4. The Generalized Pigeonhole Principle states that for any function f from a finite set X to a finite set Y and for any positive integer k, if n(X) > k · n(Y), then there is some y in Y such that y is the image of at least k + 1 distinct elements of X.
Here let X be the set of people and Y be the set of
astrological star signs. There are 12 star signs, so n(Y) =
12. Since n(X) = 25 we can let k = 2.
Thus n(X) > 2·n(Y) and so there must be at least three
people in the group with the same star sign.