{"task": {"agent_timeout": 600, "task": "omnimath_2505", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nFor some positive real $\\alpha$, the set $S$ of positive real numbers $x$ with $\\{x\\}>\\alpha x$ consists of the union of several intervals, with total length 20.2. The value of $\\alpha$ can be expressed as $\\frac{a}{b}$, where $a, b$ are relatively prime positive integers. Compute $100a+b$. (Here, $\\{x\\}=x-\\lfloor x\\rfloor$ is the fractional part of $x$.)\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": []}