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Duelling Idiots and Other Probability Puzzlers (Princeton Puzzlers)

3.0 out of 5 stars 5 customer reviews
ISBN-13: 978-0691102863
ISBN-10: 0691102864
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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. --This text refers to an out of print or unavailable edition of this title.

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."--Mathematics 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."--Des Higham, MSOR Connections
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Product Details

  • Series: Princeton Puzzlers
  • Paperback: 296 pages
  • Publisher: Princeton University Press (July 1, 2002)
  • Language: English
  • ISBN-10: 0691102864
  • ISBN-13: 978-0691102863
  • Product Dimensions: 5.5 x 0.7 x 8.5 inches
  • Shipping Weight: 13.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #3,113,304 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: 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!
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By A Customer on October 26, 2000
Format: 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.
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Format: Paperback Verified Purchase
I bought the book after reading the kindle sample.

I find in the first section of the full version that this book might be useful "as a supplement as you take an elementary course in probability"... "If you don't know what that sentence said, this book may be just a bit too much for you, at least for now."

Ouch. I was looking for something a little simpler...

My suggestion: if you're a noob like me, stay away, even if you found the kindle sample interesting.

At least until you finish your elementary course in probability.
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By A Customer on October 28, 2001
Format: Hardcover
There is surely a need for a book like this but sadly this one doesn't do the
job. The author clearly has no idea what's really required. On p 20 he has
the results of five runs of 10,000 simulations to estimate the probability
P(A) of an event A. Now P(A) is known here, so these simulations are just an
ATTEMPT to verify that the program is working correctly. The author merely
notes that "the estimates for P(A) are a bit on the high side." No kidding!
All five runs produced consistently high estimates, and combining the runs
there's only one chance in 87 that the overall estimate would be so high
(ASSUMING the program were working properly). Of course, it's POSSIBLE that
the procedure is correct, that such high estimates just happened by a long
shot, but my email suggesting that the simulations be rerun drew no reponse.
Given this failure to demonstrate that a KNOWN probability can be estimated
properly, goodness only knows how good/bad UNknown probability estimates are.
Little wonder so many bombs are missing their targets in Afghanistan.
Turning to how the random numbers were generated I promptly noticed the table
of autocorrelations on p 184. These are not only bad, the zero-lag
correlation (a variable with itself) is 1.023!!! Given that it should be
nothing but EXACTLY 1 I initially thought this was a social comment on the
age of the generator, but machines were NEVER THAT bad. Rather, you'll find
the reason in the mishmash just above the table.
Indeed, in what little I read, statistical concepts are massacred. Further,
on p 27 there's an expression for pi which is actually mathematical nonsense
(ie, it is incorrect). At that stage I quit reading, it's so painful.
Nonetheless, I'll give the author two stars for TRYING to fill a void. He
just needs someone to correct everything, which is obviously no small task.
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Format: Hardcover Verified Purchase
The best puzzle books start with problems that are interesting and non trivial, and offer unexpected solutions. They appeal to a crowd with different levels of education and offer a new idea or two to all. They will lead an unsuspecting layman to a new beautiful mathematical subject, and treat a pro with a lighthearted yet technically sound look at the concepts he is already familiar with.

"Dueling idiots" is none of that. To read it you must be more than familiar with probability theory, and at ease with going through rather tedious calculations and using mathlab. Yet all a sophisticated reader finds here is technical sloppiness and absence of fresh ideas.

I am giving it two stars rather than one because it could provide some probability theory buff with a nice set of "real life" applications -- good as an auxiliary text book for an undergraduate probability class e.g. Apart from that, you will find a better puzzle book almost anywhere you look.
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