{"task": {"agent_timeout": 600, "task": "omnimath_4036", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nAn [i]anti-Pascal[/i] triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from $1$ to $10$.\n\\[\\begin{array}{\nc@{\\hspace{4pt}}c@{\\hspace{4pt}}\nc@{\\hspace{4pt}}c@{\\hspace{2pt}}c@{\\hspace{2pt}}c@{\\hspace{4pt}}c\n} \\vspace{4pt}\n & & & 4 & & &  \\\\\\vspace{4pt}\n & & 2 & & 6 & &  \\\\\\vspace{4pt}\n & 5 & & 7 & & 1 & \\\\\\vspace{4pt}\n 8 & & 3 & & 10 & & 9 \\\\\\vspace{4pt}\n\\end{array}\\]\nDoes there exist an anti-Pascal triangle with $2018$ rows which contains every integer from $1$ to $1 + 2 + 3 + \\dots + 2018$?\n\n[i]\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": []}