Consider a 3×7 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 4×6 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. ceiling functionfunctioncombinatorics proposedcombinatorics