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Impossible?: Surprising Solutions to Counterintuitive Conundrums [Paperback]

Julian Havil
3.5 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

17 April 2011

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable--and all of it mathematically irrefutable.

Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly--why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion--how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible?

Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.


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Product details

  • Paperback: 264 pages
  • Publisher: Princeton University Press (17 April 2011)
  • Language: English
  • ISBN-10: 0691150028
  • ISBN-13: 978-0691150024
  • Product Dimensions: 1.6 x 15.4 x 23.5 cm
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 1,081,839 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

"Havil once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem . . . . Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment."--J.T. Noonan, Choice

"This sequel to the author's book Nonplussed! supplies another set of brain-stretching problems and ideas. Its subtitle is 'Surprising Solutions to Counterintuitive Conundrums'; the surprise often consisting of the fact that it is possible to obtain a solution at all! . . . This is another excellent book by Havil, following in the Martin Gardner tradition."--Alan Stevens, Mathematics Today

"Julian Havil has quietly joined the ranks of the very best writers of popular mathematics. His two volume set Impossible? and Nonplussed! Mathematical Proof of Implausible Ideas not only belong in every library, but in the hands of every young person interested in mathematics and especially in the hands of their teachers."--John J. Watkins, Mathematical Intelligencer

"Impossible? is an immensely thought-provoking book. Even if you skim or skip the more complex abstract math, you may have a hard time letting these puzzles go, so strongly do they flout common sense. You'll just have to do your best to put them our of your mind when you need to get some sleep, but if the situation ever arises, be sure to take Monty up on his offer."--Ray Bert, Civil Engineering

"I would highly recommend this book as a reference for the mathematician who likes recreational mathematics, or as a good read for the recreational enthusiast with a penchant for more rigor."--Blair Madore, MAA Reviews

From the Inside Flap

"Julian Havil's Impossible? is a superb discussion of problems easily understood by a high schooler, yet with solutions so counterintuitive as to seem impossible. Topics include the notorious Monty Hall three-door problem, the Gamow-Stern elevator paradoxes, the Kruskal count card trick, Cantor's 'paradise' of alephs, and the mind-blowing Banach-Tarski paradox, all analyzed in depth by a master who does not hold back equations that provide elegant proofs. There are surprises on almost every page."--Martin Gardner

"This book is a fascinating and thoroughly enjoyable read. Havil offers an engaging collection of counterintuitive results and seemingly impossible problems. Some of the material is truly astonishing, and the author conveys his sense of surprise very effectively. Each problem ultimately yields to careful and well-presented analysis. The history of many of the results is discussed, and further references are provided."--Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles

"I thought it impossible for Julian Havil to exceed Nonplussed!, his previous collection of perplexing math puzzlers. And yet he has done just that with the sequel Impossible?, an accomplishment that has left me nonplussed."--Paul J. Nahin, author of An Imaginary Tale

--This text refers to the Hardcover edition.

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Most Helpful Customer Reviews
14 of 14 people found the following review helpful
2.0 out of 5 stars Review of Impossible? By Julian Havil 18 July 2008
Format:Hardcover
This is not a book for the layman. I found this book heavy going and problems with lack of explanation in places.
However there are a number of gems which are definitely worth exploring. These are:
Simpson's Paradox. This is an example where (a/b) > (c/d) and (p/q) > (r/s) but
(a+p)/(b+q) maybe less than (c+r)/(d+s).
Connection between the continued fraction of 1/e and the optimal number of r out of n.
Why the infinite sum 1/n is called the harmonic series.
Why order is lost in complex numbers.
Moreover there are some fantastic quotes by various mathematicians such as the following by De Morgan:
The ratio of log of -1 to square root of -1 is the same as circumference to diameter of a circle.
This book must be read in conjunction with the author's other title `Nonplussed!' because he refers to it in a number of places. I have not read `Nonplussed!' but I do think a book like this should be totally independent of any other text.
A major problem with the book is progression is too fast. It is difficult to digest an idea and the author has moved on to higher dimension. A good example of this is the `Monty Hall' problem. The author describes the Monty Hall problem and within a couple of pages he has moved onto various extensions and generalisations of the problem. It would have been better to progress at a slower rate so that the reader understands the initial problem and then is able to follow the extensions on this problem.
In general I found myself taking a lot of time to get through it, because I had to keep going back and looking at things again and again in a bid to understand.
There are a number of typos in particular the brief appendix at the end seems to be full of them. The infinite series for sin and cosine is wrong. It should have alternating signs. There is no fig 4 which relates to subintervals. The proof of log(2) is irrational is incorrect.
This sort of text should have a lot more diagrams.
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1 of 2 people found the following review helpful
5.0 out of 5 stars Another gem 9 Mar 2009
Format:Hardcover
Julian Havil has produced yet another gem that should find a place in the collection of any fan of recreational mathematics. He again demonstrates that it's possible to make mathematics accessible, fun, fascinating and intriguing - with the equations, not in spite of them! I defy anyone to read this book and not be surprised at least once. From the extraordinary logic problems in the first chapter to the exotic theorems in the last this book continues the theme of his previous book, Nonplussed: Mathematical Proof of Implausible Ideas, that the world is often weirder than common sense might first make you think. Beware: this book is densely packed with ideas that will make you want to explore more. Good.
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Amazon.com: 3.5 out of 5 stars  6 reviews
39 of 45 people found the following review helpful
4.0 out of 5 stars you may be a little too surprised by these surprises to be surprised 21 Oct 2008
By James H. Waters - Published on Amazon.com
Format:Hardcover|Verified Purchase
i warn the potential purchaser that this may not be quite what you expect. There is a demand for substantial mathematical sophistication - which was a little beyond my level (i do have a doctorate, but not in math, and had to stop taking math courses after my sophomore year in college because matrix algebra was about all i could handle). i don't doubt that the book is delightful for those strong in math and i probably would give it 5 stars except that the title strikes me as a bit misleading. probably your average college graduate would not know enough to find these conundrums counterintuitive, and the solutions, likewise, are probably not much more surprising than that the conundrums are supposedly common-sensical. not a criticism of the material, more of the packaging.

james h waters phd
8 of 8 people found the following review helpful
3.0 out of 5 stars Intriguing Topics, Careless Editing 30 May 2011
By Henry S. Valk - Published on Amazon.com
Format:Paperback|Verified Purchase
As expected from this author, the topics are well chosen and the counter-intuitive results intriguing.
However,contrary to my experience with Havil's earlier books, "Impossible" seems to reflect hasty preparation and/or careless editing, hence the lower rating. An earlier review referred to the error in the proof of the irrationality of log2. To this can be added a number of others. For example: wrong signs in the Taylor expansions of sinx and cosx (p.226);numerous P(n-k,k)instead of P(n-k-1)in the coin toss discussion (p.97); log n - 2/3 instead of log n -3/2 (p.101);over-counting by a factor 3! in the mathematical expression for the number of ways of picking one pair(not two pairs as stated)in a poker hand, and the omission of -40 and -1098240 in the last line of the odd card discussion (p.106). While It should be emphasized that this is not a book for the casual reader,even the reader with some measure of mathematical sophistication will be frustrated by such errors and misprints;certainly, an unnecessary impediment to what could be a enjoyable journey for one seriously interested in mathematical conundrums.
12 of 16 people found the following review helpful
4.0 out of 5 stars I liked what I saw so far. 30 Sep 2009
By Peter Gacs - Published on Amazon.com
Format:Hardcover
I am a mathematician, so my opinion is probably biased. This is the kind
of popular book on mathematics that would have appealed to me in my young age
and seems still very enjoyable and instructive (I have only skimmed it so far).
The main reason for my review is that, the book not giving an email address for the
author, this place seemed the easiest one to point out a computation error
that invalidates the proof of irrationality of log 2 in the appendix.
The correct computation will lead to a correct proof, but a different one, which
as expected, must use the uniqueness of prime factorization.
1 of 1 people found the following review helpful
3.0 out of 5 stars Thought-provoking, with some flaws 11 Nov 2012
By Jay P - Published on Amazon.com
Format:Paperback
This is an interesting and thought-provoking book that presents a series of mathematical problems and puzzles, the answers to which are often surprising. It is a book from which most people (who read it thoroughly) would learn about some interesting areas of mathematics, and discover new ways to look at some perhaps already-familiar topics.

Understanding much of what the author is saying requires some background in math, but definitely not a degree in the subject. An introductory course in calculus would be helpful, because the book does use lots of simple calculus, and some familiarity with basic probability ideas would also be good to have. (I should admit, however, that I didn't fully understand either of the last two short chapters, so there are some areas that are more advanced.) Someone with less of a math background would still be able to understand some of the problems, at least partly (for instance, anyone who has played poker would be able to understand the gist of what he shows about the effect of wild cards) and get something out of the book, but would have a hard time following many of the series of equations - which are used to demonstrate what the author is saying and which help to explain the reason behind a surprising result.

There are, unfortunately, a number of errors in some of the mathematical expressions and equations, which made the book more difficult and frustrating to read: sometimes, I thought I was misunderstanding something, when the problem was that the algebra was wrong. There are also some places where the author's explanation is too short, isn't clear, or where an equation doesn't reflect what is said in the text. This seems like it would be more confusing to a reader with a less-advanced background.

Despite these reservations, I still found the book to be worth reading. Mostly, it isn't fast or easy reading, but it's a book that taught me a few things, often stimulated my thinking, and I still find myself pondering the implications of some of the chapters.
2.0 out of 5 stars Errors 29 Jan 2014
By mbl - Published on Amazon.com
Format:Kindle Edition
There are errors everywhere and many things are obscure. You simply can't read this book all the way through. You can pick some pieces here and there though.
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