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Using the numbers [2, 4, 8], create an arithmetic expression that equals 6. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-0", "num_completions": 7, "num_expressions": 7, "numbers": [2, 4, 8], "source": "synthetic_exact_countdown", "target": 6, "verifier": "countdown"}
countdown
7
train_multi_answer
Using the numbers [6, 9, 11], create an arithmetic expression that equals 26. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-1", "num_completions": 3, "num_expressions": 3, "numbers": [6, 9, 11], "source": "synthetic_exact_countdown", "target": 26, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [6, 8, 9], create an arithmetic expression that equals 12. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-2", "num_completions": 5, "num_expressions": 5, "numbers": [6, 8, 9], "source": "synthetic_exact_countdown", "target": 12, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 7, 11], create an arithmetic expression that equals 14. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-3", "num_completions": 5, "num_expressions": 5, "numbers": [4, 7, 11], "source": "synthetic_exact_countdown", "target": 14, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 4, 5], create an arithmetic expression that equals 7. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-4", "num_completions": 6, "num_expressions": 6, "numbers": [2, 4, 5], "source": "synthetic_exact_countdown", "target": 7, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [5, 9, 10], create an arithmetic expression that equals 18. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-5", "num_completions": 5, "num_expressions": 5, "numbers": [5, 9, 10], "source": "synthetic_exact_countdown", "target": 18, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 7, 8], create an arithmetic expression that equals 18. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-6", "num_completions": 3, "num_expressions": 3, "numbers": [3, 7, 8], "source": "synthetic_exact_countdown", "target": 18, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 10, 11], create an arithmetic expression that equals 19. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-7", "num_completions": 5, "num_expressions": 5, "numbers": [2, 10, 11], "source": "synthetic_exact_countdown", "target": 19, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [6, 8, 11], create an arithmetic expression that equals 25. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-8", "num_completions": 3, "num_expressions": 3, "numbers": [6, 8, 11], "source": "synthetic_exact_countdown", "target": 25, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [4, 11, 12], create an arithmetic expression that equals 19. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-9", "num_completions": 5, "num_expressions": 5, "numbers": [4, 11, 12], "source": "synthetic_exact_countdown", "target": 19, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 3, 9], create an arithmetic expression that equals 21. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-10", "num_completions": 2, "num_expressions": 2, "numbers": [2, 3, 9], "source": "synthetic_exact_countdown", "target": 21, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [3, 4, 7], create an arithmetic expression that equals 6. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-11", "num_completions": 5, "num_expressions": 5, "numbers": [3, 4, 7], "source": "synthetic_exact_countdown", "target": 6, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [7, 11, 12], create an arithmetic expression that equals 30. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-12", "num_completions": 3, "num_expressions": 3, "numbers": [7, 11, 12], "source": "synthetic_exact_countdown", "target": 30, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [3, 10, 12], create an arithmetic expression that equals 25. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-13", "num_completions": 3, "num_expressions": 3, "numbers": [3, 10, 12], "source": "synthetic_exact_countdown", "target": 25, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 9, 12], create an arithmetic expression that equals 5. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-14", "num_completions": 5, "num_expressions": 5, "numbers": [2, 9, 12], "source": "synthetic_exact_countdown", "target": 5, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 4, 8], create an arithmetic expression that equals 14. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-15", "num_completions": 3, "num_expressions": 3, "numbers": [2, 4, 8], "source": "synthetic_exact_countdown", "target": 14, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 4, 5], create an arithmetic expression that equals 11. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-16", "num_completions": 3, "num_expressions": 3, "numbers": [2, 4, 5], "source": "synthetic_exact_countdown", "target": 11, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [4, 6, 8], create an arithmetic expression that equals 12. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-17", "num_completions": 5, "num_expressions": 5, "numbers": [4, 6, 8], "source": "synthetic_exact_countdown", "target": 12, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 8, 11], create an arithmetic expression that equals 15. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-18", "num_completions": 5, "num_expressions": 5, "numbers": [4, 8, 11], "source": "synthetic_exact_countdown", "target": 15, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [6, 8, 12], create an arithmetic expression that equals 24. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-19", "num_completions": 2, "num_expressions": 2, "numbers": [6, 8, 12], "source": "synthetic_exact_countdown", "target": 24, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [2, 5, 6], create an arithmetic expression that equals 9. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-20", "num_completions": 5, "num_expressions": 5, "numbers": [2, 5, 6], "source": "synthetic_exact_countdown", "target": 9, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 4, 11], create an arithmetic expression that equals 9. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-21", "num_completions": 6, "num_expressions": 6, "numbers": [2, 4, 11], "source": "synthetic_exact_countdown", "target": 9, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [5, 7, 8], create an arithmetic expression that equals 10. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-22", "num_completions": 5, "num_expressions": 5, "numbers": [5, 7, 8], "source": "synthetic_exact_countdown", "target": 10, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 4, 12], create an arithmetic expression that equals 18. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-23", "num_completions": 3, "num_expressions": 3, "numbers": [2, 4, 12], "source": "synthetic_exact_countdown", "target": 18, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [4, 6, 12], create an arithmetic expression that equals 24. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-24", "num_completions": 2, "num_expressions": 2, "numbers": [4, 6, 12], "source": "synthetic_exact_countdown", "target": 24, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [4, 8, 10], create an arithmetic expression that equals 5. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-25", "num_completions": 5, "num_expressions": 5, "numbers": [4, 8, 10], "source": "synthetic_exact_countdown", "target": 5, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [8, 11, 12], create an arithmetic expression that equals 31. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-26", "num_completions": 3, "num_expressions": 3, "numbers": [8, 11, 12], "source": "synthetic_exact_countdown", "target": 31, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [3, 6, 8], create an arithmetic expression that equals 30. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-27", "num_completions": 2, "num_expressions": 2, "numbers": [3, 6, 8], "source": "synthetic_exact_countdown", "target": 30, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [2, 4, 5], create an arithmetic expression that equals 10. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-28", "num_completions": 6, "num_expressions": 6, "numbers": [2, 4, 5], "source": "synthetic_exact_countdown", "target": 10, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [2, 3, 12], create an arithmetic expression that equals 30. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-29", "num_completions": 2, "num_expressions": 2, "numbers": [2, 3, 12], "source": "synthetic_exact_countdown", "target": 30, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [3, 5, 12], create an arithmetic expression that equals 14. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-30", "num_completions": 5, "num_expressions": 5, "numbers": [3, 5, 12], "source": "synthetic_exact_countdown", "target": 14, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 6, 7], create an arithmetic expression that equals 4. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-31", "num_completions": 5, "num_expressions": 5, "numbers": [3, 6, 7], "source": "synthetic_exact_countdown", "target": 4, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 9, 10], create an arithmetic expression that equals 22. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-32", "num_completions": 3, "num_expressions": 3, "numbers": [3, 9, 10], "source": "synthetic_exact_countdown", "target": 22, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [5, 8, 10], create an arithmetic expression that equals 4. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-33", "num_completions": 5, "num_expressions": 5, "numbers": [5, 8, 10], "source": "synthetic_exact_countdown", "target": 4, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [7, 11, 12], create an arithmetic expression that equals 6. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-34", "num_completions": 5, "num_expressions": 5, "numbers": [7, 11, 12], "source": "synthetic_exact_countdown", "target": 6, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [6, 8, 9], create an arithmetic expression that equals 7. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-35", "num_completions": 5, "num_expressions": 5, "numbers": [6, 8, 9], "source": "synthetic_exact_countdown", "target": 7, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 6, 9], create an arithmetic expression that equals 27. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-36", "num_completions": 5, "num_expressions": 5, "numbers": [2, 6, 9], "source": "synthetic_exact_countdown", "target": 27, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 5, 7], create an arithmetic expression that equals 4. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-37", "num_completions": 6, "num_expressions": 6, "numbers": [2, 5, 7], "source": "synthetic_exact_countdown", "target": 4, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [3, 6, 9], create an arithmetic expression that equals 27. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-38", "num_completions": 2, "num_expressions": 2, "numbers": [3, 6, 9], "source": "synthetic_exact_countdown", "target": 27, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [2, 6, 11], create an arithmetic expression that equals 3. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-39", "num_completions": 3, "num_expressions": 3, "numbers": [2, 6, 11], "source": "synthetic_exact_countdown", "target": 3, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 10, 12], create an arithmetic expression that equals 24. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-40", "num_completions": 3, "num_expressions": 3, "numbers": [2, 10, 12], "source": "synthetic_exact_countdown", "target": 24, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [3, 7, 10], create an arithmetic expression that equals 20. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-41", "num_completions": 3, "num_expressions": 3, "numbers": [3, 7, 10], "source": "synthetic_exact_countdown", "target": 20, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 4, 8], create an arithmetic expression that equals 24. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-42", "num_completions": 2, "num_expressions": 2, "numbers": [2, 4, 8], "source": "synthetic_exact_countdown", "target": 24, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [2, 9, 11], create an arithmetic expression that equals 4. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-43", "num_completions": 6, "num_expressions": 6, "numbers": [2, 9, 11], "source": "synthetic_exact_countdown", "target": 4, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [5, 11, 12], create an arithmetic expression that equals 6. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-44", "num_completions": 5, "num_expressions": 5, "numbers": [5, 11, 12], "source": "synthetic_exact_countdown", "target": 6, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 6, 10], create an arithmetic expression that equals 15. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-45", "num_completions": 5, "num_expressions": 5, "numbers": [4, 6, 10], "source": "synthetic_exact_countdown", "target": 15, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [9, 10, 12], create an arithmetic expression that equals 13. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-46", "num_completions": 5, "num_expressions": 5, "numbers": [9, 10, 12], "source": "synthetic_exact_countdown", "target": 13, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 8, 12], create an arithmetic expression that equals 1. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-47", "num_completions": 3, "num_expressions": 3, "numbers": [3, 8, 12], "source": "synthetic_exact_countdown", "target": 1, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 3, 10], create an arithmetic expression that equals 15. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-48", "num_completions": 8, "num_expressions": 8, "numbers": [2, 3, 10], "source": "synthetic_exact_countdown", "target": 15, "verifier": "countdown"}
countdown
8
train_multi_answer
Using the numbers [3, 4, 12], create an arithmetic expression that equals 11. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-49", "num_completions": 5, "num_expressions": 5, "numbers": [3, 4, 12], "source": "synthetic_exact_countdown", "target": 11, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [5, 8, 12], create an arithmetic expression that equals 1. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-50", "num_completions": 5, "num_expressions": 5, "numbers": [5, 8, 12], "source": "synthetic_exact_countdown", "target": 1, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [5, 8, 10], create an arithmetic expression that equals 3. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-51", "num_completions": 5, "num_expressions": 5, "numbers": [5, 8, 10], "source": "synthetic_exact_countdown", "target": 3, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 4, 5], create an arithmetic expression that equals 1. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-52", "num_completions": 5, "num_expressions": 5, "numbers": [2, 4, 5], "source": "synthetic_exact_countdown", "target": 1, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 6, 8], create an arithmetic expression that equals 2. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-53", "num_completions": 7, "num_expressions": 7, "numbers": [4, 6, 8], "source": "synthetic_exact_countdown", "target": 2, "verifier": "countdown"}
countdown
7
train_multi_answer
Using the numbers [3, 6, 9], create an arithmetic expression that equals 12. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-54", "num_completions": 5, "num_expressions": 5, "numbers": [3, 6, 9], "source": "synthetic_exact_countdown", "target": 12, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 6, 8], create an arithmetic expression that equals 17. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-55", "num_completions": 3, "num_expressions": 3, "numbers": [3, 6, 8], "source": "synthetic_exact_countdown", "target": 17, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 7, 9], create an arithmetic expression that equals 1. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-56", "num_completions": 6, "num_expressions": 6, "numbers": [2, 7, 9], "source": "synthetic_exact_countdown", "target": 1, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [4, 7, 9], create an arithmetic expression that equals 2. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-57", "num_completions": 6, "num_expressions": 6, "numbers": [4, 7, 9], "source": "synthetic_exact_countdown", "target": 2, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [6, 10, 11], create an arithmetic expression that equals 15. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-58", "num_completions": 5, "num_expressions": 5, "numbers": [6, 10, 11], "source": "synthetic_exact_countdown", "target": 15, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 9, 12], create an arithmetic expression that equals 36. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-59", "num_completions": 5, "num_expressions": 5, "numbers": [3, 9, 12], "source": "synthetic_exact_countdown", "target": 36, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 9, 10], create an arithmetic expression that equals 3. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-60", "num_completions": 5, "num_expressions": 5, "numbers": [4, 9, 10], "source": "synthetic_exact_countdown", "target": 3, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 8, 12], create an arithmetic expression that equals 5. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-61", "num_completions": 2, "num_expressions": 2, "numbers": [4, 8, 12], "source": "synthetic_exact_countdown", "target": 5, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [2, 5, 6], create an arithmetic expression that equals 13. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-62", "num_completions": 3, "num_expressions": 3, "numbers": [2, 5, 6], "source": "synthetic_exact_countdown", "target": 13, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [5, 6, 9], create an arithmetic expression that equals 20. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-63", "num_completions": 3, "num_expressions": 3, "numbers": [5, 6, 9], "source": "synthetic_exact_countdown", "target": 20, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [3, 5, 7], create an arithmetic expression that equals 15. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-64", "num_completions": 3, "num_expressions": 3, "numbers": [3, 5, 7], "source": "synthetic_exact_countdown", "target": 15, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [6, 10, 12], create an arithmetic expression that equals 4. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-65", "num_completions": 5, "num_expressions": 5, "numbers": [6, 10, 12], "source": "synthetic_exact_countdown", "target": 4, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 3, 9], create an arithmetic expression that equals 8. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-66", "num_completions": 5, "num_expressions": 5, "numbers": [2, 3, 9], "source": "synthetic_exact_countdown", "target": 8, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 6, 11], create an arithmetic expression that equals 13. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-67", "num_completions": 6, "num_expressions": 6, "numbers": [4, 6, 11], "source": "synthetic_exact_countdown", "target": 13, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [6, 9, 12], create an arithmetic expression that equals 15. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-68", "num_completions": 5, "num_expressions": 5, "numbers": [6, 9, 12], "source": "synthetic_exact_countdown", "target": 15, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [5, 8, 11], create an arithmetic expression that equals 14. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-69", "num_completions": 5, "num_expressions": 5, "numbers": [5, 8, 11], "source": "synthetic_exact_countdown", "target": 14, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 5, 8], create an arithmetic expression that equals 10. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-70", "num_completions": 5, "num_expressions": 5, "numbers": [4, 5, 8], "source": "synthetic_exact_countdown", "target": 10, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 4, 12], create an arithmetic expression that equals 24. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-71", "num_completions": 6, "num_expressions": 6, "numbers": [2, 4, 12], "source": "synthetic_exact_countdown", "target": 24, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [4, 7, 11], create an arithmetic expression that equals 22. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-72", "num_completions": 3, "num_expressions": 3, "numbers": [4, 7, 11], "source": "synthetic_exact_countdown", "target": 22, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [8, 9, 11], create an arithmetic expression that equals 12. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-73", "num_completions": 5, "num_expressions": 5, "numbers": [8, 9, 11], "source": "synthetic_exact_countdown", "target": 12, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 6, 10], create an arithmetic expression that equals 12. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-74", "num_completions": 2, "num_expressions": 2, "numbers": [3, 6, 10], "source": "synthetic_exact_countdown", "target": 12, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [5, 8, 10], create an arithmetic expression that equals 7. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-75", "num_completions": 5, "num_expressions": 5, "numbers": [5, 8, 10], "source": "synthetic_exact_countdown", "target": 7, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [8, 9, 12], create an arithmetic expression that equals 5. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-76", "num_completions": 5, "num_expressions": 5, "numbers": [8, 9, 12], "source": "synthetic_exact_countdown", "target": 5, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 7, 12], create an arithmetic expression that equals 21. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-77", "num_completions": 5, "num_expressions": 5, "numbers": [4, 7, 12], "source": "synthetic_exact_countdown", "target": 21, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [5, 8, 10], create an arithmetic expression that equals 13. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-78", "num_completions": 5, "num_expressions": 5, "numbers": [5, 8, 10], "source": "synthetic_exact_countdown", "target": 13, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 5, 6], create an arithmetic expression that equals 26. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-79", "num_completions": 2, "num_expressions": 2, "numbers": [4, 5, 6], "source": "synthetic_exact_countdown", "target": 26, "verifier": "countdown"}
countdown
2
train_multi_answer
Using the numbers [4, 8, 9], create an arithmetic expression that equals 13. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-80", "num_completions": 5, "num_expressions": 5, "numbers": [4, 8, 9], "source": "synthetic_exact_countdown", "target": 13, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 9, 11], create an arithmetic expression that equals 6. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-81", "num_completions": 5, "num_expressions": 5, "numbers": [4, 9, 11], "source": "synthetic_exact_countdown", "target": 6, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 7, 11], create an arithmetic expression that equals 21. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-82", "num_completions": 3, "num_expressions": 3, "numbers": [3, 7, 11], "source": "synthetic_exact_countdown", "target": 21, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 4, 10], create an arithmetic expression that equals 20. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-83", "num_completions": 6, "num_expressions": 6, "numbers": [2, 4, 10], "source": "synthetic_exact_countdown", "target": 20, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [4, 6, 9], create an arithmetic expression that equals 7. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-84", "num_completions": 5, "num_expressions": 5, "numbers": [4, 6, 9], "source": "synthetic_exact_countdown", "target": 7, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [4, 5, 12], create an arithmetic expression that equals 13. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-85", "num_completions": 5, "num_expressions": 5, "numbers": [4, 5, 12], "source": "synthetic_exact_countdown", "target": 13, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 11, 12], create an arithmetic expression that equals 26. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-86", "num_completions": 3, "num_expressions": 3, "numbers": [3, 11, 12], "source": "synthetic_exact_countdown", "target": 26, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [10, 11, 12], create an arithmetic expression that equals 9. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-87", "num_completions": 5, "num_expressions": 5, "numbers": [10, 11, 12], "source": "synthetic_exact_countdown", "target": 9, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 8, 10], create an arithmetic expression that equals 5. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-88", "num_completions": 5, "num_expressions": 5, "numbers": [3, 8, 10], "source": "synthetic_exact_countdown", "target": 5, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 8, 9], create an arithmetic expression that equals 20. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-89", "num_completions": 3, "num_expressions": 3, "numbers": [3, 8, 9], "source": "synthetic_exact_countdown", "target": 20, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [2, 7, 11], create an arithmetic expression that equals 6. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-90", "num_completions": 5, "num_expressions": 5, "numbers": [2, 7, 11], "source": "synthetic_exact_countdown", "target": 6, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [5, 7, 10], create an arithmetic expression that equals 12. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-91", "num_completions": 5, "num_expressions": 5, "numbers": [5, 7, 10], "source": "synthetic_exact_countdown", "target": 12, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [5, 6, 9], create an arithmetic expression that equals 8. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-92", "num_completions": 5, "num_expressions": 5, "numbers": [5, 6, 9], "source": "synthetic_exact_countdown", "target": 8, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 5, 7], create an arithmetic expression that equals 1. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-93", "num_completions": 5, "num_expressions": 5, "numbers": [3, 5, 7], "source": "synthetic_exact_countdown", "target": 1, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 8, 9], create an arithmetic expression that equals 19. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-94", "num_completions": 3, "num_expressions": 3, "numbers": [2, 8, 9], "source": "synthetic_exact_countdown", "target": 19, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [5, 9, 12], create an arithmetic expression that equals 16. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-95", "num_completions": 5, "num_expressions": 5, "numbers": [5, 9, 12], "source": "synthetic_exact_countdown", "target": 16, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [3, 8, 11], create an arithmetic expression that equals 1. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-96", "num_completions": 6, "num_expressions": 6, "numbers": [3, 8, 11], "source": "synthetic_exact_countdown", "target": 1, "verifier": "countdown"}
countdown
6
train_multi_answer
Using the numbers [6, 7, 10], create an arithmetic expression that equals 9. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-97", "num_completions": 5, "num_expressions": 5, "numbers": [6, 7, 10], "source": "synthetic_exact_countdown", "target": 9, "verifier": "countdown"}
countdown
5
train_multi_answer
Using the numbers [2, 7, 8], create an arithmetic expression that equals 17. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-98", "num_completions": 3, "num_expressions": 3, "numbers": [2, 7, 8], "source": "synthetic_exact_countdown", "target": 17, "verifier": "countdown"}
countdown
3
train_multi_answer
Using the numbers [4, 6, 12], create an arithmetic expression that equals 18. Use each given number exactly once. You may use +, -, *, /, and parentheses. Return exactly one final answer and no explanation: the expression inside \boxed{}.
{"instance_id": "train_multi_answer-0-99", "num_completions": 5, "num_expressions": 5, "numbers": [4, 6, 12], "source": "synthetic_exact_countdown", "target": 18, "verifier": "countdown"}
countdown
5
train_multi_answer
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ModeBench

ModeBench measures both correctness and the variety of correct answers produced by language models. Each problem has an executable verifier and a canonical definition of answer identity, so distinct wording alone does not count as a new solution.

This release contains three frozen benchmark levels across Graph Coloring, Countdown, Python Factors, MathIR, and PantryPlan. It preserves every original feature, row, and row order. The answer field is a serialized executable specification, not a target answer to include in the model prompt.

Level 1 · Level 2 · Level 3 · Loading · Evaluation · Manifest · Validation

The accompanying model and research-artifact archive contains experiment-specific model indexes and mappings to the paper results. Dataset publication does not imply completed Level-3 training results.

Level 1

The original benchmark uses 384 training problems and 128 primary evaluation problems per domain. PantryPlan additionally has its original 64-row development split. Graph Coloring also includes a separate 128-row unique_answer evaluation subset; it is published as the auxiliary level1_graph_coloring_unique_answer configuration and is not the primary multi-answer paper evaluation.

Level 2

Level 2 is the frozen modebench_harder_v2_matched_r5 release. It changes problem structure while retaining the verifier and canonicalizer contracts. Each domain has 384 training, 128 development, and 128 evaluation rows. Support histograms follow the recorded matched reference construction; refer to the original identity manifest for the precise reference splits and scaling factors.

Level 3

Level 3 is the E122-frozen modebench_level3_matched_v3 release, with 384 training, 128 development, and 128 evaluation rows per domain. It preserves Level-2 support histograms. Admission used adaptive second-round matching to fixed historical Level-1 measurements: Graph and Python have fresh v3 confirmation, while Countdown, MathIR, and Pantry retain prior split bytes and confirmation evidence. This is not a claim of statistical equivalence, or of five fresh same-round confirmations.

The original identity manifest still records pending_fresh_candidate_confirmation. That historical record is preserved verbatim. The later confirmation report records matched_fixed_reference and binds that exact dataset identity. Neither record has been rewritten for publication.

Loading

from datasets import load_dataset

ds = load_dataset("od2961/ModeBench", "level2_countdown")
train = ds["train"]
development = ds["dev"]
evaluation = ds["eval"]

# Raw problem text goes to the policy. Keep the executable answer spec private
# from the policy and use it only in the verifier.
problem = evaluation[0]["problem"]
reference_spec = evaluation[0]["answer"]

Use level1_, level2_, or level3_ followed by graph_coloring, countdown, python_factors, mathir, or pantry_plan. Only existing splits are exposed; Level 1 generally has no dev split. No test split is invented. The Parquet files load through the standard datasets loader without remote dataset code. Pin a dataset revision for reproducible experiments.

Evaluation

Use the original held-out eval rows and the frozen prompt, decoding, and verifier settings for a stated comparison. Use dev only where the original release provides it. Do not fit prompts, choose checkpoints, or tune methods on evaluation outcomes; training, development, and evaluation roles remain separate after public release.

The same executable validation produces acceptance and canonical identity. Report correctness and distinct correct identities separately: with K sampled answers, pass@K is whether any answer verifies, and distinct@K counts unique verified canonical keys. The reported main benchmark uses K=8; the papers specify the seeds, draws, and training checkpoints. Evaluation and prompt guide documents the supplied verifier interface and its versioned source.

The support-count metadata and reference specifications are for construction, checking, and analysis. Do not supply gold support catalogues or hidden evaluation references to the policy. Original prompt strings are retained; prompt formatting distinguishes raw problems from the model-specific chat and decoding interfaces.

Files and provenance

MANIFEST.json records every source identity, feature schema, ordered-row digest, split mapping, and Parquet digest. VALIDATION.json records full row and feature round trips, unchanged source files, canonical problem-identity checks, and support matching. code/oat_drgrpo/ preserves verifier and template source files byte for byte; provenance/ preserves original identities and construction/admission records.

License provenance

The original repository's Apache-2.0 source-code license is preserved in licenses/source_repository_APACHE_2.0.txt, and copied source copyright notices remain intact. The frozen dataset roots contain no separate dataset-specific license declaration; this export does not invent new dataset license terms. PantryPlan ingredient provenance records USDA FoodData Central Foundation Foods under CC0/public-domain source terms in pantry_ingredient_source.json.

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