# omnimath / omnimath_3728

- 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

An economist and a statistician play a game on a calculator which does only one
operation. The calculator displays only positive integers and it is used in the following
way: Denote by $n$ an integer that is shown on the calculator. A person types an integer,
$m$, chosen from the set $\{ 1, 2, . . . , 99 \}$ of the first $99$ positive integers, and if $m\%$ of the
number $n$ is again a positive integer, then the calculator displays $m\%$ of $n$. Otherwise,
the calculator shows an error message and this operation is not allowed. The game consists of doing alternatively these operations and the player that cannot do the operation
looses. How many numbers from $\{1, 2, . . . , 2019\}$ guarantee the winning strategy for the
statistician, who plays second?

For example, if the calculator displays $1200$, the economist can type $50$, giving the number
$600$ on the calculator, then the statistician can type $25$ giving the number $150$. Now, for
instance, the economist cannot type $75$ as $75\%$ of $150$ is not a positive integer, but can
choose $40$ and the game continues until one of them cannot type an allowed number

## 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