I'm just getting into magic squares. I've memorized the magic square taught by Harry Lorayne int "The Magic Book.

Harry mentions that he wouldn't repeat it for the same group because they might notice the pattern.

I work restaurants and while I don't think I would repeat it for the same group I would be concerned with people comparing the results if I give them the square as a souvenir.

I recently noticed that the square I memorized "wraps" on itself. I'm pretty sure I could fold the piece of paper into a cylinder either vertically or horizontally and then cut it apart anywhere and it would still work. Right?

Also, it doesn't matter if you write the numbers vertically or horizontally and you can mirror reflect the whole thing and it still works.

So it seems to me I can start writing my 8 in any square I want and move in any direction I want as long as I am careful to follow the rules of "wrapping" and all will still work in the end. this combined with the fact that the key numbers change depending on the two digit number numbed by the spectator means that the square I come up with will not be very likely to look at all like any others I've ever written.

I played with it tonight and checked the math and it seemed to work. I just wanted some confirmation that this was correct or some warnings if I am wrong.

If I can come up with magic squares that don't resemble each other just by reflecting and shifting this one square, what are the advantages of learning the more complicated squares I have seen others discussing?

I'm a newbie in this area so be kind. Thanks!

Mike you might want to check out Doug Dyment's site, deceptionary.com . He sells an inexpensive booklet called MindSights. In it is his solution to the exact issue you are talking about. He provides templates for various rotations and reflections as well as some clever ruses to disguise any appearance of repetition.

The rest of the booklet contains other items which are unrelated but also excellent. Highly recommended.

Thanks, I'll check it out.

Bill Fritz has a great set of lecture notes and videos ......or free.

In his routine, the magic square is different every time, and the math has been minimized.

Thanks Scott,

That answers my question about what are the benefits of more advanced magic squares compared to just learning the one in "The Magic Book".

On the page you link to he shows that the magic square I know how to make has four numbers that stand out from the rest and might point to the method. His method fixes this,

But, I don't really think this is anything that someone would pick up on. For all they know this is just the way Magic Squares look (If they even noticed it).

I think I'll be quite happy to do the one I now know and add my own reflections in case people compare squares (I know in my Restaurant work people WILL do that).

I'm still going to look at his method and I do think it is an improvement. I just had a heck of a time learning to memorize the one square and calculate just those 4 numbers on the fly. I don't think I'm going to want to calculate all 16 numbers even if it is relatively easy.

I am currently writing an ebook called "Mostly Perfect" which improves and simplifies the Fritz/Farrar/Meyer method for constructing a 4x4 magic square for any total. The square is even more "balanced" and only one simple calculation is needed.

Mike

Similarly, I have taught (at my private workshop):
My technique is not based on the Fritz approach, though, and does not require learning sets of numbers.

Thanks guys,

You are all very generous. I know magic square aren't for every one but my philosphy is to have a lot of tools in your toolbelt. I have card stuff, sponge balls, fire wallet, balloons, etc and now a little mathemagic. It's great if someone asks you about poker and you have poker trick or if they say they saw a math wizard you can say "well I can't do that but let me try a little something..."

My new magic squares eBook, "Mostly Perfect" is now available at Lybrary.com (link in my signature).

Mostly Perfect describes a new variation that simplifies the computation of the Orville Meyer (also Bill Fritz, Mark Farrar) 4x4 method for ANY total, and that produces even more balanced and elegant squares (the difference between the highest and lowest number in the square is never greater than 16). The summation constant can be found in at least 36 ways.

The eBook also comes with a browser application (no Internet connection needed) that facilitates learning of the method.

As a (relatively) modest improvement over the Meyer method, I have accordingly priced the 29-page eBook relatively modestly at $6.00.

Mike

Mike,

I don't check TMC very often, but I just came across this thread where you mention your Mostly Perfect book.

Having bought, downloaded and read it, I love the simplifications to the formula, and the way that your method creates such a well-balanced square. (Like you, this has always seemed like a flaw in the many "instant" methods that exist.)

It's well-written and well-presented, and I love the training tool that you also provide.

The only downside, for me, is that the basic square you use is different to the one I've been using for over 30 years, so I may have to see how things can be re-worked so that I don't need to learn another basic square.

And thanks for the mentions, too!

Once I've had time to digest it more fully, I'll write a detailed review on my Magic Squares Book blog.

Thanks for great contribution to the world of magic squares literature.

Many thanks for your kind words Mark. I really appreciate it, especially as your own important work in this area has been a great help to me.

The Mostly Perfect computational method will work with any basic 'Diabolic' / 'Most Perfect' 4x4 square, so you shouldn't need to learn a new one. The learning tool, however, only works with the basic Harry Lorayne square. I chose this square because it is already known to many mentalists.

Mike

Further to my earlier post, I can confirm that Mike's method works fine with the base magic square I use.

Mike,

You're welcome.

I could probably change the learning tool to work with my own square, if I had the time.



Mark

I've just published a full review of Mike Daniels' Mostly Perfect on one of my blogs: http://www.magicsquaresbook.com/blog/rev......daniels/

You can now download a FREE EXTRACT of Mostly Perfect from Lybrary.

http://www.lybrary.com/mostly-perfect-p-124662.html

Mike

I previously posted:
I can now add that "On The Square" is finally available in my book, Idiopraxis.

How is Mark's different from Doug's? Not asking for methods but any statable differences that can be compared?

I don't know Doug's method. My "Mostly Perfect" method produces squares for any whole-number total (greater than 33) that sum to the target total in at least 36 different ways (up to 52). Doug says his method produces between 28 and 36 ways. "Mostly Perfect" squares are extremely elegant (no repeated values, and the 16 values never have a range of more than sixteen). You have to memorise one basic square. The mental arithmetic needed to adjust this to any named total is pretty easy, but Doug's may be easier.

Mike

Mindpro asked:
I assume that this actually refers to Mike's method, not Mark's.

The mathematics of magic squares is fixed, so any attempts to deal with the problem of producing perfect (and near-perfect) squares are going to have the same underpinnings. Consequently, there are many similarities between Mike's approach and mine. What distinguishes them is the attention paid to lots of little details.

In Mike's, you must memorize the old Harry Lorayne square to use as a construction pattern; in mine, I use a different pattern that can be learned as a pattern, not just a rote memorization of 16 numbers. In Mike's, the math is a bit more difficult; I do essentially the same math, but have found ways to simplify the operations (the hardest thing you ever need to do is divide a guaranteed-even number by two). Finally, Mike's method is defined for magic square totals of 34 and larger, where mine works for 20 and larger (this is nice because it includes the range of adult ages, making it suitable for age-related presentations).

Those are the main differences as I recall them.

Both methods produce the same number of magic totals (up to 52), but I only mention the ones that are likely to be used in a presentation to "normal" audiences (i.e., not mathematicians).

Great effect on the verge of being overdone.