The rook is placed on the a1 square of the chessboard. In one move, it is allowed to slide it any number of squares to the right or up. The player who places the rook on the h8 square wins. Who wins with correct play?
On each move, the second player can return the rook to the a1-h8 diagonal.

## Solution

We will describe the winning strategy for the second player. With his first move, the first player must remove the rook from the a1-h8 diagonal. The second player can return the rook to the diagonal with his move. We arrive at a situation similar to the initial one. The only difference is that the rook is now closer to the h8 square. By adhering to this strategy, the second player will be the first to reach the h8 square.

## Answer

the second player wins.