{"task": {"agent_timeout": 600, "task": "omnimath_74", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nA social club has $2k+1$ members, each of whom is fluent in the same $k$ languages.  Any pair of members always talk to each other in only one language.  Suppose that there were no three members such that they use only one language among them.  Let $A$ be the number of three-member subsets such that the three distinct pairs among them use different languages.  Find the maximum possible value of $A$.\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": []}