What?!? You haven't finished your Christmas shopping for your favorite geek yet? In that case, I have some updates to the 2005 Grey Matters Gift Guide:

Starting with my personal favorite, Pi-related items, ThinkGeek has reponded to those of you who think it's too cold for Pi T-shirts and Pi babydolls, by bringing us the Pi hoodie!

Of course, staying inside can also help keep you warm. However, to really get that blood circulating in the brain, I suggest playing Polarity. Imagine magnets meet Reversi (also known as Othello), and you'll start to get the idea.

Here's a great post from John Biesnecker, an American who is currently living in China. He shares his experiences and often amusing personal mnemonics as he learns to read and write Chinese characters.

This post is a good example of why, as useful and as powerful as mnemonics can be, it's often best if you keep them private.

Even if you've never thought about competing in the World Memory Championships, about which I've written before, you may still wonder what it would be like, and how you would stack up. If so, I have great news for you!

Tony Buzan, founder of the World Memory Championships and the Buzan Centres, has created an ongoing online memory contest that anyone can enter as much as they wish. This contest is called the World Memory Challenge!

The challenge consists of at least 3 tests, more if the website determines you can handle further tests. The tests consist of things like memorizing the order of playing cards and other symbols, matching pairs of cards, and even matching names with faces. To get an idea of how the various challenges are presented, check out the online tutorial first.

A score is kept as you play, but you don't see it until you go as far as you can with the tests. The site lets you see your full ranking details if you enter your e-mail address. To compare your scores in various ways, the site also keeps track of constantly updated statistics, so you can see how you measure up against the average in your own country, against other countries, by gender, age and even occupation!

If, like me, you would be interested in seeing how well the average reader of Grey Matters does, please post your best scores in the comments! I'll keep my best score updated in my profile, for those who are interested.

Oh, and if you need any help improving on the tests, then simply spend more time reading this blog!

So, you have a friend or family member who's a math and/or memory geek, but you're not sure what to get them for the holidays? Not to worry, the 2005 Grey Matters Gift Guide is here!

What better place to start than a T-shirt featuring a mnemonic on it? This T-shirt from ThinkGeek.com features the classic mnemonic for the formula for sulfuric acid:

Johnny was a chemist's son,
But Johnny is no more.
What Johnny thought was H₂O,
was H₂SO₄!

Of course, where math and memory skills meet, Pi is always there! For those who enjoy the classic challenge of Pi, you can encourage their achievements with a T-shirt featuring 4,493 digits of Pi! Don't forget, though, that there are ladies out there who take on the challenge. For them, there's the same t-shirt design available in babydoll style.

I can here some of you saying, "Sure, T-shirts are a great Christmas gift in some places, but what about those of us in the northern hemisphere?" No problem! Just wrap yourself in a nice, warm blanket, featuring the first 410 digits of Pi. I'll even help you memorize 400 digits of Pi at no extra charge. You're on your own for the remaining digits, however.

Before we leave the Pi-related gifts, why not tell the world how easy memorizing Pi can be, with an "Simple As 3.141592..." T-shirt?

That last T-shirt is put out by the good people at mental floss magazine (yes, I meant to type the magazine name entirely in lower case). Mental floss's motto is "::Feel Smart Again::". Although it is one of the more inexpensive gifts in this guide, a mental floss subscription can help your favorite geek or trivia lover feel smart all year (assuming you're not trying to avoid that)!

Speaking of reading material, there is a great selection of Memory & Mnemonics ebooks from Lybrary.com, including the hard-to-find "How To Develop A Perfect Memory", about which I wrote in my second blog post.

If your favorite geek leans more towards math, then the Martin Gardner's Mathematical Games CD-ROM, containing all 30 years of the mathematical master's Scientific American columns should be just the thing.

For someone who likes to perform the calendar recall feat, but never seems to have a portable perpetual calendar around for verification, perhaps a Calendar Wheel, or a nice wooden perpetal calendar from Sculptures-Jeux would come in handy.

But for something really special, let's consider the Knight's Tour. The mathematicians can do the Knight's Tour their way, and the memorizers can do the Knight's Tour in a completely different way, but they both still need a way to demonstrate the feat. To answer that want (need?), we have the Knight's Tour Excalibur by Devin Knight, complete with 3 different size chessboards for different audience sizes, as well as plenty of extras. For those who would like to be able to do the Knight's Tour, but don't want to put in the work, it even includes a method that makes performing the Knight's Tour much simpler, yet doesn't interfere if you wish to perform the legitimate versions!

I'm just doing my part to make your holidays happier and geekier.

Thanks to a recent e-mail discussion with some friends who also share an interest in memory work, we've managed to devise a simple way to find out when and how frequently "Friday the 13th" will occur in a given year.

First, you'll need to be able to perform the standard calendar feat. There are several variations in the formula, so I'll assume that you're using the version taught here. Once you've become comfortable practicing this version, you'll be ready to move on to the Friday the 13th version of the feat.

Start with the number 6. From this, subtract the code number for the year. You're done.

Yes, that's it. The resulting number will give you the month code for all months in that same year that contain a Friday the 13th.

As an example, let's figure out in which months a Friday the 13th will occur in 2006. The key number for 2006 is, interestingly, 6 (See here and here for details on how this was determined). Subtracting 6-6, we get 0.

Which months have a code number of 0? Only January and October do. Therefore, in 2006, only January and October will have a Friday the 13th. Checking the 2006 Calendar, we can verify that this correct.

Don't forget to adjust for leap years when necessary. In leap years, January is 6 and February is 2.

Why does this work? The original calendar formula has you add up numbers representing the date, month and year to get the day of the week, so it stands to reason that we can start with the day of the week, and subtract the date and year to obtain a month number.

Friday is equal to 5. Keeping in mind that we can add multiples of 7 without affecting the outcome, we'll add 14 to 5, getting 19. From this, we can subtract the date in which we're interested, the 13th, without working with negative numbers. 19 minus 13 equals 6. From 6, all we need is the key number for the year, which runs from 0 to 6. The result can only be the key number for the months containing a Friday the 13th!

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Just when you think there's nothing more amazing about magic squares, someone goes and proves you wrong. I've run across some amazing magic squares, including ones that are gigantic, or work with multiplication instead of addition, or can be toured by a chess knight and so on.

Here's an 8 by 8 magic square. See if you can guess what is so unique about it:

14    56    55    54    53     7     8    13
1     24    16    45    44    43    23    64
63    15    40    26    27    37    50     2
62    48    29    35    34    32    17     3
4     47    33    31    30    36    18    61
5     19    28    38    39    25    46    60
59    42    49    20    21    22    41     6
52     9    10    11    12    58    57    51

True, it does total 260 horizontally, vertically and diagonally, and uses all the numbers from 1 to 64, but that is hardly unique among magic squares.

Here comes the truly magic part. Let's see what would happen if we removed the top and bottom rows, as well as the leftmost and rightmost columns:

24    16    45    44    43    23
15    40    26    27    37    50
48    29    35    34    32    17
47    33    31    30    36    18
19    28    38    39    25    46
42    49    20    21    22    41

Surprise! We still have a magic square! This 6 by 6 square totals 195 horizontally, vertically and diagonally.

Would you believe we can trim this magic square again, and still get yet another magic square?

40    26    27    37
29    35    34    32
33    31    30    36
28    38    39    25

This 4 by 4 magic square totals 130 in all the directions of the previous squares!

These unique constructs are referred to as nested magic squares, and it is possible to create them for any size square starting at 5 by 5.

The above examples were taken directly from the Nested Magic Squares webpage, which teaches methods for creating your own nested magic squares. For those of you who use Matlab, or an Excel-compatible spreadsheet, files are included so you can experiment with these squares yourself.

Just for fun, the author has also included some ginormous magic squares in ascii format, like the 99 by 99 nested magic square (multiple monitors may help in viewing this properly)!

No, there's no practical use for nested magic squares yet (which I consider to be one of their better qualities), but I'll take the experience of wonder wherever I can get it.