Duelling Idiots and Other Probability Puzzlers
The book is a collection of 21 essays, each built around one or two probability problems. The author plays with the problems: solving them, modifying them, simulating them on a computer. Indeed simulations constitute a considerable part of the book. (MATLAB scripts take up 65 out of 270 pages, with additional 22 pages devoted to the history and theory of random number generators.) All discussed problems come with solutions - some with solutions at the text proper, some at the end of the book.
Most of the essays follow a definite plan: a problem, its solution, a modification, its solution. The modified problems are usually sufficiently hard to the extent that their analytic solution, when exists, is unsuitable to handle analytically. In other cases, an analytic solution is simply unavailable. The solutions are usually counterintuitive and this explains the word Puzzlers in the title. However, the book is definitely not a puzzle collection in the common sense. Most of the problems require a level of comfort with probability methods beyond that associated with casual audience. Some are intended to a reader with a one-two years Calculus experience.
The problems are truly entertaining and the manner in which the author keeps modifying them is edifying. The book's style leaves no doubt about author's enthusiasm about the subject. For him, the problems provide another opportunity to demonstrate the power of mathematics and the flexibility of its problem solving strategies. But more than that, an experienced writer, the author exploits every opportunity to tell a story: a historic background, a personal note, a real world association. For any one who can follow the author's mathematics, the book is a pleasure to read.
The book is neither a collection of solved problems nor a probability text. It will be appreciated by curious undergraduates and probability instructors as a course supplement.
Duelling Idiots and Other Probability Puzzlers, Princeton University Press, 2000. Softcover, 269 pp, $22.95. ISBN 0691102864.