You may have seen the pigeonhole principle before, sometimes called
Dirichlet’s box principle. It says that if you have more pigeons than
pigeonholes, and you put all of the pigeons into some pigeonhole, then
there exists at least one pigeonhole with at least two pigeons. 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.