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Polyominoes:
Puzzles, Patterns, Problems, and Packings
Revised and Expanded Second Edition
Solomon W. Golomb

Paperback | 1996 | $35.00 | £27.95 | ISBN: 9780691024448
198 pp. | 7 3/4 x 10 | 200 line illustrations, 5 tables
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Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes.

Reviews:

"The book covers all areas, both beginner and expert, thoroughly. Hundreds of diagrams illustrate the detailed, clearly written texts.... A classic. From a simple idea, Golomb has created a ... science."--Colin Singleton, New Scientist

"One of the most eagerly anticipated second editions in the history of mathematics, [Polyominoes] was worth it.... Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller."--Charles Ashbacher, Journal of Recreational Mathematics

"Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller."--Journal of Recreational Mathematics

Endorsements:

"Those acquainted with polyominoes will snap up this volume. And if you haven't yet discovered the fascination of these tantalizing tiles, this is the book to introduce you to them."--Martin Gardner, author of The Ambidextrous Universe

Table of Contents:

Preface to the Revised Edition
Preface to the First Edition
Ch. 1 Polyominoes and Checkerboards 3
Ch. 2 Patterns and Polyominoes 12
Ch. 3 Where Pentominoes Will Not Fit 20
Ch. 4 Backtracking and Impossible Constructions 30
Ch. 5 Some Theorems about Counting 43
Ch. 6 Bigger Polyominoes and Higher Dimensions 70
Ch. 7 Generalizations of Polyominoes 85
Ch. 8 Tiling Rectangles with Polyominoes 97
Ch. 9 Some Truly Remarkable Results 111
Appendix A. Answers to Exercises in Chapter 5 127
Appendix B. Problem Compendium 133
Appendix C. Golomb's Twelve Pentomino Problems 146
Appendix D. Klamer's Konstant and the Enumeration of N-Ominoes 152
Glossary 155
Bibliography for the First Edition 160
Comprehensive Bibliography 162
Name Index 183


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