This is a book of 256 mathematical gems meant to stimulate and entertain. However, on a deeper level, these little puzzles, accessible to a general audience, provide a setting so rich in mathematical themes. One of the larger purposes of the book is to show how everyday situations can lead an inquisitive problem solver to profound and far-reaching mathematical principles. Discussions accompanying the problems reinforce important techniques in discrete mathematics, and the solutions, which require verbal arguments, show that proofs and careful reasoning are at the core of doing mathematics. In addition, anyone reading this book will learn that asking good questions is just as important to the progress of mathematics as answering questions.

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Table of Contents

Preface

Problems

Hints

Solutions

Responses to Queries

The Treasury

About the Authors

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About the Authors

**Paul Vaderlind** was raised in Warsaw, Poland. In 1969, at the age of 21, he emigrated to Sweden. Vaderlind had been studying math at the University of Warsaw. He finished his education in Stockholm and got his PhD in the field of discrete mathematics at the department of mathematics of Stockholm University. He has taught mathematics at Stockholm since 1974. Vaderlind’s first contact with problem solving was when he, at age 10, was given this beautiful puzzles book *The Moscow Puzzles* by Boris Kordemsky (now a classic). Since then problem solving and problem constructing have been his main hobbies. He has published (in Swedish) several books on this subject for both adults and children. Besides his work at the university Vaderlind is engaged in mathematical competitions and in the education of gifted youth. For several years he was the leader of the Swedish team to the IMO. He has two children and lives in a suburb of Stockholm.

**Richard K. Guy** has taught mathematics at all levels from kindergarten to post-graduate, in Britain, Singapore, India, and Canada. He has been involved in the publications program of The Mathematical Association of America (MAA) for quite some time, serving for 25 years as the editor of the Unsolved Problems Section of *The American Mathematical Monthly*, as well as serving on several MAA editorial boards. The MAA selected him as the Hedrick Lecturer in 1978, and he won the Lester R. Ford Award for Expository Writing in 1989. He is the author of a dozen books, notably among them *Winning Ways*, with Elwyn Berlekamp and John Conway; *The Book of Numbers*, with John Conway; *Unsolved Problems in Number Theory*, and *Unsolved Problems in Geometry*, with Hallard Croft and Ken Falconer.

**Loren Larson** was Professor of Mathematics at St. Olaf College from 1963-1996, and Benedict Distinguished Visiting Professor of Mathematics at Carleton College, 1999-2001. He has been active in the MAA as Governor of the North Central Section, and as Associate Director of the William Lowell Putnam Mathematical Competitions. His publications include: *Algebra and Trigonometry Refresher for Calculus Students*, *Problem-Solving through Problems*, and *The Wohascum County Problem Book*, with George Gilbert and Mark Krusemeyer published by the MAA.