Various committees
Source: 2015 BAMO-8 #2
February 22, 2016
countingGroupsB8combinatoricsOlympiadcommittees
Problem Statement
Members of a parliament participate in various committees. Each committee consists of at least people, and it is known that every two committees have at least one member in common. Prove that it is possible to give each member a colored hat (hats are available in black, white or red) so that every committee contains at least members with different hat colors.