Ramsey Theory - clique of size 3

In group of six people, three are friends or strangers

Ramsey theory is a branch of mathematics that looks for ordered subsets in random systems when they get large enough. The simplest problem in Ramsey theory is the following: What is the smallest number of people to guarantee a clique of size 3? A clique in this context is defined as a set of people who are either friends or strangers. To make the problem simpler, we will give the answer. A clique of size 3 is guaranteed among six people. The problem we will pose is to prove that this is true.

Prove that in a group of six people, there must be three people who are friends (know each other) or strangers (do not know each other).

Solution is here