# omnimath / omnimath_1526 - 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 Kelvin and 15 other frogs are in a meeting, for a total of 16 frogs. During the meeting, each pair of distinct frogs becomes friends with probability $\frac{1}{2}$. Kelvin thinks the situation after the meeting is cool if for each of the 16 frogs, the number of friends they made during the meeting is a multiple of 4. Say that the probability of the situation being cool can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are relatively prime. Find $a$. ## 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