There are 64 pawns placed on a chessboard. Each square contains a pawn. Two players are on the same side of the chessboard. Each player takes turns and removes a pawn along with all pawns above it and to its right. The player who picks the pawn at the bottom-left corner loses. Who can definitely win the game?



Dan Hoey solved this puzzle:

A move at (1, 1) by the first player removes all pawns at (x, y) where x ≥ 1 and y ≥ 1. In that case the only pawns left are at (x, 0) and (0, y), and the first player wins by mirroring the second player's strategy.

Rajesh Balakrishnan solved this puzzle:

First guy knocks off b2! Then always mirror the opponent's moves symmetrically across the diagonal and win.


This puzzle is taken from folklore.

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