# omnimath / omnimath_2461 - 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 group of 101 Dalmathians participate in an election, where they each vote independently on either candidate \(A\) or \(B\) with equal probability. If \(X\) Dalmathians voted for the winning candidate, the expected value of \(X^{2}\) can be expressed as \(\frac{a}{b}\) for positive integers \(a, b\) with \(\operatorname{gcd}(a, b)=1\). Find the unique positive integer \(k \leq 103\) such that \(103 \mid a-bk\). ## 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