Consider a pyramid with a regular $n$-gon as its base. We colour all the segments connecting two of the vertices of the pyramid except for the sides of the base either red or blue. Show that if $n=9$ then for each such colouring there are three vertices of the pyramid connecting by three segments of the same colour, and that this is not necessarily the case if $n=8$.
Problem
Source: Bundeswettbewerb Mathematik 2021, Round 1 - Problem 4
Tags: combinatorics, graph theory, Coloring, Graph coloring, geometry, edge coloring