{"task": {"agent_timeout": 600, "task": "omnimath_1380", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nWe can view these conditions as a geometry diagram as seen below. So, we know that $\\frac{e}{f}=\\frac{3}{4}$ (since $e=a-b=\\frac{3}{4} c-\\frac{3}{4} d=\\frac{3}{4} f$ and we know that $\\sqrt{e^{2}+f^{2}}=15$ (since this is $\\left.\\sqrt{a^{2}+c^{2}}-\\sqrt{b^{2}+d^{2}}\\right)$. Also, note that $a c+b d-a d-b c=(a-b)(c-d)=e f$. So, solving for $e$ and $f$, we find that $e^{2}+f^{2}=225$, so $16 e^{2}+16 f^{2}=3600$, so $(4 e)^{2}+(4 f)^{2}=3600$, so $(3 f)^{2}+(4 f)^{2}=3600$, so $f^{2}\\left(3^{2}+4^{2}\\right)=3600$, so $25 f^{2}=3600$, so $f^{2}=144$ and $f=12$. Thus, $e=\\frac{3}{4} 12=9$. Therefore, \\boldsymbol{e f}=\\mathbf{9} * \\mathbf{1 2}=\\mathbf{1 0 8}$.\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": []}