MathDB
5 of n people may sit at a circle on a table among friends / strangers

Source: Czech-Polish-Slovak Junior Match 2013, Team p3 CPSJ

March 21, 2020
combinatorics

Problem Statement

In a certain group there are n5n \ge 5 people, with every two people who do not know each other exactly having one mutual friend and no one knows everyone else. Prove 55 of nn people, may sit at a circle around the table so that each of them sits between a) friends, b) strangers.