P5 Combinatorics 2018 Turkey TST
Source: Turkey Team Selection Test 2018 P5
March 26, 2018
combinatorics
Problem Statement
We say that a group of students is a team if any two students in this group are friends. It is known that in the school any student belongs to at least one team but if any two students end their friendships at least one student does not belong to any team. We say that a team is special if at least one student of the team has no friend outside of this team. Show that any two friends belong to some special team.