Question

In a group of n > 20 people, there are some (at least one, and possibly all) pairs of people that know each other. Knowing is symmetric; if A knows B, then B knows A. For some values of n and k, this group has a certain property: If any 20 people are removed from the group, the number of pairs of people that know each other is at most (n − k)/n times that of the original group of people. For k=41 and 39, what possible values of n are there.

Answer 1

This is a toughie. As I suspected, google can help. Make a start here, and see where that takes you.

https://math.stackexchange.com/questions/3961864/in-a-group-of-n20-people-in-which-some-pairs-know-each-other-20-people-are-r