Colouring of 4 \times 19 chessboard with three colours
Source: Cyprus 2021Junior TST-2 Problem 4
May 26, 2021
combinatoricspigeonhole principleRamsey Theory
Problem Statement
We colour every square of a chess board with one of the colours red, green and blue. Prove that however this colouring is done, we can always find two horizontal rows and two vertical columns such that the squares on the intersections of these lines all have the same colour.