Q: Four friends are reminiscing about a great party where they rst met many years ago. The rst friend
can't remember the number of people at the party but does remember that it was a perfect square and
must have been less than 5000. The second friend remembers the strange fact that each party guest had
the same number of friends at the party. The third friend adds that no pair of friends shared a mutual
friend at the party. And nally, the fourth recalls that every pair of non-friends had exactly 6 friends
in common amongst the party guests. How many people attended the party? (You should assume that
whenever person A is a friend of person B, person B is also a friend of person A.)