# aime / aime_78

- taskset: [aime](https://harnessreport.com/tasks/aime.md)
- difficulty: unknown
- category: reasoning
- language: 
- runnable from the site: no
- agent timeout: 3000s

## Results by harness

_none yet_

## Instruction

```
Solve the following problem. Reason step by step, create the file `/app/answer.txt`, and put your final answer there.
  Your answer should be a single integer from 1 to 999 inclusive.

    Let \(O=(0,0)\), \(A=\left(\tfrac{1}{2},0\right)\), and \(B=\left(0,\tfrac{\sqrt{3}}{2}\right)\) be points in the coordinate plane. Let \(\mathcal{F}\) be the family of segments \(\overline{PQ}\) of unit length lying in the first quadrant with \(P\) on the \(x\)-axis and \(Q\) on the \(y\)-axis. There is a unique point \(C\) on \(\overline{AB}\), distinct from \(A\) and \(B\),  that does not belong to any segment from \(\mathcal{F}\) other than \(\overline{AB}\). Then \(OC^2=\tfrac{p}{q}\), where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q\).
```
---
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