{"task": {"agent_timeout": 600, "task": "omnimath_292", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nFor any odd positive integer $n$, let $r(n)$ be the odd positive integer such that the binary representation of $r(n)$ is the binary representation of $n$ written backwards. For example, $r(2023)=r\\left(11111100111_{2}\\right)=11100111111_{2}=1855$. Determine, with proof, whether there exists a strictly increasing eight-term arithmetic progression $a_{1}, \\ldots, a_{8}$ of odd positive integers such that $r\\left(a_{1}\\right), \\ldots, r\\left(a_{8}\\right)$ is an arithmetic progression in that order.\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": []}