Define a winning strategy for one of the two players engaged in the following game:
Initially a rook is placed on the bottom left corner of a 8 × 8 chessboard. A move consists of
advancing the rook any positive number of squares either up or to the right.
The players take turns.
One that cannot make a move loses.
The 2nd player can force a win.
The rook starts on the main diagonal. The first player must move it off the main diagonal, by moving up or right by n squares. The 2nd player can always return it to the main diagonal, by moving up if the first player moved right, or right if the first player moved up. Eventually the 2nd player moves it to the top right square, for the win.