You may have seen the pigeonhole principle before, sometimes called the Dirichlet principle. It says that if you have \(n\) pigeonholes, and more than \(n\) pigeons, and you put all of the pigeons into some pigeonhole, then there exists at least one pigeonhole with at least one pigeon. While it sounds quite simple, it’s a powerful technique. The difficult thing is often choosing the appropriate pigeons and pigeonholes.
It has multiple applications in various situations.
Today we will see how to use it in geometric problems.