Magic Squares for the Mathematically Challenged...FREE!

Published on Sunday, November 21, 2010 in , , , , , , ,

Bill Fritz' Magic Squares for the Mathematically ChallengedPerformer Bill Fritz, known to Magic Cafe denizens as Mr. Mindbender, has done some incredible work on a performance magic square. Today, he is very generously sharing it for free with Grey Matters readers!

Bill Fritz' new work, Magic Squares for the Mathematically Challenged, consists of notes and a series of 8 videos detailing a performance piece in which you create a magic square for any number from 35 to 100, as given by a spectator.

Before going through the notes and videos, you need to be familiar with what is referred to as the Foundation Magic Square. Regular Grey Matters readers will be familiar with the Instant Magic Square taught here, but it has a few flaws. First, if you use this approach for several people at the same event, they can compare their squares and quickly figure out how you're doing it.

Even if you only perform this for one person, if they choose a number like 99, the resulting magic square can still suggest the method:

 8 11 79  1
78  2  7 12
 3 81  9  6
10  5  4 80
As you can see, the numbers 78 through 81 stand out, and it's not hard to figure out that this has to do with the method.

The Foundation Magic Square solves this by allowing for adjustment to all 16 numbers, instead of just 4. If you look at a magic square for 99 using the Foundation Magic Square approach, you get results like this:
25 22 19 33
20 32 26 21
31 17 24 27
23 28 30 18
See the difference? All the numbers are in the same range, so none of the numbers stand out.

You can have a Foundation Magic Square automatically generated for you on this page. Try it out with different numbers, and see if you can start determining the pattern, using the green magic square up in the corner as a clue to the starting point. The method behind the magic square's construction is detailed here.

You can also start understanding the Foundation Magic Square concept by using your favorite spreadsheet, and seeing the effects different numbers have on the square. Those familiar with the Peg System will have a simple way to memorize the basic magic square.

Mentally finding the adjustment numbers and the remainder can be tricky during actual performance, especially when you have to keep the presentation moving as you do so. Isn't there an easier way?

Yes! It is precisely this challenge that inspired Bill Fritz to create Magic Squares for the Mathematically Challenged! Whether you're up to the math or not, I think you'll find his approach to getting the required numbers easy to use. Watch how quickly Bill Fritz determines the needed numbers in the first screencast, which I recommend viewing in fullscreen mode:

Intrigued? I thought so. Without further ado, here are the Magic Squares for the Mathematically Challenged notes themselves (downloadable at link), which I also recommend viewing in fullscreen:

Here are the complete set of links to the screencasts, as they're referred to in the notes (viewing in fullscreen recommended):

SCREENCAST #1: The Challenge
SCREENCAST #2: Introduction
SCREENCAST #3: The Concept
SCREENCAST #6: Exceptions
SCREENCAST #7: Examples
SCREENCAST #8: Presentation Tips

Don't skip the Presentation Tips video, as there are some very handy and impressive handling tips that further help the work. If the Post-It Note Magic Square presentation sounds familiar, it may be because I linked to Bill's original description of it at the end of June's snippets post.

Bill, thank you very much for sharing your incredible work on the Foundation Magic Square for free here on Grey Matters!

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