Reviews (26)

IQ: Intelligence Quotient or Interview Questions?
William Poundstone's previous books on logic, philosophy and science have long been favorites of mine, so a book on, ostensibly, interviewing at Microsoft sounded intriguing.

Actually, the book's cover is somewhat misleading -- Microsoft reportedly doesn't use puzzle questions (much) anymore, and Poundstone spends almost as much time recounting the history of IQ testing, the psychology of puzzles, and pondering the changes in modern industrial workers -- so this book actually fits right in with Poundstone's other works.

Do puzzles really measure intelligence?Nope, high aptitude at puzzle solving measures only one thing -- the ability to solve puzzles -- as Poundstone points out while discussing the curious membership of Mensa.And most observers today agree that no single parameter can define intelligence, which is a many-faceted and only-dimly-understood concept anyway.

Perhaps most revealingly, Poundstone recounts studies which show that an interviewer usually makes up his mind about a candidate within the first few seconds of meeting her, and the rest of the interview is merely an exercise in confirming first impressions.

So much for careful testing, eh?

Depends on what you're looking for...
I bought and read this book thinking it was focused on solving puzzles.Looking back it was probably my mistake.This book focuses mainly on the recent history of puzzles, and to an extent the merit of IQ tests.Focusing mainly on Microsoft, the book goes through their previous hiring rituals.There are few puzzles directly talked about in the book, most of which puzzle buffs will likely have come across in some form or another.Like I said, it's not a bad book, I finished in about 2 days, but don't expect too much material directly related to puzzle solving.

Reviews (7)

Wonderful text on creative process
Very enjoyable read and useful information for companies and people engaged in creative activities.Presents interesting research and great content regarding innovation.Perkins' style is well-suited to general audiences and he provides good references for more technically demanding readers.I highly recommend this book.

Easy to understand, harder to apply
Problem solving, according to Perkins, is a little like looking for gold. From there we draw analogies about the landscape and the different stages of problem solving itself: false hits, stuck in canyons, etc.
There's no denying that such a description fits and anyone reading this book is going to recognise the very same limitations in there own thinking. The problem, however, is in the application. Though Perkins enjoys telling a few anecdotes where he coaches the person to a successful solution by highligting which of the thinking modes they're 'stuck in', in real life (and without knowing the final solution) it becomes something of a problem to apply.
It's an enjoyable read but it kind of makes me wonder whether this book will lead to many 'euraka' moments.

Running through the streets naked...
I have read many books on problem solving and breakthrough thinking. This is by far the most accessible. David Perkins is co-director of "Project Zero", an educational research group at Harvard Graduate School. He has a PhD in mathematics and artificial intelligence from MIT, so he is very qualified to be writing on this subject.

Perkins covers a lot of ground in this book and manages to explain his theory of problem solving from many different aspects using varied problems and examples.

The title refers to Archimedes and his breakthrough discovery of the displacement of water to calculate volume. This is the first example, which is drawn from this near mythological event. Perkins continues to delve deeper into how breakthroughs in thinking occur.

He outlines a series of steps that he believes are key to breakthrough thinking. These are abstracted from many different examples of breakthrough thinking. (Long Search, Little Apparent Progress, Precipitating Event, Cognitive Snap, Transformation).

From certain aspects this is the easy part, defining a set of steps that seem to be common in breakthroughs. The interesting part for a reader will be, can Perkins describe a series of steps that can define how the mind can actually achieve breakthroughs? Defining the steps always seems reminiscent of seeing the instructions for tying a bow tie, steps 1 to 4 seem reasonable, and then suddenly in step 5 you have a tied bow tie. But how do you get from step 4 to step 5 is always left a mystery that needs to be worked out. Obviously with a little fiddling, and knowing the end result, tying a bow tie, is a breakthrough that most people can achieve. But how to get from precipitating event to cognitive snap (or Eureka) is a little trickier to define. Is there really a series of steps to achieve breakthroughs?

Perkins spends the rest of the book, delving deeper and exploring this subject. He tackles some of the common pitfalls of thinking that can hamper someone's ability to solve a problem. Breakthrough problems by their very nature need to breakthrough current assumptions and thought patterns. Perkins uses the analogy of the Klondike gold rush to explore the principles further. How do you find a small amount of gold in a large area? Perkins feels this is analogous to finding solutions to breakthrough problems. He describes some common pitfalls, using this analogy (Wilderness of Possibilities, Clueless Plateau, Narrow canyon of exploration, Oasis of False Hope).

Perkins uses many puzzle examples throughout the book. Some of the puzzles are old, but still useful to explore. He defines the different kinds of puzzles, the ones that can be solved by a linear progression of thought, and then the second kind that needs a breakthrough in thinking (not always on a large scale), this is where linear logical progression will not reveal the answer. He uses the pitfalls as defined and shows how each of them can side track the puzzler from finding the solution.

At first, the nature of the Klondike analogy, seems to be too contrived and can be off-putting. But Perkins manages to demonstrate the different aspects of breakthrough thinking using it. The book is filled with puzzles that will be fun for anyone who loves puzzles. Perkins explores many aspects of thinking, delving into artificial intelligence and evolution. Sometimes I felt that some of the chapters were probably irrelevant, but on the whole, this book is very cohesive and manages to follow through a logical progression through the many facets of breakthrough thinking. It is very accessible, and its simple nature, could be mistaken for lack of substance. But there is a lot of information, and the reader will learn many techniques and can actually put together a set of steps to "help" them solve problems. Obviously it is not going to give a step-by-step manual to come up with the next "Theory of Evolution" but there is a lot of information here that can be used practically to help solve puzzles, and help solve real world problems.Perkins never succumbs to boasting that this is an exhaustive set of principles to achieve breakthroughs in thinking.

This is a very rewarding book, but if you are looking for a "how to" guide, you will not find it here. But you can extract many helpful insights from this book that will help you solve problems.

I highly recommend this book for anyone interested on breakthrough thinking.

Note: This is published in paperback under a different title "The Eureka Effect"

Reviews (15)

Informative and Lacks Inspiration
This is not a how-to-book.The Root-Bernsteins present thirteen characteristics of what they view as genius.With each chapter they list examples from art, literature, and a variety of other disciplines.I have never encountered references to Sir Arthur Conan Doyle and Bruno Schulz within two pages of each other.The book lacks enthusiasm.Someone like Desmond Morris or Steven Pinker could of made this material really compelling.Still this book is more insightful than one that encourages someone to visualize certain object to make you an Einstein.

Comprehensive and insightful
Sparks of Genius is an excellent analysis of the variety of different types of "tools" or techniques that innovators and creators use.I agree with many of the other reviewers that the authors provide copious examples.For some, this was overdoing it, but for myself, the examples were well selected and properly used to illustrate the tools at issue.I never felt bored or annoyed by them.

Unlike some reviewers, I felt that the authors did provide a solid theoretical or conceptual framework, and not merely a laundry list of examples.Indeed, I was particularly impressed by their identification and explanation of the reasons behind the deep linkages between artistic and scientific endeavors, and by the interesting explorations of the interplay of artistic and scientific discovery in many noted thinkers.Science education in general would be much more interesting to theaverage student if standard textbooks fleshed out the often artistic interests of the great scientists as well as the Root-Bernsteins.

I would take the Root-Bernsteins to task however, for the rather prosaic presentation of their material. In particular, its a shame for them to so heavily emaphasize visualization and multimodal representation, and to cite the work of Edward Tufte, and then present such a conventionally design book of text and relatively limited and often poorly placed figures, oddly located "appendices" etc.The illustrations, layouot, typesetting, and overall design should have itself been reflective of their subject matter. Perhaps a second edition would rectify this oversight.

Finally, I note that they could have better "rationalized" or categorized the various "tools" they identify, and thereby perhaps shortened the book.For example, Body Thinking is really just another type of Imagining, that is imaging with the body.These captures could have been combined.

Overall, an excellent, enjoyable read.Most non-fiction works like this take me weeks to read.This one I literally could not put down.Recommended.

weak
Skip this book in favor of spending time inventing YOUR OWN genius.If you think this is a manual for becoming smart, forget it.The gifts are doled out at birth and the best we can hope to do is make the most of what we have.

Reviews (5)

Great book presenting a theory of learnable intelligence
What is the nature of intelligence? How and to what extent can intelligence be developed? What aspects of intelligence can de identified and what aspects especially demand attention? While the classic view of intelligence implies that intelligence is a fixed, genetically determined characteristic of individuals this book presents a different perspective: a theory of learnable intelligence clarifying to what extent and how our intelligence can be amplified. Three dimensions of intelligence are identified: 1) neural intelligence: neurological speed and precision; in large part genetically determined, 2) experiential intelligence: extensive common knowledge and skill and specialized knowledge and skill; learned, 3) reflective intelligence: strategies for memory, problem solving, mental self-monitoring, meta-cognition; learned. Perkins argues that reflective intelligence offers the best opportunity for improving intelligent thought and behavior. Perkins identifies important pitfalls in human thinking and reasoning and shows how to avoid them. The author acknowledges that intellectual talent is a real phenomenon and does not deny any intellectual differences in intellectual talent. He argues that most people can learn to use whatever intellectual talents they have much better than they normally do. This book, which reminds of the work of Robert Sternberg, is a true must for anyone interested in theories of intelligence.

Smart Start
I own this book and it's a smart start to learning about intelligence.P.S. The boy from the Phillipines has a good assessment of this book.As to the reviewer who said he needed to go to college before he spoke or wrote--well at least HE can spell and type!

too much too much
regalman@usa.net

The author spends way to much time on error, sometimes his own. His facts are wrong about Copernicus -Copernicus was not an astronomer-he was a mathematician. See the web page - university of florida - history of science. I am afraid if he can't a simple fact right about Copernicus, where else is he wrong. He studied astronomy, but was a mathematician. Ptolemy used mathematics (equants) to prove his theory not idealism.He did not just a patch a leak. Talk about intelligence, the author should stick to terms and definitions and stay away from poetry like-patch a leak. That doesn't sound to scientific to me. Before he talks about science, he ought to study history of philosophy. This author must have relied on unreliable sources, he certainly didn't look up information himself. He ought to have given up in the chapteron telescopes and intelligence. Ohhh, boy...

Reviews (16)

Teacher & Engineer
It is one of my frist book on structuring analysis. I would hightly recomend you to buy this book as the price is not as hihg as its value.

Thinking Skills

Highly recommended reading to develop thinking skills beyond average.

Interfaculty and interdisciplinary approach to problem solving.

A must read for students and those who left out the first chance to read this magnificent book.

Good reference for problem analysis - Bush should read this
I found this book whilst searching for a framework for basic problem solving. This book provides 14 good techniques, the most important I believe are Causal Flow Diagram, Hypothesis Testing and Utility Matrix.

Actually I was triggered to buy this book is because the author was an ex-CIA. I guess when he left, he brought all his techniques with him in his head!

I wish the Bush Administration and Tony Blair should refer to this book (especially the Hypothesis Testing) when they have "irrefutable evidence" that Saddam Hussein has WMD in his cellar.

Reviews (8)

Excellent
This book is an excellent collection of creative-thinking techniques that will make you more creative in your business and personal lives. This ranks close to the classic book on creative-thinking "Thinkertoys" by Michael Michalko.

Original and good
This book is both original and good. The part that is good is not original and the part that is original is not good.

Innovative Tools for Practical Problem Solving
James M. Higgins' packs every one of his 220 pages with solid content. He collected problem-solving techniques from organizations and individuals from all types of business and several countries. He wrote them up, summarized them, and presented them to us in easy-to-read, digestible, format. Most important, he explains them so that they can be taken and used.

Higgins spends two short chapters discussing problem solving and innovation, then he gets down to the techniques. He has techniques for recognizing and identifying problems, analyzing the environment, brainstorming problem-solving ideas, and choosing solutions. One of my favorite facts about this book is that he has 38 techniques for individuals to brainstorm ideas, yet also has another 32 group brainstorming techniques. He really includes something for everyone in this smorgasbord.

I have adapted and used a number of these successfully: the Lotus Blossom and Two Words Techniques have been excellent brainstorming processes for me. I have shown a large number of people the Why-why diagram for uncovering the root causes of problems. I have shared my copy of this book with five or six people, each of whom went out and bought their own copy.

Reviews (26)

Somewhat useful, but mostly obvious, arbitrary and ...
...not terribly well written.

I think the method is overblown. It can be useful in a group setup since it delineates and formalizes the roles and different aspects of mental attack, so to say. However, all of them are rather obvious and you'd do precisely this thing on your own even if you didn't know about "the six thinking hats" trick or didn't think of the process this way. And why six? I think, one could express the same idea with ten (or three). It is somewhat arbitrary I think. Also, the transition, borders so to say, between different mental postures is blurred and, again, somewhat arbitrary, I think. Anyway, no harm in skimming this book when you got nothing else to do, just don't expect any breakthroughs coming out if it.

Simple, interesting, easy to remember and helpful
Though I despise the author's self boasting and over exaggeration of the impact and influence which he wrote in the preface that "The Six Hats method may well be the most important change in human thinking for the past twenty-three hundred years" and "the introduction of it increased thinking productivity by 493 percent in a simple experiment with three hundred senior public servants", I am obliged to describe it simple, interesting, easy to remember and helpful.

In short, the six hats refer to six different perspectives(white-facts, red-emotions, yellow-positive views, black-negative views, green-creative/alternatives, blue-organizing/goals). The author suggests that by putting one hat/perspective at a time, thinking and thus problem solving will be much enhanced, both on an individual and on a group discussion setting when all participants are required to put on the same color of hats together sequentially.

Of course the reality is more complicated and difficult than what the author paints as office politics always come into play. Nevertheless, this book reminds me of "Who Moved My Cheese? An Amazing Way to Deal with Change in Your Work and in Your Life by Spencer Johnson and Kenneth H. Blanchard" in that readers can easily recall the concept well. Anyway, it's an outstanding book not to be missed.

Reviews (11)

Not quite a breakthrough
It's fair to say that the breakthrough touted by the authors occured quite some time back - I don't think that any of the 7 principles suggested could be said to be new or even that they are brought together in a new framework.
Regardless, if you haven't used these principles before then it is likely to be something of a breakthrough. The authors present a remarkably well planned overview of the steps needed to come to creative solutions to problems.
Many readers are likely to find hints of De Bono, Senge and even some NLP in the reading. That shouldn't detract from the book though - it brings some rather disparate structures together to achieve an extremely beneficial approach to thinking and problem solving.
4 stars because it could have been edited down by 50 pages without detracting from the message.

Many thanks to Professors Nadler and Hibino
This is an excellent book. It is well written. The authors have excellent credentials and convincingly outline the seven principles of creative problem solving in the most lucid terms.

Readers will find that many of the individual ideas, concepts, considerations and perspectives are familiar. However, as Proust stated, the real voyage of discovery consists not in seeking new landscapes, but in having new eyes. Professors Nadler and Hibino show that you, and any group that you are part of, can significantly increase your chances of achieving breakthroughs if you adopt a certain approach to solving problems and making decisions. It is a purpose-directed approach. The focus is on the solution, not the problem.

They proceed to outline this approach in some detail. It includes a holistic set of steps to guide your use of the seven principles. They also describe a number of optional tools. When adapted to your own style and circumstances, and used in context, these tools really do maximise your chances of achieving breakthroughs e.g.

· `Exploration and expansion of purposes' enables you to creatively find the right problem to work on

· `Solution after next' helps to unfetter the team's creativity, to rise above current limitations, wrong assumptions and misconceptions - whether conscious or subconscious - and to ensure that today's solution is future-oriented and innovative

· `System matrix' facilitates a comprehensive consideration of all aspects of a solution thus maximising the chances of successful implementation

The thinking skills outlined in this book and ensuing practice can serve you well for the rest of your life. These skills are so fundamental, they can be beneficially applied in countless ways and in countless situations - both business and personal.

I first read this book six months ago and have no hesitation in recommending it.

Reviews (20)

A delightful and satisfying classic
Are you like a dog with a bone when you're working on a brain teaser? After pages of scribbles, do you get a big grin on your face when you turn to the answers and say: "I'm right!" Then this book is for you.

And if you're not yet a die-hard problem-solver? You should step right up, too. You may get hooked.

G. Polya's book is based on the fact that, if we study how someone does something successfully, we can learn to do it successfully as well. How To Solve It is an application of 'heuristics' to solving problems.

There are certain mental operations useful in solving problems, any sorts of problems. Polya (who was an eminent mathematician and former Professor of Mathematics at Stanford University) describes and illustrates the most usual and useful of these operations, in a way that is irresistible and eye-opening.

These useful mental operations are organized according to when they come into play during the four steps to solving a problem. 1. You have to understand the problem. (Not as easy as it sounds.) 2. Find the connection between the data given and the unknown. Conceive the idea of a plan for the solution. 3. Carry out the plan. 4. Examine the solution obtained.

If you take some time and try to solve the problems selected to illustrate each mental operation, you will be well-rewarded. You will likely discover something surprising about your own problem-solving methods, and improve them in the process. You will definitely discover many new ideas and techniques to add to your arsenal.

For example, a first impulse when confronted with a problem is often to try to 'swallow it whole' -- to try to meet all of the conditions of the problem at once. G. Polya suggests keeping only part of the condition, and dropping the other part. This can lead you straight to a solution you might otherwise have completely missed.

His techniques help you to stand back and get to the heart of the problem, rather than getting lost in it.

Something else I liked very much about his book is his encouragement to guess, or to reason 'plausibly.' While the final proof must be strictly logical, "Anything is right that leads to the right idea." Problem-solving has every right to be fun, as well as purposeful.

Buy it!
The issue is that solving problems is not made interesting and fulfilling experience.

This book beautifully explains the process of problem-solving. It starts from simple problems, lays down the fundamentals and leads to more complex problems.

One of the gems is the simple formula:
1. Understand the problem
2. Devise a plan (seeing how various items connect
3. Carry out the plan
4. Look back at the completed solution, review and discuss it.

It is also a good reference to teach kids how to approach problems.

Buy it and it will be a very handy reference.

Very helpful to my programming work
Polya prescribes different forms to approaching a problem through some guide questions that a solver should ask ("Is there a related problem"). The exposition is quite short, majority of the book is devoted to a glossary of heuristic terms which prove very helpful. Polya uses common problems in high school geometry to demonstrate his point which make it easily understandable.

Reviews (14)

Essential for budding (and experienced) problem-solvers
I join the ranks of previous reviewers here who honestly feel that having read this book in high school would have almost certainly changed my life.I, too, did very well in high school math competitions, but the maturity I am gleaning from this gem may have vaulted me into a different league.

It contains hundreds of problems from various levels of competition, from AIME problems all the way through some of the toughest Putnam problems (which, if you know anything about the Putnam, are about as hard as competition problems come).But the biggest help are the vital insights and exciting ways of looking at these problems.Don't take my word for it--many past IMO contestants have suggested this book too.

Particularly helpful is the way the author divides the book into sections based on often-used concepts and techniques.For example, you will see applications of the pigeonhole principle from the most basic (e.g. "In a drawer with socks of 2 colors, show that after picking any 3 socks, we must have a pair of same-colored socks.") through some rather difficult ones (1994 Putnam A4, an Erdos problem, and more).

The same goes for a multitude of others--the invariants section includes both the classic chocolate bar-cutting problem and Conway's rather difficult checker problem.Then, not only does he solve the latter beautifully, but incorporates nontrivial questions that ensure the reader has completely understood the solution (e.g., "Could we have replaced lambda with an arbitrary integer?Why not?").

You don't have to be a math competition buff to gain from this book, however.If you're simply interested in mathematical puzzles and problems, and are looking to expand your repertoire, this book will help you.Anyone with a good dose of intelligence and motivation will benefit.

For an additional problem book, check out Mathematical Olympiad Challenges by Andreescu and Gelca.For purely Putnam treatment, there are several volumes written by Kedlaya.And if you're a CS student, looking for honing those CS math skills to be razor sharp, you should definitely look into Concrete Mathematics by Graham, Knuth, and Patashnik.

Happy solving.

The Book I wish I had in High School
When I was in high school, I placed second in the Alabama State Mathematics Contest and won many others. However, I might could have been competitive with the IMO style problems had I had this book and would be much better off today had I seen this book earlier.

This book is for the exceptionally brilliant and the mentally tough.It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run.

For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key.

If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented.

PATIENCE PATIENCE PATIENCE!

Brilliant
As a high school student that is essentially bored with the regular, ho-hum classes that my school offers, this book is perfect.It gives a problem-solving foundation for math enthusiasts desiring to compete nationally in contests like the AMC, AIME, and USAMO.The problems are excellent and cover a wide range of difficulty (past ASHMEs, USAMOs, and, finally, IMOs); and the solutions are well-written, logical, and intelligible.In short, if you are looking to "get better" at problem solving, this is the book for you.

Reviews (2)

Interesting puzzles, but who's Dr. Ecco?
Presumably, this collection of mathematical puzzles is for fans of one Dr. Ecco whose life is full of adventures.For people not familiar with the character, the book appears very dull and the characters contrived, uninteresting, and, well, kind of lame.The narration is a little over the top, but all in all, the book is not terribly written.

The puzzles on the other hand are pretty interesting.Ranging from solving codes through organizing buildings in space to transporting monkeys, the puzzles are a nice way of teaching mathematical concepts.As the descriptions of the puzzles and Dr. Ecco's solutions thereof progress, the reader is asked to participate on different levels in solving of the puzzles.Cybernovices and cyberexperts can learn about math in a fun way.

I recommend this book for those interested in solving puzzles of any kind who are not detered by corny storylines.If you are not sure whether you'd like this book, I recommend you flip through it at a book store to make sure.

Ecco strikes again
As a fan of Ecco's Puzzling Adventures, I was eager to take a look at his cyberpuzzles.Ecco and his protege Shasha have done it again, and I recommend this book to anyone looking for interesting, challenging, thoughtful problems.

The book is a fun and intersting read on its own, but I have also drawn on the book's puzzles in teaching (a course on logic and discrete math).

Reviews (5)

fun with puzzles
I bought The Puzzling Adventures of Dr. Ecco just before going on vacation, and was hooked before the plane took off.It is the perfect book for puzzle-lovers, including a broad range of topics across many levels of difficulty.My husband and I sat long after our lunches had been cleared on several occasions, working them out together.The author's humor and imagination in creating his characters adds to the delight of having one's brain teased (and then satisfied -- the solutions are in the back).Buy this book!

Dr. Ecco --- A Mathematical Version of Sherlock Holmes
When this book first came out from W. H. Freeman, I could not contain my excitement. I had been trying to intoduce a course in matheamtics that would have a broad appeal. With a very few exceptions, university students take mathematics courses because they are told to do so, and will leave the subject behind as soon as the minimum requirement is meet. I wanted students to have a chance to explore mathematics, but was hard pressed to put together a functional package.

"The Puzzling Adventure of Dr. Ecco" was an answer to my prayers. Discrete mathematics is an ideal introductio to the borader realm of the whole subject since it requires very little technical background, and there is the additional attraction in being related to computing science. However, there was considerable opposition to the introduction of such a course, and it was not until five years later that it became a pilot project. Dennis' credibility as a serious researcher helped tremendously in the final push.

Once the course got going, there was no stoppig it.Enrollment went up from 24 in the initial year to over 150 at present, while the course is still the only one not required by any program. It draws students from diverse background, from the Faculties of Science, Education, Arts, Business, Engineering and Pharmocology.

Much of the success of the course is due to the top quality of the book. The problems are well chosen, with a variety of topics as well as levels of difficulty. However, it is how each problem is treated that brings out how much thought has gone into the writing.

I will give one example, the problem of transporting oil from Houston to Moscow. The theoretical foundation is the Maxi-Flow Mini-Cut Theorem, which provides an algorithm to compute the maximal flow. Usuaully, students ignore the minimum cut altogether because the theorem guarantees that the flow they find will be maximal. Here, Dr. Ecco is asked where additional planes should be added. If none is added to the routes that constitute the minimal cut, they will be wasted. Thus the companion idea of the minimal cut is clearly brought back to center stage.

The book is written with a great sense of humour, with much commentary on comtemporary society. It has been said that from the many volumes of detective fictions Agatha Christie had written, future social scientists could find invaluable data. This book reflects the thinking of one segment of the intelligentia at the time.

As a final note, the University of Alberta has published a companion volume titled "Professor Scarlet's Notebook", which serves as a background textbook but specifically tailored for use with Dr. Ecco. It is available for US$10 from:

Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G2G1, Canada.

Andy Liu,1998 Canadian UniversityProfessor of the Year, and3M Teaching Fellow.

unique puzzle book with computer-science-inspired problems
What I really like about this book is its unique focus; Shasha has written problems that illustrate concepts from math and computer science,without requiring any prior background.

It's written in an entertaining style, the problems can be understood and enjoyably worked on by everyone from bright middle school students to graduate students -- and even if you have a lot of other puzzle books, many of these problems will be new to you.

My only complaint is that there aren't more puzzles here! The Dr. Ecco story-line is nicely written, and the puzzles are presented cleverly, but all that creative writing takes up a lot of space. Still, this is a small issue, I enjoyed reading the book, I loved the puzzles, and they are very easy to share with friends and students.

Reviews (3)

Riddled with errors, but ---
I have never seen so many typos, omissions, and errors in a published book.Many of the examples are poorly introduced, theorems are mentioned that don't exist in the book, etc.Other than Rubik's cube, most of the other puzzles are presented in a completely incomprehensible manner.It's very annoying, in a book that's otherwise just what I want.It does give a good quick and dirty intro to the group theory needed, however.

In depth group theory via games and puzzles
I am old enough to remember the original appearance of the Rubik's cube puzzle. I examined it a few times while in a store, but never put any effort into it. Later, I looked at some of the literature that explained how "easy" it was to solve the puzzle. The solution involves the use of some advanced topics in group theory, so it is a puzzle with a mathematical twist. However, that is not the only application of group theory, there are many ways in which it can be used. Joyner shows us many of them, and provides the foundation before he tackles the problems.
This is an excellent book that can be used to either refresh your understanding of group theory or teach it to advanced undergraduates. The objects being manipulated are easy to understand, sometimes easy to build or acquire and the explanations are easy to follow. They are also different from those found in the standard group theory text. Puzzles are an area that fascinates many people, so it is often an advantage to present mathematical instruction in the form of a puzzle rather than in the standard sequence of background notation, theorem and then proof.
Finally, the author is to be commended for donating all of the profits from the book to the Earth Island Institute. It is a non-profit organization dedicated to environmental projects throughout the world. Therefore, not only can a purchase of this book do your mathematical skills some good, it can also improve the quality of life for everyone on the planet.

Published in the recreational mathematics newsletter, reprinted with permission.

For the love of Puzzles...
I just got this book yesterday and I have not read it fully, but I had to write a quick review to say how excited I am about this book. The Rubik's Cube craze hit when I was young. I loved solving the cube and have loved puzzles ever since. I did start trying to describe a solution mathematically when I was at college, but got side tracked and bogged down in some of the math. So this book was a great find for me. I am going to enjoy reading this book and following the mathematical proof. Even though there does seem to be a lot of equations and for the casual reader this might put them off, but from my first browse of the book the math isn't too complex and should be something that anyone who has taken some introductory math courses at the college level should be able to follow.

Reviews (8)

A book about the unexpected and the beautiful in math.
Yes, as several reviewers pointed out, the title is a bit misleading.But in my opinion it shortchanges the book!This is a book about unexpected and beautiful mathematical realities, and can be read (almost) like a novel.One pauses, of course to think, but without any pain.The clarity of the presentation makes the contents accessible to anyone.The footnoting and bibliographical information make further research easy.The illustrations are exact and plentiful.It's even beautifully laid out and printed, (I refer to the hardcover edition).An absolute classic.Give a copy to a bright young mind to counteract the horrible effects of the average math "education" prevalent in our public and private schools.If you own 100 books on math, this could still easily become your favorite.

Interesting Read
I have never read any books on "recreational mathematics" so didn't know quite what to expect from this book--in general I found it entertaining and interesting, with a broad range of topics, including physics, statistics, logical paradoxes, higher dimensions, etc.You don't really have to be a math person to enjoy this book; almost anyone interested in stimulating topics should find at least parts of it interesting.

The book consists of numerous short articles with bibliographies for each.If one article bores you, move on to the next...I found the articles on statistics, logical paradoxes, a 2D Universe (Planiverse) and others very interesting and enjoyable.It is important to understand that this book is not a puzzle book per se; although almost every articles includes some task for hard-core readers to perform ("Prove that...", or "How many..."), it is really intended as reading material.

A few negatives:the articles almost all seem to have been written in the 1950s or 1960s (!); each article has an addendum which attempts to bring it up to date.Although this didn't matter that much to me, since I have never read anything on recreational mathematics, I doubt that much of the material would be new for anyone that reads the topic regularly.Similarly, it would have been more interesting to discover what topics are currently "hot" in this field.Also, the author spends too much time for my taste on trivial mathematical games such as folding paper into different shapes rather than on really thought-provoking mathematical topics (purely a personal preference, I suppose).

The imporatance of Mathematics
Martin Gardner is the grand old man of popular mathematics.He especially likes the math behind puzzles, riddles and logical conundrums.Logic and mathematics is the source of his thinking on the Skepticism he professes in his writings on pseudoscience, religion, the paranormal, UFO's, and other outlands of science and rational thinking.

This book is a collection of his best columns from Scientific American magazine.It was of the good reasons to read the magazine.Like many other things in the last few years, that publication jumped the shark at some point.Gardner was one of the reasons to still read it for a while there.

Gardner, however, is not just interested in the mathematics.The men, and history of the questions is also important to him.That is because it forms a context to the questions and the discovery of the answers.Context is very important to the author.Without it, you really don't know where you are.

If you like the writing of such good folks like Douglas Hofstadter, Jeremy Bernstein, Eli Maor, John Allen Paulos, Richard Feynman, Stephen Jay Gould, Isaac Asimov, Carl Sagan, Arthur C. Clarke or Ed Regis, than you will probably like the writing of Gardner.

Mathematics is something that people don't read a lot. At least not recreationally. Normally because they don't understand that it forms the basis of real logical thought.A real understanding of the modern world requires one of the understand science.And science that isn't, at least in part, based on mathematics isn't real science.It is something more of our leaders should take a real interest in.How can we expect our leaders to make good decisions on cloning or when-life-begins if they have no real understanding of science and mathematics?

Reviews (3)

the editorial review math is exactly correct!
Ok, since there is some confusion on the issue, let me explain how the 2/3 comes about.We are looking for the probability that the second marble is white, given that the first one pulled out of the bag was.

First intuitively - if you think about it, if there had been 2 white marbles in the bag to start with you're more likely to have pulled out a white marble on the first draw than you would have if the bag started with one white and one black.That is, knowing that you pulled out a white marble, it's more likely that both marbles were white than it is that there was one of each.

Now mathematically - this is called conditional probability. Because of the problem description, before drawing the bag could either contain one of each color or two white marbles, each of these options with probability .5 (50%).If the bag has one of each, your probability of drawing white first is .5, and if it has two whites your probability of drawing white first is 1 (100%).

So, the (compound) probability that the bag has one of each *and* you get white first is .5 x .5 = .25 and the probability that the bag has both white and you get white first is .5 x 1 = .5.So, the total probability of getting white first is the sum of the probabilities of these two possible ways of that occuring, .75.

Now, the actual probability that was requested was that of there being a white marble in the bag after taking out a white one...that is, what's the probability of the bag having had 2 white marbles if you know it had at least one.This should be the same as the probability of getting two white marbles divided by the probability that the first marble was white.

Probability notation for this conditional probability is
P(W2|W1) = P(W1 & W2)/P(W2)

Which then is .5/.75, which is equal to 2/3 - the number given in the editorial.The result does maybe initially seem to be a strange number, but there is no wiggle room here.It's correct.

Letter to the editorial review
The Editorial has single handedly solved a modern dilemma in the world of Mathematics.I do believe it has been said that it is better to be assumed a fool then to open your mouth and remove all doubt.The final conclusion is that the contradiction leads us to realize a possible incompleteness in the system.Here is how:

Solution #1 As the state of the bag, after the operation, is necessarily identical with its state before it, the chance is just what it was, viz. 1/2. Solution #2 Let B and W1 stand for the black or white counter that may be in the bag at the start and W2 for the added white counter. After removing white counter there are three equally likely states:

Inside bag------Outside bag
W1--------------W2
W2--------------W1
B ---------------W2

In two of these states a white counter remains in the bag, and so the chance of drawing a white counter the second time is 2/3.This contradiction of the first solution might indicate that the system offers an incomplete answer (not that the first answer was wrong).