Question 88
Pete and Basil play the following game on a checkered $n \times n$ board. Initially the whole board is white except for one corner square which is black; a rook is put onto this square. The players move alternately, Pete moves first. On each turn, a player moves a rook to another square horizontally or vertically. Immediately after that, all the squares passed by a rook (including the square where the move results) become black. It is prohibited to move a rook to or across any black square. The player who cannot move loses. Which of the players has a winning strategy? (N. Polyansky)