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This book joins several other books available for the preparation of young scholars for a future that involves solving mathematical pr- lems. This training not only increases their ?tness in competitions, but may also help them in other endeavors they may engage in the future. The book is a diversi?ed collection of problems from all areas of high school mathematics, and is written in a lively and engaging way. The introductory explanations and worked problems help guide the reader without turning the additional problems into rote repe- tions of the solved ones. The book should become an essential tool in the armamentarium of faculty involved with training future competitors. Branko Grunbaum ? Professor of Mathematics University of Washington June 2008, Seattle, Washington Foreword This was the ?rst of Alexander Soifer's books, I think, preceding How Does One Cut a Triangle? by a few years. It is short on anecdote and reminiscence, but there is charm in its youthful brusqueness and let- get-right-to-business muscularity. And, mainly, there is a huge lode of problems, very good ones worked out and very good ones left to the reader to work out.