Question 15
Petya and Vasya play on an $n\times n$ board, where $n\gt1$. Initially the board is white except for one corner cell, which is black and contains a rook. The players alternate moves. On each move a player moves the rook horizontally or vertically, and all cells through which it moves, including its destination, are recolored black. The rook may neither pass through black cells nor stop on them. A player unable to move loses; Petya moves first. Who wins with optimal play?