Reviews (4)

Read the Adams book instead
If you just plan to skim the text and do not intend to try applying the ideas presented to actual knots, then you may not notice this small book's many errors. But if you wish to verify what the text says and try your hand at some knot calculations, then this is not the book for you. Perhaps the worst example is the author's comment that the figure-eight knot and the trefoil not have the same Conway polynomial. They don't. After an hour of calculating and recalculating, it is frustrating to discover that the author, not the reader, is the one in error. That kind of elementary error makes one question the author's basic competence and knowledge of the field.

Another error is made when giving an example of calculating the Conway polynomial for a link with two separate circles (page 68): the right-hand side of the equation should have no term in x. Figure 2.15 (algebraic representation of a braid) also has an error: the upper-right-hand braid elementary braid is b2, not b1. (The text below the diagram is correct, but the diagram itself has it wrong.)

For a beginner who is learning the subject, the necessity of sorting out the author's errors is unacceptable. A book with so many errors should have an errata (list of corrections) on the web, but I searched and found none.

I though the braid chapter was well-written. I have not studied braids before and it made the situation pretty clear.

On the plus side, the drawings are excellent, the best I have seen in any knot book. For example, figure 3.3 (page 40) has a nice diagram clearly showing various "problems" that might happen momentarily during Reidemeister moves. In this case, a picture is worth a thousand words.

I did not enjoy the author's mini-digressions into non-mathematical applications of knots. They went on too long and didn't relate well to the mathematics in the book.

Finally, this author seems to have a bit of an attitude. He makes it sound like he almost beat Kaufmann to discovering Kaufmann's bracket. Then he goes on to point out that the Celtic people discovered a form of it centuries ago (beating Kaufmann). Sounds like sour grapes to me. He makes frequent comments such as "the attentive reader will notice," which I found annoying after a while. Readers do not like to be insulted.

After a full day with this book, I am tossing it into the trash. The Knot Book by Colin Adams is solid on the math and a better overall introduction to the math side.

It is not that bad, but full of mistakes
I actually read the French version, and skimmed through the Englih one. When I read it in French, I was baffled by the number of mistakes per page. So I reread it, keeping a list of mathematical mistakes and typos(?). It averaged 1.7/page. I send it in to the French editor, but I realized that they kept the mistakes in the English version!

On the other hand, I thought explanations were pretty good.

So I would certainly not recommend it as a starter, but if you know enough of knot theory, the mistakes should keep you entertained...

This book is bad!
Don't buy this book if you're a mathematician!

Either something really disturbing has happened during one of the translations (russian->french->english), or I seriously doubt mr. Sossinsky's ability to teach anyone about knot theory.

Almost every single calculation in the book is wrong. Some of the errors are plain typo's, admitted. But others are so disturbingly wrong that I had to read the passages several times to believe that a mathematician could have written this.

One notable example is when the author calculates (correctly for once) the Conway polynomial of the trefoil knot to be 1+x^2. Then goes on (this is so good, I just have to quote it):

"A calculation similar to this one shows that the Conway polynomial for the figure eight knot (Figure 1.2) is equal to x^2+1: it is the same as that for the trefoil. The Conway polynomial does not distinguish the trefoil from the figure eight knot; it is not refined enough for that."

In fact, the figure eight knot has Conway polynomial 1-x^2. Scary that an expert on knot theory can make this error (three times in a row!). -Afterall, the simplest counterexample to whether the Conway polynomial is a perfect invariant is a very, very basic thing to know!

Other mistakes are rather amusing (even whilst still being annoying). For instance, the author confuses a figure-eight knot with an unknot, shortly after casually mentioning that his intuition of space is "fairly well developed".

Another thing that annoys me as a mathematician is the author's "personal digressions", trying to explain how the minds of mathematicians work and why mathematics can be beautiful in the same way as arts and music. The worst one of them is concerned with how the author *almost* discovered the Kaufmann construction of the Jones Polynomial before Kaufmann did. (At least, that's how it sounds to me.) In my opinion, either you try to explain some math, or you do pocket philosophy. -Not both at once!

On the good side, the actual subjects treated in the book are very well chosen. (Except, the author promises twice to get back to telling about the Alexander polynomial but he never does...) (And that last thing reminds me: The book has no index!!!)

So, my advise is: read the contents pages and go learn the theory from elsewhere.

Untangling Mathematically
It is always surprising and pleasing to find that mathematicians are busy in their ivory towers looking at non-numerical concepts and even using small subjects to turn out tomes that are impenetrable to us non-mathematicians. If you want to spend a little time learning how mathematicians think about the lowly subject of knots, there is now a little book with good illustrations and explanations that may go over the heads of most people, but nonetheless demonstrates the high degree of effort in this mathematical field. _Knots: Mathematics with a Twist_ (Harvard) by Alexei Sossinsky (who is a professor of mathematics at the University of Moscow; this work is translated by Giselle Weiss) demonstrates well the complexity of a field that might at first seem unpromising but actually has important relevance to the real world.

The diagrams here, and there are many of them, are a great help. You could make your knot cross over and under an infinite number of different ways. But how different, and how can you tell the difference between one knot and another? There is, according to Sossinsky, no algorithm that works in every case of classification, not even an algorithm that can be taught to a computer. This is true even though the attempts at classification, with graphic or symbolic notation which cannot be reproduced here, are quite complicated. So, being able to tell one knot from another is the as yet unattained Holy Grail of knot theory. Interestingly, if you tie a knot, however simple, into a string, you cannot tie another knot, however complicated, into the string so that one knot will, when it meets the other, untie the string. The proof of the impossibility of one knot canceling out another is nicely sketched here. The chapters here are written more-or-less independently of one another, so that if one stumps you, you can try the next with a clean slate. For needed relief, Sossinsky has put in digressions (and labeled some of them as such) which any reader ought to be able to enjoy, like the one about the slime eel that knots itself for defenses (left trefoil knot). Some of the coincidences between knots, algebra, quantum theory, and other disparate lines of thought are really quite lovely, and indicate once again that no one knows where research in pure mathematics may lead or how practical it may turn out to be.

Sossinsky has a witty style, and acknowledges how strange this mathematical world must be for visitors. At one point in demonstrating the procedure for composing a knot from primes, he parenthetically says of the task of making a rigorous definition of what he has described intuitively, "I will leave to the reader already corrupted by the study of mathematics the task." He is a genial guide to a strange land. ... Read more

Reviews (2)

If you like to think, this is the book for you
Gardner has penned another whimsical, informative and totally amusing book (again). The entire thing is a MENSA member's dream come true - a work equally at home in the entertainment and education fields.

This is not just one dreary problem after another. Instead, Gardner offers commentary on subjects as far-ranging as time, molecules, chess, cards and electricity. And always he manages to pause for a quick puzzle or two (or three). Terrific read.

A fun book of brainteasers!
Wheels, Life and ... is an enthralling and thoroughly enjoyable book for anyone interesed in math brainteasers. It covers a wide range of intriguing topics, from simple word puzzles to complex mathematical ideas. Knotted threads and geometric fantasies mingle effortlessly with Zeno's paradox and the challenging game of life! I couldn't stop reading one teaser after another, wracking my brain on some tantalising clue. If you're fascinated by mindgames, buy it. Its a Martin Gardner! ... Read more

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Reviews (3)

Another Fine Math You've Got Me Into
This is one of the best recreational math books I have ever read.The humorous real life scenarios lead to deep mathematical concepts.I use this book in a class for future mathematics teachers.Hopefully, it will inspire them to make math fun for their students.

Another Fine Math You've Got Me Into..,.
This is one of the best recreational math books I have ever read.It presents scenarios from real life that lead to real math.Humor abounds in the stories but deep mathematical concepts abond in the solutions.I use this book as a required text for a mathematics course for future teachers.Hopefully, they too can make mathematics as much fun as Mr. Stewart.

Humor with a mathematical flavor
The author is the comedic equal of the team associated with the title. Puns fly fast and furious, and the slow of wit will not catch them all. A master of the verbal slapstick, his wit makes you simultaneously grin andgroan. The worthy successor to Martin Gardner in writing a regularmathematics column for `Scientific American', he is the clown prince ofmathematics.
Some of the catchy titles and subjects are:

1. Tile and error, tiling a rectangular surface.
2.Knights of the flattorus, about knight tours of a chessboard.
3.Another vine math you'vegot me into, a combinatorial problem of planting several varieties ofgrapes in plots so that all pairs are together in one and only one plot,etc.
4.Sofa, so good, on moving a sofa through tight places.

All subjects are presented with clarity and thoroughly resolved by the endof the chapter.
This work is the rarest of mathematical books. Itpresents solid, sophisticated mathematics in a manner that people couldread just for the jokes. A vine piece of work.

Published in Journalof Recreational Mathematics, reprinted with permission. ... Read more

Reviews (1)

I loved this book.
This book contains many mathematical, and numeralogical puzzles and analyses. The author details all of his meetings and interveiws with Dr. Matrix. Dr. Matrix was a numerologist from the 50's to 1980, he was also a scam-artist involving mathematical scams. ... Read more

Reviews (1)

Numbers Go On Steroids
If you're drawn to things like magic squares, Fibonacci number puzzles or fractal geometry, you'll find "Number Mosaics" by A. R. Kanga irresistible. "Number Mosaics" is recreational mathematics on steroids. The author weaves ordinary numbers into geometrical arrangements such as spirals, stars, lattices and ladders, exploring the arithmetical properties they generate, much like magic squares. He takes a neglected corner of the arithmetical universe and spins a fascinating gossamer web, articulating a novel theory of numbers.

While this is not a text on traditional number theory, it's not George Gammow's "One, Two, Three... Infinity," either. This book is quite narrow in focus. It's not a popularization, since this is probably the only treatment of the subject in existence. It's as if Kanga hit on a vein of numerical ore, exhaustively mining and refining it into a unique theory of - Number Mosaics! The closest thing I have read is, "Magic Squares and Cubes," by W. S. Andrews, which is both a survey and a presentation of novel material.

In contrast, most popular books on mathematics today take the reader on a wide-ranging tour of dozens of topics, but don't offer original treatments such as Number Mosaics does. A sampling of my personal favorites includes: "Fractals, Chaos, Power Laws - Minutes From An Infinite Paradise," by Manfred Schroeder (1990) - This book demands some high-school math to get the most out of but is well written and chock full; "The Story Of [the square-root of minus-one], An Imaginary Tale," by Paul J. Nahin (1998); "The Divine Proportion," by H. E. Huntley (1970); "The Mathematical Tourist," by Ivars Peterson; and an excellent book by Devlin. And there are the classics by such writers as Martin Gardiner, Hogben, Kasner, Newman, Klein and many others.

If you're interested in grander vistas than that offered by "Number Mosaics," other writers have developed novel mathematical theories of much greater significance. In his monumental "Synergetics" and "Synergetics II," Buckminster Fuller develops a unique structural "Theory Of Everything" based upon, among other things, a repudiation of the Cartesian coordinate system and its 90 degree axes, which he replaces with a axis system based on 60 degrees. This has born fruit in the field of solid-state physics with the invention of "fullerines," perhaps better known as "Bucky-balls," synthetic carbon molecules with extraordinary physical properties.

Benoit Mandlbrot's epochal "The Fractal Geometry Of Nature" summarizes the work of this pioneer, which has altered the course of science and engineering, from weather prediction to telecommunications to astronomy to population fluctuations.

Another highly original, if far less influential thinker is Arthur Young, whose books include, "The Reflexive Universe," - also a kind of "Theory Of Everything" - and, "The Geometry Of Meaning." The latter is a brilliant synthesis of the calculus, physics, aerodynamics, astrology, Aristotelian philosophy and phenomenology. Despite this intimidating description the book is highly readable even for the mathematically uninitiated, yet presents ideas of genuine significance. I highly recommend both books.

Douglas Hofstadter's classic "Godel, Escher, Bach" gives us his imaginative insights into the connections between the paradoxical logic of Godel's Uncertainty Theorem, the visual paradoxes of M. C. Escher's engravings and J. S. Bach's perpetual canons, via dialogues a la Lewis Carrol. His "Metamagical Themas" is also of interest.

Straddling popularization and originality is the provocative, "Laws Of The Game, How The Principles Of Nature Govern Chance," by Manfred Eigen and Ruthild Winkler (1981).

I cannot fail to mention one of the most enduring classics of "underground" mathematics, G. Spencer-Brown's "Laws Of Form." A slim volume, it is slow going, but is the kind of book that will continue to yield precious insights twenty years after the first reading. Brown claims to have simplified mathematical logic by adding to the accepted list of logical results - true, false and meaningless - the result, "imaginary". He claims to have used this imaginary logical operator to be the first to prove the famous four-color theorem, but apparently this claim has not received any attention from mathematical officialdom.

While all the above-mentioned books have far greater general relevance than "Number Mosaics," the field of mathematics is full of once "useless" curiosities that eventually became the keys to powerful new technologies. Case in point: Imaginary numbers. Perhaps one day, the curious "Universals" in "Number Mosaics" will prove to have applications which we cannot even imagine today. ... Read more

Book Description

Mathematics can be fun for everyone, and this book shows it. It grew out of the author's popularisation of mathematics via live, call-inTV shows and widely published articles. The questions, comments, and even the answers here come largely from the callers and readers themselves, and so the book covers the kind of mathematical problems that people are interested in, not those that professional mathematicians, writers or even publishers think people should be interested in. The book makes no attempt to fit any mould. Although written by a research mathematician, it goes where the callers and readers have directed it, over a wide range of topics and levels. Everyone paging through it will be captured by something of interest, whether they consider themselves interested in mathematics or not. ... Read more

Reviews (1)

Fun problems submitted to a call-in show
Despite the math phobia that afflicts so much of the population, it is limited in extent. All but the most committed hater of mathematics understands how valuable it is and respects those who can use math. This book is a catalog of questions submitted to a call-in show, which is certainly one of the most unusual ways to solicit mathematics problems. The world seems to be overpopulated with call-in shows, some of which get downright weird. To many people, discussing personal problems over the airwaves is the preferred way to deal with them. This is clearly a case of a call-in show that adds something to society rather than airing some of the ills that afflict it.
The problems presented in the book are fascinating, in that they start with simple ideas concerning how the world works. My two favorites are "Do Airplanes Get Lighter as Passengers Eat Lunch?" and "Can a Computer Have Free Will?" These are the type of problems that kindle the interest of lay people. Interesting, sometimes profound questions where the answers require a bit of deep thought. Some of the best brain teaser problems with simple solutions that you will ever find are in this collection. I have used a few of them as test problems to try the patience of my students.
It is gratifying to see such an endeavor succeed. Mathematics has so much to offer our society, but like artisans throughout history it is truly the society in general that supports the practitioners. Programs like this convince us all that, despite the occasional spouting of math phobia, our society does indeed respect mathematics as a pillar of human achievement. ... Read more

Reviews (3)

Eye Twitchers
I've been into Dell Crosswords and Especially Logic Problems since I was 16; my father's word puzzle love facilitated my addiction.

I use a logic problem to lull me to sleep every evening. Yearly I upgrade my thesaurus for the latest, and more wordly edition to keep up with the curves thrown by the international crosswords. Try to keep my mind a step above the "rust".

Back in my Trig and Calc days, they drilled into me the need to constantly write down known variables, and chart info, to keep track of your formulas and progress in solving a problem. Logic Problems reinforce this practice.

I've got my kid thinking in charts with his schoolwork, especially homework.

Challenging and fun
I have always loved logic problems better than any other puzzles. This book definitely delivers some hefty problems. Though it contains only 75 of them, each are involved enough to keep you working on each one for a good while. The only drawback is that the answer section in the back does not have charts. I would have like to seen a graph to quickly see if I'm right or not. Though, each problem does have a talk through section and a concise summary of answers.

Overall, each problem is challenging and has a variety of subjects to keep you involved with it. If you like logic problems, I highly recommend this. It's definitely worth it.

Excellent problems to solve
In my capacity as a teacher, I want students to have practice THINKING..and this is what logic puzzles such as the ones here provide. This book includes the organizational charts, the solution to the puzzles, as well as an explanation for the solutions. It would be excellent if they would include the answer in chart form as well. (I translate these for foreign language classes..the language is simple enough for a beginning level class. Very challenging ! ... Read more

Book Description

Requiring only a basic background in plane geometry and elementary algebra, this classic poses 28 problems that introduce the fundamental ideas that make mathematics truly exciting. "Excellent . . . a thoroughly enjoyable sampler of fascinating mathematical problems and their solutions" — Science Magazine.
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Reviews (2)

The Real Beauty and Exhiliration of Math
This is a superb book, and the best way to first sample the delights of math for its own sake. Don't let the subtitle "Selections from Mathematics for the Amateur" turn you off. True, the math involved is elementary, not going beyond high school algebra and geometry. But the material won't be found in most textbooks, having been chosen with elegance and beauty, rather than utility, in mind (which isn't to say that it doesn't have its important uses). Even the professional mathematician who has already seen most of the contents will profit from studying the book's exemplary treatment of its topics. The authors are some of the best math expositors who have ever lived. Each idea in the book is developed admirably, and strikes the perfect balance between conciseness and lucidity. You probably can't do better in choosing an introduction to prime and perfect numbers, the four-color problem, regular polyhedra, Pythagorean triples, pedal triangles, periodic decimal fractions, Waring's problem, the number 30 (sic!), and many other fascinating intellectual tibdits.

At Dover's low price, this book is a great buy. Get it! If you have more mathematical knowledge, then I also recommend "Proofs from the Book" by Aigner, et al., which is written for mathematicians in a similar style.

An excellent collection of problems at the elementary level
Written by two top-notch mathematicians, requiring the mathematics that a high school student can do, this book takes you on a journey that is easy to follow and yet shows the power of mathematics. It is an excellent book for high school enrichement or early undergraduates.

Even if you are a mathematician you will be suprized at many of the results and enjoy trying to solve some of the problems. Many of the problems are quite hard. Even though some of the problems are the standard ones, many are off the beaten track. No matter what your level of expertise, I am sure you will enjoy this book. ... Read more

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Reviews (2)

One of the classics of Puzzledom
Dudeney was one of the two fathers of puzzles today. Amusements in Mathematics has many of Dudeney's best puzzles. An excellent book.

Intriguing math teasers for ages 11 up, brilliantly answered
This excellent collection of teasers has inferential problems in arithmetic and algebra, and includes geometry, mazes, magic squares and a lot of chess-board tours. The answers are often gems in themselves -- things mentioned in passing and left to the reader to establish -- e.g. "... of the twelve ways that eight queens can be placed on a chessboard without attacking one another..." At twelve years old I spent many an hour finding those twelve ways. There is a small problem with the age of the book, first published in 1917. You could buy an airplane for 400 pounds ($1,680) then, and the money puzzles in the first chapter assume familiarity with British pounds, shillings and pence (and ha'pennies and farthings). The Dover edition of 1958 included a preface on British coins and stamps, and another on the game of cricket, but this edition was in 8vo rather than the original quarto, making some of the diagrams very small. I received my copy in 1936, at age eleven, and have cherished it ever since. I still find challenges in it in spite of my Masters degree in Mathematical Physics! ... Read more

Book Description

131 activities, ranging from matchstick and coin puzzles through ferrying, railway shunting, dissection, topological and domino problems to a variety of magical number arrays with surprising properties are included. ... Read more

Reviews (1)

Much more fun than 2 movie tickets
For about the price of 2 movie tickets, you get over 100 puzzles, games and challenges that range from fairly simple, to nearly impossible. I love working on them when I'm riding the train. These are not typical straight-forward, busywork problems. They really stretch your mind.

This is my first Brian Bolt book, but after reading this one, I'm planning to start a collection. ... Read more

Book Description

Clear instructions for 101 tricks and problems, many based on important math principles. Calculations have been concealed; tricks are carefully streamlined for quick understanding and flawless performance. Master such number phenomena as Lightning Calculations, Giant Memory, Magic Squares, nearly 100 more.
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Reviews (1)

Gotta have it!
If you see a book written by Karl Fulves on magic that has the words Self-Working in the title then buy it. There is a wealth of knowledge in each of these books. -Diamond Jim Tyler ... Read more

Book Description

Dr. Ecco is a mathematical detective and puzzle solver. In this book readers are invited to join him in solving nearly 40 puzzles inspired by methods in computer science and mathematics, including The Tower of Lego, the Odd Doors Problem, Spies and Double Agents, Gossiping Defenders, Code Breaking and many more. No special skills needed, just a clear head and a little imagination. Solutions.
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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 University Professor of the Year, and 3M 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.

And of course, Dover offers it at a great price!

A Combination of Puzzles and Operations Research
This walk on the puzzle side of life is a joyous jaunt through mathematics. The fictional Dr. Ecco, a dedicated omniheurist or puzzle solver, devotes his life to resolving the difficulties of others. The majority of the problems are in applied mathematics, and are typical of the real world. Professor Scarlet provides the narration and his serving as a foil to Dr. Ecco has much in common with the partnership of Dr. Watson and Sherlock Holmes.

The topics include coding, the flow of goods through transit points, production bottlenecks, road and mass transit construction, information transfer and conducting elections. Detailed solutions to all problems are given at the end of the book. The majority can be solved using only cleverness, although a mathematical background is certainly helpful.

Superbly narrated and with a tight grasp on life, this book is an existence proof of the premise that learning mathematics can be fun. An excellent supplemental text for any course that involves problems in operations research.

Published in Journal of Recreational Mathematics, reprinted with permission

Exciting and challenging puzzle book
This book is really fun. I am a person who really enjoys this kind of books, but this one was one of the best. I loved it!! ... Read more

Book Description

truly challenging conundrums for the expert puzzlist. Algebraic amusements, geometric exercises, diophantine diversions, problems in logic and deduction, probability posers, insight puzzles and assorted number theory problems. 130 woodcut illustrations by Ed Kysar.
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Reviews (3)

Fun little book!!!
I agree with the first reviewer! The problems are fun to read and think about. Unlike many problem books that state problems in a long-winded and confusing style, this book contains a series of interesting puzzles that are presented in a nice brief, easy to read format. The drawings are cute as well! It was this book, and others like it, that helped spark my interest in mathematics and problem solving from a young age. Now I use puzzles of this type for my own students! They make nice extra credit problems on exams! :-)

Puzzles for problem solvers
I actually have the 1st edition hardbound book that is copyrighted in 1964. It is also 217 pages and must be identical to the new editions.

This book is filled with puzzles that were chosen for "originality, elegance of solution, and imaginative appeal." "The book singles out problem themes and solutions calling for ingenuity rather than perseverance."

The book is arranged according to the types of problems. Here's how the chapters are broken up: 1)Algebraic Amusements, 2)Geometric Exercises, 3)Solving in Integers, 4)Problems in Logic and Deduction, 5)Probability Posers, 6)Insight Puzzles, 7)Assorted Number Theory Problems.

The problems vary from simple to difficult. Overall, there's a good selection of mathematical brain-teasers.

so-so
This book, while challenging, may be too easy for those past 7th grade, yet to hard for those below fifth. also, the layout is extremely confusing ... Read more

Book Description

Martin Gardner begins Riddles with questions about splitting up polygons into prescribed shapes and he ends this book with an offer of a prize of $100 for the first person to send him a 3 x# magic square consisting of consecutive primes. Only Gardner could fit so many diverse and tantalizing problems into one book.

This material was drawn from Gardner's column in Issac Asimov's Science Fiction Magazine. His riddles presented here incorporate the responses of his initial readers, along with additions suggested by the editors of this series. In this book, Gardner draws us from questions to answers, always presenting us with new riddles- some as yet unanswered. Solving these riddles is not simply a matter of logic and calculation, though these play a role. Luck and inspiration are factors as well., so beginners and experts alike may profiably exercise their wits on Gardner's problems, whose subjects range from geometry to word play to questions relating to physics and geology.

We guarantee that you will solve some of these riddles, be stumped by others, and be amused by almost all of the stories and settings that Gardner has devised to raise these questions. ... Read more

Reviews (1)

Gardner is again, as always, at his best
I would be thoroughly justified in causing my online thesaurus to heat up and spout smoke from my searching for new superlatives to describe the mathematical writing of Martin Gardner. His problems and puzzles have been a constant source of interest and entertainment from the first time I encountered them decades ago, and this collection is more of the same. These thirty six puzzles were first published in Gardner's regular column that used to appear in Isaac Asimov's Science Fiction Magazine, which is where I first read them.
Gardner has been quoted as saying that the reason that he does so well in writing about mathematics is that he really doesn't know that much about it. I consider this his only serious published mistake. He has shown an amazing depth of understanding of most areas of mathematics, which is necessary for one to write about it so well.
These puzzles cover the usual broad spectrum of a Gardner collection, everything from the 'magic' of numbers to encounters with bizarre aliens is the setting for a puzzle. Detailed solutions to all are included, some of which are in serial form, with answer number one raising a question solved in answer two, sometimes all the way to answer four.
No one has done more to make mathematics interesting and palatable to the general public than Martin Gardner. Whether he is writing problems or puzzles, he is capable of turning a math problem into a story or a story into a math problem. If he were ever to grab a piece of chalk and start teaching, he would put the rest of us to shame. ... Read more

Book Description

Amazon.com

Are there games that keep tripping you up? Puzzles that make you want to kick yourself when you discover the answer? Marcel Danesi's book can change all that. He walks you through the most common types of puzzles and shows you how to navigate the pitfalls of each so that you can avoid being taken in by misdirection. You'll learn how to systematically work out solutions as you follow him step by step through detailed examples and then practice on puzzles that will make you feel like your genius self again. But if you're already a master, just buy this for the puzzles themselves--they're terrific! ... Read more

Reviews (3)

The world needs more books like this!
I wanted to echo Charles Ashbacher's positive and fairminded review of this book (and counter the hostile and unfair review by the first reviewer). This book by Marcel Danesi is designed to provide people with an accessible way to approach logic puzzles (as Ashbacher pointed out, there is a good deal of *mathematical* puzzles as well but they do not require a great deal of math background). If -- as the negative reviewer argued -- this book is on a introductory level, so much the better! There are a lot of people who would like to and should get into logic puzzles and games.

This book is a great way to avoid some of the pitfalls and intimidating obstacles faced by puzzle-solvers -- whether you are a novice or an *expert.*

As for the comments made by the 1st reviewer ... it really is unfair to bash this book based on some sort of egotistical grounds as that particular reviwer seems to be doing. If this book is mostly for *beginners* -- and I believe, on the contrary, that it would be great for puzzle enthusiasts as well -- then there is absolutely nothing wrong with that! Everyone needs to be able to walk before they can run and if beginners get a taste for puzzle-solving from a book like this and go on to harder puzzles, then great for them! Frankly, in this world today, we need to encourage more people to get into logic rather than discourage people by the kinds of arrogant attitudes displayed by the 1st reviewer.

Also recommended: *Problem Solving Through Recreational Mathematics* by Averbach & Chein, *Puzzles for Pleasure* by Barry Clarke, *Mensa Logic Brainteasers*, and Marcel Danesi's new book *The Puzzle Instinct* (which not only provides puzzles but also discusses puzzles from an anthropological perspective ... i.e., how puzzles are a part of various important themes in human culture throughout recorded history).

A basic introduction to the basics of many puzzles
Humans love puzzles. They appear in artifacts thousands of years old and are part of every culture. One can open almost any newspaper in the United States and find a crossword puzzle and some other kind of problem for solution. Logic puzzles are also popular and can be used to teach the basics of mathematics and problem solving. Furthermore, the skills needed to solve them can be learned, and this book is designed to teach them.
The author teaches a course in solving puzzles at the University of Toronto, and much of this material is from that course. However, the level is one where anyone with an interest in puzzles will be able to understand it. Most of the techniques used to solve the problems involve the construction of charts and working through the various options. With the exception of the alphametics, very little mathematics is involved, and then it is the most basic of algebra.
There are also some points in this book that mathematics teachers could incorporate into their classes. For years I have used alphametics in my introductory classes in programming. They are an excellent example of coding a series of nested loops that exhaustively searches for a solution. I have also occasionally used a logic problem as a filler in mathematics exams as high up as advanced calculus. Students seem to enjoy them.
If you are fascinated by puzzles and would like to improve your skill, then this is a book for you. Many puzzles are presented and solutions to all are included. Happy puzzling!

Not for a serious puzzler.
To be fair, this book does do a decent job of illustrating some useful, if elementary, techniques for solving popular classes of problems. However, most people who would find such a book interesting have already seen the old chestnuts in here and know how to solve them. A serious puzzler would rather complain about how the problems are ambiguous, well-known, trivial, poorly stated, and/or poorly solved. I'd recommend this to an elementary school teacher trying to teach a unit on logic. But for everyone else, I suggest looking elsewhere. Fortunately, I got my copy free from the publisher. To me, that's about what it's worth. ... Read more

Book Description

The International Mathematical Olympiad (IMO) is the World Championship Competition for High School students, and is held annually in a different country.More than eighty countries are involved.Containing numerous exercises, illustrations, hints and solutions, presented in a lucid and thought- provoking style, this text provides a wide range of skills required in competitions such as the Mathematical Olympiad.More than fifty problems in Euclidean geometry invo9lving integers and rational numbers are presented.Early chapters cover elementary problems while later sections break new ground in certain areas and area greater challenge for the more adventurous reader.The text is ideal for Mathematical Olympiad training and also serves as a supplementary text for student in pure mathematics, particularly number theory and geometry.Dr. Christopher Bradley was formerly a Fellow and Tutor in Mathematics at Jesus College, Oxford, Deputy Leader of the British Mathematical Olympiad Team and for several years Secretary of the British Mathematical Olympiad Committee. ... Read more

Reviews (1)

Gardner weaves the magic of math
Gardner weaves the magic of mathematics again in this awesome math "thriller". After 'Time Travel', this is the second book I read, and I think Gardner does a wonderful job of going about math in a non-boring way. At some points of time, I had difficulty understanding whether I am supposed to be a complete novice or an advanced student, hence the 4 stars. ... Read more

Amazon.com

The Last Recreations collects the final works of Martin Gardner, the renowned "Mathematical Games" columnist for Scientific American. No prior knowledge of mathematics are necessary here; all will enjoy learning about topics ranging from Bulgarian solitaire to taxicab geometry, with experienced expositor Gardner as guide. Letters and updates concerning his column are also included in this book. ... Read more

Reviews (2)

whoa! slow down!
Maybe its that I'm looking at the past through rose colored glasses, but when I read this I did'nt experience the same sense of wonder that I did when I was 13. Martin touches on very very cool topics, but my main gripe is that he whizzes through everything, often just giving a pointer to another book, which is great in that it encourages more exploration but is frustrating at the same time. But if you havent encountared recreational mathematics before, take a look, Martin does a wonderful job in making math FUN!

Whoah! Nostalgia!
Reading this takes me back to time spent in my school's library poring over Gardner's columns in Scientific American. Several of the columns in this book I first read as a nerdy 14 year old and was staggered then (as I am now) by the elegance and beauty of the ideas they contained. Now I read it with a far greater appreciation of the problems and ideas expressed, but that doesn't compare with the sheer sense of wonder I experienced first time around. ... Read more

Reviews (1)

Another Great Collection from Martin Gardner
This book is another great collection of problems, discussions, and mathematical curiosities from Martin Gardner - and one of his best.

In this book, Martin Gardner has assembled an absorbing discussion on the theoretical aspects and possibility of time travel, including the many paradoxes that may arise; two problem collections to give to try out yourself and give to your friends; two chapters on tangrams and tiling each; along with 15 more chapters on interesting topics such as the melody-making machines, anamorphic art, block packing and more.

Particularly interesting are the chapters "Six Sensational Discoveries" and "Dodgem and Other Simple Games." The former is a collection of six April Fool's jokes he published in April of 1975. The latter is an extensive and occupying discussion of simple games that one can play with friends, along with winning strategies for some and just mathematical theories for others.

I strongly recommend this book for those interested in mathematical curiousities and the likeness. It is especially interesting for children of ages 6-12; they may not understand everything, but certain chapters they will remember and revisit forever! ... Read more