Counting,Recounting and Matching

Although we start our mathematical education by learning to count, it is this very thing which is one of the most difficult things to carry out in practice. In this article, we discuss a very simple method which is available in a very general form under the name of Fubini’s principle (see Box 1). In its simplest form, it is the obvious observation that counting in two different ways produces the same sum. However, the various examples we discuss will hopefully convince the reader that the principle is surprisingly effective.