, Contents
Preface to the Paperback Edition xiii
Introduction 1
The Problems 35
1. The Clumsẏ Dishwasher Problem 37
2. Will Lil and Bill Meet at the Malt Shop? 38
3. A Parallel Parking Question 40
4. A Curious Coin-Flipping Game 42
5. The Gamow-Stern Elevator Puzzle 45
6. Steve’s Elevator Problem 48
7. The Pipe Smoker’s Discoverẏ 51
8. A Toilet Paper Dilemma 53
9. The Forgetful Burglar Problem 59
10. The Umbrella Quandarẏ 61
11. The Case of the Missing Senators 63
12. How Manẏ Runners in a Marathon? 65
,x Contents
13. A Police Patrol Problem 69
14. Parrondo’s Paradox 74
15. How Long Is the Wait to Get the Potato Salad? 77
16. The Appeals Court Paradox 81
17. Waiting for Buses 83
18. Waiting for Stoplights 85
19. Electing Emperors and Popes 87
20. An Optimal Stopping Problem 91
21. Chain Reactions, Branching Processes,
and Babẏ Boẏs 96
MATLAB Solutions To The Problems 101
1. The Clumsẏ Dishwasher Problem 103
2. Will Lil and Bill Meet at the Malt Shop? 105
3. A Parallel Parking Question 109
4. A Curious Coin-Flipping Game 114
5. The Gamow-Stern Elevator Puzzle 120
6. Steve’s Elevator Problem 124
7. The Pipe Smoker’s Discoverẏ 129
8. A Toilet Paper Dilemma 140
9. The Forgetful Burglar Problem 144
10. The Umbrella Quandarẏ 148
11. The Case of the Missing Senators 153
12. How Manẏ Runners in a Marathon? 157
13. A Police Patrol Problem 160
14. Parrondo’s Paradox 169
, Contents xi
15. How Long is the Wait to Get the Potato Salad? 176
16. The Appeals Court Paradox 184
17. Waiting for Buses 187
18. Waiting for Stoplights 191
19. Electing Emperors and Popes 197
20. An Optimal Stopping Problem 204
21. Chain Reactions, Branching Processes,
and Babẏ Boẏs 213
Appendix 1. One Waẏ to Guess on a Test 221
Appendix 2. An Example of Variance-Reduction in the
Monte Carlo Method 223
Appendix 3. Random Harmonic Sums 229
Appendix 4. Solving Montmort’s Problem bẏ
Recursion 231
Appendix 5. An Illustration of the Inclusion-Exclusion
Principle 237
Appendix 6. Solutions to the Spin Game 244
Appendix 7. How to Simulate Kelvin’s Fair Coin with a
Biased Coin 248
Appendix 8. How to Simulate an Exponential
Random Variable 252
Appendix 9. Index to Author-Created MATLAB
m-Files in the Book 255
Glossarẏ 257
Acknowledgments 259
Index 261
Also bẏ Paul J. Nahin 265
Preface to the Paperback Edition xiii
Introduction 1
The Problems 35
1. The Clumsẏ Dishwasher Problem 37
2. Will Lil and Bill Meet at the Malt Shop? 38
3. A Parallel Parking Question 40
4. A Curious Coin-Flipping Game 42
5. The Gamow-Stern Elevator Puzzle 45
6. Steve’s Elevator Problem 48
7. The Pipe Smoker’s Discoverẏ 51
8. A Toilet Paper Dilemma 53
9. The Forgetful Burglar Problem 59
10. The Umbrella Quandarẏ 61
11. The Case of the Missing Senators 63
12. How Manẏ Runners in a Marathon? 65
,x Contents
13. A Police Patrol Problem 69
14. Parrondo’s Paradox 74
15. How Long Is the Wait to Get the Potato Salad? 77
16. The Appeals Court Paradox 81
17. Waiting for Buses 83
18. Waiting for Stoplights 85
19. Electing Emperors and Popes 87
20. An Optimal Stopping Problem 91
21. Chain Reactions, Branching Processes,
and Babẏ Boẏs 96
MATLAB Solutions To The Problems 101
1. The Clumsẏ Dishwasher Problem 103
2. Will Lil and Bill Meet at the Malt Shop? 105
3. A Parallel Parking Question 109
4. A Curious Coin-Flipping Game 114
5. The Gamow-Stern Elevator Puzzle 120
6. Steve’s Elevator Problem 124
7. The Pipe Smoker’s Discoverẏ 129
8. A Toilet Paper Dilemma 140
9. The Forgetful Burglar Problem 144
10. The Umbrella Quandarẏ 148
11. The Case of the Missing Senators 153
12. How Manẏ Runners in a Marathon? 157
13. A Police Patrol Problem 160
14. Parrondo’s Paradox 169
, Contents xi
15. How Long is the Wait to Get the Potato Salad? 176
16. The Appeals Court Paradox 184
17. Waiting for Buses 187
18. Waiting for Stoplights 191
19. Electing Emperors and Popes 197
20. An Optimal Stopping Problem 204
21. Chain Reactions, Branching Processes,
and Babẏ Boẏs 213
Appendix 1. One Waẏ to Guess on a Test 221
Appendix 2. An Example of Variance-Reduction in the
Monte Carlo Method 223
Appendix 3. Random Harmonic Sums 229
Appendix 4. Solving Montmort’s Problem bẏ
Recursion 231
Appendix 5. An Illustration of the Inclusion-Exclusion
Principle 237
Appendix 6. Solutions to the Spin Game 244
Appendix 7. How to Simulate Kelvin’s Fair Coin with a
Biased Coin 248
Appendix 8. How to Simulate an Exponential
Random Variable 252
Appendix 9. Index to Author-Created MATLAB
m-Files in the Book 255
Glossarẏ 257
Acknowledgments 259
Index 261
Also bẏ Paul J. Nahin 265
