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Polyominoes will delight not only students and teachers of mathematics at all levels, but will be appreciated by anyone who likes a good geometric challenge. There are no prerequisites. If you like jigsaw puzzles, or if you hate jigsaw puzzles but have ever wondered about the pattern of some floor tiling, there is much here to interest you. A polyomino is a shape cut along the lines from square graph paper; the pronunciation of polyomino begins as does polygon and ends as does domino. Tilings, also called tessellations of mosaic patterns, are older than civilization itself. Tiling with polyominoes provides challenges that range from the popular jigsaw-like puzzles to easily understood mathematical research problems. You will find unsolved puzzles and problems of both kinds here. Answers are provided for most of the problems that have known solutions. It is only fair to repeat here the warning stated in the preface to this book, 'Playing with polyominoes can be habit forming.'

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CHOICE Review

It is a fuzzy border that separates recreational from serious mathematics. Recreational topics must be accessible and possess charm. Serious topics should admit systematic development, interact with other parts of mathematics, and pose nontrivial yet approachable problems. A polyomino the word is a portmanteau of "polygon" and "domino" is a geometrical figure consisting of several identical squares aligned edge to edge. Questions to consider concern the possibility of fitting various polyominoes together, jigsaw-style, to cover larger regions of the plane. Basically, the study of polyominos is recreational mathematics, but some problems in the area do have a fundamental character. For example, it may or may not be possible to tile the entire plane with infinitely many copies of a given polyomino, but no one knows of a fully general criterion for deciding. For the undergraduate, polyominoes offer a fun opportunity to try mathematical reasoning firsthand. The profusion of problems contained in this book, ranging from the easy to the unsolved, make it an excellent guide. Polyominoes might also present interesting challenges to the novice computer programmer, but the present volume does not speak to this.-D. V. Feldman, University of New Hampshire