Friends at a Party
Source: OMM 2009 6
July 15, 2014
combinatorics unsolvedcombinatorics
Problem Statement
At a party with people, it is known that among any people, there are either people who all know one another or people none of which knows another. Show that the people can be separated into two rooms, so that everyone in one room knows one another and no two people in the other room know each other.