{"task": {"agent_timeout": 600, "task": "omnimath_2594", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nTwo unit squares $S_{1}$ and $S_{2}$ have horizontal and vertical sides. Let $x$ be the minimum distance between a point in $S_{1}$ and a point in $S_{2}$, and let $y$ be the maximum distance between a point in $S_{1}$ and a point in $S_{2}$. Given that $x=5$, the difference between the maximum and minimum possible values for $y$ can be written as $a+b \\sqrt{c}$, where $a, b$, and $c$ are integers and $c$ is positive and square-free. Find $100 a+10 b+c$.\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": []}