Grey Matters is back, and the computer troubles are now over! I thought I'd return to blogging with July's snippets.

• There's a new group of British street performers that are right in the spirit of Grey Matters. They're called Maths Busking and they entertain with mathematical feats, in an attempt to get more people to see how interesting and engaging math (or “maths”, as they say in Europe) can be.

There's a great Maths Busking intro video over at Guardian.co.uk (Flash required), and an amusing video of BBC reporter Ruth Alexander's turn at Maths Busking (Flash required) on the BBC site.

• Speaking of things that fit well within the spirit of Grey Matters, there's now a blog called New Mental Magic. It focuses on teaching easy ways to do math in your head. Give it a look.

• For those who like to keep their MAGIC Magazine database up to date, I've just added the information for the July 2010 issue of MAGIC. On that same page, you can also get data for issue from November 2009 through June 2010, as well. All the other data is available at the MAGIC Magazine link at the beginning of this paragraph.

• The July 2010 issue of MAGIC features a very large tribute section to the late Martin Gardner, including a look at the mini-column he wrote in MAGIC for many years. Even if you don't regularly read MAGIC, this issue is well worth picking up for Martin Gardner fans.

• If you haven't been keeping up with my Twitter feed (as seen in the righmost column of this blog), I've been posting a series of videos (and one text page, so far) teaching various memory methods. You can find the posts at these links: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10

• Most readers of Grey Matters know that I have a special place in my heart for Pi, even going so far as to start this blog on 3/14. So, it was a little jarring to hear it suggested that Pi is Wrong! (PDF). The basic idea is that what we call 2*Pi should really be Pi, because of how most formulas involving Pi work out. Michael Hartl explores this idea further in The Tau Manifesto: No, Really, Pi is Wrong.

If all the talk of radians confuses you, check out BetterExplained's Intuitive Guide to Angles, Degrees and Radians.

• One last goody – the movie The Phantom Tollbooth is available online again for free! Instead of being in an unwieldy 14 parts, as it was previously, it's down to a more manageable 2 parts. Check out the movie, and enjoy!

Unfortunately, due to computer trouble, I'm not able to provide a full post today. I'm getting the trouble cleared up, and I'll be back with much more for Grey Matters readers soon.

In the meantime, you can still keep up with mental goodies by following my Twitter feed (at the link or over in the rightmost column.

Thanks for your patience!

The United States of America is 234 years old today. In honor of that, we're going to challenge your brain's knowledge of the USA!

Don't worry. I'll start slow. Before any kind of exercise you need to stretch, don't you?

Start by imagining that Puerto Rico becomes the 51st state. According to the Flag Act of 1818, a new flag containing 51 stars would be released on the following July 4th.

What exactly would the US flag look like? Skip Garibaldi has examined our past flags, and used that knowledge to work out what the US flag would look like with up to 100 stars. He also discovered that we'll be faced with a quandry if we ever have 69 or 87 states.

The adoption of the Declaration of Independence on July 4th, 1776 is, of course, why we celebrate it as Independence Day.

The late Martin Gardner has actually managed to turn the first sentences of the Declaration of Indpendence into a magic trick, with a little help from Martin Kruskal.

We're passed the warm-up, and we're going to start with the big challenges. Sporcle is curious to know how many signers of the Declaration of Independence you can name in 10 minutes. Mental Floss, on the other hand, wants to know if you can identify the states that some of the lesser known Declaration of Independence signers were representing.

If you've read this far thinking, “Would the Founding Fathers really support celebrating Independence Day with these sorts of brain challenges?”, I'd like to think at least one would support this approach: Ben Franklin. He loved magic squares! A little over 4 years ago, the Sunday Times even posted Ben Franklin's Magic Square Challenge, whose goal was to complete this square so that it totals 2,056 in as many directions as possible.

From those original 13 states, the USA has grown to 50 states. To help you learn the 50 states in a fun way, explore the visual USA state mnemonics over at 50 States of Mind. They're fun, educational, and will help with the following quizzes.

The first quiz? Name all 50 states in 10 minutes, of course. If you know your states, can you name all 50 state capitals in 10 minutes?

Now that you have all that information, how well can you filter it out? One classic challenge is to name all 8 states that begin with the letter M in 1 minute. Did you find that tough? Study those states with Lou Ryder, and then go back and try again.

For a similar challenge, try and name all 21 states whose names end in the letter A in 4 minutes. No, I don't have any resources to help you learn this one.

Don't get too used to states with certain letter patterns. Geography is about physical features. Can you name the 23 states that border the Atlantic Ocean, the Pacific Ocean, or the Gulf of Mexico in 3 minutes?

I'd love to hear how well you did on any of these challenges. Let me know in the comments!

Have a safe and happy July 4th!

I've posted quite a bit about magic squares in the past, but most of them required some calculations to present.

This week, Scam School teaches the Easy Magic Square Cheat, where you look like a genius with far less work than it would appear!

Check out the video below, and after I'll delve into more detail about this presentation.



There's really two parts to this presentation: The first matrix, which forces the number 34, and the magic square you've simply memorized as a result.

The forcing matrix is actually quite a versatile tool, and can be developed for almost any size and almost any number. Doug Dyment's article, How to Construct a Forcing Matrix, is an excellent introduction to this topic. It even includes a downloadable Excel spreadsheet, so you can understand the ideas hands-on.

Martin Gardner gives an even more thorough examination of the forcing matrix in chapter 2 of his book Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games (see a partial chapter preview here).

This nice thing about working with a fixed total in this presentation, is that you can present a magic square without practicing any calculations. As long as you rehearse the arrangement taught in the video, you'll be able to look like a math whiz doing fast and difficult calculations.

Are there other calculation-free magic square presentations? Of course!

Here's one: Introduce the basic concepts of the magic square, and point out that it's long been thought by mathematicians that the smallest possible magic square is a 3 by 3 arrangement (Why are there no 2 by 2 magic squares?).

You then bet that you can show an arrangement of fewer squares that makes a magic square. This sounds impossible. How is it done? You show them this. At first, it doesn't even seem to be a square, but when you pull out the mirror, it not only becomes a square, but a magic square, as well!

Werner Miller is also responsible for another great magic square presentation, in which your Windows computer, iPhone, or iPod Touch handles all the needed calculations for you. It's called the Age Square:

• iPhone/iPod Touch online version
• Windows offline executable version

Here's the presentation and the method behind Werner Miller's Age Square:



In my recently-added 15-puzzle tutorial, I include a magic square solution that doesn't require any calculations, either. You do need to practice solving the 15 puzzle itself, though. Doug Dyment, who wrote the above forcing article, also helped me find the arrangement used in that feat.

Returning to Werner Miller, who must dream in magic squares, our final calculation-free magic square presentation is his Holey Number puzzle/paradox. As a matter of fact, I present this feat mixed with the previously-mentioned 15 puzzle, in a presentation I described here.

If you've tried any of these magic square presentations out, or simply have any questions or comments about them, please let me know in the comments!

Picking up from the Fairy Tales post, let's talk specifically about Rip Van Winkle. Shortly before the American Revolution, he wandered up into the Catskill Mountains, where he is supposed to have run into a group of men playing a variation of nine-pins/skittles (shortly before drinking their liquor and sleeping for 20 years).

Let's take a closer look at one variation of nine-pins, introduced in 1857 in Henry Ernest Dudeney's The Canterbury Puzzles as kayles (rhymes with ”tales”).

The rules of kayles are fairly simple. A ball is rolled at a line of wooden pins. The ball is of such a size that it could knock down either a single pin, or two pins that were right next to each other. Two players take turns, and the winner is the person who knocks down the last pin.

When playing with a real ball, the challenge is a combination of strategy (which pins will give you an advantage?) and skill (can you knock down the pins you want?). For the rest of this article, we're going to assume that the game is played by two skillful players who can hit the pins they desire everytime. This way, we can examine the strategy.

Let's start with a line of 5 object (coins, for example), using an O to represent an individual coin in the set-up:

OOOOO

O.OOO

O.O..

OOOOO.OOOOO

OOOO..OOOO

OOO.OOOOOOO

OOO..OOOOOO

OOO..OO.OOO

OOO..OO...O

OOO..OO....

.OO..OO....

Between discussing the memorization of poetry (as well as memorizing speeches, monologues, and lyrics) and nostalgic, fun, and free learning resources with a friend recently, he brought up one of the oldest ways of teaching, learning, and memorizing that I'd completely ignored: Fairy tales!

Granted, you don't usually memorize fairy tales like you would a poem or speech. The important part is the lessons learned at the end. It's because of this that fairy tales tend to change from teller to teller, which is part of their fun. It's also a self-working mnemonic technique, as the lesson you need to remember is associated with all sorts of weird and vivid images.

As technology advanced, there were, of course, frequent efforts to re-tell these fairy tales in the new mediums. So, if you're ready to go, let's check out some of the oldest stories told in some of the most modern of ways – television!

Jim Henson's The Storyteller – This was actually a show within another show. In the show The Jim Henson Hour, the second half (this is why the playlist doesn't feature parts 1, 2, and 3 of most of the videos) would usually be dedicated to a segment simply titled The Storyteller, featuring John Hurt. The combination of Jim Henson's direction, and the depth of research into the fairy tales that are told made for a breathtaking and enjoyable experience every week!

Shelley Duvall's Faerie Tale Theatre – Yes, this is the same Shelley Duvall whom you remember from movies like The Shining and Popeye. This series featured a wide variety of directors, including Tim Burton and Francis Ford Coppola, so as to bring different attitudes to each of the 26 episodes, along with many well-known actors. They even had noted children's book's authors frequently design the sets!

Grim Tales – This British series featured exclusively on the fairy tales told by the Brothers Grimm. It's also the “edgiest” of all the series on this list. Rik Mayall would tell each story in his pajamas and bathrobe, while sitting in a chair that had paws and ostrich legs. Somehow, it all worked, but you need to experience it to see how.

Grimms Fairy Tale Classics – While employing a similar name to the previously-mention Grim Tales, this series couldn't be more different. This was a fairy tale series tailored to younger viewers. Originally from Japan, this anime-style fairy tale anthology series is instantly recognizable to Nickelodeon viewers by its memorable intro.

Long Ago and Far Away – This PBS series was hosted by James Earl Jones. It featured a wide variety of fairy tales from other countries (including several Hungarian folk tales), so it often included ones that weren't familiar to Western audiences. Probably the most recognizable episode of this show would have to be The Man Who Planted Trees.

Do yourself a favor, and sit through at least one tale from any one of the above shows.

The above links aren't exhaustive, so searching for more episodes by their above titles will help you find even more episodes.

Why do I keep coming back to Scam School videos? Because they're so often an entertaining and effective way of learning mathematical concepts.

This week, Scam School teaches Bob Hummer's 3-Object Divination. This is strangely reminiscent of 3-card monte, but with a mind-reading twist.

Watch the video below, and see if you can work out the method before watching the explanation (Stop on or before the 5:27 mark):



Were you able to work out the method? Whether or not you were, finish watching the video, and make sure you understand the method.

There are several great things about the routine. First, it's a great example of how even simple logic can be made to appear as a near-impossible feat. Second, because the logic is the method, you can (as noted in the video), apply this principle to any three objects. You could play this big and use large objects on a stage, if you so desired.

This trick was originally marketed by Bob Hummer in 1951 as "Mathematical Three-Card Monte". You can read more about the original version in Martin Gardner's book, Mathematics, Magic and Mystery. Thanks to Google Books, you can read about it online for free: Part 1, Part 2, Part 3.

Notice in Bob Hummer's original version, you don't turn around. Instead, you have them call out the objects as they're switched, then turn around. Depending on how you're presenting this feat, this touch may make it more or less impressive. Having the moves called out can make it seem more technical, while watching the moves has a more casual appearance.

Since Bob Hummer's original version of this routine, there have been some great thinkers turning their minds to this very routine. Harry Lorayne has developed a nice addition to this routine where you never turn around to examine the objects (this version can even be done over the phone!). This was originally published in Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American, and is now also available in Harry Lorayne's own book, Mathematical Wizardry.

Magician Max Abrams developed a great version of this classic, but routined it as a test of the spectator's ESP. It features the interesting twist that the performer mixes the cards, yet is still engaging. It also comes across less as a puzzle, and more as a shared experience. It's called Hummeracle!, and can be found in the March 1990 issue of Genii magazine.

Take a deeper look at this great routine. It's well worth your time.

The Knight's Tour lessons have long been a popular section of Grey Matters. Thanks to the efforts of the people at the Mind Magician site (formerly psychicscience.org), I've been able to add videos to the lessons over there!

There are two new videos, the first of which shows how to solve the standard Knight's Tour, and the second shows the advanced version, where you learn how to let someone choose the starting and ending squares.

The board used in these videos is also available online for free, and is a wonderful instructional tool

Here's the basic version, which has also been added to the Using The Patterns tab of the Knight's Tour lessons:


Once you've practiced that approach and are comfortable with it, you can then move on to the advanced Knight's Tour. This video can also be found in the Advanced tab of the Knight's Tour lessons:


Over on the new Downloads page, you'll find several versions of the Knight's Tour you can use to practice, including my Knight's Tour+ iPhone/iPod Touch app.

For those of you who enjoy practicing the Day of the Week For Any Date feat, Mind Magician also features an excellent tool for practicing this feat, as well as an alternate approach to determining the date.