>I won't even ask. I'll just chalk it up to "My tax dollars at work".:-)

I have good news on this front :) I'm working on this problem at home as a "hobby." It's a famous math/combinatorial problem called "Ramsey Numbers."

Suppose you have a world where every two people are friends or enemies. What is the smallest number of total people such that 3 people are either all mutual friends or all mutual enemies? The solution is pretty easy here, it's 6, and that's a Ramsey Number. It's larger mutual friend/enemy groups than 3 that become increasingly difficult to solve...