The purpose of this chapter is to present a few sample problems to illustrate the theme of the whole volume. A systematic development of the subject is started in the next chapter. While some of the sample questions introduced here can be solved with no theoretical background, the solution of others must be postponed until the necessary theory is developed.

The idea of this book is to examine certain aspects of the question “how many?”. Such questions may be very simple; for example, “How many pages are there from page 14 to page 59, inclusive?” In some cases, the answer may be nothing more than a matter of common knowledge, as for example the number of days in October, or the number of yards in a mile. In other cases, the answer may require technical information, such as the number of chemical elements known at the present time, or the number of cubic centimeters of displacement in the engine of a certain automobile. But our concern is with questions that involve thought. They may also require some prior knowledge, which will be supplied if it is not common information. Some mathematical formulas are helpful, and these will be developed in due course. However, many problems require nothing more than a little ingenuity. We begin with such a question.

Problem. It any calendar year how many Friday the thirteenths can there be? What is the smallest number possible?