Los Angeles Math Circle

1/23 -- Group B: The Pigeonhole Principle (Prof. Blake Mellor, Loyola Marymount University)

If you want to put 11 pigeons into 10 pigeonholes, you find you have to put at least two pigeons in the same hole. This seemingly obvious statement is an example of the Pigeonhole Principle, and is a surprisingly powerful idea. We will discuss some generalizations and reformulations of this famous principles, and apply it to problems ranging from easy exercises to problems from the Putnam exam, the most difficult mathematics competition in the country.