This book is the result of twenty years of puzzle collecting. For these many years I have endeavored to gather everything belonging to the realm of mathematical entertainment from all available sources. As an editor of newspaper columns on scientific entertainment, I found my readers keenly interested in this kind of pastime, and these readers proved to be among my best sources for all sorts of problems, both elementary and intricate.
Puzzles seem to have beguiled men in every civilization, and the staples of scientific entertainment are certain historic problems which have perplexed and diverted men for centuries.
Besides a number of these, this book contains many problems never before published. Indeed, the majority of the problems have been devised by me or have been developed out of suggestions from readers or friends.
This book represents only a relatively small selection from an inexhaustible reservoir of material. Its purpose is to satisfy not only mathematically educated and gifted readers but also those who are on less good terms with mathematics but consider cudgeling their brains a useful pastime. Many puzzles are therefore included, especially in the first chapters, which do not require even a pencil for their solution, let alone algebraic
formulas. The majority of the problems chosen, however, will appeal to the puzzle lover who has not yet forgotten the elements of arithmetic he learned in high school. And finally, those who really enjoy the beauties of mathematics will find plenty of problems to rack their brains and test their knowledge and ingenuity in such chapters as, for example, "Whimsical Numbers" and "Playing with Squares"
The puzzles in this book are classified into groups so that the reader with pronounced tastes may easily find his meat.
Those familiar with mathematical entertainment may miss certain all-too-well-known types, such as the famous magic squares. I believe, however, that branches of mathematical entertainment which have long since developed into special sciences belong only in books that set out to treat them exhaustively. Here we must pass them by, if only for reasons of space. Nor have geometrical problems been included.
Lack of space has also made it impossible to present every solution fully. In a great many instances, every step of reasoning, mathematical and other, is shown; in others, only the major steps are indicated; in others still, just the results are given. But in every single class of problems, enough detailed solutions are developed and enough hints and clues offered to show the reader his way when he comes to grips with those problems for which only answers are given without proof. I hope that with the publication of this book I have attained
two objectives: to provide friends of mathematics with many hours of entertainment, and to help some of the myriads who since their school days have been dismayed by everything mathematical to overcome their horror of figures.