f(bobby) = bobby^a
f' = a * bobby?

We already established that 3 are not enough. Neither 4: Allan knows Brian, Brian knows Cate and Cate is Daphne's cousin who happens to be Allan's coworker. Each of them has 2 friends but those 2 friends don't know eachother so there is a no sets of 3 friends, nor sets of complete strangers. Same goes for 5, A knows B, B knows C, C knows Daphne who brought his boyfriend Eddy who knows Allan. Same situation.

Now if Frank joins as well we have 6 and the party gets more complicated. So Allan has 5 party fellows whom he can either know or not know. So he can have at least 3 friends (and 2 strangers), or 3 strangers (and two friends). Let's say he knows B, C and D but not properly introduced to E and F yet. To solve the problem we need to establish all possible relations between Brian, Cora and Daphne. If they know eachother (or don't know eachother) they form the required set of 3 friends or strangers all by themselves. If they only know one then the two of them make the set with Allan who knows all of them. Other cases (4 friends/1 stranger 5/0 or viceversa) are treated the same way, just ignore the intruder(s).