The Facebook group Olympiad training has at least five members. There is a certain integer k with following property: for each k-tuple of members there is at least one member of this k-tuple friends with each of the other kā1.
(Friendship is mutual: if A is friends with B, then also B is friends with A.)
(a) Suppose k=4. Can you say with certainty that the Facebook group has a member that is friends with each of the other members?
(b) Suppose k=5. Can you say with certainty that the Facebook group has a member that is friends with each of the other members? combinatoricsgroup theory