Problem

Source: South African Mathematics Olympiad 2022, Problem 5

Tags: combinatorics, graph theory, Graph coloring



Let $n \geq 3$ be an integer, and consider a set of $n$ points in three-dimensional space such that: every two distinct points are connected by a string which is either red, green, blue, or yellow; for every three distinct points, if the three strings between them are not all of the same colour, then they are of three different colours; not all the strings have the same colour. Find the maximum possible value of $n$.