A 3x7 grid of squares
Source: Gulf MO 2012, Problem 3
June 14, 2012
ceiling functionfunctioncombinatorics proposedcombinatorics
Problem Statement
Consider a grid of squares. Each square may be coloured green or white.
(a) Is it possible to find a colouring so that no subrectangle has all four corner squares of the same colour?
(b) Is it possible for a grid?
Subrectangles must have their corners at grid-points of the original diagram. The corner squares of a subrectangle must be different. The original diagram is a subrectangle of itself.