The creation and solution of magic squares has certainly escalated over the last several years. But, I hasten to add, for me and possibly many others, it was Harry Lorayne's books and tapes that piqued my interest not only in magic squares but in the broader area of mathematical magic. I am forever indebted to him for introducing me to this form of entertainment.

I have today released a new magic square method: "Birthday Magic Square" https://www.lybrary.com/birthday-magic-square-p-923360.html There is zero math and the effect turns out to be stronger for spectators. This has become my favorite impromptu magic square effect. People are loving it.

Thanks Chris! It was really a refreshing booklet! I can really recommend it!

The good thing about the new generations born after 2002 is that if you split their birthdays in four pieces (example 2008-may-31), you will get 31, 5, 20, 8 and no number will stand out as suprisingly high as the case is where people is born 1950-1999.

Gus, thanks. I am very happy you liked my recent publication. With my method all numbers cluster around the numbers that have been entered by the spectator. And on top you have a bit of flexibility to shape in which direction they will lean.

It's not enough to just read Jim Solberg's books once. I'm constantly finding new ideas and suggestions because my knowledge and point of view are also changing. For example, I just found an excellent idea to force a magic sum in Jim's new book.
Thank you for sharing your knowledge!

very good work! I like the concept of the basic square with the zones. to enter in the trick with 4 different numbers instead of a "two digit number between 34 and 99" makes it "more random"...

I will release the new update of Melencolia I next week. Stay tuned!

I finished my update. Read more at Lybrary.com. Enjoy!

The Melencolia update is a big deal, folks. HCS is correct in saying it is the first workable solution for the 6x6 magic square of consecutive numbers for mathemagicians. For those who do not know, the 6x6 case is so unique that it needs special handling. Up until now, the published methods were too awkward to use in a live performance, even though the size is within reason. Larger sizes have workable methods, but would take too long for most audiences. The point is, this is a breakthrough development. Bravo, hcs!

Thank you very much for your kind words! I appreciate that very much. But also your three books are an invaluable source! I read them again and again to get inspirations.

Just when we thought that the only news to be had was about the coronavirus and along comes Version 3.30 of Melencolia! Christmas in March. What a wonderful treat and pleasant news for a change. Looking forward to reading it.

Thank you very much for your kind words! I appreciate that very much!

My ebook about magic squares, "Melencolia I" has seen a substantial update by me. It includes groundbreaking developments for magic squares. If you have purchased an earlier version at Lybrary.com, go to your digital shelf and download the new version.

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TABLE OF CONTENTS

INTRODUCTION

PART I - DUERER MAGIC SQUARE

1 CONSTRUCTION OF THE DUERER MAGIC SQUARE
1.1 A TRADITIONAL METHOD
1.2 A MORE MAGICAL WAY
1.2.1 SINGLY-EVEN MAGIC SUMS
1.2.2 DOUBLY-EVEN MAGIC SUMS
1.3 COMPLEMENT SUM
1.4 RESTRICTION TO EVEN MAGIC SUMS
1.5 ADJUSTING THE SQUARE
1.6 SQUARE AND CUBE SUMS
2 SUMMATION PATTERNS OF DUERER-TYPE MAGIC SQUARES
2.1 EVEN MAGIC SUMS
2.2 ODD MAGIC SUMS

3 TRANSFORMATION CHARACTERISTICS
3.1 STANDARD POSITION
3.2 TRANSFORMATION INTO ANOTHER ASSOCIATED MAGIC SQUARE
3.3 TRANSFORMATION INTO A MOST-PERFECT MAGIC SQUARE

4 ZIGZAG APPROACH FOR SEMI-MAGIC SQUARES
4.1 CONSTRUCTION
4.1.1 FIRST HIGH ZIGZAG PASS
4.1.2 FIRST FLAT ZIGZAG PASS
4.1.3 SECOND FLAT ZIGZAG PASS
4.1.4 SECOND HIGH ZIGZAG PASS
4.2 NORMAL SEMI-MAGIC SQUARE
4.3 ADJUSTING A SEMI-MAGIC SQUARE
4.4 TRANSFORMATION OF A SEMI-MAGIC INTO A MAGIC SQUARE

5 FOURSOME APPROACH FOR MAGIC SQUARES
5.1 FOURSOME SQUARE - ANY EVEN MAGIC SUM
5.1.1 CONSTRUCTION
5.1.2 FIRST AND SECOND PASS: HIGH AND FLAT SUMMIT
5.1.3 THIRD AND FOURTH PASS: FLAT AND DEEP VALLEY
5.1.4 NORMAL SQUARE
5.1.5 ADJUSTING THE SQUARE
5.2 INSTANT SQUARE - ANY MAGIC SUM
5.2.1 BASIC SQUARE
5.2.2 ADJUSTING THE SQUARE
5.3 INSTANT OLGO SQUARE - ANY MAGIC SUM
5.4 BALANCED INSTAN OLGO SQUARE - ANY MAGIC SUM
5.4.1 BALANCED SQUARE; WITHOUT A REMAINDER
5.4.2 BALANCED SQUARE; A REMAINDER OF ONE
5.4.3 BALANCED SQUARE; A REMAINDER OF TWO
5.4.4 BALANCED SQUARE; A REMAINDER OF THREE
5.4.5 BALANCED SQUARE; AN EVEN MAGIC SUM ONLY

PART II - JUPITER

6 MELENCOLIA - THE MODIFIED DUERER MAGIC SQUARE
6.1 ORIGINAL AND THE MODIFIED DUERER MAGIC SQUARE
6.2 CLOTH HANGER TRANSFORMATION
6.3 FOURSOME ATTRIBUTE
6.4 PRESENTATION APPROACHES

7 SUMMATION PATTERNS OF MELENCOLIA-TYPE MAGIC SQUARES
7.1 EVEN MAGIC SUMS
7.2 ODD MAGIC SUMS
7.3 FLOW OF THE SUMMIT AND VALLEY PATTERNS

8 ADJUSTING MELENCOLIA-TYPE MAGIC SQUARES - ANY MAGIC SUM
8.1 SINGLY-EVEN MAGIC SUMS; WITHOUT A REMAINDER
8.1.1 FIRST PASS: HIGH SUMMIT
8.1.2 SECOND PASS: FLAT SUMMIT
8.1.3 THIRD PASS: FLAT VALLEY
8.1.4 FOURTH PASS: DEEP VALLEY
8.1.5 COMPLETED SQUARE
8.1.6 SIMPLE FORCING MATRIX TO AVOID CALCULATIONS
8.2 DOUBLY-EVEN MAGIC SUMS; A REMAINDER OF TWO
8.2.1 FIRST PASS: HIGH SUMMIT
8.2.2 SECOND PASS: FLAT SUMMIT
8.2.3 THIRD PASS: FLAT VALLEY
8.2.4 FOURTH PASS: DEEP VALLEY
8.2.5 COMPLETED SQUARE
8.3 ODD MAGIC SUMS; A REMAINDER OF ONE
8.3.1 FIRST PASS: HIGH SUMMIT
8.3.2 SECOND PASS: FLAT SUMMIT
8.3.3 THIRD PASS: FLAT VALLEY
8.3.4 FOURTH PASS: DEEP VALLEY
8.3.5 COMPLETED SQUARE
8.3.6 DOUBLE SET OF COMPLEMENTARY PAIRS
8.4 ODD MAGIC SUMS; A REMAINDER OF THREE
8.4.1 FIRST PASS: HIGH SUMMIT
8.4.2 SECOND PASS: FLAT SUMMIT
8.4.3 THIRD PASS: FLAT VALLEY
8.4.4 FOURTH PASS: DEEP VALLEY
8.4.5 COMPLETED SQUARE
8.5 ODD MAGIC SUMS; AN ALTERNATIVE HANDLING
8.5.1 ODD MAGIC SUMS; A REMAINDER OF ONE
8.5.2 ODD MAGIC SUMS; A REMAINDER OF THREE
8.6 TRANSFORMATION INTO ANOTHER ASSOCIATED MAGIC SQUARE
8.7 TRANSFORMATION INTO A MOST-PERFECT MAGIC SQUARE
8.8 SMALL MAGIC SUMS
8.8.1 SOME APPROACHES
8.8.2 A NEW SCENARIO

9 SWINGING MELENCOLIA - ANY STARTING NUMBER IN ANY CELL
9.1 SINGLY-EVEN MAGIC SUMS
9.1.1 HIGH SUMMIT
9.1.2 FLAT SUMMIT
9.1.3 FLAT VALLEY
9.1.4 HIGH SUMMIT
9.1.5 DIFFERENT START CELLS
9.2 DOUBLY-EVEN AND ODD MAGIC SUMS
9.2.1 DOUBLY EVEN MAGIC SUMS; A REMAINDER OF TWO
9.2.2 ODD MAGIC SUMS; A REMAINDER OF ONE
9.2.3 ODD MAGIC SUMS; A REMAINDER OF THREE
9.3 PSYCHOMETRIC SWINGING
9.3 CONCEALING THE SWINGING MELENCOLIA METHOD

10 4X4 MUSINGS
10.1 SPECTATOR'S HEIGHT
10.2 ANY NUMBER IN ANY CELL
10.3 SPECTATOR'S YEAR OF BIRTH
10.4 LIGHTNING MAGIC YEAR SQUARE
10.5 COUNTING BACKWARDS
10.6 COUNTING A SEQUENCE OF ODD OR EVEN NUMBERS
10.7 CONCEALING COUNTING SEQUENCES
10.8 TWO PERSONAL NUMBERS
10.9 ANNEMANN-LIKE PRESENTATION OF THE MAGIC YEAR SQUARE
10.10 MAGIC BIRTHDAY SQUARE
10.10.1 GRAECO-LATIN APPROACH
10.10.2 ARITHMETICAL APPROACH
10.10.3 THREE LUCKY NUMBERS APPROACH
10.10.4 NO-BRAINER APPROACH

PART III - MARS

11 SUPER-MAGIC 5X5 SQUARE
11.1 ANY STARTING NUMBER
11.2 ANY MAGIC SUM

12 ALMOST-SEQUENTIAL PANDIAGONAL 5X5 MAGIC SQUARE
12.1 ANY STARTING NUMBER IN ANY CELL
12.2 MAGIC SUM DIVISIBLE BY 5 - CLOSED CYCLE
12.3 ANY MAGIC SUM AND ANY START CELL
12.3.1 WITHOUT A REMAINDER
12.3.2 A REMAINDER OF ONE
12.3.3 A REMAINDER OF TWO
12.3.4 A REMAINDER OF THREE
12.3.5 A REMAINDER OF FOUR
12.3.6 PUT IT ALL TOGETHER

13 5X5 SUMMATION PATTERNS
13.1 BASIC AND PANDIAGONAL MAGIC PATTERNS
13.2 CROSS AND X MAGIC PATTERNS
13.3 KNIGHT'S AND EXCEPTION MOVES

14 SIGIL OF LIFE
14.1 ROUTINE
14.2 EXPLANATION
14.3 ANOTHER STORYLINE

15 ANY NUMBER IN ANY CELL - FORCING A MAGIC SUM

PART IV - SUN

16 6X6 MAGIC SQUARE

17 NEW CONSTRUCTION METHOD
17.1 PATTERNS
17.1.1 PATTERN I
17.1.2 PATTERN II
17.1.3 PATTERN III
17.1.4 COMPLETED SQUARE
17.2 ANY MAGIC SUM
17.3 ANY NUMBER IN ANY CELL

18 BORDERED 6X6 MAGIC SQUARE
18.1 CONSTRUCTION OF THE INLAID 4x4 MAGIC SQUARE
18.2 CONSTRUCTION OF THE OUTER BORDER
18.3 ALTERNATIVE OUTER BORDER
18.4 "LEFT TO RIGHT" ADDITION

19 ONE MORE THING
19.1 SINGLY-EVEN MAGIC SUMS
19.2 INLAID SQUARE
19.3 BORDERED SQUARE
19.4 BLOWING UP THE THING FURTHER

RECOMMENDED READINGS AND FINAL THOUGHTS
GLOSSARY
APPENDICES
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If you have not yet read this ebook and you have an interest in magic squares, I strongly recommend the ebook:
https://www.lybrary.com/melencolia-p-921956.html

My favorite trick is One More Thing. I dedicate One More Thing to Jim Solberg with sincere gratitude.

It is nothing short of impressive how this marvelous encyclopedia is developing and growing. Hats off to hcs for his constant dedication and the generosity to share his vast knowledge with us.

@Nicolino
Very much appreciated!

While as a retailer of Melencolia I do benefit from its sales, I have also explored, performed, and investigated magic squares for 30 years. Actually my entry into magic was through magic squares, which is rather unique in terms of entry points into a magic passion. What Hans-Christian has written here is astonishing. It pushes the methodology to new frontiers. Folks with a passion for magic squares, or math, or clever methods where you use your brain rather than your fingers will experience a lot of joy reading this ebook.

For anyone who loves tricks with magic squares, there is a lot to absorb from the latest version of Melencolia. You can study it for a long time, which is reason enough to thank hcs for his incredible generosity. However, if you are not sure it is worth the trouble to make that effort, I would like to alert you to a huge payoff. Take a peek at the end of the manuscript, where there is an effect he calls One More Thing. Ignore the method on first reading and just imagine the response of the audience. If that does not inspire you to learn the method, you should give up magic squares.

@Chris and Jimso
Thank you very much for your warm words and recommendations!

I can see that this thread hasn’t had a post in just over 4 years, but I sincerely hope that @hcs, @Jimso, @Chris and others are still keeping an eye on things…and that it is the right thread to post in.

I purchased Melencolia 1 from Lybrary earlier this week and was gob-smacked with the detail contained within. Up until now, like many others, my magic square (MS) process has followed the automatic/instant kind of methodology and has been relatively simple to implement - albeit with pretty good effect. After some research, I decided to expand my knowledge on MS. That research seemed to indicate that Hans-Christian Solka‘s work is considered seminal, therefore, off to Lybrary I went. The version I purchased was version 3.50, so I believe that it has encapsulated all of Mr Solka’s thinking to date. I am happy to provide proof of purchase, if required.

However, here is my dilemma! It is massive! I am not a mathematician, and although I deeply appreciate the work undertaken to analyse this topic, I am not particularly inclined to need to understand every step of its evolution and the breadth of its potential application. I am a hobbyist magician, looking to add a very good MS routine to my set.

I did a skim through, to pick up where might be a good place to start, but that merely reinforced the enormity of the thinking applied by the clearly masterful author. In the first instance, I am merely looking to build upon my elementary MS skills and be capable of building MS with the following characteristics:
- use any 2 digit number (> 33), either odd or even
- have the numbers appear random, though not too far apart in value (the instant squares that I have been building use 1-13, then jump up quite a bit for large 2 digit solutions)
- a solution with sequential numbers is not yet essential (maybe later)
- a solution where the spectator can nominate the starting square and value is not yet essential, although I would like to get there eventually

With the above in mind, is there one chapter that would make a good starting point for me, before I move to the next level?

Thank you in advance.

Not the answer you are looking for, but I do think you may be better served by Werner Miller's E-Z Square series https://www.lybrary.com/e-z-square-1-9-p-923355.html Get the first volume in the series to see if his approach works better for you. I consider Melencolia something for more advanced students of Magic Squares. It can be a bit overwhelming at first sight. However, it does reward the amount of work you put into it. For two different takes on how a Magic Square can be performed take a look at "Birthdate Magic Square" and "The Ultimate Magic Square" two methods I came up with some time ago.

Thank you Chris. I have taken your advice and purchased E-Z Square 1 and 2 from Lybrary.

Hopefully, that will get me started on the right track . . .

Cheers!