Problem

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

Tags: rectangle, combinatorics, Coloring, 2020, Indonesia MO, Indonesian MO



Problem 4. A chessboard with $2n \times 2n$ tiles is coloured such that every tile is coloured with one out of $n$ 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.