The 36-Cell Square: A Gateway to the Mystical Realms

A magical square with 36 cells is a grid of numbers arranged in such a way that the sum of each row, column, and diagonal is the same. This sum is known as the magic constant. In a 36-cell grid, the magic constant would be the sum of all the numbers in the grid divided by 6. To create a magical square with 36 cells, the numbers 1 to 36 are arranged in a grid, typically starting with the number 1 in the top-left corner and incrementing by 1 as you move to the right and down. The numbers are then wrapped around to the next row or column if necessary. The main idea of a magical square with 36 cells is that it is a unique arrangement of numbers that forms a special pattern.

The main idea of a magical square with 36 cells is that it is a unique arrangement of numbers that forms a special pattern. This pattern is achieved by following specific rules and algorithms for arranging the numbers. Once the numbers are arranged correctly, the magic constant can be calculated and used to validate the square.

Magical square with 36 cells

A year ago I published a book entitled Magic Square Methods and Tricks. It contains entirely new methods for constructing four-by-four magic squares and various magic tricks that use those methods. The book got excellent reviews and gratifying feedback from readers, including several highly respected magicians. However, some readers (including some of my own family) thought that I was a bit cavalier in saying that the mental math was easy. So I set out to eliminate that requirement. To my surprise, I found that I could simplify the methods without sacrificing versatility and even extend them to work for larger magic squares. The simplified methods require no more than counting through a sequence of numbers in order while following a couple of rules that describe a path through the cells. Others have previously described such path-based methods, but without discovering the full range of possibilities. For example, you can start with any number in any cell, count upwards or downwards, and by ones, twos, or threes using the same rules. For magic sums that are even, you will always get 52 successful patterns in a four-by-four magic square; for odd sums, there will always be 36.

When I extended the concepts to five-by-five squares, I discovered that the rules to describe the path could be even simpler and the results could be even more impressive. The well-known stair method is easy, but the magic square it produces barely satisfies the definition. My new method can start in any cell, use any sequence in either direction, and will always produce a magic square with 120 predictable, symmetric, easily remembered patterns. If you want to count the predictable ones that are non-symmetrical (and hard to remember), the number is an astonishing 690. Again, you can fill out the square as fast as you can write the numbers because you are only counting through the sequence. For the first time, there is a method for five-by-five magic squares that is practical for live performances.

The result of these new discoveries is a second book, entitled More Magic Square Methods and Tricks. The magician in me wants to keep these secrets close, so you will not see it advertised, and you will not find it everywhere. But the scholar in me says I must share, so the book will be released at Magic Live! in Las Vegas later this month and available thereafter from a very few dealers. It's a high quality linen bound hardback book with 212 pages, and it costs $50. I am well aware that only the most seriously interested parties will pay that much, and that is fine with me.

I will be glad to answer questions to readers of this forum.

I do a 5x5 magic square. I'm starting in any cell with any number. All numbers are in sequence. I do my 5x5 magic square in less then one minute.
I shared this method only with only a few magicians to keep it secret.

I recently published an extremely simple method for a 4x4 magic square based on Dürer's square. Once learned the method is impossible to forget!
http://www.lybrary.com/melencolia-p-921956.html

I have this manuscript and recommend it, along with several others from lybrary.com. Anyone who is interested in magic squares should be aware of the modern methods for constructing them. There are several similar methods with interesting variations, but all of them are better than the old methods.

My latest book contains a comprehensive examination of pattern-based methods for both four-by-four and five-by-five squares. However, it does not expose or replace any of the work of these other authors. If you are reading this topic, you should want all of them.

Hi Jimso, thank you for letting us know about your new book. I have your first book but I haven't had a chance to read it yet. I have been lately interested in learning magic square methods and I'd be interested in getting your new book. I would really prefer an ebook version for many reasons. Is that something you have considered?

Yes, I thought long and hard about that. For several reasons, I rejected it. The material is really more suited to a hard copy. In the preface, I compare it to a recipe book that you come back to over and over, rather than something you read through and discard. There is a lot of depth that you will not fully appreciate on one, or even two or three, readings. Secondly, it is very hard to protect e-books from piracy. They are so easy to copy and redistribute that you might as well just put everything on an open website. Thirdly, I consider the secrets to be worth protecting from those who are mere curious. The book is expensive enough to discourage casual lookers.

Thanks for your interest, and I hope you find the material to be worth the investment.

Thank you for your response. I understand your concerns about piracy. I prefer an ebook because it is hard for me to read physical books due to a neck/back issue. A computer screen is ideal. I can also read on my phone when I'm traveling. I would even pay more for an ebook than a physical book. Anyway, I am still very interested and will order the physical book.
Best Wishes

I was asked in an email if I would provide the table of contents, as I did for the first book. Happy to do so.

Preface i
Section I. Methods

1. Preliminaries 1
2. Sequential Squares of Order Four 13
3. Sequential Squares of Order Five 29
4. Almost-Sequential Squares 42
5. Multi-Sequential Squares 50
6. Presentation 61

Section II. Tricks

7. Any Chosen Sum 73
8. Improvising with One Chosen Number 76
9. Sight Unseen 83
10. A Cosmic Connection 85
11. Two Chosen Numbers 91
12. Four Chosen Numbers 97
13. Five Chosen Numbers 104
14. Ten Chosen Numbers 114
15. The Answer to Everything 118
16. How Do You Say Hello to an Alien? 119
17. The Poker Legend 124
18. The Spectator Deals 130
19. Are You Psychic? 139
20. Odds and Ends 143

Section III. Theory

21. Magic Squares of Order Five 155
22. Why Sequential Methods Work 171

I. Successful Patterns for Order Four 185
II. Regular Patterns for Order Five 188
III. Additional Patterns for Order Five 194

I stand corrected on one statement I made above. Forum member hcs pointed out to me an old obscure reference to a method for five-by-five squares that would be practical in live performances. So I was wrong to say that it is now possible for the first time. My book goes far beyond that historical reference, but I am grateful to have the record clarified. Thanks to Hans-Christian for that correction.

Very good ideas. Thanks.

The book is now available for ordering through Stevens Magic Emporium, www.stevensmagic.com. It will also be available at Magic Live! next week. For the initial release, those are the only sources.

The first print run sold out, but more are on the way. You can still place an order with Stevens, and it will be sent as soon as available.

For those who want to see reviews before ordering (understandably), it may be a while because the magazines have a lag time of several months. Maybe someone who has the book will post a review here.

I'm sure Jimso wrote the new gold standard. His two books are a "must read" for every seriously writer about magic squares. My full recommendation for a purchase.

The book is back in stock now at Stevens. I was surprised by the demand, so I apologize to those who had to wait while more were printed.

A review of 'More Magic Square Methods and Tricks' by James J. Solberg
(Sun Mountain Publications, 2017).

Hardback with dust wrapper, octavo, 200pp.

$50.00. Available from Stevens Magic Emporium, (www.stevensmagic.com)

Jim Solberg kindly sent me a complimentary review copy of this follow-up to his 2016 book 'Magic Square Methods and Tricks'.

This second book introduces radically new methods of magic square construction that, uniquely, require almost no mental calculation or mathematical knowledge. Once a few basic patterns and structural principles are learned, creating a magic square requires nothing more than the ability to count! As well as methods for 4x4 squares, Jim also shows how constructing 5x5 squares is now not only possible, but actually even simpler!

Jim writes very clearly and the book is conveniently subdivided into sections on Methods, Tricks, and Theory. The new constructional methods are both easy to apply and extremely versatile, though they take a bit of practice before they become sufficiently familiar.

The Tricks section includes a variety of excellent effects and novel presentational ideas which go well beyond the standard 'instant magic square' first popularized by Harry Lorayne.

The shorter Theory section will be of interest to advanced students of magic squares, as well as to those familiar with Jim's first book, but can be ignored if you simply want to create elegant magic squares and perform the various effects.

This second book, like the first, represents a major advance in our understanding of how magic squares are constructed. Although it builds upon the ideas presented in Jim's first book, you do not need to be familiar with the earlier work in order to learn the much easier methods taught here. Serious students of the genre will, however, undoubtedly want both books in their collection.

I just bought the book primarily for the 5X5 square. Anxious to receive it.

Now if we could get Dr. Solka to release his method for a 5x5 square I would be an extremely happy man. His Melencolia booklet was outstanding.

"A poor workman always blames his tools"

I'm very appreciate your warm words!
Regarding a publication of my 5x5 magic square a few artists would lose their exclusivity. They asked me NOT to publish the routine.
May be in the future.

Regarding Melencolia I have interesting news. In the next weeks I will public the 2nd edition (revised, 32 pages, extended with new discoveries and clever ideas for even AND odd magic sums, easy as before, free for the owners of the first edition).

I got a sneak peek at the 2nd addition, which adds quite a bit to the first. It was already excellent, so now even more so.

For a size 3x3, the minimum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it is 111, then 175, 260, …

Magical squares have a long history and have been studied by mathematicians for centuries. They are often used in recreational mathematics and puzzles. The properties of magical squares have been explored in depth, and different methods and formulas have been developed to generate them. In conclusion, a magical square with 36 cells is a grid of numbers arranged in such a way that the sum of each row, column, and diagonal is the same. It is a unique and interesting pattern that has been studied and enjoyed by mathematicians and puzzle enthusiasts for centuries..

Reviews for "Unraveling the Code of the 36-Cell Magical Square"

- Sarah - 2 stars - I found "Magical square with 36 cells" to be quite confusing and overwhelming. The gameplay mechanics were not clear and the instructions provided were insufficient. I spent a lot of time trying to figure out how to play the game rather than actually enjoying it. Additionally, the visuals were quite bland and uninspiring. Overall, I was disappointed with my experience playing this game.

- John - 1 star - I did not enjoy playing "Magical square with 36 cells" at all. The game lacked any real excitement or challenge. The puzzles were too simple and repetitive, making it feel like I was just going through the motions rather than engaging my brain. The design and graphics were also subpar, making it difficult to stay engaged. I quickly lost interest and ended up uninstalling the game after a short playthrough. I would not recommend it.

- Emily - 2 stars - I was excited to try "Magical square with 36 cells" based on the description, but unfortunately, it did not live up to my expectations. The game felt monotonous and lacked variety. Each level felt like a repeat of the previous one, with no real new challenges or surprises. The controls were also clunky and unresponsive at times, which added to my frustration. Overall, I did not find this game enjoyable or engaging.

The Sacred Geometry of the 36-Cell Magical Square