{"task": {"agent_timeout": 600, "task": "omnimath_194", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $n$ be a positive integer.  There are $\\tfrac{n(n+1)}{2}$ marks, each with a black side and a white side, arranged into an equilateral triangle, with the biggest row containing $n$ marks.  Initially, each mark has the black side up.  An operation is to choose a line parallel to the sides of the triangle, and flipping all the marks on that line.  A configuration is called admissible if it can be obtained from the initial configuration by performing a finite number of operations.  For each admissible configuration $C$ , let $f(C)$ denote the smallest number of operations required to obtain $C$ from the initial configuration.  Find the maximum value of $f(C)$ , where $C$ varies over all admissible configurations.\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": []}