Covany Gardner
Math 108
Enrichment Paper #2
For my second enrichment paper, I chose to do it on the Dirichlet box, or more
commonly called the Pigeonhole Principle. It pretty much states “suppose we have four pigeons
but only three pigeon holes. No matter how we assign a hole to each pigeon, at least two
pigeons have to share the same hole.” Other examples of that would be that in a certain city,
there are at least two people that have the same amount of hairs on their heads. Or there is at
least two people who wake up at the same exact time. This is not probability or likelihood; they
are not happening by chance. If you have a group of 13 people, at least two of them have
birthdays in the same month. Using the quote, the pigeons are the 13 people, and the pigeon
holes are the 12 months. Now think of having 7 pigeons but only 3 pigeonholes, at least three
pigeons have to share pigeonholes. Andrew Wiles at Princeton University used the pigeonhole
principle in his proof of Fermat’s last theorem. The Pigeonhole Principle is used as an analytical