 Incidentally, solving for "n" gives the approximate formula of Frank H. Mathis cited above.This derivation only shows that "at most" 23 people are needed to ensure a birthday match with even chance; it leaves open the possibility that is 22 or less could also work.Given a year with days, the generalized birthday problem asks for the minimal number such that, in a set of randomly chosen people, the probability of a birthday coincidence is at least 50%.