Introduction 7 the Ishango Bone 10 210 Holy Days 11 210 Frustrum 12
Total Page：16
File Type：pdf, Size：1020Kb
The Josephus Problem 69 239 The Miner 104 256 The Explorer’s Problem 70 239 The Blind Abbot 105 256 Monkey Nuts 71 240 The Captive Queen 106 257 The Book of Precious Things 72 240 A Spiral Walk 107 257 A Medieval Riddle 73 241 Eight Queens 108 258 Introduction 7 The Luo River Scroll 39 224 The Mariner 74 241 The Dinner Party 109 258 The Ishango Bone 10 210 Buridan’s Ass 40 224 The Memory Wheel 75 242 The Monkey and the Pulley 110 259 Holy Days 11 210 Hi Shi’s Third Paradox 41 225 Jia Xian’s Triangle 76 242 Kirkman’s Schoolgirls 111 259 Frustrum 12 211 The Zero Proof 42 225 The Old One 77 243 The Counterfeit Bill 112 260 Triangles of Babylon 13 211 Crocodile Tears 43 226 The Trouble With Rabbits 78 243 The Travelling Salesman 113 260 Ahmes' Loaves 14 212 The Ladder of Horus 44 226 The Ring Game 79 244 Ethiopian Mathematics 114 261 As I was going to Amenemhet III's 15 212 The Sieve of Eratosthenes 45 227 The Well 80 244 Cantor’s Infinities 115 261 A Question of Quantity 16 213 Archimedes’ Revenge 46 228 Tartaglia’s Wine 81 245 Nobody 116 262 A Fractional Issue 17 213 The Nine Chapters 47 229 Topsy-Turvy 82 245 Tesseract 117 262 Strong Grain 18 214 The Cistern Problem 48 229 The Wanderer 83 246 Bertrand’s Box 118 262 Progressive Loaves 19 214 Dog and Hare 49 230 The Hound 84 246 Nothing Lost 119 263 Dates 20 215 The Chickens 50 230 Regiomontanus’ Angle 85 246 Hilbert’s Hotel 120 263 The Rule of Three 21 215 Leg and Thigh 51 231 The Problem of Points 86 247 Wine/Water Problem 121 264 Progressive Shares 22 216 Men Buy a Horse 52 231 Modesty 87 247 The Barber Paradox 122 264 Squaring the Circle 23 216 Greed 53 231 Dürer’s Square 88 248 Mamma’s Age 123 264 Square Trial 24 217 Posthumous Twins 54 232 An Odd Gift 89 249 Papa’s Problem 124 265 Sumerian Riddle 25 217 The Ship of Theseus 55 232 Clock Striking Problem 90 249 Kite Problem 125 265 Ramesses’ Star 26 218 Men Find A Purse 56 233 The Dinner Party 91 250 The Barrel of Beer 126 266 The Riddle of the Sphinx 27 218 The Unwanted 57 233 Tricking the Landlord 92 250 The Century Puzzle 127 266 The Quiet One 28 219 The Five Sons 58 234 Round and Round 93 250 The Labourer’s Puzzle 128 266 Visitors 29 219 Sun Tzu’s Classic Problem 59 234 Bachet’s Scales 94 251 A Fence Problem 129 267 Cretans 30 219 The Trouble With Camels 60 235 Rupert’s Cube 95 251 Pierrot’s Puzzle 130 267 Zeno’s Dichotomy 31 220 The Snail and the Well 61 235 The Newton—Pepys Problem 96 252 The Four Sevens 131 267 Zeno’s Arrow 32 220 Alcuin’s Camel 62 236 Sunday 97 252 Mr Gubbins in the Fog 132 268 Zeno’s Stadium 33 221 Brothers and Sisters 63 236 The Tourist 98 253 The Basket of Potatoes 133 268 Achilles and the Tortoise 34 221 Alcuin’s Flasks 64 237 The Bridges of Königsberg 99 253 The Lockers 134 268 The Heap 35 222 The Eastern Merchant 65 237 Walking the Walk 100 254 Odd Multiplication 135 269 Four Brothers 36 222 Alcuin’s Grain 66 238 The Tethered Goat 101 254 Curious Numbers 136 269 The Shoot 37 223 The Hundred Steps 67 238 Buffon’s Needle 102 255 Changing Places 137 269 The Nursery 38 223 Alcuin’s Riddle 68 239 The Thunderer 103 255 The Nine Counters 138 270 7 Donkey Riding 139 270 Weary Willie and Tired Tim 175 287 The Spot on the Table 140 271 Berry’s Paradox 176 287 Catching the Thief 141 271 Crossword 177 288 What Was the Time? 142 272 The Horse Paradox 178 288 The Thirty-Three Pearls 143 272 Washing Day 179 289 The Three Villages 144 273 A Rope Around the Earth 180 289 Puzzles are one of the areas of human experience Eternal 145 273 Schrödinger’s Cat 181 290 that transcend all cultural barriers. Every nation The Village Simpleton 146 273 Hempel’s Ravens 182 290 on Earth has puzzles, and probably has done for Whapshaw’s Wharf Mystery 147 274 Two Trains 183 291 as long as humankind has been able to reason. The Spider and the Fly 148 274 The Unexpected Hanging 184 291 Faced with the unknown, our natural curiosity Circling the Squares 149 275 The Sultan’s Dowry 185 291 drives us to find some sort of resolution. When we Charley and Miss Lofty 150 275 Fermi’s Paradox 186 292 know that the mystery has been set in front of us Cast Ashore 151 276 The Prisoner’s Dilemma 187 292 as a test, the urge to solve it – to prove ourselves – The Bank of Monte Carlo 152 276 Book Stack 188 293 becomes almost unbearable. The St Patrick’s Day Parade 153 277 Two Envelope Problem 189 293 The Boarding House Pie 154 277 Postage Stamp Problem 190 294 Deduction is probably mankind’s single greatest tool. The ability to Domestic Complications 155 278 Stable Marriage Problem 191 294 reason and theorize – to connect cause and effect into a model of The Convent 156 278 Quine’s Paradox 192 295 the world – has led us from the early caves to our current society of Old Beacon Tower 157 278 Suiri 193 295 wonders. Without it, there would be no technological progress, no Casey’s Cow 158 279 The Birthday Paradox 194 296 real understanding of others, no written language... no humanity. Our Hot Cross Buns 159 279 Kakuro 195 296 capacity for logical reasoning is the main quality that separates us Cypher Dispatch Puzzle 160 280 Wordsearch 196 297 from the rest of the animals. So perhaps it’s no surprise that we all get The Fighting Fishes of Siam 161 280 The Monty Hall Problem 197 297 enjoyment from exercising that ability. The Golf Puzzle 162 281 Meta Tic-Tac-Toe 198 298 Puzzles give us the chance to exercise our mental muscles. That is not Puzzling Scales 163 281 Sudoku 199 298 just a metaphor; in many important senses, it is a literal description of A Legal Problem 164 282 Nonogram 200 299 the way our minds work. Push your mind’s limits, and your brainpower The Necklace 165 282 Slitherlink 201 299 will get stronger, more flexible, faster – fitter. Ignore it, and it will get The Boxer Puzzle 166 283 Hashiwokakero 202 300 weaker and flabbier, exactly the same way that a body does. Recent The Patrolman’s Puzzle 167 283 Nugget Number 203 300 scientific discoveries have shown that the brain really does respond to Turf Puzzle 168 284 The Sieve of Conway 204 301 mental exercise, and solving puzzles can even help to stave off the effects Astronomical Puzzle 169 284 Gokigen Naname 205 301 of diseases like Alzheimer’s. Patch Quilt Puzzle 170 285 Fillomino 206 302 The parallels between physical and mental exercise run deeper, too. Primitive Railroading Problem 171 285 Masyu 207 302 Like physical exercise, mental exercise gives us a sense of achievement, The Rogue’s Letter 172 286 Magic Square Matrix 208 303 improves our mood, and can give us a lot of pleasure. Achievement in The Squarest Game 173 286 Numberlink 209 303 A Swarm of Good Bees 174 286 8 9 puzzle solving and logical thought can even be a mark of status, similar A well-documented craze for lateral thinking and logical deduction to that of an athlete. In China and Japan, mental agility has been puzzles and riddles swept through ancient Greece from the 5th regarded as a highly skilled competitive sport for centuries, with some of century BC, lasting for several hundred years. That carried on over into the top stars becoming household names. ancient Rome in the form of advanced mathematical and logical work. The Chinese invented Magic Square puzzles around 100BC, calling A Historical Overview of Puzzling them “Lo Shu”, river maps. Other Chinese puzzle advances followed, including the first sets of interlocking puzzle rings around 300AD, the Just as puzzles can be found in all corners of the world, they can also game of Snakes and Ladders by 700AD, and the first versions of playing be found in the archaeological records of all the ancient cultures for cards in 969AD, with a deck of cards made for the Emperor Mu-Tsung. which we have substantial remains. Puzzles are as widespread in time as These had little in common with modern playing cards, however. The they are in space. The oldest mathematical devices that we have found deck of cards we know now almost certainly came from Persia some so far are actually earlier than the oldest true writing we’ve discovered. hundred years later, arriving into Europe with Spanish sailors. The devices are a set of carvings in the form of the so-called Platonic The traditional puzzle game of Fox and Hounds arose in the 12th Solids, dated around 2700BC. Each is a three-dimensional shape made century in Scandinavia. Despite persistent rumours of great antiquity, from a number of identical regular polygonal 2-D shapes. There are Tangrams – one of the most famous Chinese puzzles – remain unknown only six Platonic Solids, of which the cube is by far the best known.