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Using ALL of the numbers 12, 4, 7, 1, 2, 5, 21, 88, create an expression that equals 109. You must use each number exactly once. You may use +, -, *, /.
{"numbers": [12, 4, 7, 1, 2, 5, 21, 88], "target": 109, "operators_used": ["/", "+", "/", "/", "/", "*", "+"], "expression": "12 / 4 + 7 / 1 / 2 / 5 * 21 + 88"}
countdown
[ { "content": "You are a helpful assistant that solves math problems by reasoning step-by-step. Show your work clearly and provide complete solutions. You MUST use ALL of the given numbers exactly once in your solution. When you have a final answer, wrap it in <answer></answer> tags.", "role": "system" }, ...
[ [ "Okay, let's see. I need to use all the numbers 12, 4, 7, 1, 2, 5, 21, 88 exactly once with +, -, *, / to make 109. Hmm, this might take a while. Let me start by listing out the numbers again to make sure I have them all: 12, 4, 7, 1, 2, 5, 21, 88. Eight numbers total. So, I need to combine them with operatio...
[ 32941 ]
[ 4 ]
[ [ "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies.", "Continue exploring alternative solution strategies." ] ]
[ [ "Okay, let's see. I need to use all the numbers 12, 4, 7, 1, 2, 5, 21, 88 exactly once with +, -, *, / to make 109. Hmm, this might take a while. Let me start by listing out the numbers again to make sure I have them all: 12, 4, 7, 1, 2, 5, 21, 88. Eight numbers total. So, I need to combine them with operatio...
iterative
[ "budget_reached" ]
[ null ]
false
[ 0 ]
[ [ [ "88 + 21 + (12 - 7 - 5) * (4 - 2 - 1)" ], [ "88 + 21 + (12 - 4 - 7 - 1) * (5 - 2)" ], [ "88 + 21 + ((7 * 2) - 12) * (5 - (4 + 1))" ], [ "88 + 5 * 4 + 1 + (21 - 12 - 7 - 2)", "88 + 5 * 4 + 1 + (21 - 12 - 7 - 2)" ] ] ]
[ [ [ true ], [ true ], [ true ], [ true, true ] ] ]
[ [ [ { "answer_block": "88 + 21 + (12 - 7 - 5) * (4 - 2 - 1)", "error": null, "final_answer": 109, "is_correct": true } ], [ { "answer_block": "88 + 21 + (12 - 4 - 7 - 1) * (5 - 2)", "error": null, "final_answer": 109, "is_...
[ [] ]
[ [ { "canonical_form": "88 + 21 = 109", "canonical_key": "arith:21+88->109", "end_char": 1708, "end_char_in_round": null, "has_free_variables": false, "is_legal": null, "is_multi_operand": false, "is_valid_arithmetic": true, "match_type": null, "offset_...
[ [ "88 + 21 = 109", "21 * 5 = 105", "12 * 7 = 84", "88 + 12 + 7 = 107", "88 + x = 109", "x = 21", "100 - 88 = 12", "(12 - 7 - 5) * (4 - 2 - 1) = 0", "(12 - 7 - 5) = 0", "(4 - 2 - 1) = 1", "88 + 21 = 109", "12 - 7 - 5 = 0", "4 - 2 - 1 = 1", "(12 - 7 - 5) * (4 - ...
[ { "has_free_variables": 4, "invalid_arithmetic": 3, "merged_text_length": 72633, "multi_operand": 47, "offsets_found": 68, "total_attempts_created": 81, "total_spans_from_llm": 82, "unevaluable": 4, "unique_canonical_keys": 36, "valid_arithmetic": 74 } ]
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