Table of Contents

Acknowledgements ix

Introducing Soames and Watsup 1

Note on Units 3

The Scandal of the Stolen Sovereign 5

Number Curiosity 6

Track Position 7

Soames Meets Watsup 8

Geomagic Squares 12

What Shape is an Orange Peel 13

How to Win the Lottery? 14

The Green Socks Caper Incident 15

Consecutive Cubes 20

Adonis Asteroid Mousterian 20

Two Square Quickies 21

Caught Clean-Handed 22

The Adventure of the Cardboard Boxes 23

The RATS Sequence 28

Birthdays are Good for You 28

Mathematical Dates 28

The Hound of the Basketballs 30

Digital Cubes 36

Narcissistic numbers 36

Piphilology, Piems, and Pilish 39

Clueless 41

A Brief History of Sudoku 42

Hexakosioihexekontahexaphobia 45

Once, Twice, Thrice 47

Conservation of Luck 47

The Case of the Face-Down Aces 49

Confused Parents 52

Jigsaw Paradox 53

The Catflap of Fear 53

Pancake Numbers 58

The Soup Plate Trick 59

Mathematical Haiku 62

The Case of the Cryptic Cartwheel 63

Two by Two 66

The V-Shaped Goose Mystery 67

Eelish Mnemonics 70

Amazing Squares 71

The Thirty-Seven Mystery 72

Average Speed 74

Four Clueless Pseudoku 74

Sums of Cubes 75

The Puzzle of the Purloined Papers 77

Master of All He Surveys 80

Another Number Curiosity 81

The Opaque Square Problem 81

Opaque Polygons and Circles 83

85

The Sign of One 85

Progress on Prime Gaps 90

The Odd Goldbach Conjecture 92

Prime Number Mysteries 94

The Optimal Pyramid 101

The Sign of One: Part Two 105

Initial Confusion 109

Euclid's Doodle 110

Euclidean Efficiency 114

123456789 Times X 115

The Sign of One: Part Three 115

Taxicab Numbers 119

The Wave of Translation 121

Riddle of the Sands 123

Eskimo α 125

The Sign of One: Part Four-Concluded 126

Seriously Deranged 128

Tossing a Fair Coin Isn't Fair 129

Playing Poker by Post 131

Eliminating the Impossible 135

Mussel Power 138

Proof That the World is Round 140

123456789Times X Continued 145

The Price of Fame 145

The Riddle of the Golden Rhombus 146

A Powerful Arithmatic Sequence 147

Why Do Guinness Bubbles Go Downwards? 149

Random Harmonic Series 151

The Dogs That Fight in the Park 153

How Tall is That Tree? 155

Why Do My Friends Have More Friends Than I Do? 156

Isn't Statistics Wonderful? 158

The Adventure of the Six Guests 158

How to Write Very Big Numbers 162

Graham's Number 166

Can't Wrap My Head Around It 167

The Affair of the Above-Average Driver 169

The Mousetrap Cube 171

Sierpinski Numbers 172

James Joseph Who? 173

The Baffleham Burglary 174

The Quardrillionth Digit of α 175

Is α Normal? 177

A Mathematician, a Statistician, and an Engineer 179

Lakes of Wada 180

Fermat's Last Limerick 183

Malfatti's Mistake 184

Square Leftovers 186

Coin Tossing over the Phone 189

How to Stop Unwanted Echoes 191

The Enigma of the Versatile Tile 194

The Thrackle Conjecture 201

Bargain with the Devil 202

A Tilling That Is Not Periodic 203

The Two Colour Theorem 206

The Four Colour Theorem in Space 208

Comical Calculus 210

The Erdos Discrepancy Problem 211

The Greek Integrator 214

Sums of Four Cubes 219

Why the Leopard Got Its Spots 221

Plygons Forever 223

Top Secret 223

The Adventure of the Rowing Men 224

The Fifteen Puzzle 229

The Tricky Six Puzzle 230

As Difficulty as ABC 232

Rings of Regular Solids 235

The Square Peg Problem 238

The Impossible Route 239

The Final Problem 243

The Return 246

The Final Solution 247

The Mysteries Demystified 249