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Turkey Team Selection Test
2018 Turkey Team Selection Test
5
5
Part of
2018 Turkey Team Selection Test
Problems
(1)
P5 Combinatorics 2018 Turkey TST
Source: Turkey Team Selection Test 2018 P5
3/26/2018
We say that a group of
25
25
25
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.
combinatorics