New Book: Magic Square Methods and Tricks
New Book: Magic Square Methods and Tricks
I have discovered a couple of new ways to construct 4by4 magic squares. These are not just variations of the standard 'adjustment' technique or any other previously known method, but entirely new ways. (I am fully aware of how unlikely that seems, but I did my homework.) They require no memorization, no cribs, and no mental calculation harder than adding two numbers. In addition, you have unprecedented control over the outcome, which presents an opportunity for some really baffling tricks. For example, you can create a reversible squareone that still works when rotated upside downfor any magic sum between 150 and 250. Or you can build one for any even magic sum over 70 that consists of only odd numbers. Many new tricks become practical with these tools.
I will admit to mixed feelings about exposing these secrets. On the one hand, I would like to share them with serious magicians who could use the methods in their own performances. On the other hand, I know that eventually some idiot will post a video on the Internet that exposes everything, at which point the magic of magic squares will be spoiled. Once the world becomes aware that they are actually quite simple to construct, no one will be impressed. Of course, the same is true for every new idea in magic, and if no one ever shared, the art would die.
Someone said that the best way to hide a secret of magic is to put it in a book, because only the most committed will bother to read it. So I wrote a book. It is a 240 page quality clothbound and dustjacketed book of the oldfashioned variety (i.e., not cheap). It is available now for preorder from magicbookshop.com.
I will admit to mixed feelings about exposing these secrets. On the one hand, I would like to share them with serious magicians who could use the methods in their own performances. On the other hand, I know that eventually some idiot will post a video on the Internet that exposes everything, at which point the magic of magic squares will be spoiled. Once the world becomes aware that they are actually quite simple to construct, no one will be impressed. Of course, the same is true for every new idea in magic, and if no one ever shared, the art would die.
Someone said that the best way to hide a secret of magic is to put it in a book, because only the most committed will bother to read it. So I wrote a book. It is a 240 page quality clothbound and dustjacketed book of the oldfashioned variety (i.e., not cheap). It is available now for preorder from magicbookshop.com.
Re: New Book: Magic Square Methods and Tricks
I am curious if you have studied the work of Werner Miller and in particular his series of EZ square ebooks. How does your method differ from the many other magic square methods already published?
Lybrary.com http://www.lybrary.com/
preserving magic one book at a time
preserving magic one book at a time

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Re: New Book: Magic Square Methods and Tricks
The one on the cover of the book has 00 in one of the squares...
Part of me is curious as to what new methods have been discovered (as Chris suggests, I've read most of what Werner has published, with pretty much all the others), but the rest of me is probably going to stick with Chuck Hickok's (which is the, subjectively, the best).
Good luck with the book, though. It's always nice to see a new book produced.
Part of me is curious as to what new methods have been discovered (as Chris suggests, I've read most of what Werner has published, with pretty much all the others), but the rest of me is probably going to stick with Chuck Hickok's (which is the, subjectively, the best).
Good luck with the book, though. It's always nice to see a new book produced.
Ian Kendall Close up magician in Edinburgh and Scotland
Re: New Book: Magic Square Methods and Tricks
I am honored that two such distinguished figures whose work I know and respect would take an immediate interest and reply.
I can certainly understand skepticism about my claim, and I expect the doubts to remain until the book gets a good public hearing. However, as I said, I did my homework. To answer your your question directly, Chris, yes, I am familiar with Miller's fine manuscripts, as well as your own, and the others at lybrary.com. I got all of them from you, and they are recommended in the book.
I am also familiar with Hickok's method, which is admirably simple but is only a special case of mine (and not quite as easy). I managed to track down and purchase a rare copy of his original manuscript just to be sure I was not missing something. In fact, I spent more money in researching the topic than I am likely to make from the book because I could not believe that my easy methods could have been overlooked over the long history of magic squares. The methods of Chuck Hickok and Lewis Jones are, in my opinion, the best prior to my own.
I gave preview copies to four people you might know: Art Benjamin, Andi Gladwin, Marshall Petersen, and Caleb Wiles. All responded with enthusiasm.
I can certainly understand skepticism about my claim, and I expect the doubts to remain until the book gets a good public hearing. However, as I said, I did my homework. To answer your your question directly, Chris, yes, I am familiar with Miller's fine manuscripts, as well as your own, and the others at lybrary.com. I got all of them from you, and they are recommended in the book.
I am also familiar with Hickok's method, which is admirably simple but is only a special case of mine (and not quite as easy). I managed to track down and purchase a rare copy of his original manuscript just to be sure I was not missing something. In fact, I spent more money in researching the topic than I am likely to make from the book because I could not believe that my easy methods could have been overlooked over the long history of magic squares. The methods of Chuck Hickok and Lewis Jones are, in my opinion, the best prior to my own.
I gave preview copies to four people you might know: Art Benjamin, Andi Gladwin, Marshall Petersen, and Caleb Wiles. All responded with enthusiasm.

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Re: New Book: Magic Square Methods and Tricks
Hi Jim,
Thanks for the reply.
I have to ask, though  on the cover of the book, one of the squares shows 00. Now, one could argue that this is not a valid entry into a magic square; is this something that happens often, or is that a one off?
Thanks, Ian
Edit: I was lucky, and got a copy of Chuck's manuscript before it became scarce. My copy is number 153
Thanks for the reply.
I have to ask, though  on the cover of the book, one of the squares shows 00. Now, one could argue that this is not a valid entry into a magic square; is this something that happens often, or is that a one off?
Thanks, Ian
Edit: I was lucky, and got a copy of Chuck's manuscript before it became scarce. My copy is number 153
Ian Kendall Close up magician in Edinburgh and Scotland

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Re: New Book: Magic Square Methods and Tricks
I am not an expert. But I know that Lewis Jones has published some work in this area as well.
Worth being aware of since he is such a talented creator.
Worth being aware of since he is such a talented creator.
Re: New Book: Magic Square Methods and Tricks
There is indeed a 00 on the square on the cover, and I generally try to avoid such values. However, in this case, I wanted the magic square with the smallest possible magic sum that can be rotated, reflected in a mirror (or viewed from the back, which is what I put on the back cover), or both, and still be a magic square with the same magic sum. Only the one with the magic sum of 88 and, unfortunately, a 00 entry could meet those requirements. There is nothing in the methods that restricts the values, but you still have the normal constraints of arithmetic. For example, if the magic sum is too small, you might have to use negative values. Inside the book, I have one with the magic sum of 1776 that can be viewed in all of those orientations without any duplicates or zero entries. I built it into a story trick involving Benjamin Franklin, who you probably know was an expert in magic squares.
Ian, you are indeed lucky to have that Hickok manuscript. I paid plenty for my copy (#161) and even more for some other rare manuscripts, but I must say I am proud to own all of them.
Joe, I completely agree that Lewis Jones has a beautifully described and fairly versatile method that I first saw in Ahead of the Pack (with Jack Avis), and then again in SemiAutomatic Card TricksVII by Steve Beam. As I said above, I like his approach almost as much as my own, and recommend all of his work in my book. I am a big fan of his thinking.
Ian, you are indeed lucky to have that Hickok manuscript. I paid plenty for my copy (#161) and even more for some other rare manuscripts, but I must say I am proud to own all of them.
Joe, I completely agree that Lewis Jones has a beautifully described and fairly versatile method that I first saw in Ahead of the Pack (with Jack Avis), and then again in SemiAutomatic Card TricksVII by Steve Beam. As I said above, I like his approach almost as much as my own, and recommend all of his work in my book. I am a big fan of his thinking.

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Re: New Book: Magic Square Methods and Tricks
I missed the bit where you mentioned Lewis Jones.
Apologies!
Good luck with your book  it sounds very good.
Apologies!
Good luck with your book  it sounds very good.

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Re: New Book: Magic Square Methods and Tricks
While it's probably a very through work, I'd find 240 pages on a Magic Square a little intimidating.
Re: New Book: Magic Square Methods and Tricks
Quite so, and also the price is daunting if you are not already a big fan of magic squares. But let me explain.
The two new methods are really very simple, and are fully explained and demonstrated in the first 14 pages. I taught the first one to my five year old grandson in a few minutes, which means there is no arithmetic at all and it is easy to remember. The second method requires adding just two numbers at a time mentally, but is more direct and therefore better suited to performance.
The rest of the book explores some of the things you can do with the new methods. Some aspects go pretty deep, but others are essentially selfworking. It started as a short manuscript, but so many ideas that started flowing as soon as I had the insight that it grew into a 240 page book. In fact, I cut it off at that point despite having many more possibilities. I am already compiling notes for a second volume.
In the opening of the book, I explain how to get what you want out of the book without reading it from cover to cover. It is more of a reference book to come back to again and again, which is why I made it a durable hardback.
All of that being said, you will not fully appreciate the contents unless you already know the usual magic square methods, which you can easily find for free on the internet. I don't expect (or want, actually) the book to sell to the merely curious, but I think that knowledgeable magicians who want to perform magic square tricks will find real value in it.
If you want to know more about the contents, check out the announcement at H&R (magicbookshop.com) or pm me. I am happy to send the table of contents to anyone who asks.
Thanks, Tom, for your post that gave me the opportunity to explain.
The two new methods are really very simple, and are fully explained and demonstrated in the first 14 pages. I taught the first one to my five year old grandson in a few minutes, which means there is no arithmetic at all and it is easy to remember. The second method requires adding just two numbers at a time mentally, but is more direct and therefore better suited to performance.
The rest of the book explores some of the things you can do with the new methods. Some aspects go pretty deep, but others are essentially selfworking. It started as a short manuscript, but so many ideas that started flowing as soon as I had the insight that it grew into a 240 page book. In fact, I cut it off at that point despite having many more possibilities. I am already compiling notes for a second volume.
In the opening of the book, I explain how to get what you want out of the book without reading it from cover to cover. It is more of a reference book to come back to again and again, which is why I made it a durable hardback.
All of that being said, you will not fully appreciate the contents unless you already know the usual magic square methods, which you can easily find for free on the internet. I don't expect (or want, actually) the book to sell to the merely curious, but I think that knowledgeable magicians who want to perform magic square tricks will find real value in it.
If you want to know more about the contents, check out the announcement at H&R (magicbookshop.com) or pm me. I am happy to send the table of contents to anyone who asks.
Thanks, Tom, for your post that gave me the opportunity to explain.
Re: New Book: Magic Square Methods and Tricks
I'm a big fan of Magic Squares  I'll definitely be ordering this.
Will it only be available from H&R?
Andrew
Will it only be available from H&R?
Andrew
Cornerboy Begrudger
Re: New Book: Magic Square Methods and Tricks
H&R will be the sole source initially. I have dealt with them as a customer for a long time, and I know that Marshall Petersen provides good service (prompt shipment, good packaging, quick responses to questions, etc.). Also, Richard Hatch and Charlie Randall (the original H and R) gave me good advice and encouragement when I was still planning the book, for which I am very grateful.
H&R has a large customer base, but it does not include everyone, so at some point I will offer it through other dealers, but only those I know and trust. I have heard stories and had personal experiences that lead me to believe that more than a few dealers are, shall we say, less than reputable. In my view, the good ones should be rewarded with our business, both as suppliers and customers.
And yes, H&R ships internationally.
By the way, if are the eagertobefirst type, you may want to get your order in. Marshall informed me that most of his first batch is already sold. If you are the waitandseethereviews type (as I am), don't worry; there will not be a long delay for replenishment.
H&R has a large customer base, but it does not include everyone, so at some point I will offer it through other dealers, but only those I know and trust. I have heard stories and had personal experiences that lead me to believe that more than a few dealers are, shall we say, less than reputable. In my view, the good ones should be rewarded with our business, both as suppliers and customers.
And yes, H&R ships internationally.
By the way, if are the eagertobefirst type, you may want to get your order in. Marshall informed me that most of his first batch is already sold. If you are the waitandseethereviews type (as I am), don't worry; there will not be a long delay for replenishment.
Re: New Book: Magic Square Methods and Tricks
Thanks Jimso  I'll get my order in.
Cheers
Andrew
Cheers
Andrew
Cornerboy Begrudger
 Steve Bryant
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Re: New Book: Magic Square Methods and Tricks
If you go to the Joe Stevens web site (stevensmagic.com), you can find a wealth of information in the Gemini Archives. One of my favorite contributors was Mike Rogers. Here is his work on the magic square:
https://www.stevensmagic.com/1995/mike ... logyhoax/
 Steve
https://www.stevensmagic.com/1995/mike ... logyhoax/
 Steve
Re: New Book: Magic Square Methods and Tricks
This is a great contribution, Steve. As Mike Rogers explicitly said, there is nothing new or special in the magic square method, but he managed to build a presentation that buried the very involvement of a magic so deep that the method of construction does not matter. When the square is finally revealed, it comes as a complete surprise. This is an inspiring example of creativity in presentation.
By the way, Stevens is another of those 'good guys' among magic dealers that we should all support.
By the way, Stevens is another of those 'good guys' among magic dealers that we should all support.
Re: New Book: Magic Square Methods and Tricks
The book is now shipping and, according to the dealer, "receiving great reviews so far."
Re: New Book: Magic Square Methods and Tricks
A couple of people have asked if there was a way to get a signed copy. I will be at Magic Live! next month and will be glad to sign books and answer questions there. I will periodically stop by the booth for H&R, where the book will be sold. Next year, I will be attending Magifest in January, the joint IBM/SAM convention in July, and (of course) the Genii convention in October.
 Michael Daniels
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Re: New Book: Magic Square Methods and Tricks
A review of 'Magic Square Methods and Tricks' by James J. Solberg
(Sun Mountain Publications, 2016).
Hardback with dust wrapper, octavo, 240pp.
$60.00. Available from H & R Magic Books (http://www.magicbookshop.com)
James Solberg kindly sent me a complimentary review copy of this new book. I was particularly excited to read it because of Solberg's claim that he presents two easy, but previously unknown, methods for constructing 4x4 magic squares. The 4x4 squares are of special interest to magicians because they are best suited for tricks and demonstrations of apparent mathematical skill, including the 'instant magic square' for any named total popularized by Harry Lorayne.
The book has six main sections. Section I demonstrates and explains the two new 'Basic Methods' of construction that Solberg has discovered. While the first 'Step Method' is of theoretical interest and quite cute, it is the second 'Slot Method' that has the major practical applications and forms the basis for almost all the material that follows
Are these methods genuinely new discoveries? Well, they are certainly new to me, and Solberg reports that he has been unable to find any previous description of them despite two years’ extensive research. This now begs the equally important question: 'Are the methods any good?' The answer, I suggest, depends on your interests and purposes.
Mathematicians will certainly love the general theory that Solberg presents, which is itself based on a standard mathematical and engineering approach (Dr Solberg is a mathematical engineer as well as magician). While the method is essentially quite simple, it is extremely versatile and capable of generating countless examples of many different types of magic square.
Magicians who want to extend their repertoire beyond the classic instant magic square will also find the new method of immense value. Having said that, there is quite a learning curve involved and expertise with the method will not be acquired without considerable practice. The book's blurb claims that you can create magic squares without memorizing anything and that 'you will never have to add more than two numbers at a time'. This might lead many to underestimate the magnitude of the task involved. There is certainly some memory required (especially for the 'Advanced Methods' described in Section II). Also, while it is correct that you never need to add more than two numbers at a time, this fails to mention that (except for the simplest of squares) some of the numbers to be added must themselves be calculated. If all you want to do is learn how to perform the classic instant magic square, there are, in my opinion, easier methods, some of which can generate more elegant looking squares than those created by the procedures described in this book.
Section II (Advanced Methods) delves more deeply into the theory behind 4x4 magic squares, identifying the different categories of squares, and explaining various procedures for adjusting squares in order to meet the specific criteria you seek (such as to sum to a certain total, or to maximize the number of ways in which this total can be achieved, or how to create reversible squares). This is an important chapter, much of which is required study for many of the presentations that follow (including the instant magic square).
In Section III (Presentation) Solberg gives useful practical tips, advice and strategies for designing and presenting magic square effects so that your audiences will be interested and entertained by them. This is particularly important given the inherently dry and intellectual nature of magic square construction.
Section IV (Basic Tricks) teaches nine effects that vary in difficulty from 'easy' to 'moderate'. Some of these are very easy once you understand the basic construction methods (e.g., spectator chooses the starting cell for a simple 116 square). Others are a little more challenging (e.g., spectator chooses the cell for any digit from 1 to16). Also included are two procedures for creating an instant magic square for any sum from 34 to 80. The Section closes with three engaging applications. First is 'The Birthday Square', created after writing in the spectator's birth month, day, century and year (or any other date). Next, 'A Calendar Trick' creates a magic square by rearranging the numbers in a freely selected 4x4 box of calendar dates. Finally, there is a quite elaborate (though not difficult) 'Compatibility Test', involving creating a square based on quiz answers given by a couple.
Section V (Advanced Tricks) teaches eleven effects that vary in difficulty from 'moderate' to 'advanced'. A twelfth effect is technically 'easy' but involves learning an elaborate script. The Section begins with two methods for extending the instant magic square for totals greater than 80. Next, there is a very strong but quite long routine, most suited to stage work, in which two magic squares are simultaneously created for two different target sums, while the performer is blindfold and the spectators randomly call out which cells (from either square) should be entered next. Solberg claims that this is easier than it sounds! Further demonstrations of mathematical prowess follow in which the spectator is allowed to choose 3, 4, or even 7 numbers to enter into the square which the performer then makes magic. There is also a novel procedure that uses coins in the cells rather than numbers. The Section ends with a twoperson routine, and two entertaining presentations that incorporate extended stories.
Section VI (For Further Study) includes a short but interesting history of magic squares, followed by a rather thorough and uptodate annotated list of books, articles, online resources, DVDs and props. Solberg has certainly done his research! Serious students of magic squares (whether mathematicians or magicians) will almost certainly find some nice surprises here. The Section ends with an account of how Solberg discovered his methods.
Overall, this is an important book that makes a major and original contribution to the literature on 4x4 magic squares. It will appeal to mathematicians who specialize in number theory, and to magicians who want to feature magic squares in their repertoire and who are willing to get to grips with the underlying methods and presentations. Yet this is not an especially difficult book, even for readers who are not particularly mathematical. Solberg writes very well and everything is laid out concisely, clearly, and in a logical order. On the other hand, it is not really a book to dip into casually in the hope of cherry picking a few tricks. Those magicians who do put in the legwork will develop a skill for life, as well as facility with a general method that has enormous versatility in terms of its potential for creating new magic square effects and presentations.
Highly recommended.
Michael Daniels
(Sun Mountain Publications, 2016).
Hardback with dust wrapper, octavo, 240pp.
$60.00. Available from H & R Magic Books (http://www.magicbookshop.com)
James Solberg kindly sent me a complimentary review copy of this new book. I was particularly excited to read it because of Solberg's claim that he presents two easy, but previously unknown, methods for constructing 4x4 magic squares. The 4x4 squares are of special interest to magicians because they are best suited for tricks and demonstrations of apparent mathematical skill, including the 'instant magic square' for any named total popularized by Harry Lorayne.
The book has six main sections. Section I demonstrates and explains the two new 'Basic Methods' of construction that Solberg has discovered. While the first 'Step Method' is of theoretical interest and quite cute, it is the second 'Slot Method' that has the major practical applications and forms the basis for almost all the material that follows
Are these methods genuinely new discoveries? Well, they are certainly new to me, and Solberg reports that he has been unable to find any previous description of them despite two years’ extensive research. This now begs the equally important question: 'Are the methods any good?' The answer, I suggest, depends on your interests and purposes.
Mathematicians will certainly love the general theory that Solberg presents, which is itself based on a standard mathematical and engineering approach (Dr Solberg is a mathematical engineer as well as magician). While the method is essentially quite simple, it is extremely versatile and capable of generating countless examples of many different types of magic square.
Magicians who want to extend their repertoire beyond the classic instant magic square will also find the new method of immense value. Having said that, there is quite a learning curve involved and expertise with the method will not be acquired without considerable practice. The book's blurb claims that you can create magic squares without memorizing anything and that 'you will never have to add more than two numbers at a time'. This might lead many to underestimate the magnitude of the task involved. There is certainly some memory required (especially for the 'Advanced Methods' described in Section II). Also, while it is correct that you never need to add more than two numbers at a time, this fails to mention that (except for the simplest of squares) some of the numbers to be added must themselves be calculated. If all you want to do is learn how to perform the classic instant magic square, there are, in my opinion, easier methods, some of which can generate more elegant looking squares than those created by the procedures described in this book.
Section II (Advanced Methods) delves more deeply into the theory behind 4x4 magic squares, identifying the different categories of squares, and explaining various procedures for adjusting squares in order to meet the specific criteria you seek (such as to sum to a certain total, or to maximize the number of ways in which this total can be achieved, or how to create reversible squares). This is an important chapter, much of which is required study for many of the presentations that follow (including the instant magic square).
In Section III (Presentation) Solberg gives useful practical tips, advice and strategies for designing and presenting magic square effects so that your audiences will be interested and entertained by them. This is particularly important given the inherently dry and intellectual nature of magic square construction.
Section IV (Basic Tricks) teaches nine effects that vary in difficulty from 'easy' to 'moderate'. Some of these are very easy once you understand the basic construction methods (e.g., spectator chooses the starting cell for a simple 116 square). Others are a little more challenging (e.g., spectator chooses the cell for any digit from 1 to16). Also included are two procedures for creating an instant magic square for any sum from 34 to 80. The Section closes with three engaging applications. First is 'The Birthday Square', created after writing in the spectator's birth month, day, century and year (or any other date). Next, 'A Calendar Trick' creates a magic square by rearranging the numbers in a freely selected 4x4 box of calendar dates. Finally, there is a quite elaborate (though not difficult) 'Compatibility Test', involving creating a square based on quiz answers given by a couple.
Section V (Advanced Tricks) teaches eleven effects that vary in difficulty from 'moderate' to 'advanced'. A twelfth effect is technically 'easy' but involves learning an elaborate script. The Section begins with two methods for extending the instant magic square for totals greater than 80. Next, there is a very strong but quite long routine, most suited to stage work, in which two magic squares are simultaneously created for two different target sums, while the performer is blindfold and the spectators randomly call out which cells (from either square) should be entered next. Solberg claims that this is easier than it sounds! Further demonstrations of mathematical prowess follow in which the spectator is allowed to choose 3, 4, or even 7 numbers to enter into the square which the performer then makes magic. There is also a novel procedure that uses coins in the cells rather than numbers. The Section ends with a twoperson routine, and two entertaining presentations that incorporate extended stories.
Section VI (For Further Study) includes a short but interesting history of magic squares, followed by a rather thorough and uptodate annotated list of books, articles, online resources, DVDs and props. Solberg has certainly done his research! Serious students of magic squares (whether mathematicians or magicians) will almost certainly find some nice surprises here. The Section ends with an account of how Solberg discovered his methods.
Overall, this is an important book that makes a major and original contribution to the literature on 4x4 magic squares. It will appeal to mathematicians who specialize in number theory, and to magicians who want to feature magic squares in their repertoire and who are willing to get to grips with the underlying methods and presentations. Yet this is not an especially difficult book, even for readers who are not particularly mathematical. Solberg writes very well and everything is laid out concisely, clearly, and in a logical order. On the other hand, it is not really a book to dip into casually in the hope of cherry picking a few tricks. Those magicians who do put in the legwork will develop a skill for life, as well as facility with a general method that has enormous versatility in terms of its potential for creating new magic square effects and presentations.
Highly recommended.
Michael Daniels

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Re: New Book: Magic Square Methods and Tricks
Thanks for the detailed review, Michael.