TOT 178 1988 Spring Train S4 pawns on an infinite chess board
Source:
May 20, 2020
combinatorics
Problem Statement
Pawns are placed on an infinite chess board so that they form an infinite square net (along any row or column containing pawns ther is a pawn , three free squares , pawn , three squares, and so on , with only every fourth row and every fourth column containing pawns). Prove that it is not possible for a knight to tour every free square once and only once. (An old problem of A . K . Tolpugo)