The Second Book of Mathematical Puzzles and Diversions

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8 Contents 16. Origami [Answers on page 1841 17. Squaring the Square 186 18. Mechanical Puzzles [Answers on page 2181 19. Probability and Ambiguity [Answers on page 2291 20. The Mysterious Dr. Matrix 233 [Answers on page 2421 REFERENCES FOR FURTHER READING 245 POSTSCRIPT 253
INTRODUCTION SINCE THE APPEARANCE of the first Scientific American Book of Mathematical Puzzles & Diversions, in 1959, popular in- terest in recreational mathematics has continued to increase. Many new puzzle books have been printed, old puzzle books reprinted, kits of recreational math materials are on the market, a new topological game (see Chapter 7) has caught the fancy of the country's youngsters, and an excellent little magazine called Recreational Mathematics has been started by Joseph Madachy, a research chemist in Idaho Falls. Chess- men - those intellectual status symbols - are jumping all over the place, from TV commercials and magazine adver- tisements to A1 Horozoitz's lively chess corner in The Satur- day Review and the knight on Paladin's holster and have- gun-will-travel card. This pleasant trend is not confined to the U.S. A classic four-volume French work, Rkcrkations Mathkmatiques, by Edouard Lucas, has been reissued in France in paperbacks. Thomas H. OJBeirne, a Glasgozu mathematician, is writing a splendid puzzle column in a British science journal. In the U.S.S.R. a handsome 575-page collection of puzzles, assem- bled by mathematics teacher Boris Kordemski, is selling in Russian and Ukrainian editions. It is all, of course, part of a world-wide boom in math -in turn a reflection of the in- creasing demand for skilled mathematicians to meet the in- credible needs of the nezo triple age of the atom, spaceship and computer. The computers are not replacing mathematicians; they
Page 1 and 2: T H E S E C O N D SCIENTIFCC - L ME
Page 3 and 4: The 2nd SCIENTIFIC AMERICAN Book of
Page 5 and 6: Material previously published in Sc
Page 7: INTRODUCTION CONTENTS The Five Plat
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
Page 55 and 56: 56 Nine Problems depicted at bottom
Page 57 and 58: 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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The Second Book of Mathematical Puzzles and Diversions

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