IMO 2016 Shortlist C3

Let n be a positive integer relatively prime to 6. We paint the vertices of a regular n-gon with three colours so that t...

IMO 2016 Shortlist C3

Category: Combinatorics

Problem

Let n be a positive integer relatively prime to 6. We paint the vertices of a regular n-gon with three colours so that there is an odd number of vertices of each colour. Show that there exists an isosceles triangle whose three vertices are of different colours.