Paul J. Nahin
Princeton University Press | 2013 | 250 páginas | rar - pdf | 1,35 Mb
link (password: matav)
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.
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 S impson’s Paradox, Radio-Direction Finding, and the Spaghetti Problem 21
Challenge Problems 30
1 Breaking Sticks 36
1.1 The Problem 36
1.2 Theoretical Analysis 36
1.3 Computer Simulation 38
2 The Twins 42
2.1 The Problem 42
2.2 Theoretical Analysis 43
2.3 Computer Simulation 44
3 Steve’s Elevator Problem 47
3.1 The Problem 47
3.2 Theoretical Analysis by Shane Henderson 48
3.3 Computer Simulation 51
4 Three 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
5 Big Quotients—Part 1 62
5.1 The Problem 62
5.2 Theoretical Analysis 62
5.3 Computer Simulation 64
6 Two Ways to Proofread 66
6.1 The Problem 66
6.2 Theoretical Analysis 67
7 Chain Letters That Never End 70
7.1 The Problem 70
7.2 Theoretical Analysis 70
8 Bingo Befuddlement 74
8.1 The Problem 74
8.2 Computer Simulation 75
9 Is Dreidel Fair? 79
9.1 The Problem 79
9.2 Computer Simulation 80
10 Hollywood Thrills 83
10.1 The Problem 83
10.2 Theoretical Analysis 83
11 The Problem of the n-Liars 87
11.1 The Problem 87
11.2 Theoretical Analysis 87
11.3 Computer Simulation 89
12 The Inconvenience of a Law 90
12.1 The Problem 90
12.2 Theoretical Analysis 90
13 A Puzzle for When the Super Bowl is a Blowout 93
13.1 The Problem 93
13.2 Theoretical Analysis 94
14 Darts and Ballistic Missiles 96
14.1 The Problem 96
14.2 Theoretical Analysis 97
15 Blood Testing 103
15.1 The Problem 103
15.2 Theoretical Analysis 103
16 Big Quotients—Part 2 107
16.1 The Problem 107
16.2 Theoretical Analysis 107
17 To Test or Not to Test? 117
17.1 The Problem 117
17.2 Theoretical Analysis 119
18 Average Distances on a Square 126
18.1 The Problem(s) 126
18.2 Theoretical Analyses 127
18.3 Computer Simulations 136
19 When Will the Last One Fail? 139
19.1 The Problem 139
19.2 Theoretical Analyses 142
20 Who’s Ahead? 147
20.1 The Problem 147
20.2 Theoretical Analysis 148
21 Plum Pudding 151
21.1 The Problem 151
21.2 Computer Simulation 152
21.3 Theoretical Analysis 153
22 Ping-Pong, Squash, and Difference Equations 156
22.1 Ping-Pong Math 156
22.2 Squash Math Is Harder! 161
23 Will You Be Alive 10 Years from Now? 168
23.1 The Problem 168
23.2 Theoretical Analysis 169
24 Chickens in Boxes 176
24.1 The Problem (and Some Warm-ups, Too) 176
24.2 Theoretical Analysis 180
25 Newcomb’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
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