Even I am interested for pdf, if available

Always looking for improvement of my current Magic square, this seems to be the one.
I'm interested, too. Just waiting on the reviews.

If you are a member of the SAM, the November issue of MUM has a review on page 60. I am still waiting for reviews in Genii and the Linking Ring, and hoping that some who have bought the book will comment here. It is not for me to review my own book, but I will say that all of the feedback that I have received has been very positive.

I should also mention that the book is available from www.magicbookshop.com (as first announced) and also www.stevensmagic.com --both highly reputable dealers who ship internationally.

For anyone who is hoping that the book will be available in pdf or e-book form, I am sorry to disappoint but that will not happen for the foreseeable future. After a lot of consideration and advice from others, the decision was to offer it in hardback form only. The book contains so much new material that it is really a reference book that you should keep handy on a shelf and come back to repeatedly, rather than something you read through once and discard. That is why I chose a high-quality, archival format.

Jim - any chance of getting a UK distributor? International rates from the US are prohibitively expensive.

Mike

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 (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 1-16 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 two-person 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 up-to-date 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

For anyone wanting to see another independent review, there is one in this month's Linking Ring. (January, 2017, page 106).