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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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 6756, "numbers": [73, 48], "target": 121, "expression": "48 + 73"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers 73 and 48 that equals 121.\nThink carefully about how these two numbers can combine through addition, subtraction, multiplication, division, or any combination thereof to achieve the desired result of 121.\n\nHere’s one way to approach ... | [
false
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""
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true
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"73 + 48 = 121"
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"It is impossible to form an exact equation using the numbers 73 and 48 that sums up to 121 while adhering strictly to the rules stated.",
"73 + 48 = 121",
"73 + 48 = 121"
]
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 6685, "numbers": [14, 54], "target": 756, "expression": "14*54"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {14, 54} that equals exactly 756.\nThink carefully about how these numbers interact with each other through addition, subtraction, multiplication, division, etc., until we find our desired result.\n\nStep 1: Multiply ... | [
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false
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"(14 * 54) + x = 756"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 6, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "(14 * 54) + x = 756", "start_line": 127, "end_line": 127, "context": "In conclusion, the answer is:", "start_pos": 4303, "en... | [{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "(14 * 54) + x = 756", "final_answer": null}] | [
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[
"((14 * 14) + 54) / 14",
"\\( 54 \\times 14 = 756 \\)",
"((14/54)*(14/54))+108",
"(14 * 14 - 54) / 14 = 756",
"(14 * 54) + x = 756",
"(14 * 54) + x = 756"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 6, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 6, "internal_spans_detailed": [{"answer": "((14 * 14) + 54) / 14", "start_line": 14, "end_line": 14, "context": "Final Equation:", ... | [[{"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "((14 * 14) + 54) / 14", "final_answer": 756.0}, {"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 54 \\times 14 = 756 \\)", "final_answer": null}, {"is_correct": false, "error": "Expression do... | {
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... | 2025-09-18 |
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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5824, "numbers": [40, 70], "target": 110, "expression": "40 + 70"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {40, 70} which will result in exactly 110.\n\nStep 1: Start with one of the numbers.\n - Let's choose 40 first.\n\nStep 2: Add another number to get close to our goal.\n - We need more than just 40 to reach 110 qu... | [
false
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""
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true
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"40 + 70"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 3, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "40 + 70", "start_line": 45, "end_line": 45, "context": "<answer>", "start_pos": 1169, "end_pos": 1177}, "total_spans_found":... | [{"is_correct": true, "error": null, "answer_block": "40 + 70", "final_answer": 110.0}] | [
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[
"40 + 70",
"40 + 70",
"40 + 70"
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5930, "numbers": [30, 31], "target": 930, "expression": "31*30"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {30, 31} that equals exactly 930.\nThink carefully about how these two numbers interact with each other through addition, subtraction, multiplication, division, etc., until we arrive at our goal of creating an express... | [
false
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""
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false
] | [
"Step 1: 30 + 31 = 61"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "Step 1: 30 + 31 = 61", "start_line": 161, "end_line": 161, "context": "What is the result when you add 30 and 31?", "start_p... | [{"is_correct": false, "error": "Incorrect final answer", "answer_block": "Step 1: 30 + 31 = 61", "final_answer": 61.0}] | [
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[
"\\( 30 \\times 31 = 930 \\)",
"No valid direct calculation exists under standard arithmetic rules leading exactly to 930 solely with 30 and 31.",
"\\u221A30 * (31 + \\u221A30)",
"\\( 31 \\times 31 - 11 + 20 - 40 \\)",
"Step 1: 30 + 31 = 61"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 5, "internal_spans_detailed": [{"answer": "\\( 30 \\times 31 = 930 \\)", "start_line": 23, "end_line": 23, "context": "final equati... | [[{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 30 \\times 31 = 930 \\)", "final_answer": null}, {"is_correct": false, "error": "Could not evaluate expression", "answer_block": "No valid direct calculation exists under standard arithmetic rules leading exactly to 930 solely with 3... | {
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... | 2025-09-18 |
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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5864, "numbers": [25, 78], "target": 103, "expression": "25 + 78"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {25, 78} which equals exactly 103.\n\nStep 1: Start with one of the numbers.\n - Let's choose 78 first.\n\nStep 2: Add another number to get close to our goal.\n - We need more than just 78 to reach 103 quickly. A... | [
false
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""
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true
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"(25 + 78)"
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"(78 + 25)",
"(25 + 78)",
"(25 + 78)"
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 6120, "numbers": [85, 76], "target": 161, "expression": "76 + 85"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers 85 and 76 that equals 161.\nThink carefully about how these two numbers can interact through addition, subtraction, multiplication, division, or any combination thereof to achieve the desired result.\n\nStep-by-step thinking process:\n\... | [
false
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""
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"Step 1: 85 + 76 = 161"
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"Step 1: 85 + 76 = 161",
"Step 1: 85 + 76 = 161"
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5533, "numbers": [45, 75], "target": 120, "expression": "45 + 75"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {45, 75} which equals exactly 120.\n- Step 1: Add 45 and 75 together.\n- Step 2: Divide the result obtained from Step 1 by 2.\n- Final Equation: (45 + 75) / 2\n\nTherefore,\n<answer>((45 + 75) / 2)</answer>\n</sample>... | [
false
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""
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true
] | [
"(45 + 75)"
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"((45 + 75) / 2)",
"45 + 75 = 120",
"(45 + 75)",
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5746, "numbers": [62, 14], "target": 868, "expression": "14*62"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {62, 14} that equals 868.\nThink carefully about how these numbers interact with each other through addition, subtraction, multiplication, division, etc., until we arrive at our goal of creating an expression equaling... | [
false
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""
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false
] | [
"\\( 62 \\times 14 = 868 \\)"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "\\( 62 \\times 14 = 868 \\)", "start_line": 70, "end_line": 70, "context": "Hence, the correct answer is:", "start_pos": 271... | [{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 62 \\times 14 = 868 \\)", "final_answer": null}] | [
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"(62 * 14) - 0 = 868",
"\\( 62 \\times 62 - 14 \\div 62 \\)",
"\\( 62 \\times 14 = 868 \\)",
"\\( 62 \\times 14 = 868 \\)"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 4, "internal_spans_detailed": [{"answer": "(62 * 14) - 0 = 868", "start_line": 21, "end_line": 21, "context": "Final Equation:", "s... | [[{"is_correct": false, "error": "Expression uses an unavailable or repeated number", "answer_block": "(62 * 14) - 0 = 868", "final_answer": 868.0}, {"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 62 \\times 62 - 14 \\div 62 \\)", "final_answer": null}, {"is_correct": false, "error"... | {
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5021, "numbers": [87, 6], "target": 522, "expression": "6*87"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {87, 6} that equals exactly 522.\nThink carefully about how these numbers interact with addition, subtraction, multiplication, division, etc., to form our desired result.\n \nFirstly, let’s consider possible combinat... | [
false
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""
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false
] | [
"(87 * 6 - 6) + 0"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "(87 * 6 - 6) + 0", "start_line": 101, "end_line": 101, "context": "<answer> (87 * 6 - 6) + 0 </answer>", "start_pos": 3633, ... | [{"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "(87 * 6 - 6) + 0", "final_answer": 522.0}] | [
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false,
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false
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[
"\\( 87 \\times 6 = 522 \\)",
"Step 1: 87\nStep 2: 87 + 6 = 93\nStep 3: 93 * 6 = 522",
"((87 - 6) / (87 - 6)) = 522",
"(87 * 6 - 6) + 0",
"(87 * 6 - 6) + 0"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 5, "internal_spans_detailed": [{"answer": "\\( 87 \\times 6 = 522 \\)", "start_line": 16, "end_line": 16, "context": "<answer> \\( ... | [[{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 87 \\times 6 = 522 \\)", "final_answer": null}, {"is_correct": false, "error": "Incorrect arithmetic in line: Step 3: 93 * 6 = 522", "answer_block": "Step 1: 87\nStep 2: 87 + 6 = 93\nStep 3: 93 * 6 = 522", "final_answer": 522.0}, {"i... | {
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... | 2025-09-18 |
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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 6819, "numbers": [90, 66], "target": 156, "expression": "90 + 66"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers 90 and 66 that equals 156.\nThink carefully about how these two numbers can interact through addition, subtraction, multiplication, division, etc., to achieve the desired result of 156.\n\nStep 1: Start with one of the given numbers (le... | [
false
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""
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false
] | [
"90/2*2-78=156"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "90/2*2-78=156", "start_line": 100, "end_line": 100, "context": "<answer> 90/2*2-78=156 </answer>", "start_pos": 3227, "end_p... | [{"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "90/2*2-78=156", "final_answer": 156.0}] | [
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false,
false,
false,
false
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] | [
[
"\\( (90 + 66) = 156 \\)",
"((90 + 66) / 90) * (90 + 66) = 156",
"(90 * 66) / 36 - 165 + 156",
"90/2*2-78=156",
"90/2*2-78=156"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 5, "internal_spans_detailed": [{"answer": "\\( (90 + 66) = 156 \\)", "start_line": 29, "end_line": 29, "context": "<answer> \\( (90... | [[{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( (90 + 66) = 156 \\)", "final_answer": null}, {"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "((90 + 66) / 90) * (90 + 66) = 156", "final_answer": 156.0}, {"is_correct": false, "error": "Expr... | {
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... | 2025-09-18 |
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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5462, "numbers": [17, 92], "target": 109, "expression": "17 + 92"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {17, 92} that equals exactly 109.\n\nStep 1: Start with one of the numbers.\n - Let's choose 92 first.\n\nStep 2: Add another number to get close to our goal.\n - We need more than just 92 to reach 109 quickly. Ad... | [
false
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""
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false
] | [
"\\( 17 + 92 = 109 \\)"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "\\( 17 + 92 = 109 \\)", "start_line": 97, "end_line": 97, "context": "Line 97 in final <answer> block", "start_pos": 3995, "... | [{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 17 + 92 = 109 \\)", "final_answer": null}] | [
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false
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[
"No valid equation found.",
"\\( 92 + 17 = 109 \\)",
"\\( 17 + 92 = 109 \\)",
"\\( 17 + 92 = 109 \\)"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 4, "internal_spans_detailed": [{"answer": "No valid equation found.", "start_line": 39, "end_line": 39, "context": "Line 39 in firs... | [[{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "No valid equation found.", "final_answer": null}, {"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 92 + 17 = 109 \\)", "final_answer": null}, {"is_correct": false, "error": "Could not evaluate expressi... | {
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 6675, "numbers": [32, 20], "target": 640, "expression": "32*20"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {32, 20} that equals exactly 640.\nThink carefully about how these two numbers interact through addition, subtraction, multiplication, division, etc., until we find our desired result.\n\nStep 1: Start with one of the... | [
false
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""
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true
] | [
"32 * 20 = 640"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 3, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "32 * 20 = 640", "start_line": 39, "end_line": 39, "context": "In conclusion, the answer is:", "start_pos": 932, "end_pos": 9... | [{"is_correct": true, "error": null, "answer_block": "32 * 20 = 640", "final_answer": 640.0}] | [
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[
"\\( 32 \\times 20 = 640 \\)",
"32 * 20 = 640",
"32 * 20 = 640"
]
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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 [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 | null | null | null | null | {"source_dataset": "countdown", "source_index": 5279, "numbers": [74, 51], "target": 125, "expression": "74 + 51"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {74, 51} which will result in exactly 125 when evaluated.\n\nStep 1: Start with one of the numbers.\n - Let's choose 74 first.\n\nStep 2: Multiply the chosen number by another number from the set.\n - We need to f... | [
false
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""
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true
] | [
"(74 + 51)"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 3, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "(74 + 51)", "start_line": 48, "end_line": 48, "context": "Hence, the correct answer is:", "start_pos": 1394, "end_pos": 1404... | [{"is_correct": true, "error": null, "answer_block": "(74 + 51)", "final_answer": 125.0}] | [
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false,
true,
true
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[
"\\( 74 \\times 51 - 354 = 125 \\)",
"(74 + 51)",
"(74 + 51)"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 3, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 3, "internal_spans_detailed": [{"answer": "\\( 74 \\times 51 - 354 = 125 \\)", "start_line": 24, "end_line": 24, "context": "Final ... | [[{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 74 \\times 51 - 354 = 125 \\)", "final_answer": null}, {"is_correct": true, "error": null, "answer_block": "(74 + 51)", "final_answer": 125.0}, {"is_correct": true, "error": null, "answer_block": "(74 + 51)", "final_answer": 125.0}]] | {
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... | 2025-09-18 |
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 [80, 7], create an equation that equals 560. You can use basic arithmetic operations (+, -, *, /) and each number can only b... | 7*80 | countdown_2arg | countdown | [
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"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {80, 7} that equals exactly 560.\nThink carefully about how these numbers interact with each other through addition, subtraction, multiplication, division, etc., until we find our desired result.\n\nStep 1: Start with... | [
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false
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"(80 * 7) - 140 = 560"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "(80 * 7) - 140 = 560", "start_line": 104, "end_line": 104, "context": "Hence, the correct answer is:", "start_pos": 3465, "e... | [{"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "(80 * 7) - 140 = 560", "final_answer": 560.0}] | [
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[
"80 * 7 = 560",
"\\( 80 \\times 7 = 560 \\)",
"(80 * 7) - 140 = 560",
"(80 * 7) - 140 = 560"
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] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 4, "internal_spans_detailed": [{"answer": "80 * 7 = 560", "start_line": 15, "end_line": 15, "context": "Final Equation:", "start_po... | [[{"is_correct": true, "error": null, "answer_block": "80 * 7 = 560", "final_answer": 560.0}, {"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 80 \\times 7 = 560 \\)", "final_answer": null}, {"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "(8... | {
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... | 2025-09-18 |
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, 80], create an equation that equals 153. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 73 + 80 | 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, 80], create an equation that equals 153. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 6089, \"numbers\": [73, 80], \"target\": 153, \"expression\": \"73 + 80\"}"} | test | null | null | null | null | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 6089, "numbers": [73, 80], "target": 153, "expression": "73 + 80"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers 73 and 80 that equals 153.\nThink carefully about how these two numbers can interact through addition, subtraction, multiplication, division, etc., to achieve the desired result.\n\nStep 1: Start with one of the given numbers (let's cho... | [
false
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""
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] | [
"(73 + 80)"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "(73 + 80)", "start_line": 75, "end_line": 75, "context": "<answer> (73 + 80) </answer>", "start_pos": 2498, "end_pos": 2508}... | [{"is_correct": true, "error": null, "answer_block": "(73 + 80)", "final_answer": 153.0}] | [
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[
"73 + 80 = 153",
"\\( 73 + 80 = 153 \\)",
"(5840 / 80) - 73 = 153",
"(73 + 80)",
"(73 + 80)"
]
] | {"judge_model": "gpt-4.1-mini", "total_spans": 5, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 5, "internal_spans_detailed": [{"answer": "73 + 80 = 153", "start_line": 19, "end_line": 20, "context": "<answer> 73 + 80 = 153 </a... | [[{"is_correct": true, "error": null, "answer_block": "73 + 80 = 153", "final_answer": 153.0}, {"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 73 + 80 = 153 \\)", "final_answer": null}, {"is_correct": false, "error": "Expression does not equal stated result", "answer_block": "(5840 ... | {
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... | 2025-09-18 |
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 [27, 84], create an equation that equals 111. You can use basic arithmetic operations (+, -, *, /) and each number can only ... | 84 + 27 | 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 [27, 84], create an equation that equals 111. You can use basic arithmetic operations (+, -, *, /) ... | [] | [] | {"metadata": "{\"source_dataset\": \"countdown\", \"source_index\": 5705, \"numbers\": [27, 84], \"target\": 111, \"expression\": \"84 + 27\"}"} | test | null | null | null | null | null | null | null | null | null | null | null | null | {"source_dataset": "countdown", "source_index": 5705, "numbers": [27, 84], "target": 111, "expression": "84 + 27"} | null | null | null | null | null | null | null | [
"<think>\n<sample>\nRewritten Question:\n\nCreate an equation using the numbers from the given set {27, 84} which equals exactly 111.\n\nStep 1: Start with one of the numbers.\n - Let's choose 84 first.\n\nStep 2: Add another number to get close to our goal.\n - We need more than just 84 to reach 111 quickly. A... | [
false
] | [
""
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] | [
"Step 1: 27 + 84 = 111"
] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "final_span_info": {"answer": "Step 1: 27 + 84 = 111", "start_line": 99, "end_line": 100, "context": "<answer>", "start_pos": 2811, "end_pos": 2842}, "tota... | [{"is_correct": true, "error": null, "answer_block": "Step 1: 27 + 84 = 111", "final_answer": 111.0}] | [
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] | {"judge_model": "gpt-4.1-mini", "total_spans": 4, "extraction_method": "llm_judge", "is_final_of_multiple": true, "question_context": true, "empty_response": false, "total_internal_spans": 4, "internal_spans_detailed": [{"answer": "\\( 84 + 27 \\)", "start_line": 23, "end_line": 23, "context": "Therefore,", "start_pos"... | [[{"is_correct": false, "error": "Could not evaluate expression", "answer_block": "\\( 84 + 27 \\)", "final_answer": null}, {"is_correct": true, "error": null, "answer_block": "27 + 84 = 111", "final_answer": 111.0}, {"is_correct": true, "error": null, "answer_block": "Step 1: 27 + 84 = 111", "final_answer": 111.0}, {"... | {
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"flips_total": 0,
"num_correct": 1,
"pass_at_n": null,
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... | 2025-09-18 |
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