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The Magic Cafe Forum Index » » Magical equations » » Magic Square Solutions Chart (3 Likes) Printer Friendly Version

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MagicMan1957
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At some point after starting this thread in 2010 I found this chart which covers most basic squares.

Image
Michael Daniels
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Quote:
On Jul 10, 2016, Jimso wrote:
Thanks for the confidence, Mike, even before you have even seen what I discovered. I believe you will be pleased with the elegance and versatility of the method.

I will also recommend your "Mostly Perfect" ebook to anyone who has not seen it. I did not want to expose methods that were not mine, so I did not explain all of the wonderful methods I found while doing my research. However, I included references to the ones I thought were worth study. Yours is certainly among them. I view all of these as adding to the stock of knowledge, rather than competing for the best method.


Thanks Jim,

Mike
Jimso
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There is no need to leave readers wondering about the other patterns. Here they are, arranged in categories. The first row are those required by the definition, but the next row will automatically succeed in every magic square regardless of how it is constructed. The third row will succeed in almost every construction method. In other words, you have to do extra work to find a magic square that does not include those patterns, but such squares do exist. The fourth and fifth rows (which I call the 'vertical' and 'horizontal' patterns) can succeed alternatively even when the magic sum is odd. That is, you can get one group but not the other, for a total of 36. When the magic sum is even, you can get both of those groups to succeed as well as the odd broken diagonals in the last row. All 52 patterns are identified in the e-books by Sam Dalal and Michael Daniels, but I believe my book is the first to explain the conditions and mathematical reasons for which the various results apply. Of course, you do not need to understand the math to use the results, but it is nice to know that there is proof for the claim. My construction methods, like the others, will produce the results without any attention to the deeper math.

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Michael Daniels
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Nice

Mike
Jimso
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In answer to question, it was buried deep on page 5 of the thread, but here it is again.
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