# Transversal achievement game on a square grid

**Problem**Two players alternately write O's (first player) and X's (second player) in the unoccupied cells of an grid. The first player (if any) to occupy a set of cells having no two cells in the same row or column is the winner. What is the outcome of the game given optimal play?

## Bibliography

* indicates original appearance(s) of problem.

### Are there a simple solution?

On February 13th, 2013 Anonymous says:

I suspect, there are no simple answer and it can be solved only by heavy calculations, that is essentally there is no solution to this problem.

### history and application

On February 22nd, 2013 mshj says:

i'm not sure but i think to solve this problem, i was wondering if any body gives me some information about the history and application of this problem

## Solution

The problem has been solved. Link:- https://arxiv.org/abs/2101.00770