Coloring the Squares of an Infinite Grid
Source: Balkan MO 2016, Problem 4
May 7, 2016
combinatoricsColoring
Problem Statement
The plane is divided into squares by two sets of parallel lines, forming an infinite grid. Each unit square is coloured with one of colours so that no rectangle with perimeter contains two squares of the same colour. Show that no rectangle of size or contains two squares of the same colour.Note: Any rectangle is assumed here to have sides contained in the lines of the grid.(Bulgaria - Nikolay Beluhov)