What is your favorite application of the Pigeonhole Principle? The pigeonhole principle states that if $n$ items are put into $m$ "pigeonholes" with $n > m$, then at least one pigeonhole must contain more than one item.
I'd like to see your favorite application of the pigeonhole principle, to prove some surprising theorem, or some interesting/amusing result that one can show students in an undergraduate class. Graduate level applications would be fine as well, but I am mostly interested in examples that I can use in my undergrad classes.
There are some examples in the Wikipedia page for the pigeonhole principle. The hair-counting example is one that I like... let's see some other good ones!
Thanks!

Things like: Pigeon hole principle with sum of 5 integers  but applied to integer polynomials. This shows, for example that any integer polynomial ( with integer inputs to guarantee integer output) that has 5x+17 terms, can be reduced to a polynomial with just 12 or fewer terms, mod 5. Stick that somewhere polynomial remainder theorem . 
