Duelling Idiots and Other Probability Puzzlers [Hardcover]

Paul J. Nahin (Author)

Book Description

ISBN-10: 0691009791 | ISBN-13: 978-0691009797 | Publication Date: October 15, 2000

What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds.

If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions.

Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.

Editorial Reviews

From Publishers Weekly

"This is a book for people who really like probability problems," says Nahin (An Imaginary Tale; Time Travel), a professor of electrical engineering at the University of New Hampshire. If duelists place one bullet in one six-shooter and take turns firing at each other, what's the chance that the guy with the first shot wins? If antiaircraft missiles tell friend from foe with a system that fails 10% of the time (so that 10% of friendly planes get attacked), how much would the friendly fire rate drop if three such systems were used instead? Though probability problems can look, from afar, like extrapolations of common sense, many require mental contortions and counterintuitive realizations that make the right solutions hard to find. Those solutions, in turn, lead readers into neat concepts from higher mathematicsDthe Markov chain (that involves matrices) and the field called geometric probability. Nahin has written neither an academic book, nor one for an audience of novices: he wants recreational-math readers who will enjoy solving these fairly complex problems and who will compare their own achievements to the several-page solutions he gives. The volume thus has three parts of roughly equal length, all packed with graphs and equations. The first gives "The Problems" and the second yields "The Solutions"; the third explains how computers generate random ("more precisely called pseudo-random") numbers, and concludes with a series of programs that simulate the problems in part one. Nahin's sophisticated puzzles, and their accompanying explanations, have a far better than even chance of fascinating and preoccupying the mathematically literate readership they seek.
Copyright 2000 Reed Business Information, Inc.

Review

Nahin's sophisticated puzzles, and their accompanying explanations, have a far better than even chance of fascinating and preoccupying the mathematically literate readership they seek. (Publisher's Weekly )

An entertaining, thought-provoking collection of twenty-one puzzles. . . .These puzzles invite the reader to think intuitively, mathematically, and creatively about the laws of probability as they apply in lighthearted, often counterintuitive ways to a diverse collection of practical and speculative situations. (hematics Teacher )

By following Nahin's informal style it is possible to set [the examples] up quickly from first principles and slip them into courses on calculus, algebra, or scientific programming. They also offer a wealth of topics for undergraduate projects. Those duelling idiots are fighting over a goldmine. (Higham, MSOR Connections )

See all Editorial Reviews

Product Details

• Hardcover: 256 pages
• Publisher: Princeton University Press (October 15, 2000)
• Language: English
• ISBN-10: 0691009791
• ISBN-13: 978-0691009797
• Product Dimensions: 8.7 x 5.8 x 1 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 3.4 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #458,362 in Books (See Top 100 in Books)

More About the Author

Paul Nahin was born in California, and did all his schooling there (Brea-Olinda High 1958, Stanford BS 1962, Caltech MS 1963, and - as a Howard Hughes Staff Doctoral Fellow - UC/Irvine PhD 1972). (The lovely lady in the photo is his wife of 49 years, Patricia.) He worked as a digital logic designer and radar systems engineer in the Southern California aerospace industry until 1971, when he started his academic career. He has taught at Harvey Mudd College, the Naval Postgraduate School, and the Universities of New Hampshire (where he is now emeritus professor of electrical engineering) and Virginia. In between and here-and-there he spent a post-doctoral year at the Naval Research Laboratory, and a summer and a year at the Center for Naval Analyses and the Institute for Defense Analyses as a weapon systems analyst, all in Washington, DC. He has published a couple dozen short science fiction stories in ANALOG, OMNI, and TWILIGHT ZONE magazines, and has written 11 books on mathematics and physics, published by IEEE Press, Springer, and the university presses of Johns Hopkins and Princeton. His new book NUMBER-CRUNCHING was published by Princeton in September 2011, and Johns Hopkins recently reprinted his 1997 book TIME TRAVEL FOR WRITERS. Princeton has just released the corrected paperback edition of his 2006 book DR. EULER'S FABULOUS FORMULA. He has just completed (for Princeton) his next book, ELECTRIC LOGIC, that treats the works of George Boole and Claude Shannon and how they created the information age (to be published 2012). Two of his other Princeton math books, CHASES & ESCAPES and DUELLING IDIOTS, are scheduled to be reprinted in 2012, each with a new Preface (the one in CHASES includes an analysis of the B-29 Enola Gay's escape maneuver from the blast wave of the atomic bomb drop on Hiroshima). He has given invited talks on mathematics at Bowdoin College, the Claremont Graduate School, the University of Tennessee, and Caltech, has appeared on National Public Radio's "Science Friday" show, and advised Boston's WGBH Public Television's "Nova" program on the script for their time travel episode. He recently gave the invited Sampson Lectures for 2011 in Mathematics at Bates College (Lewiston, Maine). When he isn't writing he is battling evil-doers on his Xbox360S and, now and then, he even wins. (And he gives a big thumb's up to Valve's terrific PORTAL 2, as well as to the oldie-but-still-goodie original Xbox greats RETURN TO CASTLE WOLFENSTEIN:TIDES OF WAR and THIEF:DEADLY SHADOWS!)

FINALLY - readers have written asking about the solutions manual to THE SCIENCE OF RADIO. I now have the pdf file (3 MB) for the solutions, and if you write to me I'll send you a copy. [e-mail]

Customer Reviews

Most Helpful Customer Reviews

24 of 24 people found the following review helpful:

4.0 out of 5 stars Excellent probability teasers and solutions!, October 11, 2000

By 

Guillermo D Irisarri - See all my reviews

This review is from: Duelling Idiots and Other Probability Puzzlers (Hardcover)

This is yet another excellent contribution by professor Paul Nahin. The format of this book is different from his previous texts, but the high quality content is still there.

The book is divided into three main parts. In the first part he presents the problems and elaborates on their history, if any, and provides hints or solves a related problem. In the second part, he provides complete solutions to the problems, both analytical and through computer simulation in most cases. Finally, in the third part, he includes all the programs (MATLAB version) used to obtain the solution to the puzzlers.

The book also includes a chapter on random number generation, a key element of Montecarlo simulation.

Some knowledge of basic probability and random variables is required to fully understand the problems and solutions. Also, knowledge of calculus is needed (particularly integral calculus). To understand the computer solutions the reader must know MATLAB. The computer simulations, however, can be rewritten using any languange. Personally, I prefer Perl and that is what I used to run some of the simulations.

I believe that the computer programs could have been included in a CD or diskette, or a download site could have been used. Then, the 67 or so pages dedicated to these programs, could have been used to provide 5-10 additional problems!

29 of 32 people found the following review helpful:

4.0 out of 5 stars Real world problems masked by somewhat frivolous statements, October 14, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Duelling Idiots and Other Probability Puzzlers (Hardcover)

Two areas where the results are often counter intuitive are quantum mechanics and probability. Even experienced mathematicians are often confused by results such as the birthday and Monty Hall problems. After years of expert analysis and commentary, the results are still disputed and disbelieved by many. While these problems are not covered in any detail here, others with sometimes unexpected results are extensively examined.
The title problem is a simple one where two individuals take turns spinning the chamber of a gun, pointing it at the other and pulling the trigger. While it is obvious that the first to go has the advantage it is surprising that the advantage is not greater than it is. Another problem of special interest during playoff season concerns the probability that the best team actually wins a seven game first with four wins series. It is a well-worn cliché that, "In a short series, anything can happen!" However, the mathematical analysis clearly supports this saying. The graph of the possible results shows that even if the probability of the stronger team winning any individual game 0.65, the weaker team still has a 20% chance of winning the series.
Monte Carlo or statistical simulation methods are used to test and verify many of the results. The software package used to perform the tests is MATLAB and 63 pages of code listings is included at the end of the book. Solutions to all problems are included and many of them require a year or more of college calculus in order to understand the solution.
Although many of the problems covered in this book have somewhat frivolous statements, they also are illustrative of situations encountered in the real world. Some in fact originated there and the statements were altered to make them more interesting to a general audience. This is a good book to use as a supplement in a course in applied probability theory.

13 of 18 people found the following review helpful:

5.0 out of 5 stars Oddballs and urns, October 26, 2000

By A Customer

This review is from: Duelling Idiots and Other Probability Puzzlers (Hardcover)

Books on probability are often boring. (Remember all those tedious problems involving people obsessed with drawing balls from urns?). In "Duelling Idiots", Nahin actually makes the subject fun by describing offbeat problems with unexpected solutions. If you like solving math puzzles, then this is a great book to look at. If you're teaching a course and want to assign a book that students might actually read, then look no further.