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In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable – and all of it mathematically irrefutable. Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly – why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion – how is this possible? What does the game show, "Let's Make A Deal" reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages?
These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible? Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs.
Acknowledgments xi
Introduction 1
Chapter 1: It's Common Knowledge 3
Chapter 2: Simpson's Paradox 11
Chapter 3: The Impossible Problem 21
Chapter 4: Braess's Paradox 31
Chapter 5: The Power of Complex Numbers 39
Chapter 6: Bucking the Odds 50
Chapter 7: Cantor's Paradise 68
Chapter 8: Gamow-Stern Elevators 82
Chapter 9: The Toss of a Coin 88
Chapter 10: Wild-Card Poker 103
Chapter 11: Two Series 113
Chapter 12: Two Card Tricks 131
Chapter 13: The Spin of a Needle 146
Chapter 14: The Best Choice 165
Chapter 15: The Power of Powers 176
Chapter 16: Benford's Law 190
Chapter 17: Goodstein Sequences 201
Chapter 18: The Banach-Tarski Paradox 210
The Motifs 217
Appendix 221
Index 233
Julian Havil is a master at Winchester College, England, where he has taught mathematics for more than thirty years. He is the author of Nonplussed!: Mathematical Proof of Implausible Ideas and Gamma: Exploring Euler's Constant.
"Julian Havil's Impossible? is a superb discussion of problems easily understood by a high schooler, yet with solutions so counterintuitive as to seem impossible. Topics include the notorious Monty Hall three-door problem, the Gamow-Stern elevator paradoxes, the Kruskal count card trick, Cantor's 'paradise' of alephs, and the mind-blowing Banach-Tarski paradox, all analyzed in depth by a master who does not hold back equations that provide elegant proofs. There are surprises on almost every page."
– Martin Gardner
"This book is a fascinating and thoroughly enjoyable read. Havil offers an engaging collection of counterintuitive results and seemingly impossible problems. Some of the material is truly astonishing, and the author conveys his sense of surprise very effectively. Each problem ultimately yields to careful and well-presented analysis. The history of many of the results is discussed, and further references are provided."
– Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles
"I thought it impossible for Julian Havil to exceed Nonplussed!, his previous collection of perplexing math puzzlers. And yet he has done just that with the sequel Impossible?, an accomplishment that has left me nonplussed."
– Paul J. Nahin, author of An Imaginary Tale
