Contents
Preface
xv
Introduction: Classic Puzzles from the Past
1
I.1 A Gambling Puzzle of Gombaud and Pascal
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
Breaking Sticks
36
1.1 The Problem
1.2 Theoretical Analysis
1.3 Computer Simulation
38
2
The Twins
42
2.1 The Problem
2.2 Theoretical Analysis
43
2.3 Computer Simulation
44
Steve’s Elevator Problem
47
3.1 The Problem
3.2 Theoretical Analysis by Shane Henderson
48
3.3 Computer Simulation
51
Three Gambling Problems Newton Would “Probably” Have Liked
52
4.1 The Problems
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
5.2 Theoretical Analysis
5.3 Computer Simulation
64
Two Ways to Proofread
66
6.1 The Problem
6.2 Theoretical Analysis
67
7
Chain Letters That Never End
70
7.1 The Problem
7.2 Theoretical Analysis
8
Bingo Befuddlement
74
8.1 The Problem
8.2 Computer Simulation
75
9
Is Dreidel Fair?
79
9.1 The Problem
9.2 Computer Simulation
80
Hollywood Thrills
83
10.1 The Problem
10.2 Theoretical Analysis
11
The Problem of the n-Liars
87
11.1 The Problem
11.2 Theoretical Analysis
11.3 Computer Simulation
89
12
The Inconvenience of a Law
90
12.1 The Problem
12.2 Theoretical Analysis
A Puzzle for When the Super Bowl is a Blowout
93
13.1 The Problem
13.2 Theoretical Analysis
94
14
Darts and Ballistic Missiles
96
14.1 The Problem
14.2 Theoretical Analysis
97
15
Blood Testing
103
15.1 The Problem
15.2 Theoretical Analysis
16
Big Quotients—Part 2
107
16.1 The Problem
16.2 Theoretical Analysis
To Test or Not to Test?
117
17.1 The Problem
17.2 Theoretical Analysis
119
Average Distances on a Square
126
18.1 The Problem(s)
18.2 Theoretical Analyses
127
18.3 Computer Simulations
136
19
When Will the Last One Fail?
139
19.1 The Problem
19.2 Theoretical Analyses
142
20
Who’s Ahead?
147
20.1 The Problem
20.2 Theoretical Analysis
148
Plum Pudding
151
21.1 The Problem
21.2 Computer Simulation
152
21.3 Theoretical Analysis
153
22
Ping-Pong, Squash, and Difference Equations
156
22.1 Ping-Pong Math
22.2 Squash Math Is Harder!
161
23
Will You Be Alive 10 Years from Now?
168
23.1 The Problem
23.2 Theoretical Analysis
169
24
Chickens in Boxes
176
24.1 The Problem (and Some Warm-ups, Too)
24.2 Theoretical Analysis
180
25
Newcomb’s Paradox
183
25.1 Some History
25.2 Decision Principles in Conflict
186
Challenge Problem Solutions
189
Technical Note on MATLAB®’s Random Number Generator
213
Acknowledgments
217
Index
219
