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. Perkins's Electric Quilt, and An Imaginary Tale (all Princeton).

"A wonderful book for trained math lovers who enjoy the mental stimulation provided by a good mathematics puzzle."--Harold D. Shane, Library Journal "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 "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 "[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 "For mathematicians with an interest in probability theory, this is a fun holiday book."--Eos blog "I found it both enjoyable and enlightening. I am happy to recommend it."--Ed Barbeau, Crux

• 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(R)'s Random Number Generator 213 Acknowledgments 217 Index 219

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. Perkins's Electric Quilt, and An Imaginary Tale (all Princeton).

"A wonderful book for trained math lovers who enjoy the mental stimulation provided by a good mathematics puzzle."--Harold D. Shane, Library Journal "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 "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 "[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 "For mathematicians with an interest in probability theory, this is a fun holiday book."--Eos blog "I found it both enjoyable and enlightening. I am happy to recommend it."--Ed Barbeau, Crux

• 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(R)'s Random Number Generator 213 Acknowledgments 217 Index 219

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. Perkins's Electric Quilt, and An Imaginary Tale (all Princeton).

"A wonderful book for trained math lovers who enjoy the mental stimulation provided by a good mathematics puzzle."--Harold D. Shane, Library Journal "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 "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 "[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 "For mathematicians with an interest in probability theory, this is a fun holiday book."--Eos blog "I found it both enjoyable and enlightening. I am happy to recommend it."--Ed Barbeau, Crux

• 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(R)'s Random Number Generator 213 Acknowledgments 217 Index 219