4 comments about Amusements in Mathematics.

1. 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!



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



3. 
   With 430 puzzles, problems, paradoxes, and brain teasers, this book is a mammoth puzzle collection, compared with most math teasers and puzzles book available. But what is important is not the quantity, but the quality and charm of the problems presented. Each problem is presented with a full length solutions that makes the book absolutely an instructive experience for the reader. In some cases the author even discussed on how others had attacked and failed the problems.
   
   Additionally the book is fully illustrated with clever diagrams and sketches, which make the reading even more pleasant for everyone. You, your freinds and family will spend many hours trying the vast array of puzzles prented in this book.



4. I found this book simply sensational, once it has hundreds of interesting puzzles on math and logic. One learns a lot by reading it.

5 comments about Geometric Puzzle Design.

1. Coffin does it again, with the quintessential wooden puzzle builder's guide. If you're fortunate enough to have previous works by Stewart, keep in mind that this is an updated version, so a lot will be repetitive. Then again, if you have the previous version, you're probably a Puzzle Junkie, in which case the updates alone are probably worth it.
   If I were going to be stuck on a desert island...and there were trees, and I had a knife and a sharpening stone...then this would be the One Book I'd want.



2. Written by veteran woodworker and expert wood puzzle designer Stewart Coffin, Geometric Puzzle Design is a one-of-a-kind guide to creating intriguing, three-dimensional wooden puzzles. Special techniques for creating oddly shaped small puzzle pieces accurately and safely, recommendations for drafting one's own original designs, mathematical concepts that can be applied as engineering tools, and much more fill this original craftsman's manual. A "must-have" for intermediate to advanced woodworkers seeking to create truly brain-teasing gifts.



3. This book covers a large number of puzzle designs, most due to the author. Most of these puzzles have become sought-after classics. The puzzles are mostly 3D interlocking burrs, but there also included are 2D designs, sliding block puzzles, and non-interlocking 3D puzzles. The author also talks about how to build puzzles, characteristics of wood, etc.
   
   I am not a puzzle builder, but enjoyed the book immesely. The author is an excellent writer and his musings about symmetry and general design considerations I found fascinating. Solutions in general are lacking and much is left to the ingenuity of the reader to keep the mystery of solving these puzzles fresh.
   
   Although you can download a pdf copy of this book for free, I enjoy the physical copy for perusal. Highly recommended.



4. as a long time collector and producer of wooden puzzles is this new puzzlebook an absolute Must for every puzzle interested people; although I have all Coffin`s former editions this new review about his designs is usefull for collectors as well as for producers of puzzles;



5. Book is well written. Theories are great. I would have prefered more instruction on making the puzzles rather than just the theory.

2 comments about Brainteaser Physics: Challenging Physics Puzzlers.

1. BRAINTEASER PHYSICS: CHALLENGING PHYSICS PUZZLERS provides a fun, casual approach to learning the science of physics, through a series of fun question-and-answer 'puzzlers' posing both classic and new problems and answers. Diagrams, equations, and scientific discussions support teach brainteaser with a survey of scientific thinking and concepts, making this perfect for high school or general-interest collections seeking reinforcements to physics principles.



2. I am a Physics teacher. I was looking for a book that had questions that I could use in class to challenge the students. this book fit the bill. It asks good every-day questions with a physics answer. It provides several levels of answers depending on the intellectual level of the students. It is a great question book to open a class with.

5 comments about The Official Book of Kakuro: Book 1.

1. Most of the puzzles in this book were satisfying. Three of the latter "Medium" puzzles are irritating: two lack unique solutions (for example, the answer key has "3 1" immediately above "1 3," which is impossible to logically distinguish from "1 3" directly above "3 1") and one is actually invalid (the answer key has "2 1 2" as the solution to one "word," and there's no other way to solve it, as the three cells in question must add up to 5.) The other 147 puzzles in this collection are free of such errors. My only other grumble is about the difficulty; I did not notice a significant difference between the difficulty of the medium puzzles and the first 40 hard puzzles, though the last 10 hard puzzles were a significant step up from the first 40. Even the hardest puzzles are not as difficult as those in the Virgin books. I'd recommend this to people who are looking for a first experience with Kakuro, but those with experience with other publishers might want to look elsewhere for additional challenge.



2. Book is too small and bulky. Hard to keep open while solving puzzles. Gridwise, all of the puzzles were very small throughout the entire book. Should be geared toward kids, not adults. Not challenging at all.



3. This was my first Kakuro book. It got me up and running quickly.



4. There are an equal number of Easy, Medium and Hard puzzles. There are also instructions and tips if you have never played before. If you are like me and have been doing Cross Sums for years, you will enjoy the medium and hard puzzles. Now I'm waiting for Extreme Kakuro!!



5. I hate Kakuro books where you are suppose to guess "wildly" and cannot be solved through pure logic. This is NOT one of those.
   
   So puzzles might seem less challenging to people who like to use "trial and error" but, for the rest of us, it has plenty of challenging situations that can be solved logically.
   
   It does include some puzzles with more than one answer. So I can't give it 5 stars. But, on the other hand, I haven't found one that doesn't.

2 comments about How Long Is a Piece of String?: More Hidden Mathematics of Everyday Life.

1. I received this book for Christmas 2003, by the 26th I only had 40 pages left. If you are looking for a book to improve your mathematical ability, this is not for you. If you like to think and wonder why things are the way they are, then this is the book for you. I found myself reading one section after another, chapter after chapter. From the reasons why pyramid schemes are destined to fail, what is the best way to pack boxes of belongings when moving house, when do you take the money and leave 'Who wants to be a Millionaire' and many more fascinating and thought provoking ideas and concepts. I liked the book so much, I bought the previous book 'Why do buses come in threes?' the same day I finished this one - and I have already read one third of that one and it is not even New Year yet. This book would make the perfect gift for anyone who likes to think! So if you think they think, I think you should get it!



2. This is a follow-up to the earlier, excellent, "Why Do Buses Come In Threes?". While the earlier book focused on those annoying little mysteries of life, this asks a set of different questions, many related to tough decisions such as how conmen get rich, or "should I phone a friend?"
   
   The answers, like before, lead us through a gentle, humorous exploration of mathematics and its relevance to everyday life. Along the way we explore (among others) geometric progression (why all pyramid schemes eventually fail), the geometry of stacking, fractals, chaos theory, the mathematics behind taxi meters, and various uses and abuses of statistics, both to detect and commit fraud.
   
   The two messages of this book are that mathematics is important, and that it's fun. It's in the same vein as the work of Martin Gardener, but with a British slant.
   
   To aid casual readers or those who've previously found the subject forbidding the maths is kept at a fairly simple level. Most of the time the concepts are communicated in words and simple graphs, but key equations are included and explained for completeness. The text is easy to read and the illustrations clear and amusing. Although aimed at those new to the enjoyment of maths, it's also a good memory jogger for those with a bit more background.
   
   I thoroughly recommend this book, and also the authors' earlier volume.

No comments about 250 Kakuro Puzzles.

No comments about Probability Models in Engineering and Science (Mechanical Engineering (Marcell Dekker)).

5 comments about The Mathematics of Oz: Mental Gymnastics from Beyond the Edge.

1. I found the puzzles and problems in this book to be original and varied, and with a wide range of difficulty levels. I enjoyed the fact that some puzzles might actually have more than one answer, which leaves room for healthy debate and for better understanding the way different people think. I think this book can be enjoyed by readers of different levels of mathematical sophistication. For example, a freshman in high school could skip the more difficult problems, like the one on Ramanujan Congruences, although this is one of the most interesting chapters. My favorite chapter is one that poses a statistics-like question, dealing with bones thrown into a pit. You have to figure out the ratio of the long piece to the short piece. Here's a sample of other chapters that I really enjoyed:

   1. The Yellow-brick Road
   2. An Experiment with Kansas
   8. The Problem of the Bones
   16. Omega Sphere
   28. Legions' Number
   29. The Problem of the Tombs
   35. Prime-poor Equations
   36. Number Satellite
   43. Ramanujan Congruences and the Quest for Transcendence
   49. The Jellyfish of Europa
   99. A Connection Between Pi and e
   103. The Scarecrow Formula
   107. The Omega Crystal
   108. Attack of the Undulating Undecamorphs
   
   I've already spent hours reading and rereading the book, and showing it to friends, and I know I'll spend many hours more!




2. This wonderful mathematical puzzle book has over 100 puzzles sure to delight readers -- from kids to adults. The problems include: mazes, sequences, probability, and more. Most puzzles are very clever and fun. I liked considering the yellow-brick road that crosses America. How many bricks would it take? I also liked the zebra numbers and circular primes. Legion's number is a number so big that it makes a a billion look puny.

   Anyone who has pondered the vastness of our mathematical universe will love this book.




3. I prefer mathematical puzzles that have two features:
   - they are interesting (i.e. they have that difficulty that make them worth trying to solve);
   - they are solvable without developing a whole new theory and without writing program code.
   In this book most problems that are interesting (very interesting and intriguing, I must admit) are not solvable in the foresaid sense, and most solvable ones are not interestin. Of course, a few are both. The picture sequences to be completed are very original, and sometimes difficult, examples of QI tests.
   However, in spite of that slight flaw, I have really enjoyed reading it. It may depends on my appreciation of Oz novels and movie, and even if this book is not likely to mark the history of mathematical entertainment, it remains a worthy reading.



4. Awesome blend of stories mixing in some interesting puzzles. Being a Kansas girl, I was intrigued by the entertaining story line set in the "Sunflower state". My son graduated from the Unversity of Kansas and there is a fictional story of the campus in the book that builds toward a puzzle. I gave the book to my son on his 25th birthday and I had marked the KU story. He turned to it and was totally endeared to the book. Couldn't be a better present for anyone who loves Kansas or puzzles. Just great!!!



5. Clifford Pickover is a fountain of ideas, and in this book, he presents a set of puzzles and problems that display some of those ideas. They range from the simple to the hard, and the premise is that Dorothy has been abducted by the alien Dr. Oz and his assistant Mr. Plex. Dr. Oz presents the puzzles to Dorothy with the general caveat that she will be rewarded if she can solve them. All of the puzzles are given a difficulty rating, although there are times when the rating seems inaccurate.
   I thoroughly enjoyed this book and got so involved with a few of the problems that I used them as the basis for a presentation I made to a gathering of college and university mathematicians. It will stretch your mental mathematical muscles.

2 comments about Math Wonders to Inspire Teachers and Students.

1. I really like this book. It contains a high concentration of nice math demonstrations. It is appropriate for students as young as 11 or 12, although such young students might not understand all of the concepts, and it is great for high school aged students who are looking for interesting little tidbits that are different from their usual course work. It is also a good book for adults who like math.
   However, it virtually identical to the author's other book "Math Charmers". It makes absolutely no sense to buy them both - they are the same nearly word for word. Amazon should not be pairing the two together in a package deal.



2. Recieved item on time, right when we were told it would arrive. Book in very good condition.

5 comments about The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions.

1. This book contains print and mathematical errors. A cute book but because of the math misprints [I refuse to believe the author cannot add] a shoddy publication very uncharacteristic of Princeton



2. A magic square is an array of numbers in which the sums of numbers in rows, columns, and diagonals are equal. A magic square uses consecutive numbers from 1 to N. Here's an example,
   
   
   4 9 2
   3 5 7
   8 1 6
   
   
   This book is different from all others I've seen on the subject, and I don't know any other books that present the large range of patterns that you'll find here. The book also focuses on discoveries in the last few years. As Pickover says, the book is essentially an exhibit of magnificent forms discovered through the centuries. All sorts of historical and quirky-human aspects are also described. Centuries ago, people believed that magic squares to had special, magical powers....



3. OK, there were a couple of typos -- keeps you on your toes. Lots and lots of examples of different variations on the magic square theme -- and puzzles for the reader to solve. Some of those puzzles are quite easy and some are quite difficult and have yet to be solved by anyone. You can't be a mathphobe to read this book, but you don't need to be a math whiz either. Anybody who likes the challenge of a good crossword or crossnumber puzzle should like this.



4. This is a book about mathematical artifacts, but it has practically no mathematical content of its own. A casual reader who wants to gaze at these beautiful objects and come away impressed but with little understanding will find this a marvellous book. However, a mathematically inclined reader is not satisfied with someone declaring that an object has such-and-such a property, he wants to know WHY.

   Chapter 1 of this book gives dozens of fascinating constructions, but for most of them not a shred of proof is offered that the arrays produced are the magic squares Pickover claims. It leaves me wondering whether or not Pickover could produce such proofs himself, even for the more simple constructions in the book.

   Pickover describes some interesting computer experiments at the end of the chapter but seems completely stymied as to why they work. The demonstration is a lovely, but simple, piece of matrix theory that I would expect my first or second year Linear Algebra students to be able to perform.
   He shows two "brute-force" proofs for the order 3 case, one by Hendricks and "another" by Johnson (at least here is an attempt at including a proof), but annoyingly seems unaware that the second is just a minor variation on the first. I wonder if Pickover actually tried to follow these proofs himself or if he just copied them for his book.

   Mathematics is not a collection of statements that the hearer must accept on "authority", it is a systematic development of theory in which every statement can be, at least in principle, demonstrated by a logical argument. The mathematics is in understanding "why", not in the acceptance of fact. Without demonstration of the claims, all that is left is the shell with no life. Beautiful, like other shells we find along the shore, but not the genuine article itself.

   I am reminded somewhat of Stephen Hawking's popularizations of physics in which the reader is deeply impressed with the beauty of the subject, but comes away knowing practically no actual physics to speak of, for the author carefully seals the machinery of physics from his reader and presents only the glamorous face. In the case of Hawking, however, the author's authority is unquestionable; I'm sure he could, if pressed, demonstrate every claim in his books from first principles. I suspect that Pickover could not.

   Aside from a few excusable errors of fact, the book shares a serious omission with almost every book on magic squares that I have seen, in that it does not present what is surely the most elementary construction known for magic squares of any odd order, as the sum of a circulant and a back-circulant matrix. Even Pickover would be able to prove that this construction works, since the reason it works is extremely obvious. Given the connection of this construction to the very important subject of orthogonal Latin Squares, you would think a serious writer would devote some space to it.

   Aside from all of the above, the material in the book is comprehensive and fascinating, drawing on a number of sources, displaying many artifacts that have titillated dabblers for millennia. As a museum piece I'd have to give the book an "A", but as a piece of mathematics, only a "D".




5. Magic squares have fascinated us for many centuries. Even in ancient Babylonian times, people considered these squares to have magical powers. Albrecht Dürer, the painter and printmaker, used them in his artworks.
   
   Most of the ideas in this book can be explored with just a pencil and paper! You can even discover new patterns in old magic squares that no one has ever found before. Even the famous eighteenth-century American Benjamin Franklin loved magic squares although he once considered them a waste of time.
   
   Pickover presents interesting people and their magic squares. From Benjamin Franklin's magic squares to four-dimensional magic tesseracts, the patterns fascinate us with their elegance. The book is a treasure and has gotten some rave reviews in the press. I enjoyed the magic spheres best of all, but I think each reader will find something new and interesting as they browse. A lot of magic squares deal with the chess board. Some focus on DNA sequences! A few were made by prisioners in jail. The author has certainly searched far and wide to assemble this massive collection.