The Second Book of Mathematical Puzzles and Diversions

More documents

Recommendations

Info

CHAPTER FIVE Nine Problems 1. THE TWIDDLED BOLTS Two IDENTICAL BOLTS are placed together so that their helical grooves intermesh [Fig. 211. If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so that it does not rotate and twiddling them in the direction shown, will the heads (a) move inward, (b) move outward, or (c) remain the same distance from each other? The problem should be solved without resorting to actual test. 2. THE FLIGHT AROUND THE WORLD A GROUP of airplanes is based on a small island. The tank of each plane holds just enough fuel to take it halfway around the world. Any desired amount of fuel can be transferred from the tank of one plane to the tank of another while the
FIG. 21. The twiddled bolts. planes are in flight. The only source of fuel is on the island, and for the purposes of the problem it is assumed that there is no time lost in refueling either in the air or on the ground. What is the smallest number of planes that will ensure the flight of one plane around the world on a great circle, assuming that the planes have the same constant ground speed and rate of fuel consumption and that all planes re- turn safely to their island base? 3. THE CIRCLE O N THE CHESSBOARD A CHESSBOARD has squares that are two inches on the side. What is the radius of the largest circle that can be drawn on the board in such a way that the circle's circumference is entirely on black squares? 4. THE CORK PLUG MANY OLD puzzle books explain how a cork can be carved to fit snugly into square, circular and triangular holes [Fig. 221. An interesting problem is to find the volume of the cork plug. Assume that it has a circular base with a radius of one unit, a height of two units, and a straight top edge of
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 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: Digital Roots ANSWERS IN THE GAME p
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
Page 59 and 60: 60 Nine Problems men who shook hand
Page 61 and 62: 62 Nine Problems As we saw earlier,
Page 63 and 64: 64 Nine Pro Blems against his own b
Page 65 and 66: 66 The Soma Cube Tix, are discussed
Page 67 and 68: 68 The Soma Cube set of the pieces
Page 69 and 70: WALL SKYSCRAPER DOG PYRAMID FIG. 29
Page 71 and 72: the top illustration of Figure 30.
Page 73 and 74: 74 The Soma Cube
Page 75 and 76: 76 The Soma Cuhe Some of these figu
Page 77 and 78: CHAPTER SEVEN Recreational Topology
Page 79 and 80: Recreational Topology FIG. 33. Stew
Page 81 and 82: Ree~eational Topology FIG. 34. The
Page 83 and 84: 84 Recreational Topology has taken
Page 85 and 86: 86 Rec~eational Topology game is pl
Page 87 and 88: 88 Recreational Topology ANSWERS TH
Page 89 and 90: 90 Phi: The Golden Ratio is commonl
Page 91 and 92: Phi: The Golden Ratio FIG. 39. The
Page 93 and 94: 94 Phi: The Golden Ratio volved in
Page 95: 96 Phi: The Golden Ratio There is a
Page 98 and 99: Phi: The Golden Ratio THE SACRAMENT
Page 100 and 101:
Phi: The Golden Ratio 101 culate ph
Page 102 and 103:
Phi: The Golden Ratio 103 The two e
Page 104 and 105:
The Monkeg and the Coconuts 105 foo
Page 106 and 107:
The Monkey and the Coconuts 107 Dir
Page 108 and 109:
The Monkey and the Coconuts 109 the
Page 110 and 111:
The Monkey and the Coconuts 11 1 le
Page 112 and 113:
Woodstock in the 12th century by Ki
Page 114 and 115:
FIG. 49. A "simply connected" maze
Page 116 and 117:
Mazes 117 tiply connected maze whic
Page 118 and 119:
A CHAPTER E L E V E N rn Recreation
Page 120 and 121:
Recreational Logic 121 man, so we p
Page 122 and 123:
Recreational Logic 123 1. In 1918,
Page 124 and 125:
Recreational Logic 125 truth. Since
Page 126 and 127:
Recreational Logic 127 stand" or "W
Page 128 and 129:
Recrecrtionnl Logic 129 solution is
Page 130 and 131:
Magic Squares 131 order three. An e
Page 132 and 133:
Magic Squares 133 FIG. 54. Albrecht
Page 134 and 135:
Magic Squares 135 can be restored b
Page 136 and 137:
Magic Sqzlnres 137 seen by transfer
Page 138 and 139:
Magic Squares 139 in Rochester, New
Page 140 and 141:
C H A P T E R T H I R T E E N James
Page 142 and 143:
James Hugh Riley Shows, Inc. 143 fe
Page 144 and 145:
James Hugh Riley Shows, Inc. 145 ha
Page 146 and 147:
James Hugh Riley Shou.s, Inc. 147 "
Page 148 and 149:
James Hugh Riley Shows, Inc. 149 ha
Page 150 and 151:
James Hug11 Riley Shows, Inc. 151 e
Page 152 and 153:
Nine More Prohlems 153 Mr. Jones ha
Page 154 and 155:
Nine More Problems 155 ing it the t
Page 156 and 157:
Nine Afore Problems 157 a journey o
Page 158 and 159:
Nine More Prohlerns 159 (This was t
Page 160 and 161:
Nine More Problems 161 (which gives
Page 162 and 163:
Nine More Problems 163 We know that
Page 164 and 165:
C H A P T E R F I F T E E N Eleusis
Page 166 and 167:
Eleusis : The Induction Game 167 pl
Page 168 and 169:
Eleusis : The Induction Game 169 To
Page 170 and 171:
Eleusis: The Indz~ction Game 171 Th
Page 172 and 173:
Eleusis : The Induction Game 173 co
Page 174 and 175:
Origami 175 past 20 years there has
Page 176 and 177:
Paper can also be folded to produce
Page 178 and 179:
Origami 179 At what spot along the
Page 180 and 181:
Origami 181
Page 182 and 183:
ADDENDUM SINCE this chapter appeare
Page 184 and 185:
Origami 185 crease. If the value to
Page 186 and 187:
Squaring the Square 187 H. Stone, n
Page 188 and 189:
FIG. 73. Sqzcnring the Sqziare FIG.
Page 190 and 191:
Squaring the Square 191 gram. But S
Page 192 and 193:
Squaring the Square 193 out any ref
Page 194 and 195:
Squaring the Square 195 and eventua
Page 196 and 197:
Squaring the Sqz~are 112 FIG. 78. 3
Page 198 and 199:
Squaring the Square 199 But I thoug
Page 200 and 201:
Squaring the Square 201 each diagra
Page 202 and 203:
Squaring the Square 203 FIG. 82. si
Page 204 and 205:
Squaring the Square 205 team solved
Page 206 and 207:
Squaring the Square 207 first is to
Page 208 and 209:
Squaring the Square 209 fifth-dimen
Page 210 and 211:
Mechanical Puzzles 21 1 about 2,000
Page 212 and 213:
Mecl~nnicnl Puzzles 213 Dissection
Page 214 and 215:
Mechanical Puzzles 215 is shown in
Page 216 and 217:
Mechanical Puzzles 217 ulated a cer
Page 218 and 219:
Mechanical Puzzles 219 symmetrical
Page 220 and 221:
Probability and Ambiguity 22 1 ple
Page 222 and 223:
Probability and Amhig~iity 223 now
Page 224 and 225:
Probability and Ambiguity 225 study
Page 226 and 227:
Probability and Ambiguity 227 that
Page 228 and 229:
Probability and Ambiguity 229 David
Page 230 and 231:
oric, or 213, a~itl A's arc 113. In
Page 232 and 233:
CHAPTER TWENTY w The Mysterious Dr.
Page 234 and 235:
The Mysterious Dr. Matrix FIG. 91.
Page 236 and 237:
The Mysterious Dr. Matrix 237 the m
Page 238 and 239:
The Mysterious DT; Matrix 239 denti
Page 240 and 241:
The Mysterious Dr. Matrix 241 read
Page 242 and 243:
The Mysterious Dr. Matrix 243 Note
Page 244 and 245:
246 References for Further Reading
Page 246 and 247:
Page 248 and 249:
Page 251 and 252:
POSTSCRIPT, 1987 No EFFORT has been
Page 253 and 254:
ABOUT THE AUTHOR MARTIN GARDNER has
show all

The Second Book of Mathematical Puzzles and Diversions

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?