  Two players take it turn to claim empty cells from an $n\times n$ grid. The
first player (if any) to occupy a transversal (a set of $ n $ cells having no
two cells in the same row or column) is the winner. What is the outcome of the
game given optimal play? Our aim in this paper is to show that for $n\ge 4$ the
first player has a winning strategy. This answers a question of Erickson.
