{"task": {"agent_timeout": 600, "task": "omnimath_3850", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $n$ be a positive integer. Compute the number of words $w$ that satisfy the following three properties.\n\n1. $w$ consists of $n$ letters from the alphabet $\\{a,b,c,d\\}.$\n\n2. $w$ contains an even number of $a$'s\n\n3. $w$ contains an even number of $b$'s.\n\nFor example, for $n=2$ there are $6$ such words: $aa, bb, cc, dd, cd, dc.$\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": []}