Six has 15's hat, then she go to fifteen and fifteen there's her hat. so, following the cycle we'll get your hat back. so then, now we have the more general problem, what's the probability that all cycles are a blank bigger than N, that everybody is going to have to would have to follow at least N talk to at least N friends or N people, N random people to get their hat back, so that's a generalized derangements problem. 