The Pigeonhole Principle (What It Is, How It Works, and How It Applies to Map Coloring)
Kenneth R. Rebman · The Two-Year College Mathematics Journal · 1979
The pigeons on the cover are confronting a very basic mathematical idea: If three of them are going into two compartments, then at least two birds must share a compartment. Now this does not seem to be a very profound observation, but we shall see that it is representative of a remarkably powerful mathematical tool called the Pigeonhole Principle. It is possible to formally derive the Pigeonhole Principle from the fundamental concept of a function defined on a finite set. (See Exercise 1.) But because the statement of the principle is really quite self-evident, we will simply accept it as our starting point.