Colouring 2n tiles and rectangles, combinatorics
Source: Indonesian MO (INAMO) 2020, Day 1, Problem 4
October 13, 2020
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Problem Statement
Problem 4. A chessboard with tiles is coloured such that every tile is coloured with one out of 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.