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A 3x7 grid of squares

Source: Gulf MO 2012, Problem 3

June 14, 2012
ceiling functionfunctioncombinatorics proposedcombinatorics

Problem Statement

Consider a 3×73\times7 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 4×64\times 6 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.