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4

Part of 2016 Balkan MO

Problems(1)

Coloring the Squares of an Infinite Grid

Source: Balkan MO 2016, Problem 4

5/7/2016
The plane is divided into squares by two sets of parallel lines, forming an infinite grid. Each unit square is coloured with one of 12011201 colours so that no rectangle with perimeter 100100 contains two squares of the same colour. Show that no rectangle of size 1×12011\times1201 or 1201×11201\times1 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)
combinatoricsColoring