{"task": {"agent_timeout": 600, "task": "omnimath_4033", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $A$ be a given set with $n$ elements. Let $k<n$ be a given positive integer. Find the maximum value of $m$ for which it is possible to choose sets $B_i$ and $C_i$ for $i=1,2,\\ldots,m$ satisfying the following conditions:\n[list=1]\n[*]$B_i\\subset A,$ $|B_i|=k,$\n[*]$C_i\\subset B_i$ (there is no additional condition for the number of elements in $C_i$), and\n[*]$B_i\\cap C_j\\neq B_j\\cap C_i$ for all $i\\neq j.$\n[/list]\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": []}