{"task": {"agent_timeout": 600, "task": "omnimath_2307", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nBrave NiuNiu (a milk drink company) organizes a promotion during the Chinese New Year: one gets a red packet when buying a carton of milk of their brand, and there is one of the following characters in the red packet \"\u864e\"(Tiger), \"\u751f\"(Gain), \"\u5a01\"(Strength). If one collects two \"\u864e\", one \"\u751f\" and one \"\u5a01\", then they form a Chinese phrases \"\u864e\u864e\u751f\u5a01\" (Pronunciation: hu hu sheng wei), which means \"Have the courage and strength of the tiger\". This is a nice blessing because the Chinese zodiac sign for the year 2022 is tiger. Soon, the product of Brave NiuNiu becomes quite popular and people hope to get a collection of \"\u864e\u864e\u751f\u5a01\". Suppose that the characters in every packet are independently random, and each character has probability $\\frac{1}{3}$. What is the expectation of cartons of milk to collect \"\u864e\u864e\u751f\u5a01\" (i.e. one collects at least 2 copies of \"\u864e\", 1 copy of \"\u751f\", 1 copy of \"\u5a01\")? Options: (A) $6 \\frac{1}{3}$, (B) $7 \\frac{1}{3}$, (C) $8 \\frac{1}{3}$, (D) $9 \\frac{1}{3}$, (E) None of the above.\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": []}