The Knight's Tour, for those not familiar with it, is a puzzle involving a standard 8 by 8 chessboard, and the chess piece known as a knight.

A chess knight can move 2 squares horizontally and 1 square vertically, or 1 square horizontally and 2 squares vertically, resulting in an L-shaped move. For example, from the position depicted below, the knight can move to any of the squares marked by an X:

The challenge of the Knight's Tour is for the knight to "tour" the entire 8 by 8 chess board, using only its L-shaped move, and without landing on any square twice. If you would like to try this online before reading further, you can try it at Be A Genius* or Worle.com.

I myself have written about two different approaches to the Knight's Tour. I've written about a memorized approach here, and an algorithmic approach here and here.

I recently ran across a great column by Frederic Friedel, which uses the occasion of 9 year old boy performing the Knight's Tour on German TV as a jumping off point for a discussion of the classic puzzle.

Especially interesting for readers of this article will be Koltanowski's presentation, combining a giant memory feat with the Knight's Tour, and the semi-magic squares (all rows and columns, but not diagonals, add up to the same total) created using only the knight's move. Interestingly, the 150-year-old question of whether it is possible for a Knight's Tour to trace a fully magic square (with rows, columns AND diagonals adding up to the same total) was answered only recently.

The article only lists a Knight's Tour application for Windows, though. To remedy that, I created a Mac OS X version (G3, G4 or G5, running OS X 10.1 or greater required). In my OS X version, you can practice hitting all 64 squares, starting and ending on the same square, and even practice starting and ending on randomly chosen squares!

To learn about the Knight's Tour in great depth, read Knight's Tour Notes, an entire website just about the history and analysis of this fascinating puzzle.

Many of you may be interested in memory technique, but may not know where to start. For those of you who fit the description, and for future reference on this site, here are some excellent free courses in basic memory techniques that can be found on the web:

Mind Tools
Memory Master
How to Develop a Super-Power Memory by Harry Lorayne
neuroMod Memory Improvement Course
Be A Genius*: Memory Basics

Euan, over at the Magic Den, posted an amusing list of why memorized decks are dumb.

Judging by the comments, I'm not sure many people get the point of the article, though.

It's satire, people! The point, at least to me, is to make you think why you're using a memorized deck. Are you using it to simply stroke your own ego, or because it is making it possible to bring more amazing experiences to your audiences?

Euan's last comment is:

If you're going to use a memorized stack you might as well just start using a marked deck or a svengali deck. Or even better, a marked svengali deck with rough and smooth thrown in for good measure.

Exactly right.

With the recent rise in popularity of the memorized deck as a magician's tool, many think that memory techniques are a relatively recent development.

In actuality, methods for memorization actually date back as far as Ancient Greece!

A good basic introduction to the history of memory techniques can be found in the book "All About Mnemonics", in Chapter 2 and Chapter 3 (Thanks to SoundNumbers.com).

The same site with the above excerpts also has a brief history of the development of the phonetic alpabet, as well.

Memory demonstrations as a form of entertainment, of course, is a more recent development, but even that dates back farther than you may expect. You can read about some of the better known memory performers in Chapter XI of Fred Barlowe's "Mental Prodigies" and on Dr. Wilson's "Famous Mnemonists" page.

If these pages intrigue you, and you wish to learn more about the wide and varied history of memory techniques, check out "The Art of Memory" by Francis A. Yates.

It seems like I've always been interested in recreational mathematics, since I first realized it could be fun. However, the interest in memory techniques came later, during college.

Through my interest in magic, I'd occasionally heard of performers who did great memory feats, but I would think, "wow", and then move on.

During a summer break from college, I finally picked up Harry Lorayne's "The Memory Book", figuring it would both help in my studies, and might possibly be used in a magic trick or two. I read through carefully, and practiced the techniques before moving on to further techniques.

It turned out that one of my classes in the following semester, 18th to 20th century Art History, would be the perfect testing place for this new-found skill. The mid-term and the final in this class consisted solely of being shown 60 paintings. To get full credit for each painting, we had to write down the name of the artist, the name of the painting and the year it was painted, within 5 years (so, for a painting done in 1775, answers ranging from 1770 to 1780 would get credit).

Further, the teacher told us which painting would be on the test.

Thanks to memory technique, I only spent 2 hours studying for the test - that's only 2 minutes per painting!

The next day, when the mid-term was given, the test was a breeze. I could see all my mental links in each painting, and got every part of each answer with no problem!

Well, there was one problem...

The teacher had never seen anyone get 100% on this test before, including the exact years for all the paintings. She could only conclude that I had cheated on the test. When I explained to her that I hadn't cheated, she replied that if that were so, then I would have no problem taking the test again under her watchful eye. I agreed.

The day before the scheduled make-up test, I strengthened my mental links, just to be sure.

The day of the test, I stayed after class, and she had re-arranged all the slides in her projector. The only light in the dark room was on me, so she could keep an eye on what I was doing. She would show slides, and then watch me write the answers down.

After only about 10 slides, she came and picked up my paper. She hadn't seen me take out any crib notes, or look at my arm, or cheat in any other way. After seeing that my first 10 answers were correct and cheat-free, she apologized and re-instated my previous 100% grade!

I suppose many people might have been bitter about being accused of cheating, but I couldn't help realize that the whole series of events came about because of the unbelievable results of a trained memory!

I think the magician in me took over and said, "If she can't believe that a trained memory was the answer, how about when it is used before audiences?"

Thus began a new passion for me, that has lasted to this day.

Hermetic Press has just announced that they are taking pre-orders for Barrie Richardson's "Act Two"! This is the sequel to his now-classic Theater of the Mind.

Any reader of this blog should read the original, especially the "Mental Gymnastics" chapter, which is full of great and original lightning calculation and memory feats. As a matter of fact, the write-up for Act Two promises (among other things):

Various feats of superhuman memory and rapid calculation convince audiences of the performer's extraordinary mental powers—and their own.

There are also many other interesting goodies promised, and if his previous book is any indication, this book is probably worth the wait. I'll be reviewing this as soon as I get a chance to go through my own copy.

First, there was ipolygraph, which apparently used a lie detector to determine a chosen card. Then came Boondoggle, which proves, as we all know, that Google knows everything, including your selected card!

Now, we have Agogle, which take Boondoggle to the next level!

First, Agogle does the classic Boondoggle effect, but with the real Google search engine.

Second, if you wish to repeat the effect, and have someone else type the question about their card into Google, you can do it.

The last effect is the one that captured my attention. In it, you claim that you have memorized the entire contents of the World Wide Web. You go to Google and ask the person for any search term that interests them. It is entered into Google and, before you click the Search button, you recall the number of pages on the WWW in which that term can be found. Once click to Google's search engine proves you correct!

Of course you haven't memorized the WWW, and the claim is completely ludicrous and impossible. I have nothing against psuedo-memory effects (many of which are ingenious, as a quick download of the latest version of MemoryEffects.pdf will show), and peformed with the right combination of humbug and flair, this is a great routine to show your friends.

A few quick additions to Grey Matters:

* MemoryEffects.PDF was updated on April 30th

* Added a link to the Psychic Entertainer's Association, which has posted a link in its members only area to Grey Matters.

* Added a link to Curious Math, a site dedicated to teaching interesting math shortcuts and strategies.