# omnimath / omnimath_4119

- 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 $r>1$ be a rational number. Alice plays a solitaire game on a number line. Initially there is a red bead at $0$ and a blue bead at $1$. In a move, Alice chooses one of the beads and an integer $k \in \mathbb{Z}$. If the chosen bead is at $x$, and the other bead is at $y$, then the bead at $x$ is moved to the point $x'$ satisfying $x'-y=r^k(x-y)$.

Find all $r$ for which Alice can move the red bead to $1$ in at most $2021$ moves.

## 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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