IMO 2010 Shortlist C2
On some planet, there are 2N countries (N © 4). Each country has a flag N units wide and one unit high composed of N fie...
Category: Combinatorics
Problem
On some planet, there are 2N countries (N © 4). Each country has a flag N units wide and one unit high composed of N fields of size 11, each field being either yellow or blue. No two countries have the same flag. We say that a set of N flags is diverse if these flags can be arranged into an N N square so that all N fields on its main diagonal will have the same color. Determine the smallest positive integer M such that among any M distinct flags, there exist N flags forming a diverse set. (Croatia)