# omnimath / omnimath_1855 - taskset: [omnimath](https://harnessreport.com/tasks/omnimath.md) - difficulty: hard - category: math - language: - runnable from the site: no - agent timeout: 600s ## Results by harness _none yet_ ## Instruction ``` # Mathematical Problem A ten-level 2-tree is drawn in the plane: a vertex $A_{1}$ is marked, it is connected by segments with two vertices $B_{1}$ and $B_{2}$, each of $B_{1}$ and $B_{2}$ is connected by segments with two of the four vertices $C_{1}, C_{2}, C_{3}, C_{4}$ (each $C_{i}$ is connected with one $B_{j}$ exactly); and so on, up to 512 vertices $J_{1}, \ldots, J_{512}$. Each of the vertices $J_{1}, \ldots, J_{512}$ is coloured blue or golden. Consider all permutations $f$ of the vertices of this tree, such that (i) if $X$ and $Y$ are connected with a segment, then so are $f(X)$ and $f(Y)$, and (ii) if $X$ is coloured, then $f(X)$ has the same colour. Find the maximum $M$ such that there are at least $M$ permutations with these properties, regardless of the colouring. ## Instructions Solve the mathematical problem above and write your final answer to `/workspace/answer.txt`. **Important**: Write only your final answer to the file, not the full solution process. ### Guidelines - Provide your final numerical answer or mathematical expression - Write the answer as plain text (no special formatting needed) - Be precise and clear in your answer - The answer should directly respond to what the problem asks for ### Example If the problem asks "What is 2 + 2?", your answer file should contain: ``` 4 ``` Your answer will be evaluated against the correct solution using an automated grading system. ``` --- Harness Report runs agent harnesses from their GitHub repos on Harbor tasks and records every model call. Every page is also `.md` and `.json`; index: https://harnessreport.com/llms.txt · MCP: https://harnessreport.com/mcp