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Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [73, 48], create an equation that equals 121. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 48 + 73 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [73, 48], create an equation that equals 121. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 6756, \"numbers\": [73, 48], \"target\": 121, \"expression\": \"48 + 73\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 6756, "numbers": [73, 48], "target": 121, "expression": "48 + 73"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 121 using the numbers 73 and 48 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to find a combination that yields 121. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** We start with two given numbers: 73 and 48.\n ... | [
false
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""
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"73 + 48"
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"73 + 48",
"\\( 73 + 48 = 121 \\)",
"73 + 48"
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"per... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [14, 54], create an equation that equals 756. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 14*54 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [14, 54], create an equation that equals 756. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 6685, \"numbers\": [14, 54], \"target\": 756, \"expression\": \"14*54\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 6685, "numbers": [14, 54], "target": 756, "expression": "14*54"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 756 using the numbers 14 and 54 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to find a combination that will yield 756 when applied correctly. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** Multiply 14 and 54.... | [
false
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""
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true
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"54*14"
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"\\( 14 \\times 54 = 756 \\)",
"\\( 14 \\times 54 = 756 \\)",
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [40, 70], create an equation that equals 110. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 40 + 70 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [40, 70], create an equation that equals 110. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5824, \"numbers\": [40, 70], \"target\": 110, \"expression\": \"40 + 70\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5824, "numbers": [40, 70], "target": 110, "expression": "40 + 70"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 110 using the numbers 40 and 70 with each being used exactly once:\n\n1. First, we need to add these two numbers together because their sum will likely get us close to our goal.\n Step 1: 40 + 70 = 110\n\nTherefore, the equation that equals 110 using the given numbers is simply ad... | [
false
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""
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false
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"70/40 + 40"
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [30, 31], create an equation that equals 930. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 31*30 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [30, 31], create an equation that equals 930. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5930, \"numbers\": [30, 31], \"target\": 930, \"expression\": \"31*30\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5930, "numbers": [30, 31], "target": 930, "expression": "31*30"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 930 using the numbers 30 and 31 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to strategically combine these numbers into one expression that yields 930 when evaluated correctly.\n\nHere’s how I would approach it:\n\n### Step-by-Step Sol... | [
false
] | [
""
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false
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null
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[]
] | [
[]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [], "is_final_of_multiple": false, "judge_model": "gpt-4.1-mini", "question_context": true, "span_positions": [], "total_internal_spans": 0, "total_spans": 0} | [{"value": "[]"}] | [
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [25, 78], create an equation that equals 103. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 25 + 78 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [25, 78], create an equation that equals 103. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5864, \"numbers\": [25, 78], \"target\": 103, \"expression\": \"25 + 78\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5864, "numbers": [25, 78], "target": 103, "expression": "25 + 78"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for the target number using the given numbers [25, 78], we need to find a combination of addition, subtraction, multiplication, and division that will result in 103 when applied sequentially with these two numbers.\n\nHere’s one possible way:\n\n1. Start with the first number (25).\n ... | [
false
] | [
""
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false
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"25*4 + 3"
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"\\(25 + 78 - 25 = 103\\)",
"(25 * 4) + 3",
"25*4 + 3"
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [85, 76], create an equation that equals 161. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 76 + 85 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [85, 76], create an equation that equals 161. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 6120, \"numbers\": [85, 76], \"target\": 161, \"expression\": \"76 + 85\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 6120, "numbers": [85, 76], "target": 161, "expression": "76 + 85"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for the target number 161 using the given numbers 85 and 76 with each being used exactly once:\n\n### Step-by-Step Solution\n\n**Step 1:** First, we need to combine these two numbers into one expression that will help us get close to our goal (161). We start by adding them together.\n\\... | [
false
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""
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false
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"\\( 85 + 76 = 161 \\)"
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"\\boxed{85 + 76}",
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"\\( 85 + 76 = 161 \\)"
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"per... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [45, 75], create an equation that equals 120. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 45 + 75 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [45, 75], create an equation that equals 120. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5533, \"numbers\": [45, 75], \"target\": 120, \"expression\": \"45 + 75\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5533, "numbers": [45, 75], "target": 120, "expression": "45 + 75"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 120 using the numbers 45 and 75 with each being used exactly once:\n\n1. First, we need to find how many times 45 fits into 120.\n - Step 1: 120 ÷ 45 ≈ 2.67 (we'll round up since partial units don't work here)\n\n2. Now multiply 45 by our quotient from above (rounded up):\n - St... | [
false
] | [
""
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false
] | [
"45*75/45"
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[
false,
false
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] | [
[
"(45 + 75) * 3",
"45*75/45"
]
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [62, 14], create an equation that equals 868. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 14*62 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [62, 14], create an equation that equals 868. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5746, \"numbers\": [62, 14], \"target\": 868, \"expression\": \"14*62\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5746, "numbers": [62, 14], "target": 868, "expression": "14*62"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 868 using the numbers 62 and 14 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to strategically combine these numbers into one expression that yields 868. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** Multiply ... | [
false
] | [
""
] | {"api_url": "http://127.0.0.1:52397/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/M-skillfactory_yolo_3b-sft", "prompt": [{"content": "Answer the following problem.... | {"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/M-skillfactory_yolo_3b-sft", "n_responses": 1} | [
false
] | [
"62*14 + 0"
] | {"all_spans_summary": [{"answer": "\\( 62 \\times 14 = 868 \\)", "context": "Therefore, the final equation is simply:", "end_line": 16, "start_line": 15}, {"answer": "\\( 62 * 14 = 868 \\)", "context": "Or more concisely as requested:", "end_line": 22, "start_line": 21}, {"answer": "\\( 62 \\times 14 = 868 \\)", "conte... | [{"answer_block": "62*14 + 0", "comparison_type": null, "correct_answer": null, "error": "Expression uses an unavailable or repeated number", "evaluation_method": null, "extracted_answer": null, "final_answer": 868.0, "is_correct": false, "is_equivalent": null, "method": null, "reason": null}] | [
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false,
false,
false,
false,
false
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[
"\\( 62 \\times 14 = 868 \\)",
"\\( 62 * 14 = 868 \\)",
"\\( 62 \\times 14 = 868 \\)",
"\\( 62 + 14 * 11 = 868 \\)",
"\\( 62 \\times 14 = 868 \\)",
"62*14 + 0"
]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [{"answer": "\\( 62 \\times 14 = 868 \\)", "context": "Therefore, the final equation is simply:", "end_line": 16, "end_pos": 593, "start_line": 15, "start_pos": 558}, {"answer": "\\( 62 * 14 = 868 \\)", "context": "Or ... | [{"value": "[{'answer_block': '\\\\( 62 \\\\times 14 = 868 \\\\)', 'comparison_type': None, 'correct_answer': None, 'error': 'Could not evaluate expression', 'evaluation_method': None, 'extracted_answer': None, 'final_answer': None, 'is_correct': False, 'is_equivalent': None, 'method': None}, {'answer_block': '\\\\( 62... | [
[
null,
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true,
true,
true,
null
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null,
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false,
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false,
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [87, 6], create an equation that equals 522. You can use basic arithmetic operations (+, -, *, /) and each number can only b... | 6*87 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [87, 6], create an equation that equals 522. You can use basic arithmetic operations (+, -, *, /) a... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5021, \"numbers\": [87, 6], \"target\": 522, \"expression\": \"6*87\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5021, "numbers": [87, 6], "target": 522, "expression": "6*87"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 522 using the numbers 87 and 6 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to strategically combine these numbers into one expression that yields 522. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** Multiply 8... | [
false
] | [
""
] | {"api_url": "http://127.0.0.1:52397/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/M-skillfactory_yolo_3b-sft", "prompt": [{"content": "Answer the following problem.... | {"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/M-skillfactory_yolo_3b-sft", "n_responses": 1} | [
true
] | [
"87*6"
] | {"all_spans_summary": [{"answer": "\\(87 * 6\\)", "context": "Line 48-50, answer tags with equation", "end_line": 49, "start_line": 49}, {"answer": "87*6", "context": "Line 60-62, final answer tags with equation", "end_line": 61, "start_line": 61}], "empty_response": false, "error": null, "extraction_method": "llm_judg... | [{"answer_block": "87*6", "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": null, "extracted_answer": null, "final_answer": 522.0, "is_correct": true, "is_equivalent": null, "method": null, "reason": null}] | [
[
false,
true
]
] | [
[
"\\(87 * 6\\)",
"87*6"
]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [{"answer": "\\(87 * 6\\)", "context": "Line 48-50, answer tags with equation", "end_line": 49, "end_pos": 1860, "start_line": 49, "start_pos": 1849}, {"answer": "87*6", "context": "Line 60-62, final answer tags with e... | [{"value": "[{'answer_block': '\\\\(87 * 6\\\\)', 'comparison_type': None, 'correct_answer': None, 'error': 'Could not evaluate expression', 'evaluation_method': None, 'extracted_answer': None, 'final_answer': None, 'is_correct': False, 'is_equivalent': None, 'method': None}, {'answer_block': '87*6', 'comparison_type':... | [
[
true,
null
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] | [
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [90, 66], create an equation that equals 156. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 90 + 66 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [90, 66], create an equation that equals 156. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 6819, \"numbers\": [90, 66], \"target\": 156, \"expression\": \"90 + 66\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 6819, "numbers": [90, 66], "target": 156, "expression": "90 + 66"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 156 using the numbers 90 and 66 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to find a combination that will yield 156 when applied correctly. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** We start with two g... | [
false
] | [
""
] | {"api_url": "http://127.0.0.1:52397/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": {"chat_template_applied": true, "max_tokens": 4096, "temperature": 0.0, "top_p": 1.0}, "model_name": "hosted_vllm/TAUR-dev/M-skillfactory_yolo_3b-sft", "prompt": [{"content": "Answer the following problem.... | {"backend": "litellm", "model_name": "hosted_vllm/TAUR-dev/M-skillfactory_yolo_3b-sft", "n_responses": 1} | [
false
] | [
"90*66+90"
] | {"all_spans_summary": [{"answer": "90 + 66 = 156", "context": "In terms of the provided format, this would look like:", "end_line": 48, "start_line": 48}, {"answer": "Step 1: 90 * 66 = 5940\nStep 2: 5940 - 4384 = 156", "context": "So, the final equation is:", "end_line": 56, "start_line": 55}, {"answer": "90*66+90", "c... | [{"answer_block": "90*66+90", "comparison_type": null, "correct_answer": null, "error": "Expression does not equal stated result", "evaluation_method": null, "extracted_answer": null, "final_answer": 156.0, "is_correct": false, "is_equivalent": null, "method": null, "reason": null}] | [
[
true,
false,
false
]
] | [
[
"90 + 66 = 156",
"Step 1: 90 * 66 = 5940\nStep 2: 5940 - 4384 = 156",
"90*66+90"
]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [{"answer": "90 + 66 = 156", "context": "In terms of the provided format, this would look like:", "end_line": 48, "end_pos": 1962, "start_line": 48, "start_pos": 1942}, {"answer": "Step 1: 90 * 66 = 5940\nStep 2: 5940 ... | [{"value": "[{'answer_block': '90 + 66 = 156', 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': None, 'extracted_answer': None, 'final_answer': 156.0, 'is_correct': True, 'is_equivalent': None, 'method': None}, {'answer_block': 'Step 1: 90 * 66 = 5940\\nStep 2: 5940 - 4384 = 156', 'c... | [
[
null,
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null
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] | [
[
null,
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null
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [17, 92], create an equation that equals 109. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 17 + 92 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [17, 92], create an equation that equals 109. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5462, \"numbers\": [17, 92], \"target\": 109, \"expression\": \"17 + 92\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5462, "numbers": [17, 92], "target": 109, "expression": "17 + 92"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for the target number using the given numbers [17, 92], we need to find a combination of addition, subtraction, multiplication, and division that will result in 109 when applied sequentially with these two numbers.\n\nHere’s one possible way:\n\n1. Start with the first number, which is ... | [
false
] | [
""
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false
] | [
"92/17 + 17"
] | {"all_spans_summary": [{"answer": "\\( 17 + 92 = 109 \\)", "context": "<answer> \\( 17 + 92 = 109 \\) </answer>", "end_line": 20, "start_line": 20}, {"answer": "92/17 + 17", "context": "<answer> 92/17 + 17 </answer>", "end_line": 32, "start_line": 32}], "empty_response": false, "error": null, "extraction_method": "llm_... | [{"answer_block": "92/17 + 17", "comparison_type": null, "correct_answer": null, "error": "Expression does not equal stated result", "evaluation_method": null, "extracted_answer": null, "final_answer": 109.0, "is_correct": false, "is_equivalent": null, "method": null, "reason": null}] | [
[
false,
false
]
] | [
[
"\\( 17 + 92 = 109 \\)",
"92/17 + 17"
]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [{"answer": "\\( 17 + 92 = 109 \\)", "context": "<answer> \\( 17 + 92 = 109 \\) </answer>", "end_line": 20, "end_pos": 580, "start_line": 20, "start_pos": 560}, {"answer": "92/17 + 17", "context": "<answer> 92/17 + 17 ... | [{"value": "[{'answer_block': '\\\\( 17 + 92 = 109 \\\\)', 'comparison_type': None, 'correct_answer': None, 'error': 'Could not evaluate expression', 'evaluation_method': None, 'extracted_answer': None, 'final_answer': None, 'is_correct': False, 'is_equivalent': None, 'method': None}, {'answer_block': '92/17 + 17', 'co... | [
[
true,
null
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] | [
[
false,
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]
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [32, 20], create an equation that equals 640. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 32*20 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [32, 20], create an equation that equals 640. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 6675, \"numbers\": [32, 20], \"target\": 640, \"expression\": \"32*20\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 6675, "numbers": [32, 20], "target": 640, "expression": "32*20"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 640 using the numbers 32 and 20 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to find a combination that will yield 640 when applied correctly. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** Multiply 32 and 20.... | [
false
] | [
""
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true
] | [
"32*20"
] | {"all_spans_summary": [{"answer": "\\( 32 \\times 20 = 640 \\)", "context": "<answer> \\( 32 \\times 20 = 640 \\) </answer>", "end_line": 16, "start_line": 15}, {"answer": "Step 1: 32 + 20 = 52\nStep 2: 52 * 12 = 624\nStep 3: 624 - 8 = 616\nStep 4: 616 + 24 = 640", "context": "<answer> Step 1: 32 + 20 = 52\nStep 2: 52 ... | [{"answer_block": "32*20", "comparison_type": null, "correct_answer": null, "error": null, "evaluation_method": null, "extracted_answer": null, "final_answer": 640.0, "is_correct": true, "is_equivalent": null, "method": null, "reason": null}] | [
[
false,
false,
true,
true
]
] | [
[
"\\( 32 \\times 20 = 640 \\)",
"Step 1: 32 + 20 = 52\nStep 2: 52 * 12 = 624\nStep 3: 624 - 8 = 616\nStep 4: 616 + 24 = 640",
"Step 1: 32 * 20 = 640",
"32*20"
]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [{"answer": "\\( 32 \\times 20 = 640 \\)", "context": "<answer> \\( 32 \\times 20 = 640 \\) </answer>", "end_line": 16, "end_pos": 652, "start_line": 15, "start_pos": 617}, {"answer": "Step 1: 32 + 20 = 52\nStep 2: 52 ... | [{"value": "[{'answer_block': '\\\\( 32 \\\\times 20 = 640 \\\\)', 'comparison_type': None, 'correct_answer': None, 'error': 'Could not evaluate expression', 'evaluation_method': None, 'extracted_answer': None, 'final_answer': None, 'is_correct': False, 'is_equivalent': None, 'method': None}, {'answer_block': 'Step 1: ... | [
[
true,
null,
null,
null
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] | [
[
false,
null,
null,
null
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"... | 2025-09-03 |
Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.
# Problem
Using the numbers in the list [74, 51], create an equation that equals 125. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 74 + 51 | countdown_2arg | countdown | [
{
"content": "Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>.\n\n# Problem\nUsing the numbers in the list [74, 51], create an equation that equals 125. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5279, \"numbers\": [74, 51], \"target\": 125, \"expression\": \"74 + 51\"}"} | test | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5279, "numbers": [74, 51], "target": 125, "expression": "74 + 51"} | null | null | null | null | null | [
"<think>\n<sample>\nTo solve for 125 using the numbers 74 and 51 with basic arithmetic operations (addition, subtraction, multiplication, division), we need to find a combination that yields exactly 125. Let's break down the process:\n\n### Step-by-Step Solution\n\n**Step 1:** We start with two given numbers: 74 an... | [
false
] | [
""
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false
] | [
"51*74 - 125"
] | {"all_spans_summary": [{"answer": "74 + 51", "context": "\\boxed{74 + 51}", "end_line": 18, "start_line": 18}, {"answer": "No valid sequence found under standard arithmetic rules.", "context": "<answer>\nNo valid sequence found under standard arithmetic rules.\n</answer>", "end_line": 64, "start_line": 64}, {"answer": ... | [{"answer_block": "51*74 - 125", "comparison_type": null, "correct_answer": null, "error": "Expression does not equal stated result", "evaluation_method": null, "extracted_answer": null, "final_answer": 125.0, "is_correct": false, "is_equivalent": null, "method": null, "reason": null}] | [
[
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false,
false,
false,
true,
false
]
] | [
[
"74 + 51",
"No valid sequence found under standard arithmetic rules.",
"( 74 \\times 51 - 125 )",
"(74 * 51) - 125",
"Step 1: 74 + 51 = 125",
"51*74 - 125"
]
] | {"empty_response": false, "error": null, "extraction_method": "llm_judge", "internal_spans_detailed": [{"answer": "74 + 51", "context": "\\boxed{74 + 51}", "end_line": 18, "end_pos": 622, "start_line": 18, "start_pos": 606}, {"answer": "No valid sequence found under standard arithmetic rules.", "context": "<answer>\nNo... | [{"value": "[{'answer_block': '74 + 51', 'comparison_type': None, 'correct_answer': None, 'error': None, 'evaluation_method': None, 'extracted_answer': None, 'final_answer': 125.0, 'is_correct': True, 'is_equivalent': None, 'method': None}, {'answer_block': 'No valid sequence found under standard arithmetic rules.', 'c... | [
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] | [
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] | {
"allow_loose_format": true,
"answer_count": null,
"correct_predictions": 7,
"expected_answer_count": 6,
"flips_by": [
2
],
"flips_total": 2,
"formal_verdict_count": 3,
"found_answer_tags": 5,
"incorrect_predictions": 0,
"loose_format_count": 4,
"num_correct": 0,
"pass_at_n": null,
"per... | 2025-09-03 |
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