Problem
COM-B2-M06-P016 Twenty People
#16
★★★★☆ Level 4 of 5
Prove that among any \(20\) people there are either \(4\) pairwise acquainted people or \(4\) pairwise unacquainted people.
Use the previous bound \(R(4,4)\le20\).
Colour the edge between two people red if they are acquainted, and blue if they are not. By the bound \(R(4,4)\le20\), in \(K_{20}\) there is either a red \(K_4\) or a blue \(K_4\).
A red \(K_4\) means \(4\) pairwise acquainted people, and a blue \(K_4\) means \(4\) pairwise unacquainted people.
A good exercise in translating a graph result back into the language of the problem.