Synopses & Reviews
What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the one-of-a-kind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book.
Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the past--from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton--and also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book.
Nahin then presents twenty-five unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB® Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.
Review
"Nahin (Duelling Idiots and Other Probability Puzzlers), University of New Hampshire professor emeritus of electrical engineering, takes intrepid, mathematically minded readers on a fresh outing through the land of probability in this collection of puzzles, complete with MATLAB computer code. Nahin draws from the usual venues of probability problems, from gambling to sports, many utilizing Monte Carlo algorithms, which use random numbers to describe the behavior of dice and flipped coins. Nahin begins with the familiar 'Gambler's Ruin' problem, then branches out to consider the number of stops an elevator might make along its route, the likelihood of a proofreader missing errors, chance of false positives in medical tests, and whether the traditional dreidel game is really fair. The book isn't written for the casual browser; Nahin assumes readers will have a solid grounding in college-level mathematics as well as basic probability and some computer programming, if not knowledge of the MATLAB software package. For those who have the prerequisites, the author offers a pleasant collection of brain-teasers on which to test their mettle. 28 line illus., 22 tables." Publishers Weekly Copyright PWxyz, LLC. All rights reserved.
Review
"A wonderful book for trained math lovers who enjoy the mental stimulation provided by a good mathematics puzzle."--Harold D. Shane, Library Journal
Review
"Prolific mathematics author Nahin presents a series of thought-provoking probability questions designed to intrigue the reader. . . . In general, the solutions rely only on basic rules of probability and algebraic manipulation, while ranging in difficulty from the very straightforward to the highly challenging."--Choice
Review
"The author's infectious enthusiasm is evident here as in his earlier books. Students at various levels and other fans of mathematics will find much to engage their interest and challenge their minds."--G. A. Heuer, Mathematical Reviews
Review
"[T]he book provides useful problems for an instructor wishing to improve their student's ability at combinatorics, statistical distribution theory and calculus (specifically integration). . . . [T]he book also provides motivation for an interested student or reader to pursue the study of probability and statistics to a deeper level."--Gabrielle Kelly, Irish Mathematical Society Bulletin
Review
"For mathematicians with an interest in probability theory, this is a fun holiday book."--Eos blog
Review
"I found it both enjoyable and enlightening. I am happy to recommend it."--Ed Barbeau, Crux
Synopsis
"Readers of this absorbing book will gain significant pleasure as well as a broadened understanding of the nuances of mathematics, along with a wonderful picture of how analytics and simulations complement each other. Nahin is a master at this. I love this book!"
--Joseph Mazur, author of What's Luck Got to Do with It?: The History, Mathematics, and Psychology of the Gambler's Illusion"This book will be of interest to anyone who loves the challenge and surprise inherent in probability theory, and who likes to tinker with their computer as a simulator. Nahin's style is easy and informal."--Julian Havil, author of The Irrationals: A Story of the Numbers You Can't Count On
About the Author
Paul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire. He is the best-selling author of many popular-math books, including Duelling Idiots and Other Probability Puzzlers, The Logician and the Engineer, Number-Crunching, Mrs. Perkinss Electric Quilt, and An Imaginary Tale (all Princeton).
Table of Contents
Preface xv
Introduction: Classic Puzzles from the Past 1
I.1 A Gambling Puzzle of Gombaud and Pascal 1
I.2 Galileo's Dice Problem 3
I.3 Another Gombaud-Pascal Puzzle 4
I.4 Gambler's Ruin and De Moivre 6
I.5 Monte Carlo Simulation of Gambler's Ruin 10
I.6 Newton's Probability Problem 13
I.7 A Dice Problem That Would Have Surprised Newton 17
I.8 A Coin-Flipping Problem 18
I.9 Simpson's Paradox, Radio-Direction Finding, and the Spaghetti Problem 21
Challenge Problems 30
1Breaking Sticks 36
1.1 The Problem 36
1.2 Theoretical Analysis 36
1.3 Computer Simulation 38
2The Twins 42
2.1 The Problem 42
2.2 Theoretical Analysis 43
2.3 Computer Simulation 44
3Steve's Elevator Problem 47
3.1 The Problem 47
3.2 Theoretical Analysis by Shane Henderson 48
3.3 Computer Simulation 51
4Three Gambling Problems Newton Would "Probably" Have Liked 52
4.1 The Problems 52
4.2 Theoretical Analysis 1 54
4.3 Computer Simulation 1 55
4.4 Theoretical Analysis 2 57
4.5 Computer Simulation 2 58
4.6 Theoretical Analysis 3 59
5Big Quotients--Part 1 62
5.1 The Problem 62
5.2 Theoretical Analysis 62
5.3 Computer Simulation 64
6Two Ways to Proofread 66
6.1 The Problem 66
6.2 Theoretical Analysis 67
7Chain Letters That Never End 70
7.1 The Problem 70
7.2 Theoretical Analysis 70
8Bingo Befuddlement 74
8.1 The Problem 74
8.2 Computer Simulation 75
9Is Dreidel Fair? 79
9.1 The Problem 79
9.2 Computer Simulation 80
10Hollywood Thrills 83
10.1 The Problem 83
10.2 Theoretical Analysis 83
11The Problem of the n-Liars 87
11.1 The Problem 87
11.2 Theoretical Analysis 87
11.3 Computer Simulation 89
12The Inconvenience of a Law 90
12.1 The Problem 90
12.2 Theoretical Analysis 90
13A Puzzle for When the Super Bowl is a Blowout 93
13.1 The Problem 93
13.2 Theoretical Analysis 94
14Darts and Ballistic Missiles 96
14.1 The Problem 96
14.2 Theoretical Analysis 97
15Blood Testing 103
15.1 The Problem 103
15.2 Theoretical Analysis 103
16Big Quotients--Part 2 107
16.1 The Problem 107
16.2 Theoretical Analysis 107
17To Test or Not to Test? 117
17.1 The Problem 117
17.2 Theoretical Analysis 119
18Average Distances on a Square 126
18.1 The Problem(s) 126
18.2 Theoretical Analyses 127
18.3 Computer Simulations 136
19When Will the Last One Fail? 139
19.1 The Problem 139
19.2 Theoretical Analyses 142
20Who's Ahead? 147
20.1 The Problem 147
20.2 Theoretical Analysis 148
21Plum Pudding 151
21.1 The Problem 151
21.2 Computer Simulation 152
21.3 Theoretical Analysis 153
22Ping-Pong, Squash, and Difference Equations 156
22.1 Ping-Pong Math 156
22.2 Squash Math Is Harder! 161
23Will You Be Alive 10 Years from Now? 168
23.1 The Problem 168
23.2 Theoretical Analysis 169
24Chickens in Boxes 176
24.1 The Problem (and Some Warm-ups, Too) 176
24.2 Theoretical Analysis 180
25Newcomb's Paradox 183
25.1 Some History 183
25.2 Decision Principles in Conflict 186
Challenge Problem Solutions 189
Technical Note on MATLAB®'s Random Number Generator 213
Acknowledgments 217
Index 219