# omnimath / omnimath_4355

- 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

[i]Nyihaha[/i] and [i]Bruhaha[/i] are two neighbouring  islands, both having $n$ inhabitants. On island [i]Nyihaha[/i] every inhabitant is either a Knight or a Knave. Knights always tell the truth and Knaves always lie. The inhabitants of island [i]Bruhaha[/i] are normal people, who can choose to tell the truth or lie. When a visitor arrives on any of the two islands, the following ritual is performed: every inhabitant points randomly to another inhabitant (indepently from each other with uniform distribution), and tells "He is a Knight" or "He is a Knave'". On sland [i]Nyihaha[/i], Knights have to tell the truth and Knaves have to lie. On island [i]Bruhaha[/i] every inhabitant tells the truth with probability $1/2$ independently from each other. Sinbad arrives on island [i]Bruhaha[/i], but he does not know whether he is on island [i]Nyihaha[/i] or island [i]Bruhaha[/i]. Let $p_n$ denote the probability that after observing the ritual he can rule out being on island [i]Nyihaha[/i]. Is it true that $p_n\to 1$ if $n\to\infty$?

## 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