{"task": {"agent_timeout": 600, "task": "omnimath_2566", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $N$ be the number of ways in which the letters in \"HMMTHMMTHMMTHMMTHMMTHMMT\" (\"HMMT\" repeated six times) can be rearranged so that each letter is adjacent to another copy of the same letter. For example, \"MMMMMMTTTTTTHHHHHHHHHHHH\" satisfies this property, but \"HMMMMMTTTTTTHHHHHHHHHHHM\" does not. Estimate $N$. An estimate of $E$ will earn $\\left\\lfloor 20 \\min \\left(\\frac{N}{E}, \\frac{E}{N}\\right)^{4}\\right\\rfloor$ 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": []}