# omnimath / omnimath_3822

- 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

Esmeralda has created a special knight to play on quadrilateral boards that are identical to chessboards. If a knight is in a square then it can move to another square by moving 1 square in one direction and 3 squares in a perpendicular direction (which is a diagonal of a $2\times4$ rectangle instead of $2\times3$ like in chess). In this movement, it doesn't land on the squares between the beginning square and the final square it lands on.

A trip of the length $n$ of the knight is a sequence of $n$ squares $C1, C2, ..., Cn$ which are all distinct such that the knight starts at the $C1$ square and for each $i$ from $1$ to $n-1$ it can use the movement described before to go from the $Ci$ square to the $C(i+1)$.

Determine the greatest $N \in \mathbb{N}$ such that there exists a path of the knight with length $N$ on a $5\times5$ board.

## 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.
```
---
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