{"task": {"agent_timeout": 600, "task": "omnimath_2516", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nSuppose two distinct competitors of the HMMT 2021 November contest are chosen uniformly at random. Let $p$ be the probability that they can be labelled $A$ and $B$ so that $A$ 's score on the General round is strictly greater than $B$ 's, and $B$ 's score on the theme round is strictly greater than $A$ 's. Estimate $P=\\lfloor 10000 p\\rfloor$. An estimate of $E$ will earn $\\left\\lfloor 20 \\min \\left(\\frac{A}{E}, \\frac{E}{A}\\right)^{6}\\right\\rfloor$ points.\n\n## Instructions\n\nSolve the mathematical problem above and write your final answer to `/workspace/answer.txt`.\n\n**Important**: Write only your final answer to the file, not the full solution process.\n\n### Guidelines\n\n- Provide your final numerical answer or mathematical expression\n- Write the answer as plain text (no special formatting needed)\n- Be precise and clear in your answer\n- The answer should directly respond to what the problem asks for\n\n### Example\n\nIf the problem asks \"What is 2 + 2?\", your answer file should contain:\n\n```\n4\n```\n\nYour answer will be evaluated against the correct solution using an automated grading system.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "math", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "omnimath", "tags": ["omni-math"]}, "runs": []}