The Pigeon-hole Principle

I've mentioned the "pigeon-hole principle" briefly before, and it crossed my radar again when James Tanton put up a video on it here:

http://www.jamestanton.com/?p=810

It is one of those intuitive mathematical concepts that seems so obvious upon first glance that one wonders why it must even be stated, or how it could possibly be of any use... and yet that is the essence and beauty of mathematics: that basic, seemingly obvious ideas can be massaged by logic to produce significant and less obvious outcomes and ramifications.

If you're familiar with the pigeon-hole principle (it is especially used in combinatorics) you understand what I mean; if you're not familiar with it, then I won't even state it lest you think it too boring to bother with, but direct you instead to another link further elucidating it:

http://mindyourdecisions.com/blog/2008/11/25/16-fun-applications-of-the-pigeonhole-principle/