{"task": {"agent_timeout": 600, "task": "omnimath_4227", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $n$ be a positive integer. A [i]Nordic[/i] square is an $n \\times n$ board containing all the integers from $1$ to $n^2$ so that each cell contains exactly one number. Two different cells are considered adjacent if they share a common side. Every cell that is adjacent only to cells containing larger numbers is called a [i]valley[/i]. An [i]uphill path[/i] is a sequence of one or more cells such that:\n\n(i) the first cell in the sequence is a valley,\n\n(ii) each subsequent cell in the sequence is adjacent to the previous cell, and\n\n(iii) the numbers written in the cells in the sequence are in increasing order.\n\nFind, as a function of $n$, the smallest possible total number of uphill paths in a Nordic square.\n\nAuthor: Nikola Petrovi?\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": []}