 = 84\nAdding them together: 24 + 84 = 108\n</final_answer>'", " Wait! I can double check this answer. 3*8 is 24, and 6*14 is ... | 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': \"<think>First, we need to multiply 13 and 2:</think>\\n<final_answer>\\nStep 1: 13 * 2 = 26\\n</final_answer>\\n\\n<think>Now, we need to multiply the result by 6:</think>\\n<final_answer>\\nStep 1: 26 * 6 = 156\\n</final_answer>\\n\\n<think>And finally, we need to add a zero to the result since we a... | ["{'generation': \"<think>First, we need to multiply 13 and 2:</think>\\n<final_answer>\\nStep 1: 13 * 2 = 26\\n</final_answer>\\n\\n<think>Now, we need to multiply the result by 6:</think>\\n<final_answer>\\nStep 1: 26 * 6 = 156\\n</final_answer>\\n\\n<think>And finally, we need to add a zero to the result since we ar... | cf4237b8a4d528b6996957344229c797765e97e4d292bb00152890f0273bfe5d | 510813f610ad2885b641030188a8c8d20ca83a50ca2a36b5355b3d8af2089c8b | b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to multiply 13 and 2:</think>\n<final_answer>\nStep 1: 13 * 2 = 26\n</final_answer>\n\n<think>Now, we need to multiply the result by 6:</think>\n<final_answer>\nStep 1: 26 * 6 = 156\n</final_answer>\n\n<think>And finally, we need to add a zero to the result since we are working with ages:</think... | [{"budget_forced_chunks": ["<think>First, we need to multiply 13 and 2:</think>\n<final_answer>\nStep 1: 13 * 2 = 26\n</final_answer>\n\n<think>Now, we need to multiply the result by 6:</think>\n<final_answer>\nStep 1: 26 * 6 = 156\n</final_answer>\n\n<think>And finally, we need to add a zero to the result since we are... | 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': \"<think>First, we need to multiply 13 by 9. </think>\\n<think>13 * 9 = 117</think>\\n<think>Now we need to subtract 12 from 117.</think>\\n<think>117 - 12 = 105</think>\\n<think>So the equation is (13 * 9) - 12 = 105.</think>\\n<final_answer>105</final_answer> Hold on, let me verify this answer. 13 x... | ["{'generation': \"<think>First, we need to multiply 13 by 9. </think>\\n<think>13 * 9 = 117</think>\\n<think>Now we need to subtract 12 from 117.</think>\\n<think>117 - 12 = 105</think>\\n<think>So the equation is (13 * 9) - 12 = 105.</think>\\n<final_answer>105</final_answer> Hold on, let me verify this answer. 13 x ... | f69cf0b77fe42a0d324ddf1ad2281a565cd8fe5a16a7ae869ce3b5af3648068e | da83e0c754606dd8653769cc1a82cbaae8fe676572547d75c872cdf58d56fc8f | 785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to multiply 13 by 9. </think>\n<think>13 * 9 = 117</think>\n<think>Now we need to subtract 12 from 117.</think>\n<think>117 - 12 = 105</think>\n<think>So the equation is (13 * 9) - 12 = 105.</think>\n<final_answer>105</final_answer> Hold on, let me verify this answer. 13 x 9 is 117, and 117 - 12... | [{"budget_forced_chunks": ["<think>First, we need to multiply 13 by 9. </think>\n<think>13 * 9 = 117</think>\n<think>Now we need to subtract 12 from 117.</think>\n<think>117 - 12 = 105</think>\n<think>So the equation is (13 * 9) - 12 = 105.</think>\n<final_answer>105</final_answer>", " Hold on, let me verify this answe... | 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, we can use the given numbers [16, 5, 7, 10] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 24.\\n\\n<think>Let's break down the numbers 16, 5, 7, and 10 into their components of multiplication and addition: 16 = 2 * 8, 5 = 5, 7 =... | ["{'generation': \"To solve the problem, we can use the given numbers [16, 5, 7, 10] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 24.\\n\\n<think>Let's break down the numbers 16, 5, 7, and 10 into their components of multiplication and addition: 16 = 2 * 8, 5 = 5, 7 = ... | 88082144b6bbe5af4c5b843fb0153a69cb4ffa01356400441326b9aeb27e7341 | 799ad6928102e3f10f3aba9eecfd691709262a50e7812cb4adcfcdd97353a464 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the given numbers [16, 5, 7, 10] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 24.\n\n<think>Let's break down the numbers 16, 5, 7, and 10 into their components of multiplication and addition: 16 = 2 * 8, 5 = 5, 7 = 7, 10 = 1 * 10. We ... | [{"budget_forced_chunks": ["To solve the problem, we can use the given numbers [16, 5, 7, 10] and apply the basic arithmetic operations (+, -, *, /). We need to find an equation that equals 24.\n\n<think>Let's break down the numbers 16, 5, 7, and 10 into their components of multiplication and addition: 16 = 2 * 8, 5 = ... | 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 will follow the standard order of operations in arithmetic, which is:\\n\\n1. **First, perform the left-to-right addition and subtraction of the numbers present.**\\n\\n \\\\[\\n 19 + 24 = 43\\n \\\\]\\n\\n Next, we will subtract 18 from ... | ["{'generation': \"To solve the problem \\\\( 19 + 24 - 18 - 2 \\\\), we will follow the standard order of operations in arithmetic, which is:\\n\\n1. **First, perform the left-to-right addition and subtraction of the numbers present.**\\n\\n \\\\[\\n 19 + 24 = 43\\n \\\\]\\n\\n Next, we will subtract 18 from t... | 63792ff69af699c4a79245246a3a0ca868fd10c8a39aac99e71d88802ba4d89e | c8b96c17d1cc42d3cdd0a3944a65fc5cdc3ce1607a49e7659cba77c65bc2a3a2 | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 19 + 24 - 18 - 2 \\), we will follow the standard order of operations in arithmetic, which is:\n\n1. **First, perform the left-to-right addition and subtraction of the numbers present.**\n\n \\[\n 19 + 24 = 43\n \\]\n\n Next, we will subtract 18 from the result:\n\n \\[\n 43 - 18 ... | [{"budget_forced_chunks": ["To solve the problem \\( 19 + 24 - 18 - 2 \\), we will follow the standard order of operations in arithmetic, which is:\n\n1. **First, perform the left-to-right addition and subtraction of the numbers present.**\n\n \\[\n 19 + 24 = 43\n \\]\n\n Next, we will subtract 18 from the resu... | 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 \\\\( 17 \\\\times 6 \\\\times 2 \\\\times 17 \\\\), we can break it down into simpler steps:\\n\\n1. First, calculate \\\\( 17 \\\\times 6 \\\\):\\n \\\\[\\n 17 \\\\times 6 = 102\\n \\\\]\\n\\n2. Next, multiply the result by 2:\\n \\\\[\\n 102 \\\\times 2 = 204\\n \... | ["{'generation': \"To solve the problem \\\\( 17 \\\\times 6 \\\\times 2 \\\\times 17 \\\\), we can break it down into simpler steps:\\n\\n1. First, calculate \\\\( 17 \\\\times 6 \\\\):\\n \\\\[\\n 17 \\\\times 6 = 102\\n \\\\]\\n\\n2. Next, multiply the result by 2:\\n \\\\[\\n 102 \\\\times 2 = 204\\n \\... | 3ebf9c654d2c23444bb49b95d6ffae3543f7edd3c874005aacb5efe0e8c72831 | 79627955b99d396c075d0879ad7a818d3b21c5d6a9f427e1405e67e23ac8e56e | f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 17 \\times 6 \\times 2 \\times 17 \\), we can break it down into simpler steps:\n\n1. First, calculate \\( 17 \\times 6 \\):\n \\[\n 17 \\times 6 = 102\n \\]\n\n2. Next, multiply the result by 2:\n \\[\n 102 \\times 2 = 204\n \\]\n\n3. Finally, multiply \\( 17 \\) by the original ... | [{"budget_forced_chunks": ["To solve the problem \\( 17 \\times 6 \\times 2 \\times 17 \\), we can break it down into simpler steps:\n\n1. First, calculate \\( 17 \\times 6 \\):\n \\[\n 17 \\times 6 = 102\n \\]\n\n2. Next, multiply the result by 2:\n \\[\n 102 \\times 2 = 204\n \\]\n\n3. Finally, multiply \... | 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 \\\\( 3 + 20 - 3 - 22 \\\\), we can break it down into simpler steps by using the distributive property of arithmetic operations.\\n\\n1. **Combine the first two numbers:**\\n \\\\[\\n 3 + 20 = 23\\n \\\\]\\n\\n2. **Combine the last two numbers:**\\n \\\\[\\n 23 - 3 = 2... | ["{'generation': 'To solve the problem \\\\( 3 + 20 - 3 - 22 \\\\), we can break it down into simpler steps by using the distributive property of arithmetic operations.\\n\\n1. **Combine the first two numbers:**\\n \\\\[\\n 3 + 20 = 23\\n \\\\]\\n\\n2. **Combine the last two numbers:**\\n \\\\[\\n 23 - 3 = 20... | 27faf0638979afa1b175846661e17479d01ceedaf0bf10d7dbb70aeb3521ef97 | 3f6f94c431163cd8cc49822757d645f85470473d307da501df3e89c4e031cae9 | 6b51d431df5d7f141cbececcf79edf3dd861c3b4069f0b11661a3eefacbba918 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 3 + 20 - 3 - 22 \\), we can break it down into simpler steps by using the distributive property of arithmetic operations.\n\n1. **Combine the first two numbers:**\n \\[\n 3 + 20 = 23\n \\]\n\n2. **Combine the last two numbers:**\n \\[\n 23 - 3 = 20\n \\]\n\n3. **Finally, subtract ... | [{"budget_forced_chunks": ["To solve the problem \\( 3 + 20 - 3 - 22 \\), we can break it down into simpler steps by using the distributive property of arithmetic operations.\n\n1. **Combine the first two numbers:**\n \\[\n 3 + 20 = 23\n \\]\n\n2. **Combine the last two numbers:**\n \\[\n 23 - 3 = 20\n \\]\... | 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. **First Step:** Combine \\\\( 11 \\\\) and \\\\( 8 \\\\):\\n \\\\[\\n 11 + 8 = 19\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 9 \\\\) from the result:\\n \\\\[\\n 19 - 9 = 10\\n \\\\]\... | ["{'generation': \"To solve the problem \\\\( 11 + 8 - 9 + 13 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Combine \\\\( 11 \\\\) and \\\\( 8 \\\\):\\n \\\\[\\n 11 + 8 = 19\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 9 \\\\) from the result:\\n \\\\[\\n 19 - 9 = 10\\n \\\\]\\... | 0cc1376e685c64555564eb12e63d0398e53a881d7ddd1ee152d5e5ae43fa7702 | 21a660424e8cbb50098eb005a75591915839535032517b245dd5062f33d5ac1b | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 11 + 8 - 9 + 13 \\), we can break it down into simpler steps:\n\n1. **First Step:** Combine \\( 11 \\) and \\( 8 \\):\n \\[\n 11 + 8 = 19\n \\]\n\n2. **Second Step:** Subtract \\( 9 \\) from the result:\n \\[\n 19 - 9 = 10\n \\]\n\n3. **Third Step:** Add \\( 13 \\) to the result f... | [{"budget_forced_chunks": ["To solve the problem \\( 11 + 8 - 9 + 13 \\), we can break it down into simpler steps:\n\n1. **First Step:** Combine \\( 11 \\) and \\( 8 \\):\n \\[\n 11 + 8 = 19\n \\]\n\n2. **Second Step:** Subtract \\( 9 \\) from the result:\n \\[\n 19 - 9 = 10\n \\]\n\n3. **Third Step:** Add ... | 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 \\\\( 3 + 18 - 7 - 17 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mu... | ["{'generation': \"To solve the problem \\\\( 3 + 18 - 7 - 17 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mul... | 0bff8a88f392bdea9bf78037fd9345e9a360c73183f41fac27009acbfcf45a45 | 284464ca2a666cb6ff9513a61057ef6b38f08efea9d5d1e57272daf5b514b30d | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 3 + 18 - 7 - 17 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Multiply next to the first n... | [{"budget_forced_chunks": ["To solve the problem \\( 3 + 18 - 7 - 17 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Mu... | 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': '<think>Step 1: We need to use the numbers 6, 15, and 18 exactly once each. We can start by multiplying the two largest numbers, 18 and 15.</think>\\n<think>Step 2: 18 * 15 = 240</think>\\n<think>Now, we need to subtract the smallest number, 6, from 240.</think>\\n<think>240 - 6 = 234</think>\\n<think... | ["{'generation': '<think>Step 1: We need to use the numbers 6, 15, and 18 exactly once each. We can start by multiplying the two largest numbers, 18 and 15.</think>\\n<think>Step 2: 18 * 15 = 240</think>\\n<think>Now, we need to subtract the smallest number, 6, from 240.</think>\\n<think>240 - 6 = 234</think>\\n<think>... | dd4b144645f3044ade5370b84d2c8ffc297f7221b9b007340f14cfbc65e21d08 | 66bdbb1dbf3161fa4bd295ada53f214a78964d34cbac8721fc230f654dd84eb9 | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: We need to use the numbers 6, 15, and 18 exactly once each. We can start by multiplying the two largest numbers, 18 and 15.</think>\n<think>Step 2: 18 * 15 = 240</think>\n<think>Now, we need to subtract the smallest number, 6, from 240.</think>\n<think>240 - 6 = 234</think>\n<think>So, the equation is ... | [{"budget_forced_chunks": ["<think>Step 1: We need to use the numbers 6, 15, and 18 exactly once each. We can start by multiplying the two largest numbers, 18 and 15.</think>\n<think>Step 2: 18 * 15 = 240</think>\n<think>Now, we need to subtract the smallest number, 6, from 240.</think>\n<think>240 - 6 = 234</think>\n<... | 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. First, add \\\\( 21 \\\\) and \\\\( 17 \\\\):\\n \\\\[\\n 21 + 17 = 38\\n \\\\]\\n\\n2. Next, add \\\\( 1 \\\\) to the result:\\n \\\\[\\n 38 + 1 = 39\\n \\\\]\\n\\n3. Finally, add \\\\( 2... | ["{'generation': \"To solve the problem \\\\( 21 + 17 + 1 + 22 \\\\), we can break it down into simpler steps:\\n\\n1. First, add \\\\( 21 \\\\) and \\\\( 17 \\\\):\\n \\\\[\\n 21 + 17 = 38\\n \\\\]\\n\\n2. Next, add \\\\( 1 \\\\) to the result:\\n \\\\[\\n 38 + 1 = 39\\n \\\\]\\n\\n3. Finally, add \\\\( 22... | 386f2658d165d4865e961a1c33162044ca2347736a789c08f0ef045ee45694e2 | b67f903481c0c503505a89ffb5d2efc0440dab837c0f5b94fc16cd0f93e5e719 | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 21 + 17 + 1 + 22 \\), we can break it down into simpler steps:\n\n1. First, add \\( 21 \\) and \\( 17 \\):\n \\[\n 21 + 17 = 38\n \\]\n\n2. Next, add \\( 1 \\) to the result:\n \\[\n 38 + 1 = 39\n \\]\n\n3. Finally, add \\( 22 \\) to the result:\n \\[\n 39 + 22 = 61\n \\]\n\... | [{"budget_forced_chunks": ["To solve the problem \\( 21 + 17 + 1 + 22 \\), we can break it down into simpler steps:\n\n1. First, add \\( 21 \\) and \\( 17 \\):\n \\[\n 21 + 17 = 38\n \\]\n\n2. Next, add \\( 1 \\) to the result:\n \\[\n 38 + 1 = 39\n \\]\n\n3. Finally, add \\( 22 \\) to the result:\n \\[\n... | 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': '<think>Step 1: Identify the numbers and the operation needed. The user wants us to use the numbers [7, 23, 11] and perform an addition operation to get a result of 19.</think>\\n<final_answer>\\nStep 1: 7 + 23 = 23\\nStep 2: 23 + 11 = 34\\n</final_answer>\\n<think>Therefore, the equation is 7 + 23 + ... | ["{'generation': '<think>Step 1: Identify the numbers and the operation needed. The user wants us to use the numbers [7, 23, 11] and perform an addition operation to get a result of 19.</think>\\n<final_answer>\\nStep 1: 7 + 23 = 23\\nStep 2: 23 + 11 = 34\\n</final_answer>\\n<think>Therefore, the equation is 7 + 23 + 1... | 11d4963569c689aaad5d7281b004c6802e6924ca6310338820f9a7a845258c03 | cd94a9feffddb511cf4bb21a2989fbef048bfdac8f9ca47a4ddea52ecdff72f0 | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: Identify the numbers and the operation needed. The user wants us to use the numbers [7, 23, 11] and perform an addition operation to get a result of 19.</think>\n<final_answer>\nStep 1: 7 + 23 = 23\nStep 2: 23 + 11 = 34\n</final_answer>\n<think>Therefore, the equation is 7 + 23 + 11 = 34.</think>\n<ans... | [{"budget_forced_chunks": ["<think>Step 1: Identify the numbers and the operation needed. The user wants us to use the numbers [7, 23, 11] and perform an addition operation to get a result of 19.</think>\n<final_answer>\nStep 1: 7 + 23 = 23\nStep 2: 23 + 11 = 34\n</final_answer>\n<think>Therefore, the equation is 7 + 2... | 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, we can use the numbers [9, 17, 16, 9] and basic arithmetic operations to create an equation that equals 16.\\n\\nStep 1: 9 * 16 = 144\\nStep 2: 17 * 9 = 153\\nStep 3: 144 + 153 = 297\\n\\nSo, the equation is: 16 = (9 * 16) + (17 * 9)\\n\\n<final_answer>\\n16 = (9 * 16) + (17 * ... | ["{'generation': \"To solve the problem, we can use the numbers [9, 17, 16, 9] and basic arithmetic operations to create an equation that equals 16.\\n\\nStep 1: 9 * 16 = 144\\nStep 2: 17 * 9 = 153\\nStep 3: 144 + 153 = 297\\n\\nSo, the equation is: 16 = (9 * 16) + (17 * 9)\\n\\n<final_answer>\\n16 = (9 * 16) + (17 * 9... | e2307676ba5945f3e2c373ae638ce1fbf09fef1f24485b95b0b9dae44c1099fb | 1b4da6d5e75ebf799898cd96ebd7861935499bc7b18b914f13cc209f4ed6b549 | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the numbers [9, 17, 16, 9] and basic arithmetic operations to create an equation that equals 16.\n\nStep 1: 9 * 16 = 144\nStep 2: 17 * 9 = 153\nStep 3: 144 + 153 = 297\n\nSo, the equation is: 16 = (9 * 16) + (17 * 9)\n\n<final_answer>\n16 = (9 * 16) + (17 * 9)\n</final_answer> Wait, h... | [{"budget_forced_chunks": ["To solve the problem, we can use the numbers [9, 17, 16, 9] and basic arithmetic operations to create an equation that equals 16.\n\nStep 1: 9 * 16 = 144\nStep 2: 17 * 9 = 153\nStep 3: 144 + 153 = 297\n\nSo, the equation is: 16 = (9 * 16) + (17 * 9)\n\n<final_answer>\n16 = (9 * 16) + (17 * 9... | null |
36 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 11 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the problem \\\\( 15 \\\\times 6 \\\\) step by step, we can break it down into simpler multiplications and then multiply the results together. \\n\\nHere's how it works:\\n\\n1. First, let's break it into \\\\( 15 \\\\times 6 \\\\):\\n - We know that \\\\( 15 \\\\times 6 \\\\) is the same... | ["{'generation': \"To solve the problem \\\\( 15 \\\\times 6 \\\\) step by step, we can break it down into simpler multiplications and then multiply the results together. \\n\\nHere's how it works:\\n\\n1. First, let's break it into \\\\( 15 \\\\times 6 \\\\):\\n - We know that \\\\( 15 \\\\times 6 \\\\) is the same ... | 055f38773f98fc1fe93514b433eb50b05677ceaa346ad81e22d44389b2c69218 | d557d1a3780d56b3ad6c44c18a367bdb95da8e17c3271d31bd3c4625235d047c | 4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 15 \\times 6 \\) step by step, we can break it down into simpler multiplications and then multiply the results together. \n\nHere's how it works:\n\n1. First, let's break it into \\( 15 \\times 6 \\):\n - We know that \\( 15 \\times 6 \\) is the same as \\( (10 + 5) \\times 6 \\).\n - Usi... | [{"budget_forced_chunks": ["To solve the problem \\( 15 \\times 6 \\) step by step, we can break it down into simpler multiplications and then multiply the results together. \n\nHere's how it works:\n\n1. First, let's break it into \\( 15 \\times 6 \\):\n - We know that \\( 15 \\times 6 \\) is the same as \\( (10 + 5... | 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': \"<think>First, we need to combine the numbers to make a total of 23. We can do this by adding or subtracting the numbers, or by breaking them down into smaller parts.</think>\\n<final_answer>\\nStep 1: 12 + 19 = 31\\nStep 2: 31 + 18 = 49\\nStep 3: 49 + 5 = 54\\n</final_answer> But according to 54 - 5... | ["{'generation': \"<think>First, we need to combine the numbers to make a total of 23. We can do this by adding or subtracting the numbers, or by breaking them down into smaller parts.</think>\\n<final_answer>\\nStep 1: 12 + 19 = 31\\nStep 2: 31 + 18 = 49\\nStep 3: 49 + 5 = 54\\n</final_answer> But according to 54 - 5 ... | 1e02d758f3506e31de59f006d92bf7c85dab20b9e23beaf41677a15949d9d257 | f793bdad9ecf5e858a215f47764758b771996046772c2ab09c13997ff97fb08f | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to combine the numbers to make a total of 23. We can do this by adding or subtracting the numbers, or by breaking them down into smaller parts.</think>\n<final_answer>\nStep 1: 12 + 19 = 31\nStep 2: 31 + 18 = 49\nStep 3: 49 + 5 = 54\n</final_answer> But according to 54 - 5 = 49, the previous ste... | [{"budget_forced_chunks": ["<think>First, we need to combine the numbers to make a total of 23. We can do this by adding or subtracting the numbers, or by breaking them down into smaller parts.</think>\n<final_answer>\nStep 1: 12 + 19 = 31\nStep 2: 31 + 18 = 49\nStep 3: 49 + 5 = 54\n</final_answer>", " But according to... | 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': \"<think>First, let's try using the numbers[8, 6, 6, 14] to multiply together and maybe stumble upon the answer.</think>\\\\n<final_answer>\\\\nStep 1: 8 x 6 = 48 (one hundred forty-eight)\\nStep 2: 48 x 6 = 288 (ninety-sixty)\\nStep 3: 288 + 14 = 202 (two thousand twenty-eight)\\n</final_answer>' But... | ["{'generation': \"<think>First, let's try using the numbers[8, 6, 6, 14] to multiply together and maybe stumble upon the answer.</think>\\\\n<final_answer>\\\\nStep 1: 8 x 6 = 48 (one hundred forty-eight)\\nStep 2: 48 x 6 = 288 (ninety-sixty)\\nStep 3: 288 + 14 = 202 (two thousand twenty-eight)\\n</final_answer>' But ... | 2282af28b6f6534d090ed13558649edf72ec5e7d388ee194c9d515d532857337 | ad151f6b94c236a705e099c3417b7c3decac063fdfea02b5158df46c0a2579bc | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, let's try using the numbers[8, 6, 6, 14] to multiply together and maybe stumble upon the answer.</think>\\n<final_answer>\\nStep 1: 8 x 6 = 48 (one hundred forty-eight)\nStep 2: 48 x 6 = 288 (ninety-sixty)\nStep 3: 288 + 14 = 202 (two thousand twenty-eight)\n</final_answer>' But to confirm, 23 = 8 * 6 +... | [{"budget_forced_chunks": ["<think>First, let's try using the numbers[8, 6, 6, 14] to multiply together and maybe stumble upon the answer.</think>\\n<final_answer>\\nStep 1: 8 x 6 = 48 (one hundred forty-eight)\nStep 2: 48 x 6 = 288 (ninety-sixty)\nStep 3: 288 + 14 = 202 (two thousand twenty-eight)\n</final_answer>'", ... | 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. Here's how we can do it step by step:\\n\\n1. First, let's group the numbers in a way that makes sense: \\\\( 8 \\\\tim... | ["{'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. Here's how we can do it step by step:\\n\\n1. First, let's group the numbers in a way that makes sense: \\\\( 8 \\\\time... | 42ba5c03d722b5c353664340bb3fdd03fef285a1d746be67dc6080b64f3ed1f2 | 6010e5495bfc0eb1aaa69f8d33dafba7002318874f2f8993a899f6c2175341be | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.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. Here's how we can do it step by step:\n\n1. First, let's group the numbers in a way that makes sense: \\( 8 \\times 9 \\), \\( 6 \\times 23 \\), an... | [{"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. Here's how we can do it step by step:\n\n1. First, let's group the numbers in a way that makes sense: \\( 8 \\times 9 \\)... | 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': '<think>First, we need to use the numbers 15, 12, and 10 to create an equation that equals 13. We can use basic arithmetic operations such as addition, subtraction, multiplication, and division.</think>\\n\\n<final_answer>\\nStep 1: We start by multiplying 15 and 12. Since 15 is greater than 10, we su... | ["{'generation': '<think>First, we need to use the numbers 15, 12, and 10 to create an equation that equals 13. We can use basic arithmetic operations such as addition, subtraction, multiplication, and division.</think>\\n\\n<final_answer>\\nStep 1: We start by multiplying 15 and 12. Since 15 is greater than 10, we sub... | 05f0d33714099cc656acf8c8eb68719411b73df92d0a070b3dc097d1897fa282 | 9182372ee604d8332a7f3e9623e2461b466d8b780a7500a2dd61955e54796104 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 15, 12, and 10 to create an equation that equals 13. We can use basic arithmetic operations such as addition, subtraction, multiplication, and division.</think>\n\n<final_answer>\nStep 1: We start by multiplying 15 and 12. Since 15 is greater than 10, we subtract 10 from 15 to... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 15, 12, and 10 to create an equation that equals 13. We can use basic arithmetic operations such as addition, subtraction, multiplication, and division.</think>\n\n<final_answer>\nStep 1: We start by multiplying 15 and 12. Since 15 is greater than 10,... | 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, we can use the numbers [9, 2, 4, 20] and basic arithmetic operations to create an equation that equals 17.\\n\\nStep 1: 20 + 2 = 22\\nStep 2: 22 * 4 = 88\\nStep 3: 88 - 9 = 79\\n\\nSo, the equation is: 20 + 2 * 4 = 79\\n\\nAnd the final answer is: <final_answer> 79 </final_answ... | ["{'generation': \"To solve the problem, we can use the numbers [9, 2, 4, 20] and basic arithmetic operations to create an equation that equals 17.\\n\\nStep 1: 20 + 2 = 22\\nStep 2: 22 * 4 = 88\\nStep 3: 88 - 9 = 79\\n\\nSo, the equation is: 20 + 2 * 4 = 79\\n\\nAnd the final answer is: <final_answer> 79 </final_answe... | 0315f9a1c2b6e1bfbf8a8edbef44189839e111a96f251ea8c1e4116c60fd5cee | e9cafd581fb89d08a111dd7726405d183419160dd52f6dd12be72064f6226e87 | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the numbers [9, 2, 4, 20] and basic arithmetic operations to create an equation that equals 17.\n\nStep 1: 20 + 2 = 22\nStep 2: 22 * 4 = 88\nStep 3: 88 - 9 = 79\n\nSo, the equation is: 20 + 2 * 4 = 79\n\nAnd the final answer is: <final_answer> 79 </final_answer> Hold on, let me verify... | [{"budget_forced_chunks": ["To solve the problem, we can use the numbers [9, 2, 4, 20] and basic arithmetic operations to create an equation that equals 17.\n\nStep 1: 20 + 2 = 22\nStep 2: 22 * 4 = 88\nStep 3: 88 - 9 = 79\n\nSo, the equation is: 20 + 2 * 4 = 79\n\nAnd the final answer is: <final_answer> 79 </final_answ... | 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': \"<think>First, we need to combine the two-digit numbers into a two-digit number and a single-digit number. We can do this by placing the two-digit number before the single-digit number.</think>\\n<think>One way to approach this is by placing the numbers in the equation randomly and then solving it. L... | ["{'generation': \"<think>First, we need to combine the two-digit numbers into a two-digit number and a single-digit number. We can do this by placing the two-digit number before the single-digit number.</think>\\n<think>One way to approach this is by placing the numbers in the equation randomly and then solving it. Le... | e7235818189cee9d7974085c723f8c0c6789bf34cec743ad9090eeb5a74018c5 | 2a9d2117ec015b63c5be448e3dbe6c88b99d39f86ca94ccadf2e18578a6d5348 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to combine the two-digit numbers into a two-digit number and a single-digit number. We can do this by placing the two-digit number before the single-digit number.</think>\n<think>One way to approach this is by placing the numbers in the equation randomly and then solving it. Let's do this step b... | [{"budget_forced_chunks": ["<think>First, we need to combine the two-digit numbers into a two-digit number and a single-digit number. We can do this by placing the two-digit number before the single-digit number.</think>\n<think>One way to approach this is by placing the numbers in the equation randomly and then solvin... | 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 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. **Think Step 1:** Consider the number 14 as \\\\( 10 + 4 \\\\). This makes the operation:\\n \\\\[\\n (10 + 4) + 1 = 13\\n \\\\]\\n\\n2. **Think Step 2:** Now, consider the number 1 as \\\\( 1 \\\\ti... | ["{'generation': \"To solve the problem \\\\( 14 + 1 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. **Think Step 1:** Consider the number 14 as \\\\( 10 + 4 \\\\). This makes the operation:\\n \\\\[\\n (10 + 4) + 1 = 13\\n \\\\]\\n\\n2. **Think Step 2:** Now, consider the number 1 as \\\\( 1 \\\\tim... | 28e1ffdd0700740151dde731e2bc7f7be8ed38e3f23333aa4e32bdaf61e5c613 | 690588146313ddc71ac5b6291a01a87d0b2a32176a8c9a537f84786c08a82d55 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 14 + 1 = 13 \\), we can break it down into simpler steps:\n\n1. **Think Step 1:** Consider the number 14 as \\( 10 + 4 \\). This makes the operation:\n \\[\n (10 + 4) + 1 = 13\n \\]\n\n2. **Think Step 2:** Now, consider the number 1 as \\( 1 \\times 14 \\). This makes the operation:\n ... | [{"budget_forced_chunks": ["To solve the problem \\( 14 + 1 = 13 \\), we can break it down into simpler steps:\n\n1. **Think Step 1:** Consider the number 14 as \\( 10 + 4 \\). This makes the operation:\n \\[\n (10 + 4) + 1 = 13\n \\]\n\n2. **Think Step 2:** Now, consider the number 1 as \\( 1 \\times 14 \\). Thi... | 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 + 4 + 24 + 10 = 16 \\\\), we can break it down into simpler steps:\\n\\n1. **Add the first two numbers:**\\n \\\\[\\n 22 + 4 = 26\\n \\\\]\\n\\n2. **Add the next two numbers:**\\n \\\\[\\n 26 + 10 = 36\\n \\\\]\\n\\nSo, the solution is \\\\( 22 + 4 + 24 + 10 ... | ["{'generation': 'To solve the problem \\\\( 22 + 4 + 24 + 10 = 16 \\\\), we can break it down into simpler steps:\\n\\n1. **Add the first two numbers:**\\n \\\\[\\n 22 + 4 = 26\\n \\\\]\\n\\n2. **Add the next two numbers:**\\n \\\\[\\n 26 + 10 = 36\\n \\\\]\\n\\nSo, the solution is \\\\( 22 + 4 + 24 + 10 =... | f3ddb34578e5f09132211961a1dd13853a41d2af86f1ac3cd4b520c9ccb55208 | 57ea06bd045d0c6c2eabfc9b26bc35cee2eb052a39546f25cd77f7c587a22742 | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 22 + 4 + 24 + 10 = 16 \\), we can break it down into simpler steps:\n\n1. **Add the first two numbers:**\n \\[\n 22 + 4 = 26\n \\]\n\n2. **Add the next two numbers:**\n \\[\n 26 + 10 = 36\n \\]\n\nSo, the solution is \\( 22 + 4 + 24 + 10 = 36 \\).\n\nTherefore, the final answer in... | [{"budget_forced_chunks": ["To solve the problem \\( 22 + 4 + 24 + 10 = 16 \\), we can break it down into simpler steps:\n\n1. **Add the first two numbers:**\n \\[\n 22 + 4 = 26\n \\]\n\n2. **Add the next two numbers:**\n \\[\n 26 + 10 = 36\n \\]\n\nSo, the solution is \\( 22 + 4 + 24 + 10 = 36 \\).\n\nTher... | 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 + 14 - 22 + 13 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: M... | ["{'generation': \"To solve the problem \\\\( 7 + 14 - 22 + 13 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mu... | d4148b73faad89dbbacfe944ac9870b26bc7780bfe26b5b6cc5809cc5575df84 | ef8dc21e0133a2b6e6a1e76ca7547457a5f356117bdb5c02d1d1b0f3e2d30c9a | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 7 + 14 - 22 + 13 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Multiply next to the first ... | [{"budget_forced_chunks": ["To solve the problem \\( 7 + 14 - 22 + 13 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: M... | 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 will follow the standard order of operations in arithmetic, which is:\\n\\n1. **First, perform the** addition and subtraction** of the numbers\u8eab\u8fb9\u7684\u64cd\u4f5c\u7b26\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u4e00\u7ea7\u8fd0\u7b97**:\\n ... | ["{'generation': \"To solve the problem \\\\( 10 + 13 - 18 + 1 \\\\), we will follow the standard order of operations in arithmetic, which is:\\n\\n1. **First, perform the** addition and subtraction** of the numbers\u8eab\u8fb9\u7684\u64cd\u4f5c\u7b26\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u4e00\u7ea7\u8fd0\u7b97**:\\n ... | f31d25479cb0879c1e473db5654734110af6012c3dec6787a432841c1e9f5e14 | c56e96674fbf187c3876e536b5237e294f4469f36773c316a0e604a3e5091630 | e629fa6598d732768f7c726b4b621285f9c3b85303900aa912017db7617d8bdb | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 10 + 13 - 18 + 1 \\), we will follow the standard order of operations in arithmetic, which is:\n\n1. **First, perform the** addition and subtraction** of the numbers\u8eab\u8fb9\u7684\u64cd\u4f5c\u7b26\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u4e00\u7ea7\u8fd0\u7b97**:\n \\[\n 10 + 13 \\quad \... | [{"budget_forced_chunks": ["To solve the problem \\( 10 + 13 - 18 + 1 \\), we will follow the standard order of operations in arithmetic, which is:\n\n1. **First, perform the** addition and subtraction** of the numbers\u8eab\u8fb9\u7684\u64cd\u4f5c\u7b26\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u4e00\u7ea7\u8fd0\u7b97**:\n ... | null |
47 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 19 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the problem \\\\( 10 + 17 - 22 + 21 \\\\), we can break it down into simpler steps:\\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 ... | ["{'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... | ec4723d791e04df97fc68140b01e5c04f54ca9d2222922ec78e3489918e89a8d | 9e01c4026ea50c024f81b0b26b4133645ef725dd9cc13cf176c1e650623b1007 | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.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 \\\\( 23 + 23 + 13 + 16 = 20 \\\\), we can break it down into simpler steps:\\n\\n1. **Combine the numbers:**\\n \\\\[\\n 23 + 23 = 46\\n \\\\]\\n \\\\[\\n 46 + 13 = 59\\n \\\\]\\n \\\\[\\n 59 + 16 = 75\\n \\\\]\\n\\n2. **Verify the steps:**\\n Let's check if... | ["{'generation': \"To solve the problem \\\\( 23 + 23 + 13 + 16 = 20 \\\\), we can break it down into simpler steps:\\n\\n1. **Combine the numbers:**\\n \\\\[\\n 23 + 23 = 46\\n \\\\]\\n \\\\[\\n 46 + 13 = 59\\n \\\\]\\n \\\\[\\n 59 + 16 = 75\\n \\\\]\\n\\n2. **Verify the steps:**\\n Let's check if ... | 8e5566982343c0690d90c6bac61b52d7dfb907ee9c94df525e5757c4c97c4262 | db237d201578701780659ed1aef2b60d06c349d2cd605d35b9c43e344346a198 | f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 23 + 23 + 13 + 16 = 20 \\), we can break it down into simpler steps:\n\n1. **Combine the numbers:**\n \\[\n 23 + 23 = 46\n \\]\n \\[\n 46 + 13 = 59\n \\]\n \\[\n 59 + 16 = 75\n \\]\n\n2. **Verify the steps:**\n Let's check if the order of operations matters by testing with... | [{"budget_forced_chunks": ["To solve the problem \\( 23 + 23 + 13 + 16 = 20 \\), we can break it down into simpler steps:\n\n1. **Combine the numbers:**\n \\[\n 23 + 23 = 46\n \\]\n \\[\n 46 + 13 = 59\n \\]\n \\[\n 59 + 16 = 75\n \\]\n\n2. **Verify the steps:**\n Let's check if the order of operatio... | 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': \"<think>First, we can add or subtract the numbers at the first glance. In this case, 14 - 4 = 10 and 8 - 1 = 7. So the equation becomes (10 + 7) * 6 + 4.</think>\\\\n<final_answer>Step 1: 10 + 7 = 17</final_answer>\\\\n<think>Now, we need to multiply 17 by 6.</think>\\\\n<final_answer>Step 2: 17 * 6 ... | ["{'generation': \"<think>First, we can add or subtract the numbers at the first glance. In this case, 14 - 4 = 10 and 8 - 1 = 7. So the equation becomes (10 + 7) * 6 + 4.</think>\\\\n<final_answer>Step 1: 10 + 7 = 17</final_answer>\\\\n<think>Now, we need to multiply 17 by 6.</think>\\\\n<final_answer>Step 2: 17 * 6 =... | 7aca7383c6015b2caa3691a0ea9a88ce61a224cc7fa4480f98bb178f67b3699a | abf814c17e6c9998a882dedeb9fefd5d9744207da8310ec3fe141485c9b0cece | 785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we can add or subtract the numbers at the first glance. In this case, 14 - 4 = 10 and 8 - 1 = 7. So the equation becomes (10 + 7) * 6 + 4.</think>\\n<final_answer>Step 1: 10 + 7 = 17</final_answer>\\n<think>Now, we need to multiply 17 by 6.</think>\\n<final_answer>Step 2: 17 * 6 = 102</final_answer>\\n<... | [{"budget_forced_chunks": ["<think>First, we can add or subtract the numbers at the first glance. In this case, 14 - 4 = 10 and 8 - 1 = 7. So the equation becomes (10 + 7) * 6 + 4.</think>\\n<final_answer>Step 1: 10 + 7 = 17</final_answer>\\n<think>Now, we need to multiply 17 by 6.</think>\\n<final_answer>Step 2: 17 * ... | 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': \"<think>First, we need to multiply 15 and 22. </think>\\n<think>15 * 22 = 330</think>\\n<think>Now we have 17 and 330. We need to multiply these two numbers.</think>\\n<think>17 * 330</think>\\n<think>17 * 30 = 510</think>\\n<think>17 * 3 = 51</think>\\n<think>Adding these two results: 510 + 51 = 561... | ["{'generation': \"<think>First, we need to multiply 15 and 22. </think>\\n<think>15 * 22 = 330</think>\\n<think>Now we have 17 and 330. We need to multiply these two numbers.</think>\\n<think>17 * 330</think>\\n<think>17 * 30 = 510</think>\\n<think>17 * 3 = 51</think>\\n<think>Adding these two results: 510 + 51 = 561<... | 47bac1a2342eda30692108659694e008e612521cbc54ffec54c8d5678789649a | 370dcedf0dfcaeedd84655684cc6bd37cdacaa0a8e5c4038cfa6e6c882e61060 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to multiply 15 and 22. </think>\n<think>15 * 22 = 330</think>\n<think>Now we have 17 and 330. We need to multiply these two numbers.</think>\n<think>17 * 330</think>\n<think>17 * 30 = 510</think>\n<think>17 * 3 = 51</think>\n<think>Adding these two results: 510 + 51 = 561</think>\n<final_answer>... | [{"budget_forced_chunks": ["<think>First, we need to multiply 15 and 22. </think>\n<think>15 * 22 = 330</think>\n<think>Now we have 17 and 330. We need to multiply these two numbers.</think>\n<think>17 * 330</think>\n<think>17 * 30 = 510</think>\n<think>17 * 3 = 51</think>\n<think>Adding these two results: 510 + 51 = 5... | 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, we can use the numbers [15, 20, 24, 17] and basic arithmetic operations to create an equation that equals 20.\\n\\nStep 1: 15 + 5 = 20\\nSo, the final answer is:\\n\\n<final_answer>\\nStep 1: 15 + 5 = 20\\n</final_answer> But I need to verify this. 20 indeed equals 20 when 15 p... | ["{'generation': \"To solve the problem, we can use the numbers [15, 20, 24, 17] and basic arithmetic operations to create an equation that equals 20.\\n\\nStep 1: 15 + 5 = 20\\nSo, the final answer is:\\n\\n<final_answer>\\nStep 1: 15 + 5 = 20\\n</final_answer> But I need to verify this. 20 indeed equals 20 when 15 pl... | e4cb65e43bd8799efe66b31342b571b532d5932afb20b4d16854be908cddc019 | d4c729d6184e5dc678411950de66cc83e11b46733769289afddd5ec13f2cf251 | f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the numbers [15, 20, 24, 17] and basic arithmetic operations to create an equation that equals 20.\n\nStep 1: 15 + 5 = 20\nSo, the final answer is:\n\n<final_answer>\nStep 1: 15 + 5 = 20\n</final_answer> But I need to verify this. 20 indeed equals 20 when 15 plus 5 on the right hand s... | [{"budget_forced_chunks": ["To solve the problem, we can use the numbers [15, 20, 24, 17] and basic arithmetic operations to create an equation that equals 20.\n\nStep 1: 15 + 5 = 20\nSo, the final answer is:\n\n<final_answer>\nStep 1: 15 + 5 = 20\n</final_answer>", " But I need to verify this. 20 indeed equals 20 when... | 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 + 15 - 6 + 24 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Combine \\\\( 18 \\\\) and \\\\( 15 \\\\):\\n \\\\[\\n 18 + 15 = 33\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 6 \\\\) from the result:\\n \\\\[\\n 33 - 6 = 27\\n \\\... | ["{'generation': \"To solve the problem \\\\( 18 + 15 - 6 + 24 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Combine \\\\( 18 \\\\) and \\\\( 15 \\\\):\\n \\\\[\\n 18 + 15 = 33\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 6 \\\\) from the result:\\n \\\\[\\n 33 - 6 = 27\\n \\\\... | 0dfd5c9b6911ee38ebcccfadea25fddef45481b0c639fa3795b35370f5d06ab6 | 10ed909db1dc7a655b9955cfebb2c5726d50b43576625d7b2e9e724c8580d160 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 18 + 15 - 6 + 24 \\), we can break it down into simpler steps:\n\n1. **First Step:** Combine \\( 18 \\) and \\( 15 \\):\n \\[\n 18 + 15 = 33\n \\]\n\n2. **Second Step:** Subtract \\( 6 \\) from the result:\n \\[\n 33 - 6 = 27\n \\]\n\n3. **Third Step:** Add \\( 24 \\) to the resul... | [{"budget_forced_chunks": ["To solve the problem \\( 18 + 15 - 6 + 24 \\), we can break it down into simpler steps:\n\n1. **First Step:** Combine \\( 18 \\) and \\( 15 \\):\n \\[\n 18 + 15 = 33\n \\]\n\n2. **Second Step:** Subtract \\( 6 \\) from the result:\n \\[\n 33 - 6 = 27\n \\]\n\n3. **Third Step:** A... | 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': \"<think>First, we need to combine the numbers to create a multiplication or division equation. One possible combination is 17 x 16, which is 272. However, this is not divisible by 21, so we need to try another combination.</think>\\n<think>Let's try 17 x 21?</think>\\n<think>no</think>\\n<think>Let m... | ["{'generation': \"<think>First, we need to combine the numbers to create a multiplication or division equation. One possible combination is 17 x 16, which is 272. However, this is not divisible by 21, so we need to try another combination.</think>\\n<think>Let's try 17 x 21?</think>\\n<think>no</think>\\n<think>Let me... | a0bbf926e8f85501032b4b6c203376301dda401daa39981885d3c09c4387a5cd | 1f6cc0a799203fca5c7ad993c753db7ebcc9bed4af86c541129c9788b48602c0 | b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to combine the numbers to create a multiplication or division equation. One possible combination is 17 x 16, which is 272. However, this is not divisible by 21, so we need to try another combination.</think>\n<think>Let's try 17 x 21?</think>\n<think>no</think>\n<think>Let me try 16 x 21.</think... | [{"budget_forced_chunks": ["<think>First, we need to combine the numbers to create a multiplication or division equation. One possible combination is 17 x 16, which is 272. However, this is not divisible by 21, so we need to try another combination.</think>\n<think>Let's try 17 x 21?</think>\n<think>no</think>\n<think>... | 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': \"<think>First, we need to use the numbers 8, 13, and 23 to create an equation that equals 18. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 23 - 13 = 10\\nStep 2: 8 * 10 = 80\\n</final_answer>\\n\\n<answer>80 - 10 = 70</answer> Wait, how? 23*2 than 23*1, why not 23-13?<sep> ... | ["{'generation': \"<think>First, we need to use the numbers 8, 13, and 23 to create an equation that equals 18. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 23 - 13 = 10\\nStep 2: 8 * 10 = 80\\n</final_answer>\\n\\n<answer>80 - 10 = 70</answer> Wait, how? 23*2 than 23*1, why not 23-13?<sep> a... | c5077f8f4a57d4767d513fa0140bb28369b0d97abe9081405ec1ce4977de6977 | e089014c0c72e03c6f566a420ec27695fdf2cf37476b848f24bcd9cd7b103b2c | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 8, 13, and 23 to create an equation that equals 18. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 23 - 13 = 10\nStep 2: 8 * 10 = 80\n</final_answer>\n\n<answer>80 - 10 = 70</answer> Wait, how? 23*2 than 23*1, why not 23-13?<sep> apologize, you're right. ... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 8, 13, and 23 to create an equation that equals 18. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 23 - 13 = 10\nStep 2: 8 * 10 = 80\n</final_answer>\n\n<answer>80 - 10 = 70</answer>", " Wait, how? 23*2 than 23*1, why not 23-13?<... | 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, we can break it down into smaller steps:\\n\\n1. Multiply the first two numbers: 3 x 14 = 42\\n2. Multiply the next two numbers: 14 x 11 = 154\\n3. Add the results from step 1 and step 2: 42 + 154 = 196\\n\\nSo the equation that equals 14 is: (3 x 14) + (14 x 11) = 196\\n\\nAnd ... | ["{'generation': 'To solve the problem, we can break it down into smaller steps:\\n\\n1. Multiply the first two numbers: 3 x 14 = 42\\n2. Multiply the next two numbers: 14 x 11 = 154\\n3. Add the results from step 1 and step 2: 42 + 154 = 196\\n\\nSo the equation that equals 14 is: (3 x 14) + (14 x 11) = 196\\n\\nAnd t... | d52f1030f65184c430fb7423fea9454bcefcbc2dd8a80a98709d4fd82e33ff99 | 1ef05c7aaa7694efc259416e25c7e5610f7a9467e8c47827e59eb90e80c7ced2 | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can break it down into smaller steps:\n\n1. Multiply the first two numbers: 3 x 14 = 42\n2. Multiply the next two numbers: 14 x 11 = 154\n3. Add the results from step 1 and step 2: 42 + 154 = 196\n\nSo the equation that equals 14 is: (3 x 14) + (14 x 11) = 196\n\nAnd the final answer in <fina... | [{"budget_forced_chunks": ["To solve the problem, we can break it down into smaller steps:\n\n1. Multiply the first two numbers: 3 x 14 = 42\n2. Multiply the next two numbers: 14 x 11 = 154\n3. Add the results from step 1 and step 2: 42 + 154 = 196\n\nSo the equation that equals 14 is: (3 x 14) + (14 x 11) = 196\n\nAnd... | 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, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 19, 23, 1, and 19. We need to use these numbers once each and apply the operations to get the target number, which is 24.\\n\\n<think>Let's start by com... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 19, 23, 1, and 19. We need to use these numbers once each and apply the operations to get the target number, which is 24.\\n\\n<think>Let's start by comb... | 4adbd29da982f2d2d00599ad14573dc4c8eb945e3de91b443e8b27003bd52042 | 9eed663edc29ed6d7f3f24e24519ddadb989ae3ec75476c63f62b5bf8f4a57e5 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 19, 23, 1, and 19. We need to use these numbers once each and apply the operations to get the target number, which is 24.\n\n<think>Let's start by combining the two 19s..... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 19, 23, 1, and 19. We need to use these numbers once each and apply the operations to get the target number, which is 24.\n\n<think>Let's start ... | 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, we can use the given numbers [20, 8, 16, 8] and apply the basic arithmetic operations (+, -, *, /). We need to create an equation that equals 22.\\n\\n<think>Let's break down the numbers:\\n20 can be 10 + 10\\n8 can be 4 + 4\\n16 can be 10 + 6\\n8 can be 8 + 8\\n\\nNow, let's u... | ["{'generation': \"To solve the problem, we can use the given numbers [20, 8, 16, 8] and apply the basic arithmetic operations (+, -, *, /). We need to create an equation that equals 22.\\n\\n<think>Let's break down the numbers:\\n20 can be 10 + 10\\n8 can be 4 + 4\\n16 can be 10 + 6\\n8 can be 8 + 8\\n\\nNow, let's us... | ebbe613099da63d1b55291f4b798ae73a232d8c4af2d918301eff2a8d08b9f58 | 76eaccefd1c4e5886e4057d7b18e969a4a9600226f4b26e60d6ef61df962b611 | 785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the given numbers [20, 8, 16, 8] and apply the basic arithmetic operations (+, -, *, /). We need to create an equation that equals 22.\n\n<think>Let's break down the numbers:\n20 can be 10 + 10\n8 can be 4 + 4\n16 can be 10 + 6\n8 can be 8 + 8\n\nNow, let's use them in an equation:</t... | [{"budget_forced_chunks": ["To solve the problem, we can use the given numbers [20, 8, 16, 8] and apply the basic arithmetic operations (+, -, *, /). We need to create an equation that equals 22.\n\n<think>Let's break down the numbers:\n20 can be 10 + 10\n8 can be 4 + 4\n16 can be 10 + 6\n8 can be 8 + 8\n\nNow, let's u... | 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. **First Step:** Calculate \\\\( 13 + 24 \\\\)\\n \\\\[\\n 13 + 24 = 37\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 6 \\\\) from the result\\n \\\\[\\n 37 - 6 = 31\\n \\\\]\\n\\n3. **T... | ["{'generation': \"To solve the problem \\\\( 13 + 24 - 6 + 15 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Calculate \\\\( 13 + 24 \\\\)\\n \\\\[\\n 13 + 24 = 37\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 6 \\\\) from the result\\n \\\\[\\n 37 - 6 = 31\\n \\\\]\\n\\n3. **Th... | 4b8548a181e3a8daf0e5e5ef30f90b7996f6638d2697da69aefcccd58369ccc7 | 0f18306e93c6b30451422876db152449239137bebb974cc06ae779d1c0cc45a4 | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 13 + 24 - 6 + 15 \\), we can break it down into simpler steps:\n\n1. **First Step:** Calculate \\( 13 + 24 \\)\n \\[\n 13 + 24 = 37\n \\]\n\n2. **Second Step:** Subtract \\( 6 \\) from the result\n \\[\n 37 - 6 = 31\n \\]\n\n3. **Third Step:** Add \\( 15 \\) to the result of the s... | [{"budget_forced_chunks": ["To solve the problem \\( 13 + 24 - 6 + 15 \\), we can break it down into simpler steps:\n\n1. **First Step:** Calculate \\( 13 + 24 \\)\n \\[\n 13 + 24 = 37\n \\]\n\n2. **Second Step:** Subtract \\( 6 \\) from the result\n \\[\n 37 - 6 = 31\n \\]\n\n3. **Third Step:** Add \\( 15 ... | 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 use the long multiplication method:\\n\\n1. Multiply 18 by 3:\\n \\\\[\\n 18 \\\\times 3 = 54\\n \\\\]\\n\\n2. Multiply 18 by 10 (which is the same as 100):\\n \\\\[\\n 18 \\\\times 10 = 180\\n \\\\]\\n\\n3. Add the two results toge... | ["{'generation': 'To solve the problem \\\\( 18 \\\\times 13 \\\\), we can use the long multiplication method:\\n\\n1. Multiply 18 by 3:\\n \\\\[\\n 18 \\\\times 3 = 54\\n \\\\]\\n\\n2. Multiply 18 by 10 (which is the same as 100):\\n \\\\[\\n 18 \\\\times 10 = 180\\n \\\\]\\n\\n3. Add the two results toget... | 82ea3a7e9d54b8c6427e04636e9e192f8eb8392c2bc9348c8bd169df6d6bab64 | d614d87b12fd03757ecddaaea21bceeba9aa9f77bb48c213e2338a8722b4f0fb | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 18 \\times 13 \\), we can use the long multiplication method:\n\n1. Multiply 18 by 3:\n \\[\n 18 \\times 3 = 54\n \\]\n\n2. Multiply 18 by 10 (which is the same as 100):\n \\[\n 18 \\times 10 = 180\n \\]\n\n3. Add the two results together:\n \\[\n 54 + 180 = 234\n \\]\n\nSo,... | [{"budget_forced_chunks": ["To solve the problem \\( 18 \\times 13 \\), we can use the long multiplication method:\n\n1. Multiply 18 by 3:\n \\[\n 18 \\times 3 = 54\n \\]\n\n2. Multiply 18 by 10 (which is the same as 100):\n \\[\n 18 \\times 10 = 180\n \\]\n\n3. Add the two results together:\n \\[\n 54 ... | 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 \\\\( 6 \\\\times 2 \\\\times 9 \\\\times 13 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step: Multiply 6 and 2**\\n \\\\[\\n 6 \\\\times 2 = 12\\n \\\\]\\n\\n2. **Second Step: Multiply 9 and 13**\\n \\\\[\\n 9 \\\\times 13 = (10 + 1) \\\\times 13 = ... | ["{'generation': 'To solve the problem \\\\( 6 \\\\times 2 \\\\times 9 \\\\times 13 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step: Multiply 6 and 2**\\n \\\\[\\n 6 \\\\times 2 = 12\\n \\\\]\\n\\n2. **Second Step: Multiply 9 and 13**\\n \\\\[\\n 9 \\\\times 13 = (10 + 1) \\\\times 13 = 1... | 04ec0523052570eab42f5d4df2df12752b6040a530a17ab530c1a34b68932cc3 | a07b20493b2474140724f67ad0df567fa239ed4d890a1d12451e43c0282a8060 | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 6 \\times 2 \\times 9 \\times 13 \\), we can break it down into simpler steps:\n\n1. **First Step: Multiply 6 and 2**\n \\[\n 6 \\times 2 = 12\n \\]\n\n2. **Second Step: Multiply 9 and 13**\n \\[\n 9 \\times 13 = (10 + 1) \\times 13 = 10 \\times 13 + 1 \\times 13 = 130 + 13 = 143\n ... | [{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 2 \\times 9 \\times 13 \\), we can break it down into simpler steps:\n\n1. **First Step: Multiply 6 and 2**\n \\[\n 6 \\times 2 = 12\n \\]\n\n2. **Second Step: Multiply 9 and 13**\n \\[\n 9 \\times 13 = (10 + 1) \\times 13 = 10 \\times 13 + 1 \\ti... | 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': \"<think>First, we need to multiply the numbers 14 and 9. We can do this by multiplying the digits in each number: 1*9 = 9 and 4*9 = 36. We then add these results together: 9 + 36 = 45. Now we need to multiply this result by 3: 45 * 3 = 135.</think>\\n<final_answer>\\nStep 1: 14 * 9 = 126\\nStep 2: 12... | ["{'generation': \"<think>First, we need to multiply the numbers 14 and 9. We can do this by multiplying the digits in each number: 1*9 = 9 and 4*9 = 36. We then add these results together: 9 + 36 = 45. Now we need to multiply this result by 3: 45 * 3 = 135.</think>\\n<final_answer>\\nStep 1: 14 * 9 = 126\\nStep 2: 126... | 886ed5f2b6b1ec35a422c1358478609a118536357450e8ce400e8f59fb3d572e | b2487dd970bb8721f302d46b97240e180f65fa3b6e19ad7c2ebf5771d607f653 | f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to multiply the numbers 14 and 9. We can do this by multiplying the digits in each number: 1*9 = 9 and 4*9 = 36. We then add these results together: 9 + 36 = 45. Now we need to multiply this result by 3: 45 * 3 = 135.</think>\n<final_answer>\nStep 1: 14 * 9 = 126\nStep 2: 126 * 3 = 378\n</final_... | [{"budget_forced_chunks": ["<think>First, we need to multiply the numbers 14 and 9. We can do this by multiplying the digits in each number: 1*9 = 9 and 4*9 = 36. We then add these results together: 9 + 36 = 45. Now we need to multiply this result by 3: 45 * 3 = 135.</think>\n<final_answer>\nStep 1: 14 * 9 = 126\nStep ... | 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': \"<think>First, we can add or subtract the numbers at the first glance. In this case, 21 + 3 = 24 is close to the target 25. Let's check other combinations.</think>\\\\n<think>Second combination, 12 + 21 = 33. This is also close to the target. </think>\\\\n<think>Third combination, 12 + 8 = 20. This i... | ["{'generation': \"<think>First, we can add or subtract the numbers at the first glance. In this case, 21 + 3 = 24 is close to the target 25. Let's check other combinations.</think>\\\\n<think>Second combination, 12 + 21 = 33. This is also close to the target. </think>\\\\n<think>Third combination, 12 + 8 = 20. This is... | 14bf1806f088e8b1c20121adc93dbe473a7bbc73cf92a5fec9a74e104fa45d4b | 99a22a74fff81f8c48fa2dafb4921d6437452b79c4215850b3b783316fe6ca3c | b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we can add or subtract the numbers at the first glance. In this case, 21 + 3 = 24 is close to the target 25. Let's check other combinations.</think>\\n<think>Second combination, 12 + 21 = 33. This is also close to the target. </think>\\n<think>Third combination, 12 + 8 = 20. This is too low, so we will ... | [{"budget_forced_chunks": ["<think>First, we can add or subtract the numbers at the first glance. In this case, 21 + 3 = 24 is close to the target 25. Let's check other combinations.</think>\\n<think>Second combination, 12 + 21 = 33. This is also close to the target. </think>\\n<think>Third combination, 12 + 8 = 20. Th... | 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, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 7, 1, and 20.\\n\\nThink: \\nStep 1: Should we multiply or divide? division seems simpler as we can directly subtract 1 from 8 to get 7,which is clos... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 7, 1, and 20.\\n\\nThink: \\nStep 1: Should we multiply or divide? division seems simpler as we can directly subtract 1 from 8 to get 7,which is close... | 05f8a72d36e87d7a5c71b839f12b84d258f67ed7ae386e28611b3519219b525e | c674bf199104dc45f397037060b82bed9ca09d088e60a8318b2aa7f82f573d61 | 4fc82b26aecb47d2868c4efbe3581732a3e7cbcc6c2efb32062c08170a05eeb8 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 7, 1, and 20.\n\nThink: \nStep 1: Should we multiply or divide? division seems simpler as we can directly subtract 1 from 8 to get 7,which is close to but less than 8.... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 7, 1, and 20.\n\nThink: \nStep 1: Should we multiply or divide? division seems simpler as we can directly subtract 1 from 8 to get 7,which is... | 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 will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mu... | ["{'generation': \"To solve the problem \\\\( 6 + 10 - 4 - 19 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mul... | 32c7d6edf9a791a9576fef36ee42924d15008a1a3cbcc17f728f099b122d86af | 20e1f5327c8fb5ca8e924289cde96faf6c2e60df0573b7c58720d6df34666d96 | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 6 + 10 - 4 - 19 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Multiply variables with numb... | [{"budget_forced_chunks": ["To solve the problem \\( 6 + 10 - 4 - 19 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Mu... | 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, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 4, 23, and 10.\\n\\n<think>Let's use the first two numbers, 8 and 4, and combine them using the addition operation:</think>\\n<final_answer>\\nStep 1... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 4, 23, and 10.\\n\\n<think>Let's use the first two numbers, 8 and 4, and combine them using the addition operation:</think>\\n<final_answer>\\nStep 1:... | 37b100781adc7aea5bd0958ae572fe10470b8db410fd9723eb5360d5452d767d | 27abc602b799c6c8ed4fa7f36db773c12da966e4d4118b130a622520943a48d5 | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 4, 23, and 10.\n\n<think>Let's use the first two numbers, 8 and 4, and combine them using the addition operation:</think>\n<final_answer>\nStep 1: 8 + 4 = 12\n</final_... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 8, 4, 23, and 10.\n\n<think>Let's use the first two numbers, 8 and 4, and combine them using the addition operation:</think>\n<final_answer>\nSt... | 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 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. **Combine the First and Third Numbers:**\\n \\\\[\\n 19 + 18 = 37\\n \\\\]\\n\\n2. **Combine the Second and Fourth Numbers:**\\n \\\\[\\n 2 + 12 = 14\\n \\\\]\\n\\n3. **Add the Results... | ["{'generation': 'To solve the problem \\\\( 19 + 2 + 12 + 18 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. **Combine the First and Third Numbers:**\\n \\\\[\\n 19 + 18 = 37\\n \\\\]\\n\\n2. **Combine the Second and Fourth Numbers:**\\n \\\\[\\n 2 + 12 = 14\\n \\\\]\\n\\n3. **Add the Results ... | c98d820c226336c2035fa0efaa4d9aa2becdcb27feac1bbf9082d6efe4f5069f | 1436914e7b70497d0e69375d7b70fd47527ca9e2cae49b0daf6cca5dd20d25a7 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 19 + 2 + 12 + 18 = 13 \\), we can break it down into simpler steps:\n\n1. **Combine the First and Third Numbers:**\n \\[\n 19 + 18 = 37\n \\]\n\n2. **Combine the Second and Fourth Numbers:**\n \\[\n 2 + 12 = 14\n \\]\n\n3. **Add the Results from the Two Combos:**\n \\[\n 37 + ... | [{"budget_forced_chunks": ["To solve the problem \\( 19 + 2 + 12 + 18 = 13 \\), we can break it down into simpler steps:\n\n1. **Combine the First and Third Numbers:**\n \\[\n 19 + 18 = 37\n \\]\n\n2. **Combine the Second and Fourth Numbers:**\n \\[\n 2 + 12 = 14\n \\]\n\n3. **Add the Results from the Two C... | 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': \"<think>First, we need to combine the numbers to create a multiplication or division equation. We can do this by grouping the numbers in pairs: [3, 17, 21, 11] can be paired as [3*7], [3*11], [2*1], and [2*11']. Now we can create the following equation:</think>\\\\n<final_answer>\\\\nStep 1: 3*7=21\\... | ["{'generation': \"<think>First, we need to combine the numbers to create a multiplication or division equation. We can do this by grouping the numbers in pairs: [3, 17, 21, 11] can be paired as [3*7], [3*11], [2*1], and [2*11']. Now we can create the following equation:</think>\\\\n<final_answer>\\\\nStep 1: 3*7=21\\\... | 3dee87e91e430e7f86936ddeb295f7a9006fcdac4e05ff39b8eb95e05789cda6 | ff841f243937fbac16fcd7bbd6cf6794fc7f246070b234a925b75877ce633207 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to combine the numbers to create a multiplication or division equation. We can do this by grouping the numbers in pairs: [3, 17, 21, 11] can be paired as [3*7], [3*11], [2*1], and [2*11']. Now we can create the following equation:</think>\\n<final_answer>\\nStep 1: 3*7=21\\nStep 2: 3*11=33\\nSte... | [{"budget_forced_chunks": ["<think>First, we need to combine the numbers to create a multiplication or division equation. We can do this by grouping the numbers in pairs: [3, 17, 21, 11] can be paired as [3*7], [3*11], [2*1], and [2*11']. Now we can create the following equation:</think>\\n<final_answer>\\nStep 1: 3*7=... | 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:\\n\\n1. First, calculate \\\\( 16 \\\\times 4 \\\\):\\n \\\\[\\n 16 \\\\times 4 = 64\\n \\\\]\\n\\n2. Next, calculate \\\\( 4 \\\\times 14 \\\\):\\n \\\\[\\n 4 \\\\times 14 =... | ["{'generation': \"To solve the problem \\\\( 16 \\\\times 4 \\\\times 14 \\\\times 12 \\\\), we can break it down into simpler steps:\\n\\n1. First, calculate \\\\( 16 \\\\times 4 \\\\):\\n \\\\[\\n 16 \\\\times 4 = 64\\n \\\\]\\n\\n2. Next, calculate \\\\( 4 \\\\times 14 \\\\):\\n \\\\[\\n 4 \\\\times 14 = ... | 98ab1b38356ecf7abfc8d59f6051f122d58b27c2757f86694bf71568c3f579e6 | cbe34bb42aa6666852658fa52a4884248cbbf63194ac9b9bcc86b2c69c103c04 | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 16 \\times 4 \\times 14 \\times 12 \\), we can break it down into simpler steps:\n\n1. First, calculate \\( 16 \\times 4 \\):\n \\[\n 16 \\times 4 = 64\n \\]\n\n2. Next, calculate \\( 4 \\times 14 \\):\n \\[\n 4 \\times 14 = 56\n \\]\n\n3. Finally, calculate \\( 12 \\times 56 \\):... | [{"budget_forced_chunks": ["To solve the problem \\( 16 \\times 4 \\times 14 \\times 12 \\), we can break it down into simpler steps:\n\n1. First, calculate \\( 16 \\times 4 \\):\n \\[\n 16 \\times 4 = 64\n \\]\n\n2. Next, calculate \\( 4 \\times 14 \\):\n \\[\n 4 \\times 14 = 56\n \\]\n\n3. Finally, calcul... | 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, we can use the basic arithmetic operations to combine the given numbers:\\n\\n9 + 20 - 18 * 16\\n\\nStep 1: 9 + 20 = 29\\nStep 2: 18 * 16 = 288\\nStep 3: 29 - 288 = -259\\n\\nHowever, the assistant provided a negative result, which is not possible in this context. It\\'s possibl... | ["{'generation': 'To solve the problem, we can use the basic arithmetic operations to combine the given numbers:\\n\\n9 + 20 - 18 * 16\\n\\nStep 1: 9 + 20 = 29\\nStep 2: 18 * 16 = 288\\nStep 3: 29 - 288 = -259\\n\\nHowever, the assistant provided a negative result, which is not possible in this context. It\\'s possible... | 3ebb28261cbe5e14b7315a28166cc1db81b47ba4e9d15a19a7de1ca91ac3fc11 | 2636ec08d0fb37b2cf450273bfe2824cdd0f5cb1b0331db5775239f4dba1e73f | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers:\n\n9 + 20 - 18 * 16\n\nStep 1: 9 + 20 = 29\nStep 2: 18 * 16 = 288\nStep 3: 29 - 288 = -259\n\nHowever, the assistant provided a negative result, which is not possible in this context. It's possible the assistant meant to sa... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers:\n\n9 + 20 - 18 * 16\n\nStep 1: 9 + 20 = 29\nStep 2: 18 * 16 = 288\nStep 3: 29 - 288 = -259\n\nHowever, the assistant provided a negative result, which is not possible in this context. It's possible... | 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, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given three numbers, 8, 3, and 9, and we need to use at least two of them along with the operations to reach the target number, which is 24 in this case.\\n\\nHere's how we... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given three numbers, 8, 3, and 9, and we need to use at least two of them along with the operations to reach the target number, which is 24 in this case.\\n\\nHere's how we ... | 7a7930e021ceeb46d974fa00bbee28c1f4e7422d48a9c96427a545e4eed0fbdf | fd72a63df0361a86a94acd60ae8292cd8ac4221f55ee795b17a95ad2540b0988 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given three numbers, 8, 3, and 9, and we need to use at least two of them along with the operations to reach the target number, which is 24 in this case.\n\nHere's how we can think about it ... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given three numbers, 8, 3, and 9, and we need to use at least two of them along with the operations to reach the target number, which is 24 in this case.\n\nHere's ... | 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': \"<think>First, we need to multiply 15 and 19. Which operation do you think would give us the closest result to 24 if we were to round naturally? </think>\\n<final_answer>\\nStep 1: Multiply 15 and 19.\\n15 * 19 = 285\\n</final_answer> But I need to verify this. 285 is far from 24, so let's try divisi... | ["{'generation': \"<think>First, we need to multiply 15 and 19. Which operation do you think would give us the closest result to 24 if we were to round naturally? </think>\\n<final_answer>\\nStep 1: Multiply 15 and 19.\\n15 * 19 = 285\\n</final_answer> But I need to verify this. 285 is far from 24, so let's try divisio... | 6233391fa323f1ae8f0498bde4e183b36b9bab90b39c8d544a67220125b83287 | 08ad970139b0652c99d841197987b916b8a1ef91494da8c899ab506134af2eb8 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to multiply 15 and 19. Which operation do you think would give us the closest result to 24 if we were to round naturally? </think>\n<final_answer>\nStep 1: Multiply 15 and 19.\n15 * 19 = 285\n</final_answer> But I need to verify this. 285 is far from 24, so let's try division. It seems 15 * 20 +... | [{"budget_forced_chunks": ["<think>First, we need to multiply 15 and 19. Which operation do you think would give us the closest result to 24 if we were to round naturally? </think>\n<final_answer>\nStep 1: Multiply 15 and 19.\n15 * 19 = 285\n</final_answer>", " But I need to verify this. 285 is far from 24, so let's tr... | 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': \"<think>First, we need to use the numbers [17, 7, 3, 8] once each in the equation. We can start by multiplying the two largest numbers, 17 and 7.</think>\\n<final_answer>\\nStep 1: 17 * 7 = 119\\n</final_answer> Wait, this result is 1 more than our target. Let's try subtracting 1 from the product ins... | ["{'generation': \"<think>First, we need to use the numbers [17, 7, 3, 8] once each in the equation. We can start by multiplying the two largest numbers, 17 and 7.</think>\\n<final_answer>\\nStep 1: 17 * 7 = 119\\n</final_answer> Wait, this result is 1 more than our target. Let's try subtracting 1 from the product inst... | d451de9faeade7c0b043fd49fe6172d6084cd97ff6acbb5e55fd09b604e52764 | 2020d77f8edf80ce2b99f12ded817ddb52c377b349252b70b0b2618f0961c036 | 785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers [17, 7, 3, 8] once each in the equation. We can start by multiplying the two largest numbers, 17 and 7.</think>\n<final_answer>\nStep 1: 17 * 7 = 119\n</final_answer> Wait, this result is 1 more than our target. Let's try subtracting 1 from the product instead.\n<think>Subtrac... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers [17, 7, 3, 8] once each in the equation. We can start by multiplying the two largest numbers, 17 and 7.</think>\n<final_answer>\nStep 1: 17 * 7 = 119\n</final_answer>", " Wait, this result is 1 more than our target. Let's try subtracting 1 from the pr... | 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': '<think>First, we need to use the numbers 16, 15, 1, and 3 to reach the target number 23. We can only use each number once.</think>\\n<final_answer>\\nStep 1: 16 + 15 = 31\\nStep 2: 31 - 1 = 30\\nStep 3: 30 + 3 = 33\\n</final_answer> But according to 33 - 3 = 30, the target number should be 30, not 23... | ["{'generation': '<think>First, we need to use the numbers 16, 15, 1, and 3 to reach the target number 23. We can only use each number once.</think>\\n<final_answer>\\nStep 1: 16 + 15 = 31\\nStep 2: 31 - 1 = 30\\nStep 3: 30 + 3 = 33\\n</final_answer> But according to 33 - 3 = 30, the target number should be 30, not 23.... | d1910265333c2aec98a24231bd582fc8e6d688f4c3a08e889f54e26f260f6ff6 | debf4e355f7604ffeeb5f3404d87d62b825d6527dc43fb065206a123921ce584 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 16, 15, 1, and 3 to reach the target number 23. We can only use each number once.</think>\n<final_answer>\nStep 1: 16 + 15 = 31\nStep 2: 31 - 1 = 30\nStep 3: 30 + 3 = 33\n</final_answer> But according to 33 - 3 = 30, the target number should be 30, not 23. I made a mistake in ... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 16, 15, 1, and 3 to reach the target number 23. We can only use each number once.</think>\n<final_answer>\nStep 1: 16 + 15 = 31\nStep 2: 31 - 1 = 30\nStep 3: 30 + 3 = 33\n</final_answer>", " But according to 33 - 3 = 30, the target number should be 30... | 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': \"<think>First, we need to use the numbers 24, 18, and 23 to create an equation that equals 19. We can only use each number once.</think>\\n<final_answer>\\nStep 1: 24 + 18 = 42\\nStep 2: 42 + 23 = 65\\n</final_answer>' Hold on, let me verify this answer. 24 + 18 equals 42, and 42 + 23 equals 65. My a... | ["{'generation': \"<think>First, we need to use the numbers 24, 18, and 23 to create an equation that equals 19. We can only use each number once.</think>\\n<final_answer>\\nStep 1: 24 + 18 = 42\\nStep 2: 42 + 23 = 65\\n</final_answer>' Hold on, let me verify this answer. 24 + 18 equals 42, and 42 + 23 equals 65. My ap... | ef1eb782cf001ce26a20ed44e1b588a2148b04dffc4bdeb09208c9415768088f | 802a5426bbc14fc70091630daf5ba791cfd4353339d08eb4744e729541630a94 | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 24, 18, and 23 to create an equation that equals 19. We can only use each number once.</think>\n<final_answer>\nStep 1: 24 + 18 = 42\nStep 2: 42 + 23 = 65\n</final_answer>' Hold on, let me verify this answer. 24 + 18 equals 42, and 42 + 23 equals 65. My apologies, the correct ... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 24, 18, and 23 to create an equation that equals 19. We can only use each number once.</think>\n<final_answer>\nStep 1: 24 + 18 = 42\nStep 2: 42 + 23 = 65\n</final_answer>'", " Hold on, let me verify this answer. 24 + 18 equals 42, and 42 + 23 equals ... | 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. **First Step:** Combine \\\\( 17 \\\\) and \\\\( 20 \\\\):\\n \\\\[\\n 17 + 20 = 37\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 10 \\\\) from the result:\\n \\\\[\\n 37 - 10 = 27\\n \... | ["{'generation': \"To solve the problem \\\\( 17 + 20 - 10 + 4 \\\\), we can break it down into simpler steps:\\n\\n1. **First Step:** Combine \\\\( 17 \\\\) and \\\\( 20 \\\\):\\n \\\\[\\n 17 + 20 = 37\\n \\\\]\\n\\n2. **Second Step:** Subtract \\\\( 10 \\\\) from the result:\\n \\\\[\\n 37 - 10 = 27\\n \\... | 6db3fbd49b81d0debd08a217bb92f3efa1f6831c4999048dd50260c4a2a8e8c0 | 3bc056dfd0233c3b03fb4c3539e85fcd8989a7fad15a268f596aa2dfc3a7bce3 | e629fa6598d732768f7c726b4b621285f9c3b85303900aa912017db7617d8bdb | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 17 + 20 - 10 + 4 \\), we can break it down into simpler steps:\n\n1. **First Step:** Combine \\( 17 \\) and \\( 20 \\):\n \\[\n 17 + 20 = 37\n \\]\n\n2. **Second Step:** Subtract \\( 10 \\) from the result:\n \\[\n 37 - 10 = 27\n \\]\n\n3. **Third Step:** Add \\( 4 \\) to the resu... | [{"budget_forced_chunks": ["To solve the problem \\( 17 + 20 - 10 + 4 \\), we can break it down into simpler steps:\n\n1. **First Step:** Combine \\( 17 \\) and \\( 20 \\):\n \\[\n 17 + 20 = 37\n \\]\n\n2. **Second Step:** Subtract \\( 10 \\) from the result:\n \\[\n 37 - 10 = 27\n \\]\n\n3. **Third Step:**... | 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': \"<think>First, we need to multiply 12 by 6 to get 72. Then, we need to multiply 10 by 72. This will give us:</think>\\n<final_answer>\\nStep 1: 12 * 6 = 72\\nStep 2: 10 * 72 = 720\\nStep 3: 720 + 72 = 792\\n</final_answer> Wait, let me try 12 * 6 = 72</final_answer> and 72 * 10 = 720</final_answer> a... | ["{'generation': \"<think>First, we need to multiply 12 by 6 to get 72. Then, we need to multiply 10 by 72. This will give us:</think>\\n<final_answer>\\nStep 1: 12 * 6 = 72\\nStep 2: 10 * 72 = 720\\nStep 3: 720 + 72 = 792\\n</final_answer> Wait, let me try 12 * 6 = 72</final_answer> and 72 * 10 = 720</final_answer> ag... | 35b1c2b18fee46db7d7d486eb513d6e14310ea4dce3e14fc7920f45913c73d48 | 82a5b9ead972f062769857dd7132e626f4b355aaba3fb500fe19fd767cae5fe9 | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to multiply 12 by 6 to get 72. Then, we need to multiply 10 by 72. This will give us:</think>\n<final_answer>\nStep 1: 12 * 6 = 72\nStep 2: 10 * 72 = 720\nStep 3: 720 + 72 = 792\n</final_answer> Wait, let me try 12 * 6 = 72</final_answer> and 72 * 10 = 720</final_answer> again</final_answer>');<... | [{"budget_forced_chunks": ["<think>First, we need to multiply 12 by 6 to get 72. Then, we need to multiply 10 by 72. This will give us:</think>\n<final_answer>\nStep 1: 12 * 6 = 72\nStep 2: 10 * 72 = 720\nStep 3: 720 + 72 = 792\n</final_answer>", " Wait, let me try 12 * 6 = 72</final_answer> and 72 * 10 = 720</final_an... | 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. **Add the two smaller numbers first:** \\n \\\\[\\n 9 + 2 = 11\\n \\\\]\\n Write down 1 and carry over 1.\\n\\n2. **Multiply the next number by the carry-over number:**\\n \\\\[\\n 5 \\\\times 1 = 5... | ["{'generation': \"To solve the problem using the numbers 5, 9, 2, and 2, we can follow these steps:\\n\\n1. **Add the two smaller numbers first:** \\n \\\\[\\n 9 + 2 = 11\\n \\\\]\\n Write down 1 and carry over 1.\\n\\n2. **Multiply the next number by the carry-over number:**\\n \\\\[\\n 5 \\\\times 1 = 5\... | b793b535bd0b3280ad4a8bc7d71b5cf4f234571620473d65acae50acc825ec57 | e8cbd5ee01dec1857224acb722f9c821b946597da44f1d2b0e054dcb5fbfde53 | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem using the numbers 5, 9, 2, and 2, we can follow these steps:\n\n1. **Add the two smaller numbers first:** \n \\[\n 9 + 2 = 11\n \\]\n Write down 1 and carry over 1.\n\n2. **Multiply the next number by the carry-over number:**\n \\[\n 5 \\times 1 = 5\n \\]\n Add the carry-over 1:\n... | [{"budget_forced_chunks": ["To solve the problem using the numbers 5, 9, 2, and 2, we can follow these steps:\n\n1. **Add the two smaller numbers first:** \n \\[\n 9 + 2 = 11\n \\]\n Write down 1 and carry over 1.\n\n2. **Multiply the next number by the carry-over number:**\n \\[\n 5 \\times 1 = 5\n \\]\n... | 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, we can use the basic arithmetic operations to combine the given numbers. The target number is 19, so we can start by adding or subtracting numbers to manipulate the target until we reach it.\\n\\n\\\\[\\n\\\\begin{think}\\n\\\\text{Given numbers:} \\\\quad 19, 10, 16, 16\\n\\\\... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations to combine the given numbers. The target number is 19, so we can start by adding or subtracting numbers to manipulate the target until we reach it.\\n\\n\\\\[\\n\\\\begin{think}\\n\\\\text{Given numbers:} \\\\quad 19, 10, 16, 16\\n\\\\t... | 9d80570a7343e6d2d68246a0e09ce47e1a6a96dc24feecbb35ad65e514cb2939 | 78b473de32b43d7c002173d5378657ba52a42625ce5708900ecdbf5b9789453f | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers. The target number is 19, so we can start by adding or subtracting numbers to manipulate the target until we reach it.\n\n\\[\n\\begin{think}\n\\text{Given numbers:} \\quad 19, 10, 16, 16\n\\text{ target:} \\quad 19\n\\text{... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers. The target number is 19, so we can start by adding or subtracting numbers to manipulate the target until we reach it.\n\n\\[\n\\begin{think}\n\\text{Given numbers:} \\quad 19, 10, 16, 16\n\\text{ t... | 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 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n - \\\\( 5 \\\\) can be thought of as \\\\( 10 - 5 \\\\).\\n - \\\\( 19 \\\\) can be thought of as \\\\( 19 \\\\).\\n\\n2. **Use the distributive property:**\\n - ... | ["{'generation': 'To solve the problem \\\\( 5 + 19 = 24 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n - \\\\( 5 \\\\) can be thought of as \\\\( 10 - 5 \\\\).\\n - \\\\( 19 \\\\) can be thought of as \\\\( 19 \\\\).\\n\\n2. **Use the distributive property:**\\n - \... | 99d6fbffa160a424f45d4b78de11360cd4b97354c1dce2e3ae62d5f2f03d5b38 | 8f74b7e3c369679f1e12c6c9ec9b3b85d51f5d6e89c2181cc67e3ed90f706203 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 5 + 19 = 24 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n - \\( 5 \\) can be thought of as \\( 10 - 5 \\).\n - \\( 19 \\) can be thought of as \\( 19 \\).\n\n2. **Use the distributive property:**\n - \\( 10 - 5 + 5 = 10 \\)\n - \\( 19 \\times... | [{"budget_forced_chunks": ["To solve the problem \\( 5 + 19 = 24 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n - \\( 5 \\) can be thought of as \\( 10 - 5 \\).\n - \\( 19 \\) can be thought of as \\( 19 \\).\n\n2. **Use the distributive property:**\n - \\( 10 - 5 + 5 = 1... | 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': \"<think>First, we need to use the numbers 17, 13, and 15 once each. We can start by adding or subtracting these numbers,</think>\\n<think>For example, we can start by adding 17 and 13:</think>',\\n<think>(17 + 13) * 15 = 30 * 15 = 450</think>,\\n<think>Now, we want to add 15 to the previous result,</... | ["{'generation': \"<think>First, we need to use the numbers 17, 13, and 15 once each. We can start by adding or subtracting these numbers,</think>\\n<think>For example, we can start by adding 17 and 13:</think>',\\n<think>(17 + 13) * 15 = 30 * 15 = 450</think>,\\n<think>Now, we want to add 15 to the previous result,</t... | 1fd81e2df0bd7f0dd3fc40b5f6617fc216f2550b4fbc63bb64c3d55a28fe4268 | 0b4c367a3bb495638c386032c2d90db43eae78f510b2126270bb3052fff05c8a | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 17, 13, and 15 once each. We can start by adding or subtracting these numbers,</think>\n<think>For example, we can start by adding 17 and 13:</think>',\n<think>(17 + 13) * 15 = 30 * 15 = 450</think>,\n<think>Now, we want to add 15 to the previous result,</think>,\n<think>So, t... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 17, 13, and 15 once each. We can start by adding or subtracting these numbers,</think>\n<think>For example, we can start by adding 17 and 13:</think>',\n<think>(17 + 13) * 15 = 30 * 15 = 450</think>,\n<think>Now, we want to add 15 to the previous resu... | 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, we can use the numbers 2, 20, 24, and 4 to create an equation that equals 24. We can use the basic arithmetic operations of addition, subtraction, multiplication, and division.\\n\\\\boxed{24} Wait, how? 2 x 20 + 24 x 4 = 48 + 96 = 144 + 48 = 192. I apologize, you are correct. T... | ["{'generation': 'To solve the problem, we can use the numbers 2, 20, 24, and 4 to create an equation that equals 24. We can use the basic arithmetic operations of addition, subtraction, multiplication, and division.\\n\\\\boxed{24} Wait, how? 2 x 20 + 24 x 4 = 48 + 96 = 144 + 48 = 192. I apologize, you are correct. Th... | 997f99b3e946a10a23c993819c4b0e619ddc9a6fa3027b29726c423e97f82ed3 | 234784e30f512a638cd6dec8311f44a87e65a74d04d0e2478165e83a9d0ecb75 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the numbers 2, 20, 24, and 4 to create an equation that equals 24. We can use the basic arithmetic operations of addition, subtraction, multiplication, and division.\n\\boxed{24} Wait, how? 2 x 20 + 24 x 4 = 48 + 96 = 144 + 48 = 192. I apologize, you are correct. The solution to the p... | [{"budget_forced_chunks": ["To solve the problem, we can use the numbers 2, 20, 24, and 4 to create an equation that equals 24. We can use the basic arithmetic operations of addition, subtraction, multiplication, and division.\n\\boxed{24}", " Wait, how? 2 x 20 + 24 x 4 = 48 + 96 = 144 + 48 = 192. I apologize, you are ... | 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. **First, let's handle the multiplication:**\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n\\n2. **Next, we add the result to 9:**\\n \\\\[\\n 9 + 18 = 27\\n \\\\]\\n\\n3. **Finally, we s... | ["{'generation': \"To solve the problem \\\\( 9 + 22 - 3 \\\\times 6 \\\\), we can break it down into simpler steps:\\n\\n1. **First, let's handle the multiplication:**\\n \\\\[\\n 3 \\\\times 6 = 18\\n \\\\]\\n\\n2. **Next, we add the result to 9:**\\n \\\\[\\n 9 + 18 = 27\\n \\\\]\\n\\n3. **Finally, we su... | 03ce236c2139b2502530b7d1a7b9f04b0a228c5b913baf576c61ea4f747ed6d7 | dda06b36cd550be53e6e802ae533a72a54ee914cd5531f6e91af805bc15e3093 | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 9 + 22 - 3 \\times 6 \\), we can break it down into simpler steps:\n\n1. **First, let's handle the multiplication:**\n \\[\n 3 \\times 6 = 18\n \\]\n\n2. **Next, we add the result to 9:**\n \\[\n 9 + 18 = 27\n \\]\n\n3. **Finally, we subtract 3 from the previous result:**\n \\[\... | [{"budget_forced_chunks": ["To solve the problem \\( 9 + 22 - 3 \\times 6 \\), we can break it down into simpler steps:\n\n1. **First, let's handle the multiplication:**\n \\[\n 3 \\times 6 = 18\n \\]\n\n2. **Next, we add the result to 9:**\n \\[\n 9 + 18 = 27\n \\]\n\n3. **Finally, we subtract 3 from the p... | 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': '<think>First, we can add 3 and 6 to get 9, and then multiply 9 by 1 to get 9. But the assistant wants us to use the numbers [3, 6, 1] and each number can only be used once. So, we need to think of something else.</think>\\n<final_answer>\\nStep 1: 3 + 6 = 9\\nStep 2: 9 * 1 = 9\\n</final_answer>\\' Wa... | ["{'generation': '<think>First, we can add 3 and 6 to get 9, and then multiply 9 by 1 to get 9. But the assistant wants us to use the numbers [3, 6, 1] and each number can only be used once. So, we need to think of something else.</think>\\n<final_answer>\\nStep 1: 3 + 6 = 9\\nStep 2: 9 * 1 = 9\\n</final_answer>\\' Wai... | 7212f88580197608ee45310d3946ace5165c460930b98ffcf2efbf62fbb9fd78 | 100530f6b8ebe121df0720a72d5b462f72fe2f623c2939e4925f50602d8c1ac8 | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we can add 3 and 6 to get 9, and then multiply 9 by 1 to get 9. But the assistant wants us to use the numbers [3, 6, 1] and each number can only be used once. So, we need to think of something else.</think>\n<final_answer>\nStep 1: 3 + 6 = 9\nStep 2: 9 * 1 = 9\n</final_answer>' Wait! I can double check ... | [{"budget_forced_chunks": ["<think>First, we can add 3 and 6 to get 9, and then multiply 9 by 1 to get 9. But the assistant wants us to use the numbers [3, 6, 1] and each number can only be used once. So, we need to think of something else.</think>\n<final_answer>\nStep 1: 3 + 6 = 9\nStep 2: 9 * 1 = 9\n</final_answer>'... | 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': \"<think>First, we need to use the numbers 15, 3, and 22 to create an equation that equals 23. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 15 + 3 = 18 (We use the largest numbers first to try to approach the target number close enough with the fewest operations.)\\nStep 2: ... | ["{'generation': \"<think>First, we need to use the numbers 15, 3, and 22 to create an equation that equals 23. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 15 + 3 = 18 (We use the largest numbers first to try to approach the target number close enough with the fewest operations.)\\nStep 2: 1... | 4cc81a73edb3c70a7f9a4e66405067bdd3cd557192e4ccc5363b1c3ffd066337 | a521bb80ce8b527bb25590df9a522d4cf8e9b94627649d903e1c6902c0f1408e | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 15, 3, and 22 to create an equation that equals 23. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 15 + 3 = 18 (We use the largest numbers first to try to approach the target number close enough with the fewest operations.)\nStep 2: 18 * 22 = 416 (We then... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 15, 3, and 22 to create an equation that equals 23. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 15 + 3 = 18 (We use the largest numbers first to try to approach the target number close enough with the fewest operations.)\nStep... | 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 will follow the standard order of operations in arithmetic, which is:\\n\\n1. **First, perform the** \"(\" prefix operations: addition and subtraction).\\n2. **Then, perform the \")\" suffix operation: multiplication**.\\n\\nLet\\'s break it down ... | ["{'generation': 'To solve the problem \\\\( 21 + 19 - 22 + 7 \\\\), we will follow the standard order of operations in arithmetic, which is:\\n\\n1. **First, perform the** \"(\" prefix operations: addition and subtraction).\\n2. **Then, perform the \")\" suffix operation: multiplication**.\\n\\nLet\\'s break it down s... | 0ae865d4dbc5cfaea27c1a97d5dd26fd6cfc693d41b25c8bb22dfbab6e87b839 | d70ed273c01a94ba8bc2003830f89de9ad22d231a38e797ec80738614d894fa3 | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 21 + 19 - 22 + 7 \\), we will follow the standard order of operations in arithmetic, which is:\n\n1. **First, perform the** \"(\" prefix operations: addition and subtraction).\n2. **Then, perform the \")\" suffix operation: multiplication**.\n\nLet's break it down step by step:\n\n### Step 1:... | [{"budget_forced_chunks": ["To solve the problem \\( 21 + 19 - 22 + 7 \\), we will follow the standard order of operations in arithmetic, which is:\n\n1. **First, perform the** \"(\" prefix operations: addition and subtraction).\n2. **Then, perform the \")\" suffix operation: multiplication**.\n\nLet's break it down st... | 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': \"<think>First, let's try to balance the numbers. We can pair 5 and 3, and then pair 2 and 6.</think>\\n<final_answer>\\nStep 1: 5*3=15\\nStep 2: 2*6=12\\nStep 3: 15+12=23\\n</final_answer> But to confirm, 23 can also be obtained by another pair: <answer> (2 + 3) * 5 / 2 </answer> However, 23 is the d... | ["{'generation': \"<think>First, let's try to balance the numbers. We can pair 5 and 3, and then pair 2 and 6.</think>\\n<final_answer>\\nStep 1: 5*3=15\\nStep 2: 2*6=12\\nStep 3: 15+12=23\\n</final_answer> But to confirm, 23 can also be obtained by another pair: <answer> (2 + 3) * 5 / 2 </answer> However, 23 is the di... | e78c916c002984bf26b644862b714de89c9d41e56e57ccb2d0f7a65240145933 | 286866cc7d3d0e46a70d9a216c094be68ed8b30cb640270203c4a394f86b9e49 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, let's try to balance the numbers. We can pair 5 and 3, and then pair 2 and 6.</think>\n<final_answer>\nStep 1: 5*3=15\nStep 2: 2*6=12\nStep 3: 15+12=23\n</final_answer> But to confirm, 23 can also be obtained by another pair: <answer> (2 + 3) * 5 / 2 </answer> However, 23 is the direct result of the ini... | [{"budget_forced_chunks": ["<think>First, let's try to balance the numbers. We can pair 5 and 3, and then pair 2 and 6.</think>\n<final_answer>\nStep 1: 5*3=15\nStep 2: 2*6=12\nStep 3: 15+12=23\n</final_answer>", " But to confirm, 23 can also be obtained by another pair: <answer> (2 + 3) * 5 / 2 </answer>", " However, ... | 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': \"<think>Step 1: We need to use the numbers 19, 10, 15, and 4 in some order within the arithmetic operations. The result should be 19.</think>\\n<final_answer>\\nStep 1: 19 = (1 + 2) * 4 = 3 * 4 = 12\\nStep 2: 19 = 10 + (15 - 4) = 10 + 11 = 21\\n</final_answer> However, 21 is not one of the target num... | ["{'generation': \"<think>Step 1: We need to use the numbers 19, 10, 15, and 4 in some order within the arithmetic operations. The result should be 19.</think>\\n<final_answer>\\nStep 1: 19 = (1 + 2) * 4 = 3 * 4 = 12\\nStep 2: 19 = 10 + (15 - 4) = 10 + 11 = 21\\n</final_answer> However, 21 is not one of the target numb... | 8a18d4ad61f45669c35df9a8a11b091e5c9e57abb679b3d8d308f8c349b25e5f | fad17fb3a3ee78823eb8e4ca95379f63edd21a5e12798b1e0789047beff91fd7 | 9400f1b21cb527d7fa3d3eabba93557a18ebe7a2ca4e471cfe5e4c5b4ca7f767 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>Step 1: We need to use the numbers 19, 10, 15, and 4 in some order within the arithmetic operations. The result should be 19.</think>\n<final_answer>\nStep 1: 19 = (1 + 2) * 4 = 3 * 4 = 12\nStep 2: 19 = 10 + (15 - 4) = 10 + 11 = 21\n</final_answer> However, 21 is not one of the target numbers, so the correct a... | [{"budget_forced_chunks": ["<think>Step 1: We need to use the numbers 19, 10, 15, and 4 in some order within the arithmetic operations. The result should be 19.</think>\n<final_answer>\nStep 1: 19 = (1 + 2) * 4 = 3 * 4 = 12\nStep 2: 19 = 10 + (15 - 4) = 10 + 11 = 21\n</final_answer>", " However, 21 is not one of the ta... | 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, we can use the basic arithmetic operations to combine the given numbers:\\n\\n23 \u00d7 13 \u00d7 9 \u00d7 17\\n\\nFirst, we can group the numbers to make the calculation easier:\\n\\n(23 \u00d7 13) \u00d7 (9 \u00d7 17)\\n\\nNow, let's calculate each part separately:\\n\\n23 \u... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations to combine the given numbers:\\n\\n23 \u00d7 13 \u00d7 9 \u00d7 17\\n\\nFirst, we can group the numbers to make the calculation easier:\\n\\n(23 \u00d7 13) \u00d7 (9 \u00d7 17)\\n\\nNow, let's calculate each part separately:\\n\\n23 \u0... | a939fd76dd91760abb7e4ac6dd9cdd69c16832cb3afe806f723809d6674d9183 | 3af93761d572522bee5fffcdc85aac9c40d522a4f5704eb204a2145e90ca8e13 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers:\n\n23 \u00d7 13 \u00d7 9 \u00d7 17\n\nFirst, we can group the numbers to make the calculation easier:\n\n(23 \u00d7 13) \u00d7 (9 \u00d7 17)\n\nNow, let's calculate each part separately:\n\n23 \u00d7 13 = 309\n9 \u00d7 17 =... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers:\n\n23 \u00d7 13 \u00d7 9 \u00d7 17\n\nFirst, we can group the numbers to make the calculation easier:\n\n(23 \u00d7 13) \u00d7 (9 \u00d7 17)\n\nNow, let's calculate each part separately:\n\n23 \u00... | 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 will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mul... | ["{'generation': \"To solve the problem \\\\( 20 + 9 - 1 + 3 \\\\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\\n\\n- **Parentheses**: Perform operations inside parentheses.\\n- **Exponents**: Calculate exponents.\\n- **Multiplication**: Mult... | 54074718fc33cde0d1ffb866e238f9ee9e73e4eb30deff57612ecfcabb7c0aa8 | 09a3501b533aecd2d38214aab61d6e005bf47b6c36df8a3cb6cc750794728110 | b7a56873cd771f2c446d369b649430b65a756ba278ff97ec81bb6f55b2e73569 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 20 + 9 - 1 + 3 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Multiply next to the first nu... | [{"budget_forced_chunks": ["To solve the problem \\( 20 + 9 - 1 + 3 \\), we will follow the standard order of operations in arithmetic, often remembered by the acronym PEMDAS, which stands for:\n\n- **Parentheses**: Perform operations inside parentheses.\n- **Exponents**: Calculate exponents.\n- **Multiplication**: Mul... | 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 will follow the steps of the thought process:\\n\\n1. **Combine the numbers**:\\n \\\\[\\n 19 + 19 = 38\\n \\\\]\\n\\n2. **Subtract 1 from the result**:\\n \\\\[\\n 38 - 1 = 37\\n \\\\]\\n\\n3. **Subtract 22 from the result**:\\n \\\... | ["{'generation': 'To solve the problem \\\\( 19 + 19 - 1 - 22 \\\\), we will follow the steps of the thought process:\\n\\n1. **Combine the numbers**:\\n \\\\[\\n 19 + 19 = 38\\n \\\\]\\n\\n2. **Subtract 1 from the result**:\\n \\\\[\\n 38 - 1 = 37\\n \\\\]\\n\\n3. **Subtract 22 from the result**:\\n \\\\... | 5e9a09fdc605b12c61135540e930f653f86cd4d1572d9149cb281ff1e69004e0 | 4a1eb49f78824faa8128953d30b3c4be9bcc3515c1d66b954e7165e50b92606f | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 19 + 19 - 1 - 22 \\), we will follow the steps of the thought process:\n\n1. **Combine the numbers**:\n \\[\n 19 + 19 = 38\n \\]\n\n2. **Subtract 1 from the result**:\n \\[\n 38 - 1 = 37\n \\]\n\n3. **Subtract 22 from the result**:\n \\[\n 37 - 22 = 15\n \\]\n\nSo, the final... | [{"budget_forced_chunks": ["To solve the problem \\( 19 + 19 - 1 - 22 \\), we will follow the steps of the thought process:\n\n1. **Combine the numbers**:\n \\[\n 19 + 19 = 38\n \\]\n\n2. **Subtract 1 from the result**:\n \\[\n 38 - 1 = 37\n \\]\n\n3. **Subtract 22 from the result**:\n \\[\n 37 - 22 = 1... | 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 + 16 + 17 + 21 = 18 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n \\\\[\\n (6 + 16) + (17 + 21)\\n \\\\]\\n\\n2. **Calculate each group:**\\n - For \\\\( 6 + 16 \\\\):\\n \\\\[\\n 6 + 16 = 22\\n \\\\]\\n... | ["{'generation': \"To solve the problem \\\\( 6 + 16 + 17 + 21 = 18 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n \\\\[\\n (6 + 16) + (17 + 21)\\n \\\\]\\n\\n2. **Calculate each group:**\\n - For \\\\( 6 + 16 \\\\):\\n \\\\[\\n 6 + 16 = 22\\n \\\\]\\n ... | 5d6946d5bae41ad89ef8b142890fcccb941af44fcb19a052c920cc994415c022 | 656e0436e2d4c37f42635c0cc65e38bc1a4c562af47a499516eb06749fdba456 | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 6 + 16 + 17 + 21 = 18 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n \\[\n (6 + 16) + (17 + 21)\n \\]\n\n2. **Calculate each group:**\n - For \\( 6 + 16 \\):\n \\[\n 6 + 16 = 22\n \\]\n - For \\( 17 + 21 \\):\n \\[\n 17 +... | [{"budget_forced_chunks": ["To solve the problem \\( 6 + 16 + 17 + 21 = 18 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n \\[\n (6 + 16) + (17 + 21)\n \\]\n\n2. **Calculate each group:**\n - For \\( 6 + 16 \\):\n \\[\n 6 + 16 = 22\n \\]\n - For \\( 17 + 21... | 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': \"<think>First, we can add 16 and 12 to get 28. Then we can subtract 14 from 28 to get 14. So the equation is:</think>\\n<final_answer>\\nStep 1: 16 + 12 = 28\\nStep 2: 28 - 14 = 14\\n</final_answer>\\n<answer>16 + 12 - 14 = 14</answer> But I need to verify this. Let's check it again. The conversatio... | ["{'generation': \"<think>First, we can add 16 and 12 to get 28. Then we can subtract 14 from 28 to get 14. So the equation is:</think>\\n<final_answer>\\nStep 1: 16 + 12 = 28\\nStep 2: 28 - 14 = 14\\n</final_answer>\\n<answer>16 + 12 - 14 = 14</answer> But I need to verify this. Let's check it again. The conversation... | d8bbffa5e5aafaa81683a064a1e22217380d39e326b48c7a3892f8be8bd55e73 | ec25b954d4c64b681f6a629e1bebf6d529c421771c4d7ef6b38b109b278a8b99 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we can add 16 and 12 to get 28. Then we can subtract 14 from 28 to get 14. So the equation is:</think>\n<final_answer>\nStep 1: 16 + 12 = 28\nStep 2: 28 - 14 = 14\n</final_answer>\n<answer>16 + 12 - 14 = 14</answer> But I need to verify this. Let's check it again. The conversation was:User: Using the n... | [{"budget_forced_chunks": ["<think>First, we can add 16 and 12 to get 28. Then we can subtract 14 from 28 to get 14. So the equation is:</think>\n<final_answer>\nStep 1: 16 + 12 = 28\nStep 2: 28 - 14 = 14\n</final_answer>\n<answer>16 + 12 - 14 = 14</answer>", " But I need to verify this. Let's check it again. The conv... | 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': \"<think>First, we need to use the numbers 4, 6, and 11 to create an equation that equals 20. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 11 + 6 = 17\\nStep 2: 17 * 4 = 68\\n</final_answer>\\n\\n<answer>68</answer> Wait! I can double check this answer. 11 + 6 = 17, 17 * 4 =... | ["{'generation': \"<think>First, we need to use the numbers 4, 6, and 11 to create an equation that equals 20. We can only use each number once.</think>\\n\\n<final_answer>\\nStep 1: 11 + 6 = 17\\nStep 2: 17 * 4 = 68\\n</final_answer>\\n\\n<answer>68</answer> Wait! I can double check this answer. 11 + 6 = 17, 17 * 4 = ... | e1fd07ae613d4433c60203d498668d3115bfa1c141ec77d811980d28281a64ce | 97371084dfc8c3d3a11b264c62dd52e390799a6af505406ad31e1b2b54b56055 | f5ca38f748a1d6eaf726b8a42fb575c3c71f1864a8143301782de13da2d9202b | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 4, 6, and 11 to create an equation that equals 20. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 11 + 6 = 17\nStep 2: 17 * 4 = 68\n</final_answer>\n\n<answer>68</answer> Wait! I can double check this answer. 11 + 6 = 17, 17 * 4 = 68, isn't 68 * 4 = 272? ... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 4, 6, and 11 to create an equation that equals 20. We can only use each number once.</think>\n\n<final_answer>\nStep 1: 11 + 6 = 17\nStep 2: 17 * 4 = 68\n</final_answer>\n\n<answer>68</answer>", " Wait! I can double check this answer. 11 + 6 = 17, 17 ... | 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, we can use the basic arithmetic operations to combine the given numbers in a way that equals the target number, 23. \\nOne such combination is:\\nStep 1: 16 + 21 = 37\\nStep 2: 15 * 2 = 30\\nNow, combining these results:\\nStep 3: 37 + 30 = 67\\nHowever, 67 is not equal to 23. ... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations to combine the given numbers in a way that equals the target number, 23. \\nOne such combination is:\\nStep 1: 16 + 21 = 37\\nStep 2: 15 * 2 = 30\\nNow, combining these results:\\nStep 3: 37 + 30 = 67\\nHowever, 67 is not equal to 23. \... | 3a1b25f4d472756ebdf562f6119b65b746b767ea84a4dd799bd070e16ecfe97b | d458798ae840986384fb19120fb9fb1a5e41c093e8037f36a443be3fcc0dcaf9 | 535fa30d7e25dd8a49f1536779734ec8286108d115da5045d77f3b4185d8f790 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers in a way that equals the target number, 23. \nOne such combination is:\nStep 1: 16 + 21 = 37\nStep 2: 15 * 2 = 30\nNow, combining these results:\nStep 3: 37 + 30 = 67\nHowever, 67 is not equal to 23. \nIt seems there might b... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations to combine the given numbers in a way that equals the target number, 23. \nOne such combination is:\nStep 1: 16 + 21 = 37\nStep 2: 15 * 2 = 30\nNow, combining these results:\nStep 3: 37 + 30 = 67\nHowever, 67 is not equal to 23... | 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, let's multiply 16 by 4:\\n - 16 * 4 = 64\\n\\n2. Now, let's multiply 1 by the result from step 1 (64):\\n - 1 * 64 = 64\\n\\n3. Finally, we need to multiply 21 by the result from step... | ["{'generation': \"To solve the problem using the numbers 16, 4, 1, and 21, we can break it down into simpler steps:\\n\\n1. First, let's multiply 16 by 4:\\n - 16 * 4 = 64\\n\\n2. Now, let's multiply 1 by the result from step 1 (64):\\n - 1 * 64 = 64\\n\\n3. Finally, we need to multiply 21 by the result from step ... | d072894f0ec9b0cfbfa2cc48b6771ecc2c365ef18772bb99cdcc43a7540ee46f | 7bde26e5b3b1575939cd70cea46432c285a6285297650ad797a14d239b460762 | b17ef6d19c7a5b1ee83b907c595526dcb1eb06db8227d650d5dda0a9f4ce8cd9 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem using the numbers 16, 4, 1, and 21, we can break it down into simpler steps:\n\n1. First, let's multiply 16 by 4:\n - 16 * 4 = 64\n\n2. Now, let's multiply 1 by the result from step 1 (64):\n - 1 * 64 = 64\n\n3. Finally, we need to multiply 21 by the result from step 2 (64):\n - 21 * 64 = 1... | [{"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, let's multiply 16 by 4:\n - 16 * 4 = 64\n\n2. Now, let's multiply 1 by the result from step 1 (64):\n - 1 * 64 = 64\n\n3. Finally, we need to multiply 21 by the result from step... | 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': '<think>First, we need to use the numbers 8, 4, and 15 to reach the target number 17. We can perform addition, subtraction, multiplication, or division operations between the numbers.</think>\\n\\n<final_answer>\\nStep 1: 15 + 4 = 19\\nStep 2: 19 * 8 = 152\\n</final_answer>\\n\\n<think>Using the numbe... | ["{'generation': '<think>First, we need to use the numbers 8, 4, and 15 to reach the target number 17. We can perform addition, subtraction, multiplication, or division operations between the numbers.</think>\\n\\n<final_answer>\\nStep 1: 15 + 4 = 19\\nStep 2: 19 * 8 = 152\\n</final_answer>\\n\\n<think>Using the number... | efcaf1a72cc1c5524e2e8c8faf13eb037aad0cfaeda5e5f50a2a2902dde53333 | 23aa6021a0c062a9b897ef9afa175819a2757915f30ab230bbb56d2e9f0d4379 | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["<think>First, we need to use the numbers 8, 4, and 15 to reach the target number 17. We can perform addition, subtraction, multiplication, or division operations between the numbers.</think>\n\n<final_answer>\nStep 1: 15 + 4 = 19\nStep 2: 19 * 8 = 152\n</final_answer>\n\n<think>Using the numbers and operations discus... | [{"budget_forced_chunks": ["<think>First, we need to use the numbers 8, 4, and 15 to reach the target number 17. We can perform addition, subtraction, multiplication, or division operations between the numbers.</think>\n\n<final_answer>\nStep 1: 15 + 4 = 19\nStep 2: 19 * 8 = 152\n</final_answer>\n\n<think>Using the num... | 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 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n - \\\\( 20 + 17 = 37 \\\\)\\n - \\\\( 37 + 24 = 61 \\\\)\\n\\n2. **Add the numbers in order:**\\n - Start with \\\\( 20 + 17 \\\\)\\n - Then add \\\\( 24... | ["{'generation': \"To solve the problem \\\\( 20 + 17 + 24 = 13 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n - \\\\( 20 + 17 = 37 \\\\)\\n - \\\\( 37 + 24 = 61 \\\\)\\n\\n2. **Add the numbers in order:**\\n - Start with \\\\( 20 + 17 \\\\)\\n - Then add \\\\( 24 ... | 06649405689279406a3c70aecf0a5a85d6c4f8da6b95412e61bf2dca98890c04 | 55ba249ea0e0bd5cabb609e0cc089c7f40c89a4d809e27c8712b899ba78b1571 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 20 + 17 + 24 = 13 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n - \\( 20 + 17 = 37 \\)\n - \\( 37 + 24 = 61 \\)\n\n2. **Add the numbers in order:**\n - Start with \\( 20 + 17 \\)\n - Then add \\( 24 \\) to the result\n\n3. **Perform the addit... | [{"budget_forced_chunks": ["To solve the problem \\( 20 + 17 + 24 = 13 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n - \\( 20 + 17 = 37 \\)\n - \\( 37 + 24 = 61 \\)\n\n2. **Add the numbers in order:**\n - Start with \\( 20 + 17 \\)\n - Then add \\( 24 \\) to the result... | 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, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 9, 14, 11, and 17.\\n\\nFirst, let's think about the problem step by step:\\n\\n1. We need to use each of these numbers exactly once in our equation.\\n... | ["{'generation': \"To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 9, 14, 11, and 17.\\n\\nFirst, let's think about the problem step by step:\\n\\n1. We need to use each of these numbers exactly once in our equation.\\n2... | 0e937e0893608a7dccea4dc5ebe2f18c3d7a0f90b5cea4b17f34fb5a0fddcb7e | 4367a333b8fbb8824e45aa74045b82d4909a70148afc968b397a44152d78cf2d | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 9, 14, 11, and 17.\n\nFirst, let's think about the problem step by step:\n\n1. We need to use each of these numbers exactly once in our equation.\n2. The numbers are all ... | [{"budget_forced_chunks": ["To solve the problem, we can use the basic arithmetic operations of addition, subtraction, multiplication, and division. We are given four numbers: 9, 14, 11, and 17.\n\nFirst, let's think about the problem step by step:\n\n1. We need to use each of these numbers exactly once in our equation... | 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 + 16 + 5 + 15 = 18 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n \\\\[\\n 22 + 16 = 38\\n \\\\]\\n \\\\[\\n 5 + 15 = 20\\n \\\\]\\n\\n2. **Add the results of the groups:**\\n \\\\[\\n 38 + 20 = 58\\n \\\\]... | ["{'generation': 'To solve the problem \\\\( 22 + 16 + 5 + 15 = 18 \\\\), we can break it down into simpler steps:\\n\\n1. **Break the numbers into groups:**\\n \\\\[\\n 22 + 16 = 38\\n \\\\]\\n \\\\[\\n 5 + 15 = 20\\n \\\\]\\n\\n2. **Add the results of the groups:**\\n \\\\[\\n 38 + 20 = 58\\n \\\\]\... | c05b04ca7ae2cc4348826abbfbaf15c8c666eac685b4eac2862b07de889f7024 | a3e4733b904b745aded4db23f1be09a0a5ea7593a933cb6bee0e85f6aba4d55f | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-05T23-42-55.567483.jsonl | ["To solve the problem \\( 22 + 16 + 5 + 15 = 18 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n \\[\n 22 + 16 = 38\n \\]\n \\[\n 5 + 15 = 20\n \\]\n\n2. **Add the results of the groups:**\n \\[\n 38 + 20 = 58\n \\]\n\n3. **Final verification:**\n \\[\n 22 ... | [{"budget_forced_chunks": ["To solve the problem \\( 22 + 16 + 5 + 15 = 18 \\), we can break it down into simpler steps:\n\n1. **Break the numbers into groups:**\n \\[\n 22 + 16 = 38\n \\]\n \\[\n 5 + 15 = 20\n \\]\n\n2. **Add the results of the groups:**\n \\[\n 38 + 20 = 58\n \\]\n\n3. **Final verif... | null |
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