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Duelling Idiots and Other Probability Puzzlers
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 "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.
- GenresMathematicsNonfiction
296 pages, Paperback
First published January 1, 2000
6 people are currently reading
124 people want to read
About the author
Paul J. Nahin
52 books124 followersPaul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire and the author of many best-selling popular math books, including The Logician and the Engineer and Will You Be Alive 10 Years from Now? (both Princeton).
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Displaying 1 - 10 of 10 reviews
January 20, 2014
This is a very good book about methods for computing probability puzzles. There are two types of methods discussed here: analytic solutions and computer simulations. The book is intended for readers with a strong mathematics background. Good algebra skills are essential, and calculus is also required to solve some of the puzzles analytically.
This book is divided into three parts. The first part is a description of 21 puzzles. The descriptions go into some detail, and provide hints. The second part contains the analytic solutions to the puzzles. The third part contains computer programs for simulating the solutions; the programs are written in Matlab, which for me is just perfect.
The puzzles have interesting names, for example, "How to Ask an Embarrassing Question", "When Idiots Duels", "Who Pays for the Coffee", "The Unsinkable Tub is Sinking!", "The Blind Spider and the Fly." The puzzles are all different; solving any one of them requires an approach different from any other. This is a well thought-out book, highly recommended for anybody with a need to try challenging puzzles that require some thought and mathematical skills.
This book is divided into three parts. The first part is a description of 21 puzzles. The descriptions go into some detail, and provide hints. The second part contains the analytic solutions to the puzzles. The third part contains computer programs for simulating the solutions; the programs are written in Matlab, which for me is just perfect.
The puzzles have interesting names, for example, "How to Ask an Embarrassing Question", "When Idiots Duels", "Who Pays for the Coffee", "The Unsinkable Tub is Sinking!", "The Blind Spider and the Fly." The puzzles are all different; solving any one of them requires an approach different from any other. This is a well thought-out book, highly recommended for anybody with a need to try challenging puzzles that require some thought and mathematical skills.
February 13, 2015
This was a surprise: a set of mostly non-trivial probability problems that uses both analytical and Monte Carlo methods to reach solutions—more or less exactly what I've been doing with my life recently.
Usually these books containing programs written by non-programmers are just frustrating to read, but this was an exception; Nahin's description of his programs is usually convincing enough, and though I didn't read through all of the source code included in the appendix (MATLAB isn't a fun language), the ones I did read were written almost exactly the way I would have written them myself (except in MATLAB). The only thing I'd fault him for programming-wise is his too-low number of trials per simulation† (usually only a thousand; that can probably be blamed on the fact that he wrote the programs in 1998 and started writing these simulations much earlier than that) and his tendency to alleviate that problem by running his program several times, presenting the results in a table, and then taking the mean, instead of just increasing the number of runs.
Not all of the problems are interesting, but most of them are more interesting than the usual problems you get in books masquerading as popular mathematics. Nahin comes across as unnecessarily condescending at times (the book was written with his undergraduate students in mind, and tends to forget there are other mathematics programs in the world—or pretends they're pitiful garbage), and his intuition for probability is sometimes surprisingly poor (though that mostly only shows in the throw-away banter, not in the problems themselves), but on the whole, this turned out to be a better little book than I was expecting.
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† One thing he doesn't try to answer, and which has been on my mind recently, is how many trials is ``enough'' for a simulation; that is, how to calculate confidence intervals.
Usually these books containing programs written by non-programmers are just frustrating to read, but this was an exception; Nahin's description of his programs is usually convincing enough, and though I didn't read through all of the source code included in the appendix (MATLAB isn't a fun language), the ones I did read were written almost exactly the way I would have written them myself (except in MATLAB). The only thing I'd fault him for programming-wise is his too-low number of trials per simulation† (usually only a thousand; that can probably be blamed on the fact that he wrote the programs in 1998 and started writing these simulations much earlier than that) and his tendency to alleviate that problem by running his program several times, presenting the results in a table, and then taking the mean, instead of just increasing the number of runs.
Not all of the problems are interesting, but most of them are more interesting than the usual problems you get in books masquerading as popular mathematics. Nahin comes across as unnecessarily condescending at times (the book was written with his undergraduate students in mind, and tends to forget there are other mathematics programs in the world—or pretends they're pitiful garbage), and his intuition for probability is sometimes surprisingly poor (though that mostly only shows in the throw-away banter, not in the problems themselves), but on the whole, this turned out to be a better little book than I was expecting.
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† One thing he doesn't try to answer, and which has been on my mind recently, is how many trials is ``enough'' for a simulation; that is, how to calculate confidence intervals.
Want to read
January 19, 2013The author explicitly intends this book to be a list of probability puzzles that are of higher calibre than the ones occasionally presented by Marilyn vos Savant in PARADE magazine (the celebrity-gossip insert that comes in the weekend newspaper). One would think that that would be a pretty low bar for a high-quality math text, but on pp 12-13, while warning against faulty reasoning by vos Savant and others (including Laplace), the author pulls a fast one himself.
The scenario concerns a markswoman who picks one of two rifles, each equally likely. Each rifle has a probability p of finding its mark. For rifle 1, p=1/2; for rifle 2, p=2/3.
The markswoman shoots 300 times with the chosen rifle, and finds her mark 175 times. Let's call this event A. The problem is to find out the probability that she picked rifle 1 and the probability that she picked rifle 2. In other words, we need to find P(p=1/2 | A) and P(p=2/3 | A).
The author first determines P(A | p=1/2) and P(A | p=2/3), which he simply calls P(1/2) and P(2/3) respectively. These give tough-to-calculate expressions (because of the factorials), but their ratio P(2/3) ÷ P(1/2) is calculated handily enough.
Next, he casually claims P(1/2) + P(2/3) = 1 (which it manifestly is not) "because p is either 1/2 or 2/3". Using this as a second equation, he "solves" for P(1/2) and P(2/3), and furthermore starts interpreting P(1/2) and P(2/3) as if they were P(p=1/2 | A) and P(p=2/3 | A) respectively. (I.e., a conflation of P(A|B) with P(B|A).)
What saves him from giving a wrong final answer is that the ratio P(p=2/3 | A) ÷ P(p=1/2 | A) happens to be equal to the ratio P(A | p=2/3) ÷ P(A | p=1/2), and the sum P(p=1/2 | A) + P(p=2/3 | A) is indeed 1, both of which can be verified by Bayes's theorem, and using the fact that in this case P(p=1/2) = P(p=2/3) = 1/2.
The scenario concerns a markswoman who picks one of two rifles, each equally likely. Each rifle has a probability p of finding its mark. For rifle 1, p=1/2; for rifle 2, p=2/3.
The markswoman shoots 300 times with the chosen rifle, and finds her mark 175 times. Let's call this event A. The problem is to find out the probability that she picked rifle 1 and the probability that she picked rifle 2. In other words, we need to find P(p=1/2 | A) and P(p=2/3 | A).
The author first determines P(A | p=1/2) and P(A | p=2/3), which he simply calls P(1/2) and P(2/3) respectively. These give tough-to-calculate expressions (because of the factorials), but their ratio P(2/3) ÷ P(1/2) is calculated handily enough.
Next, he casually claims P(1/2) + P(2/3) = 1 (which it manifestly is not) "because p is either 1/2 or 2/3". Using this as a second equation, he "solves" for P(1/2) and P(2/3), and furthermore starts interpreting P(1/2) and P(2/3) as if they were P(p=1/2 | A) and P(p=2/3 | A) respectively. (I.e., a conflation of P(A|B) with P(B|A).)
What saves him from giving a wrong final answer is that the ratio P(p=2/3 | A) ÷ P(p=1/2 | A) happens to be equal to the ratio P(A | p=2/3) ÷ P(A | p=1/2), and the sum P(p=1/2 | A) + P(p=2/3 | A) is indeed 1, both of which can be verified by Bayes's theorem, and using the fact that in this case P(p=1/2) = P(p=2/3) = 1/2.
July 6, 2007
A sloppy, poorly written book. Save your money.
February 8, 2019
A nice little book. Just a short discussion of each problem followed by the solutions. I found it quite approachable. Probably dropping the Matlab stuff and doing everything with pseudocode would have been much better.
December 28, 2015
This is a recreational puzzle book for anyone who's completed the freshmen calculus sequence and taken a first course in probability and knows how to program. Clearly not for a general audience, but still quite a bit of fun. It's semi-autobiographical, as the author selected the puzzles based on his own work and/or teaching experiences. Don't be put off by the fact that the program are written in MATLAB. If you know any programming language, the code is simple enough to understand.
Let's say you have a circuit w/ reliability p. This circuit must be truly reliable, so you grab 3 and make it a triply redundant circuit. Is the redundant version more reliable than the original? Well, it depends! Intrigued? If you fit the description above, please pick this book up and give it a whirl.
Still not convinced? One more: puzzle #5, The Curious Case of the Snow Birthdays, showed up as an interview question @ my current employer. If I hadn't read this book beforehand, I would've been stumped. So thank you, Professor Nahin, for the unexpected leg up!
Let's say you have a circuit w/ reliability p. This circuit must be truly reliable, so you grab 3 and make it a triply redundant circuit. Is the redundant version more reliable than the original? Well, it depends! Intrigued? If you fit the description above, please pick this book up and give it a whirl.
Still not convinced? One more: puzzle #5, The Curious Case of the Snow Birthdays, showed up as an interview question @ my current employer. If I hadn't read this book beforehand, I would've been stumped. So thank you, Professor Nahin, for the unexpected leg up!
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October 27, 2011No rating. This is, as billed, a book of puzzlers and problems. Unlike most amusement books, this one requires some higher level math - most probability theory or calculus. Still an interesting read. Written in a time when "source code" was not easily available, so it's printed in several pages in the book instead. I do not agree with others who way this is poorly written - there's no narrative, but it's a book of puzzles! Will read at least one more book by this author - An Imaginary Tale: The Story of "i" the square root of minus one
August 23, 2022
Despite the title, most of these problems are assignments rather than puzzles. Some are pretty hard slog, and some simply can't be done without a computer. If you make it to the end, you will have completed a freshman course on probability.
November 23, 2011
. . . but the stroke I had with the A.R.D.S. has seemed to eat-up my ability to follow these problems! Bummer!!!!!
March 22, 2015
Waste of time if you want to understand probabilities. Just puzzles.
Displaying 1 - 10 of 10 reviews