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!