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(491) 4

Part of 1996 Tournament Of Towns

Problems(1)

TOT 491 1996 Spring J A4 rook at a m x n board

Source:

8/16/2024
A rook stands at a corner of an m×nm \times n squared board. Two players move the rook in turn (vertically or horizontally through any numbers of squares). As the rook moves, it paints the squares that it visits (stopping or passing through). The rook is not allowed to pass through or stop at the painted squares. The player who cannot move, loses. Who has a guaranteed win: the first player (who starts the game) or the other, and how should he/she play?
(B Begun)
combinatorics