Question 12
In a club some pairs of members are friends. Given $k \ge 3$, we say that a club is *k-friendly* if in every group of $k$ members these can be seated at a round table so that every pair of neighbours are friends.
a) Prove that if a club is 6-friendly then it is 7-friendly.
b) Is it true that if a club is 9-friendly then it is 10-friendly?
a) Prove that if a club is 6-friendly then it is 7-friendly.
b) Is it true that if a club is 9-friendly then it is 10-friendly?