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Frontmatter
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MATHEMATICAL
JOURNEYS
Peter D. Schumer
Middlebury College
A JOHN WILEY & SONS, INC., PUBLICATION
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Copyright c
2004 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any
form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,
except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without
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Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, e-mail:
permreq@wiley.com.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best
efforts in preparing this book, they make no representations or warranties with respect to the
accuracy or completeness of the contents of this book and specifically disclaim any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created or
extended by sales representatives or written sales materials. The advice and strategies contained
herein may not be suitable for your situation. You should consult with a professional where
appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other
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Library of Congress Cataloging-in-Publication Data:
Schumer, Peter D., 1954–
Mathematical journeys / Peter D. Schumer.
p. cm.
“A Wiley-Interscience publication.”
Includes bibliographical references and index.
ISBN 0-471-22066-3 (pbk. : acid-free paper)
1. Mathematics—Popular works. I. Title.
QA93.S38 2004
510–dc22
2003062040
Printed in the United States of America.
10987654321
I dedicate this book to Amy and Andrew who are well on their way with their
own wonderful life’s journeys.
Contents
Preface
ix
Acknowledgments
xi
1 Let’s Get Cooking: A Variety of Mathematical Ingredients
1
2 The Green Chicken Contest
13
3 The Josephus Problem: Please Choose Me Last
23
4 Nim and Wythoff’s Game: Or How to Get Others to Pay Your
Bar Bill
31
5 Mersenne Primes, Perfect Numbers, and Amicable Pairs
41
6 The Harmonic Series ... and Less
49
7 Fermat Primes, the Chinese Remainder Theorem, and Lattice
Points
61
8 Tic-Tac-Toe, Magic Squares, and Latin Squares
71
9 Mathematical Variations on Rolling Dice
83
10 Pizza Slicing, Map Coloring, Pointillism, and Jack-in-the-Box
91
11 Episodes in the Calculation of Pi
101
12 A Sextet of Scintillating Problems
117
13 Primality Testing Below a Quadrillion
127
14 Erdos Number Zero
139
15 Choosing Stamps to Mail a Letter, Let Me Count the Ways
153
16 Pascal Potpourri
165
vii

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