MathDB
Which m x n grids have a valid colouring?

Source: Baltic Way 2011

November 6, 2011
geometryrectanglecombinatorics proposedcombinatorics

Problem Statement

Given a rectangular grid, split into m×nm\times n squares, a colouring of the squares in two colours (black and white) is called valid if it satisfies the following conditions:
[*]All squares touching the border of the grid are coloured black. [*]No four squares forming a 2×22\times 2 square are coloured in the same colour. [*]No four squares forming a 2×22\times 2 square are coloured in such a way that only diagonally touching squares have the same colour. Which grid sizes m×nm\times n (with m,n≥3m,n\ge 3) have a valid colouring?
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