1 comments about Green Belt Kakuro: 150 Puzzles (Martial Arts Kakuro).

1. I have purchased quite a few books of Kakuro puzzles and this book ranks up there with the best. The puzzles are large 13X22 columns and rows. I enjoy large puzzles and this book contains 150 of them. The puzzles are difficult and it takes a while to complete each one but that's part of the fun!

5 comments about Killer Sudoku: 101 Puzzles.

1. I've completed the Mensa Nasty series of regular Sudoku, Collins's Killer Sudoku Book 1, and all levels of Kakuros that appear in the backs of other books I've bought, so I'd like to think I'm fairly skilled. But I got NOWHERE in this book. As another reviewer says, pretty much the only technique available to you is Rule of 45. Very minimal opportunity to use cages, I/O's, or significant number combinations. I assumed there had to be some major breakthrough technique that I wasn't aware of and searched everywhere on the web to find it. But evidently the only techniques that exist are the ones explained very clearly in the beginning of this book. But buy it for that reason alone, and then get Collins's Killer Sudoku book. You'll have much more fun.



2. I started to do Killer Sudoku a few months ago, and became hooked. Of many puzzles I tried on books or online, this one is the best. It gives a very good introduction, and ease you into the games by giving you some Easy ones first and then progresses into 'Cool', 'Thinker', 'Brain', and the hardest 'IQ'. A total of 101 puzzles. It has been weeks now, and I am still doing a couple of them a week - enjoying tremendously as I go along.
   
   There are good reasons why the puzzles are so enjoyable - particularly in the advanced sections. The author has explored the wide variety of solving skills of Killer Sudoku. Because of the math involved, numerous scenarios are possible for designing and solving interesting Killer Sudoku puzzles, I found myself discovering novel approaches every once in a while as I progress into the harder puzzles. Such discovery is pure joy, which we addicts really appreciate. I came to the realization that, unlike the classical Sudoku, the solving techniques in Killer Sudoku are much more diversified, and many are revealed during the mind mending processes of solving (and designing).
   
   The author has also seemingly put to a lot of thoughts into the design of the puzzles. There are puzzles with unique symmetrical patterns, with unique approaches. For example, in one puzzle, the corners may be solved relatively quickly, and the center takes a lot of mind twisting and pencil works. Then there is another one, in which the first and last three columns are all filled up quickly, leaving the center three columns completely blank smiling teasingly at your face. This one, I wrote down 'Bravo' after solving it.
   
   The puzzles have apparently been well tested and selected. I cannot say the same with some other Sudoku books.
   
   A superb book. I look forward to a sequel with only hard puzzles of the same quality.



3. A killer Sudoko book that really kills your brain. It's very addictive so, for your own safety, don't do the puzzle before going to bed. It may keep you awake the whole night.



4. I've been doing Killer Sudokus for more than a year and enjoy them far more than traditional sudoku. This is a very nice collection with a range of difficulties that excludes both the easiest and very hardest I've ever seen. (Nothing as hard as the "Mind Bending" found on a popular killer sudoku website--and nothing quite as easy as the "easy" puzzles on that site either.) I'm nearly through this one and will either go back with a big eraser to start over again or buy another copy!
   
   And: if you've never done Killer Sudokus before, it includes a little primer on the tricks for doing this kind of puzzle at the front of the book.



5. great group of puzzles! these are "thinkers" and not the trivial puzzles you find in some of the other collections. However I did find two puzzles in this book with unsolvable rectangles (and therefore there is no solution to
   the puzzle).

5 comments about Brain Busters! Mind-Stretching Puzzles in Math and Logic.

1. In this most recent adventure into the Puzzling World of Barry R. Clarke, I found my mind quite well entertained. What I enjoy most about logic puzzles is their requirement for little if any prior knowledge, and each of Barry's "puzzlers" is no different. However, what is missing in most logic and mathematical puzzle books is a touch of true creativity and humor. In Brain Busters! I found that while my mathematical mind was challenged to the limit, I was also encouraged to think in new and original ways, moving from basic logic to the simple yet complex world of recreational mathematics. Barry Clarke pushes your mind to the edge with this most recent creation, and holds you there.

   As Mr. Clarke notes in the introduction, his reasons for this puzzle compilation included the pure enjoyment of creating logical and mathematical art. Fortunately for us, Barry's creations serve not only the role of entertainment, but also more importantly the role of instruction, as he leads us down different paths of twisting logic, with excellent scenery along the way. If you view mathematics as a form of poetry, you will certainly enjoy this opportunity to learn from a mathematical wizard. Brain Busters! is indeed a "mind-stretching" experience, one that allows you to see the way Barry's imagination is captured in a distinctly unique manner in each of his puzzles. His mathematical imagination is the communality that runs through each puzzle, but at the same time it is his creative touch that serves as the specificity, giving great variation to this excellent and enjoyable work.




2. Almost exactly ninety years ago, Sam Loyd's 'Cyclopaedia of Puzzles' was published in New York. This was a collection of a very large number of his puzzles which had mostly appeared in the American Press. Many were illustrated with delightful pictures at the head of the page, drawn in Sam's own hand. Barry Clarke's new book has marked similarities in layout with illustrations drawn by the author at the head of many pages and many puzzles had previously appeared in the 'Brain Twister' column in the Daily Telegraph. The drawings are remarkably like Sam Loyd's, but there the similarity stops. Sam Loyd's book was foolscap size and hard bound while Barry's has the typical Dover cover, but the real difference is in the puzzles themselves. Barry's puzzles are graded in difficulty, so that readers who do not wish to be challenged too much can start with the first section and gradually work themselves in. Also, the puzzles are ingenious and well thought out and hints are provided before the full solutions for those who need a bit of steering. This is altogether a very good read, guaranteed to keep the puzzler in the family busy over Christmas. I thoroughly recommend it.

   (Angela Newing has written for The Daily Telegraph, UK)




3. This was posted near LSAT review materials. I did not find it helpful. Too many of the questions are dissimilar from the type needed for the LSAT logic section.
   It was also frustratingly difficult, because the directions and hints were too cryptic.



4. I am a seasoned veteran of logic puzzels, lateral thinking problems, math problems, and spatial reasoning puzzles.
   
   These are not logic puzzles. They are not word problems. They are not tests of lateral thinking. Rather, they are poorly worded tricks. Everything has a "trick" to it. And not like the "roosters don't lay eggs" kind of trick, which can sometimes be fun. Not like the old game Mindtrap, which is also fun. Instead, you get these unclear paragraphs that require a few questions be answered before you can even go about thinking through a solution.
   
   The complex crosswords are fun, but there are only four of them. Not recommended.



5. The delivery time was great. The description could have been more specific - I was looking for logic puzzles of a certain type and could not tell if this book had the right type of logic puzzles from the description.

5 comments about Mathematical Puzzles: A Connoisseur's Collection.

1. this book is interesting and challenging, even to people who have studied math at the college level. the problems are short, and take about an hour to solve, at least they did for me. it was a great read and i highly recommend this as a gift for the math lover in your life.



2. I have seen the word connoisseur used to describe collections before, but when I sat down to write this review I realized that I did not know the precise usage of the term. Therefore, I pulled out my Webster's dictionary and looked it up. It was "a person who has expert knowledge and keen discrimination in some field, esp. the fine arts or in matters of taste." In terms of keen discrimination, the term applies to the puzzles in this book. They are some of the best puzzles ever published, although those who follow the field will have seen many before, although perhaps in an altered form.
   However, expert knowledge is not required to understand and solve the puzzles. The level of mathematical knowledge is that of detailed knowledge of basic algebraic and reasoning techniques. Like the very best puzzles, solving them requires a bit of "sideways" thinking. In other words, the most obvious approach to a puzzle will most likely lead to bafflement, but if you look at it just the right way, the solution is obvious. Furthermore, once the inspiration arrives, you know that you indeed have the solution.
   In all honesty, I struggled with many of these puzzles. Sometimes, I was just being stupid, and other times I doubt if the solution would have ever managed to form in my thoughts. Fortunately, solutions to nearly all of the problems are included. The final chapter contains unsolved puzzles, which seems like a bit of a misnomer, and in a real sense it is. These are really unsolved problems, their topic is just one that fits inside what is generally considered the puzzle genre.
   I loved this book, even when I was so frustrated I wanted to chop it with my very sharp axe. These puzzles will stretch you to the breaking point, which is of course a prerequisite for being among the best ever created.
   
   Published in Journal of Recreational Mathematics, reprinted with permission.



3. An interesting aspect of this puzzle book is that the sections on the solutions are longer than those describing the problems! More than most puzzle books, you will find solutions described in great detail. The solutions in fact are the best part of the book!
   
   Many of these puzzles are unbelievably difficult. In fact the last chapter contains a list of "unsolved puzzles", which is an amusing idea. Mathematicians will spend hours poring over these puzzles. This is distinctly different from any puzzle book I have ever bought! It is more for the mathematically inclined.



4. This book mainly requires that you be at ease with mathematics and mathematical terms on the level of a high school student. The solutions don't involve long calculations and calculus books. They are brain teasers that often require out-of-the-box thought and creativity. They are excellent for computer science students studying the theory of algorithms, because often the same thought process that goes into solving the more difficult problems in that field are applicable to the puzzles in this book. The puzzles can be very difficult, and several were without solution for a very long time. There is also a group of Unsolved Puzzles at the end of the book.



5. Enjoyed the book a lot. I sometimes found the questions a bit hard to understand but that I guess that is done intentionally.

5 comments about The Joy of Mathematics: Discovering Mathematics All Around You.

1. This book could have been good if the author had done a careful job of writing the text, and perhaps if the illustrations were original, and above all if the author had understood the material she was writing about. Sadly these are often not the case with this book.

   Rather, this book gives every sign of being essentially copied from bits of many dozens of other books. All the illustrations appear to be low-quality xerographic copies from other books (clearly used without any permissions).

   But worst of all, the book is chock full of misstatements, misconceptions, and sentences that don't convey any meaning.

   This book gives the non-expert reader the impression that he or she is learning something, but a great deal of the time this is just the illusion of learning.

   I will list a few of the errors and illusory learning that I can readily find:
   ________
   p. 6: The illustration of the cycloid curve should show it to be in a vertical direction where one arch meets another; instead it is at 45 degrees to the vertical.
   ________
   p. 7: It is stated that when marbles are released in a cycloid-shaped container, they will reach the bottom at the same time. This phenomenon occurs for a bowl whose cross-section is an *inverted* cycloid, but that is omitted.
   ________
   p. 13: Both the "impossible tribar" and "Hyzer's optical illusion" are NOT mathematically impossible, contrary to what is written. (They can be constructed in 3 dimensions.) Twistors are mentioned but not defined, even in a rough, metaphoric way -- just not at all.
   ________
   p. 18: It is mentioned that pi cannot be the solution of an algebraic equation with integral coefficients, but there is no discussion in the book of what such an equation is.
   __________
   p. 19: Also, it is stated that the probability of two randomly chosen integers' being relatively prime is 6/pi. Not only should the correct number be 6/(pi * pi), but the idea of randomly choosing an integer is left completely undiscussed, although there is no known way to do this.
   ________
   p. 38: The Platonic solids (aka regular polyhedra) are discussed here, but although they are defined twice, neither definition is correct. (The author neglects to mention that the faces of such a solid must be *regular* polygons.)
   ________
   p. 45: The Klein bottle is discussed and illustrated here, but there is no mention that a genuine Klein bottle cannot be constructed in ordinary 3-dimensional space. (The familiar model of a Klein bottle depicted here is a self-intersecting version of the real Klein bottle, which does not intersect itself. This is much like the fact that a picture of a knot drawn in the plane must appear as if the knot intersects itself, though it does not do so in space.)
   ________
   p. 46: The illustration at bottom purports to show what the model of the Klein bottle would look like if it were sliced in half. The halves are erroneously shown as identical, but they should be mirror images of each other.
   ________
   p. 78: The title of this page is "Fractals -- real or imaginary?"
   This is an entirely misguided question that will only confuse the reader. All mathematical concepts are real within mathematics, and do not exist (except as approximations) in the real world.

   It's a worthwhile topic in the philosophy of mathematics, and could well have been introduced in this book, but it has nothing whatsoever to do with fractals per se.
   ________
   p. 91: Here the author attempts to describe a model of hyperbolic geometry (in a circular disk) devised by Henri Poincaré. However, she gets it exactly backwards, saying that objects get smaller as they approach the boundary of the disk.
   (She may have been well-aware of how this model works, but her prose is at best completely ambiguous.)
   ________
   p. 96: Here it is stated that it has been proved that knots cannot exist in more than 3 dimensions. Apparently the author is unfamiliar with an extensive and thriving field of higher-dimensional knots. (For example, a sphere can be knotted in 4-dimensional space.)
   ________
   There are many, many more such gaffes, but I fear I have gone on too long. I just wanted to make it crystal-clear that this book is riddled with erroneous and vacuous statements.




2. Sorry to say but this book is a dud. While the concept of presenting interesting mathematical facts is great the presentation is so brief, so wrought with errors, and so incomplete that the work is not worth perusing.
   
   Some of the "chapters" have answers at the back of the book and some do not. It appears that the author could not make up her mind wether this was to be a "math tricks" book or a "popular mathematics" presentation substantiated by theory.
   
   There are many other excellent books that are more fulfilling. Journey Through Genius comes to mind.
   
   All in all a disappointing work.



3. The widely divergent reviews reflect a lack of understanding of the purpose of this book. It is meant to touch on many mathematical ideas, not to go into depth on any one idea. My son read this at age 8, then at 10, and again at 12 - getting something more out of it every time. Many of the ideas intrigued and inspired him to seek out more information on his own, to research and understand more deeply. For that purpose, it deserves the highest rating.
   
   I did not give 5 stars because there are some instances where I did find errors, these do not detract from the purpose of the book, but they are annoying to those of us who try to delve deeper. What I consistently found myself doing is researching from the internet and other print resources. But the idea originated from the overview in the book.
   
   Many recreational mathematics books are inaccessible to beginners or math phobes. This book allows you to sample many, many ideas without feeling overwhelmed by details you may not understand. If you want details, you go explore the world opened up by the book.



4. if the discoverable arithmetic of the everyday natural world interests you, try this; and then you may want to explore her other work along this line.



5. My appreciation for Theoni Pappas is enormous as for an observer and admirer of the world around her and mathematician. These factors cannot be separated, as at first you have to do more than just look around, but you have to have a beautiful mind of a child and be an intellectualist at the same time, not just to take things for granted, but as a child be curious and ask questions and finally as an intellectualist and mathematician find answers to them.
   Yet, there is more to it. It is so, as the author popularizes mathematics. She answers the basic questions about role of mathematics in our lives. Most people associate mathematics as calculating especially money, yet in mathematics the theory models or formula are created, and it occurs that they find application in our material world sometimes even centuries afterwards. Let us look at some examples in the book "The joy of mathematics": - earthquakes and logarithms- connection lies in the method to calculate earthquakes' magnitudes by means of Richter scale, which is logarithmic, - the catenary & the parabolic curves- who takes as an obvious phenomena- the Golden Gate Bridge in San Francisco- it looks gorgeous, but what it looks like is connected with construction equations, which contribute to the fundamental thing, that it really is invulnerable and cannot be destroyed by the mass itself, as well as additional natural forces. Even Galileo noticed the curve to be parabola, - Thales & the Great Pyramid- Egiptians' calculations of the height of a pyramid were based on shadows and similar triangles, -the Dome of Milan -Gothic plans incorporating the application of geometry and symmetry in architecture, and lots of stuff like that. If you like to notice more around you, astound your friends, you should read such books, as there is more beauty around you than what you just see.

2 comments about Brown Belt Kakuro: 150 Puzzles (Martial Arts Kakuro).

1. This is an excellent book for those of you who have mastered Kakuro and want a little challenge, without having to think too hard. These puzzles can be solved without guessing or very much notes. If you want a really good challenge, go for the Black Belt Kakuro puzzles.



2. I love this series. The last two books, Brown and Black Belt are more challenging.

5 comments about The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems.

1. I haven't read nearly enough Martin Gardner.
   This book tickled the math centers of my brain, which only get partially used in my work as a software engineer.

   If graph theory, game theory, topology, and numbers don't entirely scare you away, you'll find something vaguely interesting at any page you flip to in this book, and after a few more pages will have prob learned something, AND found yourself using a part of your brain that might otherwise go unused during any given day.




2. This book is certainly not a "Colossal Book of Mathematics", and if you are looking for a book full of "Classic Puzzles, Paradoxes, and Problems", this book is not it. In short, the title is wrong and deliberatly misleading. That should be enough for one not to buy this book at all, for why should one, when the author tries a con-artist trick with the title itself?
   
   A lot of the book is full of information about stuff that is tangential to mathematics at best, like Escher drawings and other art. Escher is fine, but devoting so many pages to the symmetry drawings of a certain Mr. Kim is way out of line with what a reader might expect of this book. The "fake" chapter is also in bad taste for a book of this nature. Obviously "once bitten twice shy" is not something Gardner believes in.
   
   Also an absence of adequate proofreading is evident. For example, the author claims that N is symmetrical about a horizontal axis. Also wrong (or incomplete) is Gardner's proof about why the second player can never guarantee a win in generalized tictactoe (the "proof" actually proves that the second player can't guarantee a win without looking at the first player's first move).
   
   I however liked some parts of the book, for example an argument against the parallel universe theory is almost literature (it is not Gardner's but somebody else's whose name I've forgotten). Other interesting bits and pieces exist, too numerous to describe here, but scarcely enough to warrant a purchase. On the other hand, if your local library has a copy of this book, it's not a bad one to borrow.



3. This book covers a wide variety of subjects. It is not a puzzle book in the strict sense of solving little teasers, but it is a book that starts one thinking in broader terms. Some paradoxes and concepts addressed in this book, that great thinkers spent time debating and questioning, are fun for us more common thinkers to consider as well.



4. 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?

   Which is why Martin Gardner should be considered a national treasure.




5. 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).

2 comments about First Steps for Math Olympians: Using the American Mathematics Competitions (Problem Books) (MAA Problem Book Series).

1. It's a great book, covering everything needed for the higher level AMC competitions.



2. I read this book just two weeks before the American Mathematics Contests this year as a freshman. I had never heard of these contests, but reading this book gave me everything I need to know! With its help, I qualified for the AIME (though missed the USA math olympiad by 1 question!). If you are into math contests, trust me, this will significantly raise your score.

5 comments about Entertaining Mathematical Puzzles.

1. Entertaining Mathematical Problems by Martin Gardner is a great book for all ages. This book has over 100 problems in sections ranging from topology to games. Some of the problems are simple to many, but there are some that require thought to do. Answers are included on the back. Any math lover will surely enjoy this book.
   Paul Raff (Northwestern_Wildcat@ibm.net




2. I give this book five stars. Though the problems and puzzles were created several years ago, it introduces or, at least, reintroduces the reader to humorous and thought-provoking examples highlighting how intuitive and counterintuitive processes can collide into one another.

   Martin Gardner's witty writing style makes this book a pleasant pathway to the realms of logic. Neat and concise with its stories and challenges throughout and with solutions at the very end, the book is a very ideal read, especially if you are a passenger with a very long trip ahead and who needs good quality entertainment that is also educational.




3. Nothing very exciting. Lot more books that are better value in this category on Amazon



4. As most of Martin Gardner's books, this is an enchanting
   collection of puzzles. No author has done a better job at popularizing and illustrating the beauty of mathematics.



5. "Entertaining mathematical puzzles" by Martin Gartner is collection of rather easy math puzzles of diverse mathematical topics. Only an elementary knowledge of math and the will to resist looking up the answers before completing the problems.
   
   Clear and concise comments at the beginning of each section explain the nature and importance of the math needed to solve each puzzle. A carefully explained solution follows each problem. In many cases, all that is needed to solve a problem is the ability to think logically and clearly, to be on the alert for surprising angles or hidden factors.
   
   Here is an example of what you can find inside this book:
   
   "If three cats catch three rats in three minutes, how many cats will catch 100 rats in 100 minutes?"
   
   If you like more challenging pure mathematical teasers and puzzles, you may want to try "Challenging mathematical teasers" by J. A. H. Hunter.

4 comments about Nonplussed!: Mathematical Proof of Implausible Ideas.

1. The book of Julian Havil is certainly not easy reading. Perhaps I am a dummy, but at several pages I had to read over a paragraph several times before understanding its real meaning, but the result was always worth the trouble. The calculations itself are explained thoroughly and his way of highlighting different sidesteps are often eye-openers.
   People loving Martin Gardner's articles in Scientific American, will certainly appreciate this book.



2. This book is a valuable addition to a math-puzzler's library, but contains some flaws on real-world data.
   
   For example, Havil shows, with impeccable mathematics, that if a given player has over 91.9643...% probability of winning any given point on his or her serve, that he or she has a higher likelihood of winning at the start of the game than when the score is 30-15 or 40-30. He uses this fact to back up a claim that "a high quality tennis player serving at 40-30 or 30-15 to an equal opponent has less chance of winning the game than at its start." Again, this is predicated on that 92% or better percentage of winning any given point. But in real life, high quality tennis players, even when serving, against an equal opponent does not have this high a percentage of the points gained. Take 92% as the percentage. That would mean that over 70% of the time, the non-server would not even get one point (score of 15) during a given game. If anyone watches Wimbledon or the U.S. Open, one sees that such occurrences are rare, not common. As even Havil points out, it also implies that the server will win at least 99.9% of the games. But in high-level play, set scores of 6-3, 6-4, etc. are common. With 99.9% of the games being won by the server, 99.4% of sets would go into tie-break. That's clearly not the case in the real world. But this discrepancy is needed in order to make the "paradox" that creates the "nonplussed" reaction.
   
   In the chapter on the calendar, Havil explains why the Christian feast commemorating Jesus' ascension into Heaven never falls on a Sunday by claiming that that feast is also called Holy Thursday. It's not. It's Ascension Thursday. Holy Thursday, 42 days (six weeks) before Ascension Thursday, is the day before Good Friday, and commemorates the Last Supper.



3. This book will delight readers who like to get their hands into their math. Havil sticks to mostly elementary concepts, avoiding highly abstract fields that would lose most readers. When a subject could go too far afield, Havil warns about it and presents only the part the reader needs to know, citing original source references for the interested reader. He gives complete, understandable proofs of some startling statements--proofs that leave you understanding exactly how you got there. The great thing is that you can choose to work through these problems for yourself, verifying each step, or you can just follow along with his proofs and take on faith any simple algebraic rearrangements that he may have skipped over. Compared to Havil's earlier classic on Euler's Gamma Function, this one's a bit easier to read, with numerous short sections on a variety of topics.
   
   One minor complaint is that I found some typesetting errors. One, ironically, occurs on page 49 where he uses the notation "!n" (the number of derangements of n objects) when actually he meant "n!" (the number of permutations of n objects). It's ironic because only two paragraphs later Havil warns that !n can be easily confused with n!, whereupon he adopts a new notation for !n. In the delightfully bizarre but challenging chapter on John Conway's Fractran, there are a few typos that might confuse that minority of readers who will actually try to go line-by-line through the explanation of the Fractran machine (p. 172), but if you're one of those people, discovering the errors will anyway prove your mastery.



4. I read Impossibles first and really enjoyed it a lot. This was also enjoyable, but I found myself skimming over the proofs much of the time. I did not do that with Impossibles (but I don't remember there being as much). The problems discussed were ineresting, but I did not find myself telling my other geek friends about very many.