The Liar Paradox and the Towers of Hanoi: The Ten Greatest Math Puzzles of All Time

259 Pages·2004·3.75 MB·English

by  Marcel Danesi

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The Liar Paradox
AND THE
Towers of Hanoi
THE 10 GREATEST MATH PUZZLES OF ALL TIME
Marcel Danesi
John Wiley & Sons, Inc.
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ffirs.qxd 7/2/04 12:34 PM Page i
The Liar Paradox
AND THE
Towers of Hanoi
THE 10 GREATEST MATH PUZZLES OF ALL TIME
Marcel Danesi
John Wiley & Sons, Inc.
ffirs.qxd 7/2/04 12:34 PM Page ii
Copyright © 2004 by Marcel Danesi. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
Design and production by Navta Associates, Inc.
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Library of Congress Cataloging-in-Publication Data:
Danesi, Marcel, date.
The liar paradox and the towers of Hanoi: the ten greatest
math puzzles of all time / Marcel Danesi.
p. cm.
Includes bibliographical references and index.
ISBN 0-471-64816-7 (paper)
1. Mathematical recreations. I. Title.
QA95 .D29 2004
793.74—dc22
2003027191
Printed in the United States of America
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ToAlex and Sarah;
their existence is a gift and their life is a blessing.
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CONTENTS
ACKNOWLEDGMENTS vii
Introduction 1
1 The Riddle of the Sphinx 5
2 Alcuin’s River-Crossing Puzzle 27
3 Fibonacci’s Rabbit Puzzle 47
4 Euler’s Königsberg Bridges Puzzle 67
5 Guthrie’s Four-Color Problem 85
6 Lucas’s Towers of Hanoi Puzzle 105
7 Loyd’s Get Off the Earth Puzzle 125
8 Epimenides’ Liar Paradox 141
9 The Lo Shu Magic Square 159
10 The Cretan Labyrinth 177
ANSWERS AND EXPLANATIONS 191
GLOSSARY 237
INDEX 243
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ACKNOWLEDGMENTS
I wish to thank the many people who have helped me, influenced me, and
critiqued me over the years. First and foremost, I must thank all of the stu-
dents I have had the privilege of teaching at the University of Toronto. They
were a constant source of intellectual animation and enrichment. I must
also thank Professor Frank Nuessel of the University of Louisville, for his
unflagging help over many years. I am, of course, grateful to the editors at
John Wiley for encouraging me to submit this manuscript to a publishing
house that is renowned for its interest in mathematics education. It is my
second book for Wiley. I am particularly grateful to Stephen Power, Jeff
Golick, and Michael Thompson for their expert advice, and to Kimberly
Monroe-Hill and Patricia Waldygo for superbly editing my manuscript,
greatly enhancing its readability. Needless to say, any infelicities that this
book may contain are my sole responsibility.
Finally, a heartfelt thanks goes out to my family, which includes Lucy
(my wife), Alexander and Sarah (my grandchildren), Danila (my daughter),
Chris (my son-in-law), and Danilo (my father), for the patience they have
shown me during the research and the writing of this book. I truly must beg
their forgiveness for my having been so cantankerous and heedless of fam-
ily duties.
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