{"task": {"agent_timeout": 600, "task": "omnimath_1210", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $n>1$ be a positive integer. Each unit square in an $n \\times n$ grid of squares is colored either black or white, such that the following conditions hold: - Any two black squares can be connected by a sequence of black squares where every two consecutive squares in the sequence share an edge; - Any two white squares can be connected by a sequence of white squares where every two consecutive squares in the sequence share an edge; - Any $2 \\times 2$ subgrid contains at least one square of each color. Determine, with proof, the maximum possible difference between the number of black squares and white squares in this grid (in terms of $n$).\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": []}