The Surprise Attack in Mathematical Problems

From the Foreword:

In conducting a mathematical column in the Graham Dial over the past twenty-five years, the author found that the most stimulating experience and the greatest reward for his effort came from the "surprise attack" initiated by readers in solving many of the problems.

For the most part the problems were original contributions and, strange to say, in nearly every case the prize-winning solutions by readers excelled that of the contributor, shed new light on the problem, and opened up entirely new vistas of interest.

In this book we have selected from the scores of original problems used in our column in recent years those that emphasize this feature of surprise - the unexpected approach that not only brings simplicity to the solution but often broadens the scope of the problem and adds an esoteric touch dear to the mathematician's heart.

Note that after the statement of the problem in each chapter, the word Solution appears in bold-faced type; this is a signal to the reader who wishes to tackle the problem himself to postpone further reading at this point until he has completed his own attack.