# omnimath / omnimath_1392

- 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

Let $a \neq b$ be positive real numbers and $m, n$ be positive integers. An $m+n$-gon $P$ has the property that $m$ sides have length $a$ and $n$ sides have length $b$. Further suppose that $P$ can be inscribed in a circle of radius $a+b$. Compute the number of ordered pairs $(m, n)$, with $m, n \leq 100$, for which such a polygon $P$ exists for some distinct values of $a$ and $b$.

## 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