If you're interested in learning about magic squares, the April 2005 issue of Genii magazine is a must-buy!

Memory expert Harry Lorayne has written a 7-page article in this issue entitled, "4x4 Magic Square Breakthrough??". It starts by describing a simple breakthrough that Harry discovered for making a seemingly endless variety of magic squares given any four digits by the spectator. The article goes on to show how the numbers can be placed in any row, column, diagonal, or even the four corners, and still result in a magic square with this simple approach!

For those wondering about the question marks in the title, Harry points out how learned that his breakthrough was one simple approach among many similar approaches that are just as simple.

The article concludes with different presentations inspired by Harry's new technique. One unusual approach begins with the spectator giving you both a total and in what direction they want you to start. The article also describes the use of playing cards and special dates (birthdays, weddings, etc.).

As the article itself is written, you almost get the sense of seeing Harry Lorayne's brain at work, and how he progressed through this discovery. Not only is a whole new world of approaches to the magic square is literally opened up by this article, but the resulting squares can be different every time, even when given the same starting numbers and the same orientation in which to start!

Traditionally, the magic square method most often used involves a ready-made layout that can be adjusted to a wide range of numbers (as detailed in section 3.1 of the Mentat Wiki article on Magic Squares). Improvements have been made in this method, most notably Doug Dyment's approach in his book Mindsights, that help minimize the duplication of squares, but approach in this article takes the magic square to a much wider range of possibilities.

Magic Squares with the basis described in this article have been around for some time, of course. It is only the approach that is new. As such, this approach can be incorporated in a wide variety of existing magic square routines, including those below.

In The Mind and Magic of David Berglas, there is a routine in which you make a magic square, and you then ask a spectator for their birthday, and you point out that their birthday is listed as the four corner squares of the magic square, and also add up to the magic total. Mark Farrar's version of the birthday square, in which the top row is spectator's birthday, can also benefit from this new approach (Mark's version is available as an e-book, for only $1).

The Insight Wallet includes a magic square routine that could be adapted to both the David Berglas routine and the Lorayne approach.

Even those who use Chuck Hickok's Diagonal Magic Square will see new possibilities.

Articles like this that get me thinking in new directions about classic concepts quickly become favorites of mine.


Update: Once you've learned this technique for making magic squares, you can practice at Grogono's "Make Your Own 4x4 Magic Square" page.