The Second Book of Mathematical Puzzles and Diversions

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MARTIN GARDNER Mathematical Puzzles A NEW SELECTION : from Origami to Recreational Logic, from Digital Roots and Dudeney Puzzles to the Diabolic Square, from the Golden Ratio to the Generalized Ham Sandwich Theorem. With mathematical commentaries by Mr. Gardner, ripostes from readers of Scientific American, references for further reading and, of course, solutions. With a new Postscript by the author THE UNIVERSITY OF CHICAGO PRESS
Material previously published in Scienti,fic American is copyright O 1958,1959,1960 by Scientific American, Inc. Most of the drawings and diagrams appear by courtesy of Scientijic American, in whose pages they were originally published. The University of Chicago Press, Chicago 60637 Copyright O 1961,1987 by Martin Gardner All rights reserved. Published 1961 University of Chicago Press Edition 1987 Printed in the United States of America Library of Congress Cataloging in Publication Data Gardner, Martin, 1914- The 2nd Scientific American book of mathematical puzzles & diversions. Reprint. Originally published as v. 2 of The Scientific American book of mathematical puzzles & diversions. New York : Simon and Schuster, 1961. Bibliography: p. 1. Mathematical recreations. I. Scientific American. 11. Title. 111. Title: Second Scientific American book of mathematical puzzles & diversions. QA95.Gl6 1987 793.7'4 87-10760 ISBN 0-22628253-8 (pbk.)
Page 1 and 2: T H E S E C O N D SCIENTIFCC - L ME
Page 3: The 2nd SCIENTIFIC AMERICAN Book of
Page 7 and 8: INTRODUCTION CONTENTS The Five Plat
Page 9 and 10: INTRODUCTION SINCE THE APPEARANCE o
Page 11 and 12: Introduction 11 socialism and capit
Page 13 and 14: TETRAHEDRON / The Five Platonic Sol
Page 15 and 16: 16 The Five Platonic Solids both la
Page 17 and 18: 18 The Five Platonic Solids value o
Page 19 and 20: 20 The Five Platonic Solids tance i
Page 21 and 22: 22 Tlre Five Platonic Solids ANSWER
Page 23 and 24: CHAPTER TWO w Tetrajlexagons H EXAF
Page 25 and 26: 26 Tetrnflezagons are joined by two
Page 27 and 28: A different variety of tetraflexago
Page 29 and 30: FIG. 11. How to make and flex the f
Page 31 and 32: C H A P T E R THREE Henry Ernest Du
Page 33 and 34: 34 Henry Ernest Dudeney: England's
Page 35 and 36: 36 Henry Ernest Llzcdeney: Englnvd'
Page 43 and 44: I)i,qitnl Roots FIG. 19. Symbols fo
Page 45 and 46: 46 Digital Roots Since the answer i
Page 47 and 48: 48 Digital Roots what cards are at
Page 49 and 50: Digital Roots ANSWERS IN THE GAME p
Page 51 and 52: FIG. 21. The twiddled bolts. planes
Page 53 and 54: 54 Nine Problenzs two units that is
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56 Nine Problems depicted at bottom
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Nine Problems FIG. 24. The flight a
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60 Nine Problems men who shook hand
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62 Nine Problems As we saw earlier,
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64 Nine Pro Blems against his own b
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66 The Soma Cube Tix, are discussed
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68 The Soma Cube set of the pieces
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WALL SKYSCRAPER DOG PYRAMID FIG. 29
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the top illustration of Figure 30.
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74 The Soma Cube
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76 The Soma Cuhe Some of these figu
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CHAPTER SEVEN Recreational Topology
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Recreational Topology FIG. 33. Stew
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Ree~eational Topology FIG. 34. The
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84 Recreational Topology has taken
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86 Rec~eational Topology game is pl
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88 Recreational Topology ANSWERS TH
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90 Phi: The Golden Ratio is commonl
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Phi: The Golden Ratio FIG. 39. The
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94 Phi: The Golden Ratio volved in
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96 Phi: The Golden Ratio There is a
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Phi: The Golden Ratio THE SACRAMENT
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Phi: The Golden Ratio 101 culate ph
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Phi: The Golden Ratio 103 The two e
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The Monkeg and the Coconuts 105 foo
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The Monkey and the Coconuts 107 Dir
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The Monkey and the Coconuts 109 the
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The Monkey and the Coconuts 11 1 le
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Woodstock in the 12th century by Ki
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FIG. 49. A "simply connected" maze
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Mazes 117 tiply connected maze whic
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A CHAPTER E L E V E N rn Recreation
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Recreational Logic 121 man, so we p
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Recreational Logic 123 1. In 1918,
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Recreational Logic 125 truth. Since
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Recreational Logic 127 stand" or "W
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Recrecrtionnl Logic 129 solution is
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Magic Squares 131 order three. An e
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Magic Squares 133 FIG. 54. Albrecht
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Magic Squares 135 can be restored b
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Magic Sqzlnres 137 seen by transfer
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Magic Squares 139 in Rochester, New
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C H A P T E R T H I R T E E N James
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James Hugh Riley Shows, Inc. 143 fe
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James Hugh Riley Shows, Inc. 145 ha
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James Hugh Riley Shou.s, Inc. 147 "
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James Hugh Riley Shows, Inc. 149 ha
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James Hug11 Riley Shows, Inc. 151 e
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Nine More Prohlems 153 Mr. Jones ha
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Nine More Problems 155 ing it the t
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Nine Afore Problems 157 a journey o
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Nine More Prohlerns 159 (This was t
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Nine More Problems 161 (which gives
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Nine More Problems 163 We know that
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C H A P T E R F I F T E E N Eleusis
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Eleusis : The Induction Game 167 pl
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Eleusis : The Induction Game 169 To
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Eleusis: The Indz~ction Game 171 Th
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Eleusis : The Induction Game 173 co
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Origami 175 past 20 years there has
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Paper can also be folded to produce
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Origami 179 At what spot along the
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Origami 181
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ADDENDUM SINCE this chapter appeare
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Origami 185 crease. If the value to
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Squaring the Square 187 H. Stone, n
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FIG. 73. Sqzcnring the Sqziare FIG.
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Squaring the Square 191 gram. But S
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Squaring the Square 193 out any ref
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Squaring the Square 195 and eventua
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Squaring the Sqz~are 112 FIG. 78. 3
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Squaring the Square 199 But I thoug
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Squaring the Square 201 each diagra
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Squaring the Square 203 FIG. 82. si
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Squaring the Square 205 team solved
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Squaring the Square 207 first is to
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Squaring the Square 209 fifth-dimen
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Mechanical Puzzles 21 1 about 2,000
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Mecl~nnicnl Puzzles 213 Dissection
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Mechanical Puzzles 215 is shown in
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Mechanical Puzzles 217 ulated a cer
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Mechanical Puzzles 219 symmetrical
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Probability and Ambiguity 22 1 ple
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Probability and Amhig~iity 223 now
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Probability and Ambiguity 225 study
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Probability and Ambiguity 227 that
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Probability and Ambiguity 229 David
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oric, or 213, a~itl A's arc 113. In
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CHAPTER TWENTY w The Mysterious Dr.
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The Mysterious Dr. Matrix FIG. 91.
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The Mysterious Dr. Matrix 237 the m
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The Mysterious DT; Matrix 239 denti
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The Mysterious Dr. Matrix 241 read
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The Mysterious Dr. Matrix 243 Note
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246 References for Further Reading
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POSTSCRIPT, 1987 No EFFORT has been
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ABOUT THE AUTHOR MARTIN GARDNER has
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