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Jimso
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Judging from discussions here and some recent product releases, it seems that many magicians are not yet aware that the methods for magic squares have improved a lot in the last few years. If you like the effect but were challenged by the difficulty, you should look into the newer methods by Michael Daniels (2016), Hans-Christian Solka (2017), or myself (2016 and 2017). You can do a lot more with these new methods than you can with the old instant method because you are not tied to a fixed base square. If you do a little searching in this thread, you will find earlier discussions of these developments. The methods of Daniels and Solka can be obtained in e-books from lybrary.com. Mine are in hard back books available exclusively from Stevens Magic Emporium.

My latest discoveries will soon be released in a new (third) book entitled Easy Magic Square Methods and Tricks. I believe these are the most powerful, versatile, and easy methods yet for 4x4 magic squares. There are no calculations, no memorization, and no cribs. You can start with any number in any cell, place the other numbers as fast as you can write them, and end up with fifty-two four-cell patterns matching the magic sum. You will know the fifty-two matching patterns even before you begin because they do not depend upon the starting number or position. I provide three distinct methods that produce different results (exploiting different symmetries), and there are several variations that expand the possibilities.

The new book should be available to order from Stevens within a few days.
Chris
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You should consider offering them as ebooks on Lybrary.com. We are the hub for magic square effects, effects based on math, and other self-working miracles. For all easy magic square effect lovers I also recommend the E-Z Square series by Werner Miller. He is now at volume 9. https://www.lybrary.com/werner-miller-m-7881.html
Lybrary.com preserving magic one book at a time.
Jimso
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Chris, I agree that Lybrary.com is the hub for magic square material. (I believe I have purchased all of it.) if I were to publish an e-book, that is where I would want it to be. I thought long and hard before deciding against e-book versions of any of my three books on magic squares.

Yes, a physical book is more expensive and less convenient than an e-book, but this is archival material in the old-fashioned sense of books that you keep on the shelf and learn more each time you reread. Also, I prefer to share it with just those few who are seriously interested. A lot less people will see it, but I consider that to be a good thing. I am more concerned about protecting the secrets than spreading them. So, no, I will not be offering an e-book edition.
hcs
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A review of "Easy Magic Square Methods and Tricks" by James J. Solberg
(Sun Mountain Publications, 2019; hardback with dustwrapper, 166 pp.)

The book is the third book of Mr. Solberg's Magic Square Methods and Tricks trilogy; the first book "Magic Square Methods and Tricks", 2016 and the second book, "More Magic Square Methods and Tricks", 2018. All three books are available from Stevens Magic Emporium (www.stevensmagic.com).

See also the previous threads in the Magic Café:
https://www.themagiccafe.com/forums/view......forum=99
https://www.themagiccafe.com/forums/view......forum=99

Mr. Solberg kindly sent me a complimentary review copy. Nevertheless, you will receive an independent review from someone who does such routines for real - although with a different solution (my Euphoria method) - for even and for odd magic sums.

Mr. Solberg's third book about magic squares (MS) explains three new methods to solve the "any starting cell" problem for an order four magic square of consecutive numbers. The book is intended for the magic community and a "must-have" for all "quadramagicologists".

Solving the "any starting cell" problem is the current stage of development for magic squares of order four for magic entertainers:
- MS using the exchange of numbers (Duerer, 16th century),
- MS using algebraic patterns of type A+a ... D+d (late 19th century)
- Instant MS and balanced Instant MS (the late 1920s),
- normal (for singly-even magic sums) or perfectly-balanced MS (for doubly-even or odd magic sums) of consecutive numbers with a fixed starting cell (Prof. Olgo, beginning of the 1960s),
- normal or perfect-balanced MS of consecutive numbers and any starting cell for the lowest or highest starting number in the late 2010s (Solberg and Solka).

Mr. Solberg provides solutions for pandiagonal MS (Dudeney group I), for bentdiagonal MS (Dudeney group II) and symmetric/associative MS (Dudeney group III). The book - like all books of his trilogy - will be of interest to the advanced students of magic squares. I suggest the reader learn the pandiagonal method!

It seems to me that Mr. Solberg is hiding some of his huge knowledge about Magic Squares. Even if Mr. Solberg only describes different paths from a given "starting number in any cell", the advanced student of magic squares can easily derive the respective solutions for the reverse problem - from a given magic sum (even with a remainder) to the starting number in any cell ending with a normal or perfect balanced MS. However, these solutions are a little bit more complicated "under fire" by the necessary calculations and patterns. But it can be done with minimal effort in less a minute. (A few professional magicians can do it for a given three-digit-sum with the (different to Mr. Solberg's methods) Euphoria method in about 40 seconds.)

Mr. Solberg introduces new methods of magic square construction based on his research that, uniquely, requires almost no mental calculation or deep mathematical knowledge but understanding. Once the basic patterns and principles are learned, creating a magic square requires nothing more than practice! Mr. Solberg provides the first methods for the "starting number in any cell" problem for pandiagonal and bentdiagonal magic squares!

It is even possible to use Mr. Solberg's methodology to develop further methods based on other step rules. I've done it successfully with a "U-shape" step-rule for Mr. M. Daniel's highly recommended MS ("Mostly Perfect", 2013), a mirrored Prof. Olgo MS.

I tried very hard to find bugs (in German, this behavior is called "Kruemelkackerei" :=) - the only obvious error I could find was on p. 74, it must be read IMHO as "subtract" instead of "add"! A huge achievement, which shows how carefully Mr. Solberg wrote his new book.

Mr. Solberg writes in a clear teaching style. Sometimes I would wish that he would give even more examples to make it easier for the reader.
Mr. Solberg not only provides us with new theory but also with his deep musings about presentation. Of course, this will take some practice before you become sufficiently familiar.

I highly recommend the trilogy! The new book "Easy Magic Square Methods and Tricks" represents the actual "Gold Standart" for the modern Magic Square performer! Chapeau!

Hans-Christian Solka
Melencolia I - Magic Squares for the Mental Entertainer * Smart Methods for 4x4, 5x5 and 6x6 Magic Squares * 180 A4-pages * version 3.51
adiabaticman
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Thank you for the review. One small correction. I think it should be Prof. Solberg and not Mr. Solberg. He is a Professor of Mathematics.


Quote:
On Oct 16, 2019, hcs wrote:
A review of "Easy Magic Square Methods and Tricks" by James J. Solberg
(Sun Mountain Publications, 2019; hardback with dustwrapper, 166 pp.)

The book is the third book of Mr. Solberg's Magic Square Methods and Tricks trilogy; the first book "Magic Square Methods and Tricks", 2016 and the second book, "More Magic Square Methods and Tricks", 2018. All three books are available from Stevens Magic Emporium (www.stevensmagic.com).

See also the previous threads in the Magic Café:
https://www.themagiccafe.com/forums/view......forum=99
https://www.themagiccafe.com/forums/view......forum=99

Mr. Solberg kindly sent me a complimentary review copy. Nevertheless, you will receive an independent review from someone who does such routines for real - although with a different solution (my Euphoria method) - for even and for odd magic sums.

Mr. Solberg's third book about magic squares (MS) explains three new methods to solve the "any starting cell" problem for an order four magic square of consecutive numbers. The book is intended for the magic community and a "must-have" for all "quadramagicologists".

Solving the "any starting cell" problem is the current stage of development for magic squares of order four for magic entertainers:
- MS using the exchange of numbers (Duerer, 16th century),
- MS using algebraic patterns of type A+a ... D+d (late 19th century)
- Instant MS and balanced Instant MS (the late 1920s),
- normal (for singly-even magic sums) or perfectly-balanced MS (for doubly-even or odd magic sums) of consecutive numbers with a fixed starting cell (Prof. Olgo, beginning of the 1960s),
- normal or perfect-balanced MS of consecutive numbers and any starting cell for the lowest or highest starting number in the late 2010s (Solberg and Solka).

Mr. Solberg provides solutions for pandiagonal MS (Dudeney group I), for bentdiagonal MS (Dudeney group II) and symmetric/associative MS (Dudeney group III). The book - like all books of his trilogy - will be of interest to the advanced students of magic squares. I suggest the reader learn the pandiagonal method!

It seems to me that Mr. Solberg is hiding some of his huge knowledge about Magic Squares. Even if Mr. Solberg only describes different paths from a given "starting number in any cell", the advanced student of magic squares can easily derive the respective solutions for the reverse problem - from a given magic sum (even with a remainder) to the starting number in any cell ending with a normal or perfect balanced MS. However, these solutions are a little bit more complicated "under fire" by the necessary calculations and patterns. But it can be done with minimal effort in less a minute. (A few professional magicians can do it for a given three-digit-sum with the (different to Mr. Solberg's methods) Euphoria method in about 40 seconds.)

Mr. Solberg introduces new methods of magic square construction based on his research that, uniquely, requires almost no mental calculation or deep mathematical knowledge but understanding. Once the basic patterns and principles are learned, creating a magic square requires nothing more than practice! Mr. Solberg provides the first methods for the "starting number in any cell" problem for pandiagonal and bentdiagonal magic squares!

It is even possible to use Mr. Solberg's methodology to develop further methods based on other step rules. I've done it successfully with a "U-shape" step-rule for Mr. M. Daniel's highly recommended MS ("Mostly Perfect", 2013), a mirrored Prof. Olgo MS.

I tried very hard to find bugs (in German, this behavior is called "Kruemelkackerei" :=) - the only obvious error I could find was on p. 74, it must be read IMHO as "subtract" instead of "add"! A huge achievement, which shows how carefully Mr. Solberg wrote his new book.

Mr. Solberg writes in a clear teaching style. Sometimes I would wish that he would give even more examples to make it easier for the reader.
Mr. Solberg not only provides us with new theory but also with his deep musings about presentation. Of course, this will take some practice before you become sufficiently familiar.

I highly recommend the trilogy! The new book "Easy Magic Square Methods and Tricks" represents the actual "Gold Standart" for the modern Magic Square performer! Chapeau!

Hans-Christian Solka
Watching those electrons dance on the adiabat, from Franck-Condon to the Asymptote.
adiabaticman
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Correction: Professor of Manufacturing and Industrial Engineering.
Watching those electrons dance on the adiabat, from Franck-Condon to the Asymptote.
hcs
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The announced book is here for 35 $ available:
https://www.stevensmagic.com/shop/easy-m......erg-book

You will find unique stuff in Prof. Solberg's magic square trilogy you never find somewhere else.
Maybe SME could sell all three books cheaper in a bundle?
Melencolia I - Magic Squares for the Mental Entertainer * Smart Methods for 4x4, 5x5 and 6x6 Magic Squares * 180 A4-pages * version 3.51
Michael Daniels
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Jim Solberg very generously sent me a complimentary proof copy of 'Easy Magic Square Methods and Tricks'.

While this is the third book in Jim's series on magic squares, it is a stand-alone work and you do not need to have read the first two books to be able to understand and use the methods taught here. On the contrary, this book is an ideal introduction to Jim's important work in this area, as well as to 4x4 magic squares in general. However, those already familiar with Jim's previous books or with other literature on magic squares will also find much to interest and excite them here.

In essence, this book teaches an original and easy method (requiring absolutely NO mental calculation) that allows you to construct elegant 4x4 magic squares when the spectator is allowed to freely choose ANY number in ANY starting cell. Note that this represents a fundamental change from the traditional performance approach where the spectator typically chooses the magic sum and the performer then proceeds to construct a square for that magic constant.

While some may prefer the traditional procedure, Jim makes the entirely valid point that choosing the magic sum is usually done to prove that the performer has not simply memorized a specific square and choosing a starting number and position is equally effective for that purpose. While Jim's new method DOES allow you to construct magic squares for any given total, this will require some additional mental calculation and, for this purpose, other previously published methods may be considered easier.

So, how easy is the new method? Its great advantage, of course, is that you do NOT need to do any mental calculation since the numbers being entered are generally consecutive. It is just a matter of knowing WHERE to place each number. Jim's terrific discovery is that a very few, very simple rules govern the process. The only moderately difficult part in this new method is learning the rules in the first place. Once these are fully understood, the actual construction of the square becomes childishly easy so that you can then focus entirely on selling the effect.

The book actually presents THREE variations of the basic procedure that generate three different classes of 4x4 magic square. In practice, however, you need to learn only one method. In my view (which Jim shares) the first method taught is the best and the other two are of largely theoretical and technical interest.

The book itself is very well organized and engagingly written. It covers theoretical foundations, principles of construction, structural properties, procedural and trick variations (e.g., using only odd or even numbers in every cell, or incorporating calendar dates), and useful suggestions for effective and entertaining presentations. Although, at 106 pages, the book is relatively short, it is not a quick read and, while the methods are very clearly explained, they will take some time to fully assimilate. Some helpful exercises are included along the way to enable the reader to grasp and practice the essentials.

In conclusion, this book is a brilliant addition to the literature. For magic square aficionados it is a must addition to their libraries. For those new to magic squares, or who may have steered clear because of the mental calculation involved in previous methods, they will find exactly what they need here. Finally, if you already perform a standard version of the magic square, you will be able to add interesting and highly versatile alternative presentations to your repertoire.

Very highly recommended.
slowkneenuh
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May I propose a moratorium on magic square solutions and literature? Because of my fascination with mathematical magic, each time a new publication surfaces, I feel compelled to buy it. Then after spending the right amount of time digesting it and reaching a level of comfort with it along comes another.

Of course each one improves or expands on the subject matter. Unfortunately faster than my mind, wallet and allocated bookcase space. It's amazing that after all these years there is still much to be discovered with magic squares.

My hat is off to all of you skilled inventors and authors of these publications (I have them all), but you deserve a well earned rest. Smile Smile Smile
John

"A poor workman always blames his tools"
hcs
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The bad news: Your suggestion comes too late.

I have another discovery, which extends the solutions for the "any starting number in any cell" problem of J. Solberg or myself by a climax.

After constructing the 4x4 magic square for a given starting number in any cell, I extend the magic square by a border to a 6x6 square. The numbers in this 6x6 magic square are consecutive (36 numbers; starting number till starting number plus 35).

The good news: I will add this to my book “Melencolia I” as an update. This update will be available free of charge in November 2019 - as always at Lybrary.com. I will inform you about this in this thread.

Another good news: My solution is simple! You can do it under fire! The spectators can follow and understand. You don’t need a calculator!

It is the first workable solution for a 6x6 magic square of consecutive numbers for mathemagicians.
Melencolia I - Magic Squares for the Mental Entertainer * Smart Methods for 4x4, 5x5 and 6x6 Magic Squares * 180 A4-pages * version 3.51
adiabaticman
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That's very good to hear, hcs. Looking forward to the Melancolia I update.
Watching those electrons dance on the adiabat, from Franck-Condon to the Asymptote.
Jimso
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First, I want to thank hcs and Mike for their positive reviews. Their opinions mean a lot to me because they, along with a very few others, led the way into this new generation of magic squares.

Both reviews accurately describe the contents, but I want to add a couple of clarifications. The error found by hcs was present in the proof copy he received, but I fortunately found and corrected it before the final print order, so purchasers do not have to worry about it. There are still a couple of small typos, but they should not cause any confusion.

Regarding the point raised by slowkneenuh, there has indeed been a recent surge of discoveries about methods for magic squares, and it is not over. The big game-changer was the realization that you do not have to fake the constrction (as magicians have been doing), but can do it for real by taking advantage of patterns in the structure. As Mike said, once you understand the patterns, the construction becomes childishly easy. Most of the world does not know this yet, which is why this is such a rich opportunity for magicians. I am still amazed that this was not discovered earlier, and I am certain that more revelations will follow.
ddyment
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I confess to finding the claim that "... you do not have to fake the constrction [sic] (as magicians have been doing), but can do it for real by taking advantage of patterns in the structure. ... I am still amazed that this was not discovered earlier ..." to be a bit uninformed. Magical creators (to say nothing of mathematicians) have recognized the existence of patterns in magic squares from very early in the game. Not all have made use of such patterns, but some certainly have (cf. Sam Dalal's 1993 book, Patterns of Perfection). My own most recent writings on magic squares (Idiopraxis, released in 2011) includes a very practical method for the production of classic magic squares (those summing to a predetermined total) using no trickery, and based on one of the (many) patterns that can be found in the geometry.

In the decade since that method was created, I have developed an even more elegant (thus satisfying) approach to the production of squares. That material will eventually see print, but even what exists today serves well to dispute that claim that nobody knows about patterns!
Doug Dyment's Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More
slowkneenuh
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I must confess that even though I have most literature published on magic squares and have experimented with them all (and very much enjoyed the various solutions), my aha! moment first came with Melencolia by
Hans-Christian Solka. He opened my eyes to the patterned approach with a very compelling and easy solution to use. Patterns may have been implied in the past but it was lost on me as I continued to look at them from a step approach. The pattern approach was reinforced for me by the publications of Jim Solberg.

In any case, I've learned something from every publication and would not hesitate to recommend any of them depending on the reader's interest.
John

"A poor workman always blames his tools"
Chris K
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Quote:
On Oct 30, 2019, ddyment wrote:
I confess to finding the claim that "... you do not have to fake the constrction [sic] (as magicians have been doing), but can do it for real by taking advantage of patterns in the structure. ... I am still amazed that this was not discovered earlier ..." to be a bit uninformed. Magical creators (to say nothing of mathematicians) have recognized the existence of patterns in magic squares from very early in the game. Not all have made use of such patterns, but some certainly have (cf. Sam Dalal's 1993 book, Patterns of Perfection). My own most recent writings on magic squares (Idiopraxis, released in 2011) includes a very practical method for the production of classic magic squares (those summing to a predetermined total) using no trickery, and based on one of the (many) patterns that can be found in the geometry.

In the decade since that method was created, I have developed an even more elegant (thus satisfying) approach to the production of squares. That material will eventually see print, but even what exists today serves well to dispute that claim that nobody knows about patterns!


One of my favorite things out of Idiopraxis was, in fact, ddyment's method of production a magic square. I'm excited to see his new approach whenever it does hit print. With all that being said, I am probably going to pick up a few books on magic squares from Lybrary this weekend. While I'm very happy with the method I'm using (almost exactly what Doug published in Idiopraxis), I'm always down to see what other works, such as Melencolia, might have to offer.

Finally, it should be said that Doug Dyment's website is a pretty great source of information and he offers supplements for all of his releases. https://www.deceptionary.com/
Jimso
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I will admit to using imprecise wording in my last (hastily written) post, but I cannot leave unchallenged the assertion that I am uninformed because it suggests that the material in my books might be only a rehash of previously published methods. That is definitely not the case. I have no interest in republishing previously known material.

As a retired professor with many publications and honors, I would not risk my reputation by publishing claims that were not thoroughly researched. Knowing that magic squares have been studied for a very long time and that the vast literature is widely scattered, I spent several years and considerable expense tracking down everything I could find on the subject, including rare books, obscure manuscripts, translations, and deep mathematical expositions, as well as the more common works in recreational mathematics and magic. Only after studying hundreds of documents was I confident that I had something new to offer.

Quoting directly from my latest book; "I must acknowledge the earlier work of Sam Dalal, Michael Daniels, Doug Dyment, Werner Miller, Lewis Jones, and Hans-Christian Solka. Each made important steps in advancing simplified methods for constructing customized four-by-four magic squares." In my first book (2016), I reviewed those works, as well as many older ones and other important recent advances (such as those of Art Benjamin, Chuck Hickok, Lee Sallows, and others), but I would put those in a different category of methods.

I certainly never said, or meant to suggest, that 'nobody knows about patterns' (though I can see why one could have drawn that inference). There are 10th century Arabic manuscripts that explain pattern-based methods, so of course they are not new. My comment was prompted by the observation that, despite the availability of these advances since Dalal, many magicians are still relying upon the 'adjustment' method published by Bob Nelson in 1929. Just within the past year, I have seen new releases that seem to indicate that the authors are unaware of the progress over the last twenty-five years.

My general point in response to slowkneenuh remains that, despite what is already known about magic squares, they still offer fertile ground for research and we should all expect new discoveries. (I am pretty sure his suggestion that we pause was tongue-in-cheek.) Personally, I am eager to see what Hans-Christian Solka, Doug Dyment, or anyone else has to offer.
ddyment
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I hasten to note that I did not claim that Jimso was uninformed, just that his one particular statement seemed to be so. As he appears to agree with that observation, I suspect that we are pretty much on the same wavelength. Certainly no slur was intended.
Doug Dyment's Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More
Harry Lorayne
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Hey, you might even be interested in watching my magic square presentation (within about an hour's "memory" performance) on volume 4 of my "Best Ever" DVD set. You might even want to research some of my magic square teachings in a couple of my books.
[email]harrylorayne@earthlink.net[/email]

http://www.harrylorayne.com
http://www.harryloraynemagic.com
hcs
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Quote:
On Nov 4, 2019, Harry Lorayne wrote:
Hey, you might even be interested in watching my magic square presentation (within about an hour's "memory" performance) on volume 4 of my "Best Ever" DVD set. You might even want to research some of my magic square teachings in a couple of my books.
I respectfully disagree with your last sentence! The method in the footage is outdated for about round 50 years.

In the link below, you can see Professor Olgo's (Berthold Jassinger, 1901 – 1979) presentation of a magic square in 1979 in the Marvelli Show. As you can see, he played in a class of his own. He presented at the age of 78 years a sequential square (a REAL MAGIC Square), not an "instant square". Prof. Olgo presented this kind of magic square since the early 1960s, the German Andy Häussler since the late 1980s.
https://www.youtube.com/results?search_q......ensearch

Prof. Olgo was able to construct a magic square for even and odd sums. In the case of an odd sum, the difference between his highest and the lowest number was only 16 – an almost-sequential method! His method was the state-of-the-art from about 1960 to 2017! Prof. Solberg raised in his books the art in new hights. He describes an almost-sequential method for the starting number in any start cell.

Please try to understand that we are discussing in this thread not "the discovery of magic square’s DNA". We are dealing in the meantime with the “sequence of the genome” of the square. We are walking some evolution steps higher.

An advice of a well known old magic scholar: "People should read the real stuff!"
Melencolia I - Magic Squares for the Mental Entertainer * Smart Methods for 4x4, 5x5 and 6x6 Magic Squares * 180 A4-pages * version 3.51
hcs
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Quote:
On Oct 31, 2019, slowkneenuh wrote:
I must confess that even though I have most literature published on magic squares and have experimented with them all (and very much enjoyed the various solutions), my aha! moment first came with Melencolia by
Hans-Christian Solka. He opened my eyes to the patterned approach with a very compelling and easy solution to use. Patterns may have been implied in the past but it was lost on me as I continued to look at them from a step approach. The pattern approach was reinforced for me by the publications of Jim Solberg.

In any case, I've learned something from every publication and would not hesitate to recommend any of them depending on the reader's interest.
Thank you very much for your kind words about the books of Jim Solberg and me.
Melencolia I - Magic Squares for the Mental Entertainer * Smart Methods for 4x4, 5x5 and 6x6 Magic Squares * 180 A4-pages * version 3.51
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