

Lichtagent New user Bochum  Germany  Old World 18 Posts 
Dear fellow magicians,
I'm kind of stuck in training my skills in creating instant 4x4 magic squares. The number which killed me is 67. I've tried Sam Dalal's method from Patterns of Perfection revisited and also Michael Daniels' version presented in Perfectly Possible. My problem is the sum of the outer/middle 2x2 squares  two of those squares are off by one (reminds me of Kenton Knepper ). Perhaps it's my fault, but I get those aberrations with different methods  and Michaels trainingscript accepts my solution as valid. Unfortunately I haven't found any explanation regarding this topic, but it may be due to an insufficient search not really knowing what to search for... Can someone please enlighten me about this. Thanks in advance an best season greetings Chris P.S.: When naming the cells from A to P the aberring squares are BCFG and JKNO or EFIJ and GHKL
Doctor Mirabilis Universal Cartenmaschine
https://www.fokxmagic.de/p/doctormirabilisuniversalcartenmaschine 
Larry Barnowsky Inner circle Cooperstown, NY where bats are made from 4877 Posts 
Here's a vey simple approach:
http://www.mathsbusking.com/showsmagicsquares.html 
Lichtagent New user Bochum  Germany  Old World 18 Posts 
Quote:
On Dec 21, 2016, Larry Barnowsky wrote: Hi Larry, thank you for the link. After finishing Michaels Perfectly Possible I realized that he elaborates on the theme that squares of odd sums aren't that perfect as even ones. They seem to lack quite a few of the summation patterns. While not being pleasant this is important for my presentation, since with even numbers you can go rampage when presenting the possibilities to sum up the cells, with uneven results one should be more careful in ones presentation... Thank you for your help. Cheers Chris
Doctor Mirabilis Universal Cartenmaschine
https://www.fokxmagic.de/p/doctormirabilisuniversalcartenmaschine 
Michael Daniels Inner circle Isle of Man 1551 Posts 
Hi Chris,
Yes, there is nothing unique about the number 67. The issue you describe applies to ALL oddtotal 4x4 squares. Oddtotal "mostly perfect" squares have 36 symmetrical summation patterns, which are a subset of the 52 patterns achieved by eventotal "most perfect" squares. Of the missing 16 patterns, the ones you mention are the most notable  which of the two combinations you list will occur depends on the way the square is rotated. With my Perfectly Possible method it will always be EFIJ and GHKL. If oddtotal squares are a problem for your presentation, you could always force an even total by getting the spectator to double the number they first thought of  "to make it even more difficult". Mike 
Lichtagent New user Bochum  Germany  Old World 18 Posts 
Quote:
On Dec 22, 2016, Michael Daniels wrote: Hi Mike, thanks for your further information. I knew the "normal" development as in Larry's link  having a fixed pattern and adjusting four "keycells" to reach the needed number/sum. Or as John Archer teaches in his lectures using different cribs for different ranges to minimize the offset between the fixed numbers and the newly created ones, so that the squares don't look that "premade". And for some reason the audience wanted even numbers or was that fascinated with the result when using odd sums, that I never really looked deeper in the mechanics of the magic squares until now. Some weeks ago I bought and read Sam Dalal's PoP revisited and started to develop the squares "on the fly"  and allthough it should have dawned on me much earlier I just stuck with the creation of a square for 67 (I even never looked after other odd ones afterwards since I seemingly had something misunderstood in the creation). Yesterday, after further looking into this theme I found your script/book and bought it. I really like your approach, but after understanding the method I didn't read further (my fault!), thus missing your explanation of what patterns have to fail with odd sums. This lead to my initial post above Unfortunately one doesn't find easy information about those specialties of "oddsquares" (or I didn't use the right searchterms). But thanks again for all the help, it's really appreciated. Best season greetings Chris
Doctor Mirabilis Universal Cartenmaschine
https://www.fokxmagic.de/p/doctormirabilisuniversalcartenmaschine 
Jimso New user 73 Posts 
Just to add a bit of detail, there are four levels of success that a fourbyfour magic square can achieve. Of course, the 10 basic pattersthe rows, columns, and diagonalsmust add to the magic sum in order to qualify, but there are 4 other patterns that will automatically match. So even the poorest square will have 14 successful patterns. Most methods of construction, including the 'instant' method preferred by many magicians, will achieve 10 more. Improved methods that have appeared more recently, including those of Michael Daniels, will achieve 36 predictable patterns when the magic sum is odd (the maximum possible for odd magic sums), and 52 when the magic sum is even (the theoretical limit, or 'perfection'). Those of us who realize how much success is possible find the older methods to be less than satisfying.
If you want more details, see the postings in this forum under "Magic Squares Solution Chart." 
ursmagicbalu Special user Tamil Nadu, India 965 Posts 
Quote:
On Dec 24, 2016, Jimso wrote: Unable to find this post "Magic Squares Solution Chart."
“It’s not what you do that matters, or even how you do it;
it’s what the spectators perceive you as doing that matters. That’s the MAGIC they’ll remember.” 
landmark Inner circle within a triangle 5154 Posts 
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All proceeds to Open Heart Magic charity. 
ddyment Inner circle Gibsons, BC, Canada 2394 Posts 
The easilylearned methodology that I teach (in my Calculated Thoughts book) always yields the 52 "interesting" patterns for perfect squares, and 36 for others. It's worth noting that there are additional symmetric patterns produced, but most authors ignore these, as they are not very appealing visually.
"Calculated Thoughts" is available at Vanishing Inc. and The Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More

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