(n,m)-crocodile chess piece
Source: ToT Junior O Level Autumn 1998
October 5, 2008
analytic geometrycombinatorics proposedcombinatorics
Problem Statement
Let and be given positive integers. In one move, a chess piece called an -crocodile goes squares horizontally or vertically and then goes 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.