MathDB
Colouring 2n tiles and rectangles, combinatorics

Source: Indonesian MO (INAMO) 2020, Day 1, Problem 4

October 13, 2020
rectanglecombinatoricsColoring2020Indonesia MOIndonesian MO

Problem Statement

Problem 4. A chessboard with 2n×2n2n \times 2n tiles is coloured such that every tile is coloured with one out of nn colours. Prove that there exists 2 tiles in either the same column or row such that if the colours of both tiles are swapped, then there exists a rectangle where all its four corner tiles have the same colour.