The PIGEON-HOLE principle (ESSAY!)

There are two non-bald men in New York city with exactly the same number of hairs on their heads!

This bizarre fact follows from a very simple and extraordinarily powerful principle first coined by Dirichlet in 1834 as the SchubfachPrinzip. Today it is known as the pigeon-hole principle. This chapter on the topic appears as chapter 20 of THINKING MATHEMATICS! Vol 2: Advanced Counting and Advanced Number Systems. The book appears here.

Chapter 20_The Pigeon-Hole Principle


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


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