Many regular Grey Matters readers will be familiar with Michael Daniels' Mind Magician site, where he teaches numerous math and memory feats, such as calculating cube roots in your head instantly. He's recently written a new ebook on the 4-by-4 magic square, titled Perfectly Possible. I found it to be well worth the time and money invested, and wanted to share my thoughts with Grey Matters readers.

This is going to be a difficult review, as I can't give too much away, but I also want to share with you the quality of this method. I'll start with the qualities promoted by Michael Daniels himself:

• Completely impromptu. No set-up, gimmicks, or cribs.
  
• New, improved method - minimal memory and the simplest of calculations.
  
• Suitable for close-up or stage performances.
  
• Produces elegant magic squares.
  
• Can be immediately repeated for different totals.
  
• Includes a browser application that helps you to learn and practice (Internet connection not required).
  

Ever since I started this blog, I've been waiting for this day. I started Grey Matters on 3/14/05, specifically with the goal of having its 10th blogiversary on the ultimate Pi Day: 3/14/15!

Yes, it's also Einstein's birthday, but since it's a special blogiversary for me, this post will be all about my favorite posts from over the past 10 years. Quick side note: This also happens to be my 1,000th published post on the Grey Matters blog!

Keep in mind that the web is always changing, so if you go back and find a link that no longer works, you might be able to find it by either searching for a new place, or at least copying the link and finding whether it's archived over at The Wayback Machine.

2005

Two years ago, about this time, I reviewed Presh Talwalkar's previous Infinite Tower book.

Since then, not only has Presh not only been hard at work on his Mind Your Decisions blog, but also another book guaranteed to interest Grey Matters readers! This newest book is titled The Best Mental Math Tricks. Presh was kind enough to send me an advance copy, so I'll share my review in this post.

Probably the first thing to stand out about this book, when reading the table of contents, is that it's organized almost exactly backwards to most arithmetic, and even most mental math books. It starts out with a variety of mental math shortcuts for specific situations, then moves on to squaring shortcuts, followed by multiplication shortcuts, then division shortcuts, and it closes with another variety of shortcuts.

There's nothing bad about this approach. As a matter of fact, since the subject is mental math, this actually allows the shortcuts to be described in a rough order of simpler to more complex. It's also a nice change from the standard order of adding/subtracting to multiplication/division to roots/powers.

When you learn this book is put out by the author of a blog, you might be concerned that this is just a collection of previous mental math blog posts that you could access online for free. While there is some overlap, there's plenty of material in the book that has never been posted on the author's blog. Conversely, there are also several mental math shortcuts on his blog which don't appear in the book, so Presh's book and site wind up complementing each other quite nicely.

Even when there is crossover, the entry isn't simply copied straight from the blog to the book. For example, Presh wrote a post titled Understanding the rule of 72: a popular rule that has little practical value that was highly critical of this standard shortcut. In the book, however, the rule of 72 is taught with a less critical review, while still giving the reader an understanding of when the rule is and isn't appropriate to use.

The structure of each shortcut is also well thought-out. Each one starts with a description of the shortcut itself, followed immediately by practice problems which help you internalize it. Just before providing the answers to the practice problems, however, Presh explains the proof behind each shortcut, so you can get a better understanding of why it works. This is probably one of the most useful and important aspects of the book. It's one thing to learn a rule, but another thing to understand the reasoning behind it.

If you're already familiar with mental math shortcuts, you're still likely to find enough new shortcuts to make this book worthwhile. If you're new to mental math, this book is a definite treat for the mind!

At this writing, The Best Mental Math Tricks isn't available yet, but Presh Talwalkar assures me that it will be released in the near future. When it is released, The Best Mental Math Tricks is now available at Amazon.com. I recommend to anyone interested in improving their mental math skills!

One of my favorite mental challenges, as many regular Grey Matters readers know, is the Knight's Tour. The challenge is, using only the chess knight's L-shaped move, to land on each of the 64 squares once.

Mentalist Richard Paddon recently released a download resource titled The Knight's Tour: A Scenic Journey. In this post, I'll take a close look at this new take on a classic feat.

We'll start with a quick peek at Richard Paddon himself performing the Knight's Tour, via the teaser ad:



The Knight's Tour: A Scenic Journey comes as a set of 3 files: A 45-page PDF of the same title, a 16-minute MPEG file of Paddon's performance, and the Knight's Tour Windows application used by Paddon, and programmed by Dave Everett.

In the PDF, right away, the author emphasizes the importance of developing drama in the Knight's Tour presentation. The first parts of the actual instruction, however, focus on developing the path through the board. Much of this part of the book may be familiar to readers of the “Knight's Tour” section of Paul Brook's Chrysalis Of A Polymath. However, Richard Paddon does add some new and helpful notes, such as the section on what he has dubbed “delta values”, which are familiar to those who have programmed a Knight's Tour, but little discussed in the use of performances.

In the next half of the book, Paddon discusses the presentational details. He starts with the benefits of the Knight's Tour, including its uncommon nature, and its huge potential on an emotional and theatrical scale. The thoughts behind the presentations are well laid out. Even if you disagree with any aspect of the presentation as written, you at least have a good starting point of why particular choices were made.

One of the more interesting choices is ending on a selected square, as seen in the above video. As the board empties, the chosen square becomes a more and more important focus, and becomes a natural point of building tension. The PDF winds up with a detailed description of how to use the program.

There are very few weaknesses in this product overall. One of the one that stands out to me as both a programmer and a blogger of mental feats was the choice of the Comic Sans font for the numbering of the board. If you're taking as much care as this author does to make an impact on the audience, there's probably better ways to label your board than a font designed specifically to have a comic-book appearance. On an equally minor note, the lightning in many of the shots of the performance video could be better. The importance of the video is for a more complete understanding of the presentation, so this isn't a huge drawback.

Overall, this is an excellent value for anyone seriously interested in performing the Knight's Tour. The basics of working through the path may be easily accessed in multiple sources, but the depth of knowledge that is presented, as well as the use of multiple media to demonstrate this make this the most complete lessons about all aspects of the Knight's Tour and its proper performance.

It's available for only $9.95 over at Lybrary.com and is a remarkably great value for that money. If the Knight's Tour interests you, Richard Paddon's The Knight's Tour: A Scenic Journey is a must-read.

This is the last post I'll make in 2013, so it's time to take a look back at the year in posts.

There was a lot to go over this year, so I can't hit every post, but I think you'll enjoy the highlights I've chosen!

JANUARY: I kicked the year off with the announcement of my new Moon Phase For Any Date tutorial. Closely related to the moon tutorial was the lesson on how to work out the date of Easter for any date.

I also made several happy discoveries, including the release of James Burke's unedited documentaries on YouTube, and a maze programming tutorial I hadn't seen since I was a teenager!

FEBRUARY: February seemed to be a month for mental math tutorials. Besides a few quick feats, you learned about verifying prime numbers mentally, and the unusual technique of leapfrog division. Just for fun, we even brought Pi digits to life!

MARCH: We celebrated Grey Matters' 8th blogiversary with the most posts of any month in 2013! There were several offbeat memory challenges, and numerous offbeat math lessons, such as continued fractions, getting the most out of a single equation, untangling ropes mathematically, and even Scam School's lessons about cube roots.

APRIL: This month was quiet, but we still managed to cover new uses for old calculators. With Scam School's help, there were even lessons on memorizing a list of 20 items and an impressive mobile phone magic routine!

MAY: We returned to the basics at this point in the year. YouTublerone's memory technique videos made taught in a vivid way, and mental adjustments between the Gregorian and Julian calendars were made clearer. Learning to demonstrate mental feats in an entertaining way was also on the agenda.

JUNE: James Grime shared a fun way to predict sums, and Mel Stover's work was finally given due respect on Grey Matters. An interesting lesson on how to remember and calculate temperature conversions was also one of June's highlights.

JULY: After the previous month's temperature conversion post, a few new additions were introduced to make this easier. Multiplying by ¹⁰⁄₉ was made simpler, and a technique developed for this was expanded to make numerous other mental math feats easier. Our favorite game Nim also returned.

AUGUST: The main focus of this month was a mystery feat! First, a technique for mentally multiplying by 63 was taught, followed immediately by how to mentally multiply by 72. What skill could possibly require these two abilities? I won't ruin it for you, but the answer can be found here.

SEPTEMBER: Just like May dealt with the basics, September brought complex concepts down to Earth, literally, in some cases. Quick magic tricks were an early treat, and Mental Floss' Be More Interesting gallery presented an entire buffet of techniques. Logarithms and astronomy were also explored and clarified.

OCTOBER: Picking up from September, memorizing the elements, and understanding them better with help from TED-Ed videos was the order of the day. Untangling family trees with help from Wolfram Alpha was another challenge we took on. Once again, Nim, this time in finger-dart form, put in another appearance on Grey Matters.

NOVEMBER: As the holiday season drew near, Dr. Arthur Benjamin seemed to take over the blog. His performance and lecture about mental math techniques was released shortly before his fun lecture about fibonacci numbers. Inspired by this, I also taught how to work out 3-digit cube roots, along with some handy tips and tricks.

DECEMBER: As the year drew to a close, I paused for a post about time, space, and perspective, and looked back at some classic programs that helped clarify history, math, and more. The Pebbling The Chessboard problem rounded out the year with a good look at how to turn a problem into its mathematical equivalent.

Now, it's time to start looking forward to 2014, when we'll wind up 9 years of posts, and begin working on the 10th! I hope you'll join me here on Grey Matters!

There's a book out called The Mental Calculator's Handbook by Jan van Koningsveld and Robert Fountain, which naturally piqued my interest just by the title.

How does this book compare to existing books on mental math? Check out this review and find out!

First, you'll probably want to know what kind of mental math expertise the authors have. Robert Fountain is a British calculating prodigy who was the first of only 3 current International Grandmasters of Mental Calculation.

German mental calculation champion Jan van Koningsveld has held several world records relating to mental calculation, including taking only 3 minutes and 6 seconds to solve 10 problems, each of which involved multiplying two 5-digit numbers. You can find several videos online of his performances, and even if you don't speak German, they're easy to follow due to the numbers and his results being displayed.

At first glance of the contents, The Mental Calculator's Handbook doesn't seem to be much different than, say Arthur Benjamin's The Secrets of Mental Math. The first few chapters cover addition, subtraction, multiplication, division, and fractions.

Once you delve into the chapters themselves, they do begin with basic techniques similar to other books. I was pleased to discover, however, that they do take even these basic techniques farther than most books. The exercises at the end of each section, and the detail given about the techniques is written very clearly, so it's easy to understand.

This early attention to detail and emphasizing the finer points really begins to pay off when you begin learning the techniques in the later chapters, which include working out classic feats such as finding roots, our old friend calendar calculation, and the rarely-discussed factoring of numbers into their prime components.

The section on prime factorization was an especially interesting eye-opener. I was familiar with the basic techniques from my own work on primes in mental math, but the techniques here went much farther. Testing for divisibility by 2, 3, 5, and 9 are simple enough, but when many primes provide a challenge for divisibility tests, such as 7, 11, 13, and 37. The authors turn these into almost trivial challenges by showing how working with much larger numbers, such as 999 and 1,001.

Regular Grey Matters readers won't be surprised to know that I enjoy reading about and working out calendar-related challenges, and even here I was surprised! Besides just the basics of working out the day of the week for any date, you learn how to handle questions such in which years between 2000 and 2099 will Halloween fall on a weekend, and in which months of 1961 the 29th fell on a Sunday.

The Mental Calculator's Handbook winds up with brief biographies of various past mental calculators and their performances. This section especially was a very enjoyable read, and gives you an idea of just what can happen when such feats are demonstrated, and learn the sometimes sad and often amazing ways in which these performer's lives were affected.

If you're not sure of your own interest in mental calculation, I suggest starting with a more basic book, such as The Secrets of Mental Math and see if it's something you'll enjoy. Once you're ready to pursue it further, then you're ready for The Mental Calculator's Handbook, and it's greater attention to detail and mastery of the field. As a matter of fact, this book is a great bridge between the simpler mental math books, and the far more advanced ones, such as Ronald W. Doerfler's Dead Reckoning: Calculating Without Instruments.

Overall, if you're interested in mental math, and want to go beyond the basics, The Mental Calculator's Handbook is an excellent resource to take you to those next steps.

Werner Miller has certainly been keeping busy!

Not long after the release of sub rosa 3 and 4 comes his newest book, EZ-Sqaure 5!

E-Z Square 5 is available as an ebook from Lybrary.com, available in English and in German.

As with previous books in the series, this one features a particular routine concerning magic squares. The major difference here being that these magic squares are created using playing cards, similar to Richard Wiseman's The Grid and Chris Wasshuber's Ultimate Magic Square, both of which are acknowledged in E-Z Square 5.

Werner Miller explores the possibilities through 3 main routines, and a bonus routine. The first routine is the simplest, in which the spectator generates a total by selecting 4 cards out of 16, and you quickly deal a 4 by 4 square with 16 different cards whose rows columns and diagonal give the same total. The second routine, which is my personal favorite, has the spectator cut off about half the deck, and you as the performer are able to create a 4 by 4 grid whose rows, columns, and diagonals are equal to the number of cut-off cards.

In the 3rd routine, the spectator cuts off a group of cards, and deals them into 2 piles, while the performer uses the remainder of the deck to create a 5 by 5 grid of cards. When the magic total is revealed, it proves to be the same as a number created from the top 2 values on the spectator's piles!

The bonus routine may be familiar if you've purchased Werner Miller's da capo 3, as it is Squaring the Cards. In this 4 by 4 magic square routine, the magic square's total is equal to the total of the remaining cards not used in the routine!

If you're nervous about handling the various arrangements and calculations required in normal magic square routines, EZ-Square 5 is an excellent choice, as the routining and use of playing cards takes care of much of the work automatically. As any Werner Miller fan already knows, not much more than basic card knowledge is required in his routines. I recommend E-Z Square 5 highly!

Presh Talwalkar, of the Mind Your Decisions blog, has released a new ebook full of math puzzles!

It's called What do an Infinite Tower, a Classic Physics Puzzle, and Coin Flipping Have in Common?, also known as the Infinite Tower ebook, for short.

Disclaimer: I was provided with the book by the author without charge for the purposes of review. The thoughts below are purely mine as a result of going over the ebook on my own time for the purpose of informing Grey Matters readers.

Certainly, the first thing that catches your eye is the long and unusual name. The title comes from 3 puzzles in the ebook that share a common basis. Presh Talwalkar presents these puzzles and explains them in his post announcing the ebook release.

That post, in fact, is a good introduction to the style of the book. Generally, each puzzle is introduced on 1-2 pages, and the answers are provided on following pages, so as to give you an opportunity to stop and think about it.

Yes, you could just flip to the answers on the next page right away, but this will rob you of one of the true values of the ebook. Each puzzle offers the thinker what Martin Gardner dubbed an aha! moment, a moment where insight reveals a clarity that simplifies either the problem itself, or the approach of solving the problem. Helping you experience many aha! moments for yourself is the real value.

You might expect such a book to be organized, perhaps by theme, such as, say, coin puzzles vs. sequence problems there, or by puzzle type, such as arithmetic puzzles vs. probability puzzles. Instead, the problems are roughly arranged in order of complexity of solution. In other words, only the simplest insights are needed to solve the first ones, but you need to be wary of mental traps in the latter puzzles.

Some might complain that chapters would be better organized, but even if you forget the location of a puzzle, a search can find it easily enough. With the puzzles being in order of complexity, a simple glance at the page number can give you a sort of rating, as in, "Oh, I've done pretty well with these puzzles, and I'm halfway through the book. That's a good sign!"

Incuded at the end of the ebook is bonus, but it's not a bonus puzzle. It's an article on the friendship paradox that's also available on Presh's blog here. If you're not already familiar with Mind Your Decisions, this is a good introduction to it. As with many posts there, it gets you pondering, and there's more information available online, including at TED.com and phys.org.

All in all, Infinite Tower is an enjoyable way to challenge yourself with math puzzles at your own pace. If you don't have a Kindle or Kindle app, Infinite Tower is also available as a PDF file.

If you enjoy it, you may also want to check out Presh Talwalkar's other book, Math puzzles: classic riddles in counting, geometry, probability, and game theory.

This is the last post for 2012, so it's time for look back at the highlights of Grey Matters' posts over the past year.

January

(NOTE: Check out my other Nim posts by clicking here.)

Looking around the web, I've discovered many new things related to Nim, a favorite game here at Grey Matters.

Instead of discussing a new variation of Nim, this post goes back and takes a closer look at some versions of Nim that have been discussed in previous posts.

Futility Closet just posted a puzzle called Last Cent, which is simply single-pile Nim played with 15 pennies and moves limited to taking 1, 2, or 3 pennies. If your Nim skills are rusty, try and work out the best strategy for this before moving on.

Moving on to multi-pile Nim, there's an attractive new table-top version of Nim now available, called Abacan. Below is a video review of Abacan, so you can get a better idea of how it looks and works.



It's described in the video as a game where the last player to make a move loses, but readers of Grey Matters know that you could change that rule to the last player to make a move being the winner, and only a minor change in strategy would be required.

With information from my posts on multi-pile Nim, you could work out the strategy for yourself, or you could just take the direct step of using the multi-pile Nim Strategy Calculator for a 5-pile game of piles consisting of 1, 3, 5, 7, and 9 objects.

Back in the March 1962 issue of Scientific American, Martin Gardner wrote about a game called Hexapawn, and how anyone could build a simple computer out of matchboxes and a few tokens that could learn how to win the game on its own! The article was reprinted in his book The Unexpected Hanging and Other Mathematical Diversions, and later in chapter 35 of The Colossal Book of Mathematics.

In that chapter, Martin Gardner briefly mentions that such a computer could also be built to play Nim, but doesn't give much in the way to details. Over at Tony's Math Blog, Tony discusses a Nim matchbox learning computer in more detail, if this strikes you as a fun an interesting project. He called his set “A Nim's Game Experience Learning Automaton”, or A.N.G.E.L.A., for short.

Besides Martin Gardner's classic writings on this game, there are also some excellent papers and lectures about Nim available on the web. Paul Gafni has a multi-part video on YouTube, and here's the first video:



The complete series can be found at the following links:

Intro (This is the above video.)
Part 2
Part 3
Part 4
Part 5

David Metzler also has a lecture video series on Nim, and this one is a bit more technical, with computer graphics used to help explain the concepts. Here's the first video in David Metzler's Nim lecture series:



David Metzler's complete lecture can be found at these links:

Part 1 (This is the above video.)
Part 2
Part 3
Part 4

If you liked my Chocolate Nim post, there's an online paper focusing on approaches to different versions of Chocolate Nim at virtualsciencefair.org. Even if you don't understand it right away, trying out the included Java applets and practicing with real chocolate when possible will help you pick it up quickly.

If you remember my post on fractals from summer 2011, you might be startled to learn that Nim can be examined using fractals! It turns out that the humble Sierpinski triangle turns out to be an excellent tool for examining effective Nim plays, as explained in this PDF.

For even the most ardent Nim fan, there's plenty of material here to study for quite some time. If you've made your own interesting Nim discoveries, let me know about them in the comments!

You're probably wondering why I'm reviewing three books in one post. All three are concerned with magic square routines, and there's also been some mingling of influence among the books.

In addition, they all came to my attention nearly simultaneously. In fact, the author e-mailed me and offered to send me review copies of their books literally within minutes of each other.

Introduction

Persi Diaconis, the Stanford professor who discovered that 7 riffle shuffles are the minimum required to properly mix the deck, and Ron Graham, the UCSD professor who popularized the Erdős number concept (The mathematical world's equivalent of a Kevin Bacon number), have just released a much-talked about book titled Magical Mathematics.

Is it any good? No less than the late, great founder of the field of recreational mathematics himself, Martin Gardner himself wrote the foreword, so it is definitely worth a closer look.

The first thing you notice about this book, especially if you've read previous books on math-based magic effects, is that it doesn't simply stop at explaining the effect and simply stating the mathematical principle. Magical Mathematics' strength is the way in which is delves into the principle to help you develop a better understanding, which in turn can help you spur your own creativity.

Each chapter in the first half of the book is dedicated to one particular type of principle, such as cycles, shuffling, or codes. In the later chapters, the book tends toward discussions of ideas related to those in the earlier chapters. In this latter part of the book, you learn about things like magic routines involving the I Ching, prominent people in the history of mathematical magic, and even the math behind juggling!

Grey Matters readers will recognize many of the names and principles included in this book, such as:

• Martin Gardner (of course)
• The Gilbreath Principle
• Stewart James and his effect Miraskill
• Bob Hummer and his 3-Card Monte
• Robert Neale and his Rock Paper Scissors routine

If you find you like de Bruijn Sequences, you may want to check out Leo Boudreau's work, which you can find online, as well as in his books.

Despite the cover, and even the impression you might get for quickly perusing the book, the routines aren't just limited to card tricks. There are effect here with pencil and paper, origami, chains, and many other items. Even some of the card tricks, once you understand the principle behind them, can be adapted to other objects.

The best thing about Magical Mathematics is that you can take your understanding of the trick as far as you want. Do you want to understand just enough of the effect to perform it without understanding the math? The authors describe each effect and method before explaining the mathematical basis.

Perhaps you prefer to understand the principle better so that you can create your own variations. You can take yourself through the full explanation, or even only part way if you prefer, and find inspiration either way.

If you enjoy my posts on recreational math and magic, I have no doubt you will enjoy and find great value in Magical Mathematics.

Magical Mathematics retails for $29.95, including the PDF and EPUB versions, but you can obtain the hardcover version and Kindle edition for a lower price.

To help give you a better idea of the value of this book, I've posted a Google Books preview of it below. Some of the pictures in the first chapter are removed for copyright reasons, but the publisher, Princeton University Press, has generously made the entire first chapter, including images, available for free (PDF).

Michael Daniels, the webmaster behind the Mind Magician site, has just released a new PDF eBook called Speed Dating.

This eBook is his approach to one of my favorite feats, being able to name the day of the week for any given calendar date. Naturally, I couldn't resist taking a closer look.

Here are my thoughts on the bullet points from the Lybrary.com ad for Speed Dating.

* Easy calculations – The math used in this eBook is the classic approach to the day for any date feat. Most of it is simple addition. There has always been one sticking point that catches many people, but the author offers an ingenious solution to that, which I'll come back to later.

* Uses an innovative mnemonic method which is fully described – Again, if you're already familiar with the Peg/Major system (as discussed in Memory Basics), that is fully described. What is innovative here is the way the mnemonics are coded so as to bring the required key numbers to mind as quickly as possible. I do like that memorization of the year keys is emphasized here, as that's really the only way to go when speed is important.

* Simple counting technique that makes determination of the day fast and effortless – While I mentioned the one sticking point in the classic calculations, the ingenious counting method taught in Speed Dating overcomes that obstacle, and in a way that is simple to learn and use. The best part is that it overcomes the obstacle automatically. I really wish I could be more specific here, but I can't do so without giving away too much from the eBook.

* No props or gimmicks needed – This, of course, has always been one of the best things about the day of the week for any date feat, that you can do it without resorting to special props or gimmicks. Obviously, you should have some sort of perpetual calendar with you, but with the advent of mobile devices, you can usually find perpetual calendar apps without too much trouble.

* Intermediate level mentalism – Requires about two weeks’ learning and practice in order to perfect. A suggested learning schedule is included – Please pay attention to this point. If you're just beginning to learn magic, this probably isn't the best routine to learn. Once you've become more comfortable in front of an audience, and have a better idea of what to expect, this routine can be a good one. Additionally, you'll have a better idea of how to adjust for your performances and your audiences.

* Includes a browser application that enables you to practice and test your accuracy and speed (Internet connection not required) – The included HTML program is basically the same one found under step 4 of the author's online day for any date tutorial (there are a number of differences between that page and the eBook, BTW), but given its own page. The fact that it keeps your calculation time for the last question and an average is very helpful in improving your overall time.

Probably the best thing about Michael Daniels' Speed Dating eBook is the completeness. If you've thought about learning this feat, you can learn everything you need to know from this book. The counting method, the suggested learning schedule, the performance tips, and the included program are all valuable tools because of the way they aid in the learning and encouragement.

Speed Dating is available as a PDF eBook from Lybrary.com for only $10. If you practice and use the techniques in this eBook, this is a definite bargain.

The author of Mind Performance Hacks has a new book out, called Mindhacker: 60 Tips, Tricks, and Games to Take Your Mind to the Next Level.

Disclaimer: I was provided with the book by the publisher without charge, who was asked by the authors personally to provide Grey Matters with a copy. The thoughts below are purely mine as a result of going over the course on my own time for the purposed of informing Grey Matters readers.

Many regular Grey Matters readers are probably thinking, “If it's being reviewed here, then it must be all about memory, math, and logic.” Of the 9 chapters, only 2 involve those specific topics, but they're a good place to start.

Each chapter is broken up into 5 to 10 “hacks”, individual techniques that can improve your mental acuity. The great majority of these techniques are not simple re-hashes of classic ideas, rather they're either newer ideas with a solid basis, or classic ideas taken in new directions.

The Memory chapter, for example, talks about spaced repetition (which already has its own section in my Memory Tools page), but brings a new light on it by showing how this classic technique is more widely used with the advent of computers. You may have read about the classic memory palace technique, but it's brought up to date here by relocating it, into a dungeon, surprisingly (you'll have to read the book to find out how this is a modernization).

In the Math and Logic chapter, there are great hacks about topics such as how to use knowledge of common errors to your advantage, rolling mental dice, and the benefits of mixing induction and deduction with abduction.

The other chapters in the book cover learning, time management, creativity and productivity, communication, mental fitness, and clarity. With topics like these, you might expect a dry boring textbook style, but that's not the case with Mindhacker.

Sure, each hack is detailed, but never boring. As I went through it, I couldn't help but notice the emphasis on looking at old things in new ways and engaging in exercises whenever possible. Those of you who have Mind Performance Hacks might remember the occasional use of download computer programs to help in the exercises, which also happens here. There is a great sense of fun in each hack, but it never overpowers the original purpose, so as not to lose sight of a given hack's goal.

Obviously, as a non-fiction book, this isn't meant to be read from beginning to end. There are however, two basic ways to read it. Feel the need to improve, say, your mental creativity and productivity skills? Look that up in the table of contents, and find that section to learn more. Want to reread a particular hack, or look for a specific type of help for a mental challenge? Look through the second table of contents that covers both the chapters and individual hacks. This definite gives the book a more approachable feel.

Mindhacker really is a good match to Grey Matters readers, as it is all about improving your mind, and having fun while doing so. It's approachable, educational, fun, and neither intimidating nor condescending in tone. I highly recommend Mindhacker. If you haven't already picked up Mind Performance Hacks, do your mind a favor and pick them up together.

It's been a long time since the release of both Impuzzibilities and Further Impuzzibilities, but author Jim Steinmeyer has finally released the latest in the series, Subsequent Impuzzibilities. Is it a worthy successor to the previous two books? That's the topic of today's post.

If you're not already familiar with the first books in the Impuzzibilities series, either go buy them now, or at least check out my 2006 review of both books. That way, at least we're starting at the same point.

Subsequent Impuzzibilities should be of interest to Grey Matters readers not only because it's about magic, but especially because the focus is on math-based self-working routines. Because of this focus, you can be amazed by performing the tricks as you read them. You can perform many of them over the phone, as well.

Before I get into the individual tricks, I'd like to mention that the psychology of each presentation is very finely crafted, and should be studied thoroughly as lessons in themselves. This shouldn't be surprising, since Jim Steinmeyer himself is the mind behind some of the greatest illusions and presentations of our time.

The book opens with “Eleven Roads to Heaven”, which is a great example of my point about the presentations. This 11-card routine involves repeating the same sequence of steps several times, which could quickly and easily become boring for the spectator. However, the ingenious presentation here of being able to pick out a face in a crowd the more you see it prevents the spectator's potential boredom.

In the previous book, Further Impuzzibilities, there was a trick called “Automatic Palmistry”, involving absolutely no props other than the spectator's hands. This book's “Fingertip Mindreading” is a good follow-up involving only the fingers of one of the spectator's hands.

One of the big hits of the original Impuzzibilities was the Nine Card Trick, which was popularized by no less than David Copperfield:



In Subsequent Impuzzibilities, continues examining the possibilities of this principle with “The Password Fallacy” and “A Universal Password”. In both of these routines, the routine is played as an example of the performer finding out the spectator's secret (a card name) as if they were hacking a password. I haven't seen this presentation used much in magic, yet it seems such an obvious match for many card location routines. This is where you start getting a sense for the genius of Jim Steinmeyer.

What the “Why didn't I think of that?” password approach is to presentation, the approach used in “Enigmatic Poker” and “Enigmatic Tarot” are to method. These tricks involve a somewhat unusual procedure involving the spectator telling you exactly how to shuffle, while the cards remain under much more control than it would seem. Even though they use exactly the same mixing procedure, their respective presentations justify the strange mixing in two different ways. Already I can see that this is the one thing from the book that will be adapted in myriad ways by magicians in the coming months.

Also written up earlier in the Impuzzibilities series is the “One O'Clock Mystery”, also popularized by David Copperfield:



In a similar vein, the newest book contains a number of similar effects in which several things are seemingly chosen at random, yet the outcome can be predicted in a myriad of amazing ways. “Number, Number, Number” and “A Trip Around the World” are longer routines with surprising punches, while “Force Six” and “Force Ten” are simple enough to print on your business card!

“Deal Three” is a great routine involving a different mixing procedure, this time done by the spectator. It almost seems to be a halfway point between the password routines and “Enigmatic Poker”. The person for whom you're performing can do this seemingly-fair mixing procedure as much as they want, yet you can still control the outcome. I can see this being very deceptive when mixed with the Free Will principle.

The remaining two routines from Subsequent Impuzzibilities I've saved for mentioning at the end because they both play big in their own way. “Ten in Concert” is a 3-phase routine in which the cards themselves repeatedly seem to know about the audience member's choices.

“The Magian Who Fools Himself” plays big because it can be done as a stage routine. All you need is someone from the audience, a deck of cards, a chair for the person to sit on, and something to hold the cards, such as a glass. In this effect, the spectator plays the part of the magician, and causes a card to vanish from one place and reappear in another. It's a re-working of the principle in “Teleportation”, and is an excellent lesson in why not to stop thinking about a routine.

Because these tricks are self-working, many may dismiss them. Not only will those who dismiss these tricks lose out on the presentations already there, but they won't see the potential of adapting these pieces to themselves. Also, there's nothing wrong with adding the occasional sleight or subtlety to improve them. David Copperfield's videos above are a good example of adapting and adding to routines like these.

In short, I recommend Subsequent Impuzzibilities highly, as well as all the Impuzzibilities books, not only for the tricks in the book, but for what you can learn about presentation, how to think about magic, and keeping things simple.

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Answer to Pi Day Magic 2 puzzle:
4C, 4D, KH, 9H - This arrangement could be used to cue the 6C.

Werner Miller has developed some great new approaches for magic squares, and has released them in two eBooks: E-Z Square 1 and E-Z Square 2.

E-Z Square 1

E-Z Square 2

Final Thoughts