# omnimath / omnimath_429

- 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

In a town every two residents who are not friends have a friend in common, and no one is a friend of everyone else. Let us number the residents from 1 to $n$ and let $a_{i}$ be the number of friends of the $i$-th resident. Suppose that $\sum_{i=1}^{n} a_{i}^{2}=n^{2}-n$. Let $k$ be the smallest number of residents (at least three) who can be seated at a round table in such a way that any two neighbors are friends. Determine all possible values of $k$.

## 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