Question 98
There is a group of $2n$ people, among whom there are couples of friends. It is known that every person in this group has exactly $k \ge 1$ friends (if "A" is familiar with "B", then conversely, "B" is familiar with "A"). Find such a number $k$ for which this group can always be divided into two subgroups of $n$ people so that in both subgroups each person has at least one friend?
(Bogdan Rublyov)
(Bogdan Rublyov)