Let's say you're trying to place pigeons into holes, but you have more pigeons than holes: at least two pigeons must go into the same hole. Obvious, right? Turns out this simple fact, known as the Pigeonhole Principle (or Dirichlet's Box Principle if you're boring), can be used to prove all kinds of surprising results. In this class we'll take a look at a handful of very neat problems that can be solved with this idea.