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.

Pi will always be geekily close to my heart. That is why the very first post on this blog was about Pi, and why the blog itself was started on Pi Day.

That is why I like to see people like the ambitious blogger who runs the Desktop blog, for challenging himself to memorize 1000 digits of Pi. Why he jumped from wanting to memorize only 50 digits not that long ago, to 1000 digits, is beyond me.

What is scary is that I can both understand and relate to every one of those New Year's resolutions.

Checking around other blogs for items on memory techniques, I ran into what at first appeared to be the most incredible coincidences in blog history.

It started when MSN Encarta posted an article about four tricks for improving memory. It caught plenty of people's attention, which isn't hard to do when you're Microsoft. Plenty of people naturally includes plenty of bloggers.

Full reprints of the article can be found at:

* Let's call it a day :)
* Green Place
* blacklabel
* Sampler
* weblogkoto
* I Started A Joke
* The Tunes
* WaveLinx

It may not get the coverage of MSN Encarta, but I've found Mentat Wiki to be more in-depth when it comes to memory techniques.

Update (11/17/05): This article is still making the rounds. Add STuDeNTLiFe to the list.

Over at the Explorer blog, Koh Xuan Yang has just posted some mind-boggling 9 by 9, 10 by 10 and 12 by 12 magic squares. Check them out, and be amazed!

Mindvention began here in Las Vegas today, over at the Palace Station Casino. Mindvention is a convention dedicated solely to mentalism. As I unfortunately didn't have the time available to attend the whole convention, I spent the afternoon in the dealer's room, and I'm glad I did!

Chuck Hickok was there, with his complete line of mentalist's tools, including his brand new book, Mentalism Incorporated, Volume 2. The new book contains just about everything that Chuck has published since the original book, except for his limited edition of the Diagonal Magic Square. I picked up the Diagonal Magic Square along with the new book, and I'll be pouring over the both of them in the coming days.

Mark Strivings was demonstrating his new trick, Mnemerica. The tools themselves are a clear board with 9 pegs, and 9 black disks marked 1-9, which magnetically adhere to the pegs. In the routine, the disks are mixed up, and used to create a random equation, the answer which has been predicted. The principles behind this are similar to Predict Perfect (scroll to the bottom), which I've mentioned in an earlier entry.

These are the ones that really caught my attention, but there were many other dealers with routines to catch the eye and melt the mind. This small taste of the Mindvention did prove to be the best advertising, so I may have to set aside a little more time and money for when it comes back to Vegas next year.