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(n,m)-crocodile chess piece

Source: ToT Junior O Level Autumn 1998

October 5, 2008
analytic geometrycombinatorics proposedcombinatorics

Problem Statement

Let n n and m m be given positive integers. In one move, a chess piece called an (n,m) (n,m)-crocodile goes n n squares horizontally or vertically and then goes m m squares in a perpendicular direction. Prove that the squares of an infinite chessboard can be painted in black and white so that this chess piece always moves from a black square to a white one or vice-versa.