{"task": {"agent_timeout": 600, "task": "omnimath_3728", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nAn economist and a statistician play a game on a calculator which does only one\noperation. The calculator displays only positive integers and it is used in the following\nway: Denote by $n$ an integer that is shown on the calculator. A person types an integer,\n$m$, chosen from the set $\\{ 1, 2, . . . , 99 \\}$ of the first $99$ positive integers, and if $m\\%$ of the\nnumber $n$ is again a positive integer, then the calculator displays $m\\%$ of $n$. Otherwise,\nthe calculator shows an error message and this operation is not allowed. The game consists of doing alternatively these operations and the player that cannot do the operation\nlooses. How many numbers from $\\{1, 2, . . . , 2019\\}$ guarantee the winning strategy for the\nstatistician, who plays second?\n\nFor example, if the calculator displays $1200$, the economist can type $50$, giving the number\n$600$ on the calculator, then the statistician can type $25$ giving the number $150$. Now, for\ninstance, the economist cannot type $75$ as $75\\%$ of $150$ is not a positive integer, but can\nchoose $40$ and the game continues until one of them cannot type an allowed number\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": []}