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MagicMan1957 Inner circle 1444 Posts 
At some point after starting this thread in 2010 I found this chart which covers most basic squares.


Michael Daniels Inner circle Isle of Man 1550 Posts 
Quote:
On Jul 10, 2016, Jimso wrote: Thanks Jim, Mike 

Jimso New user 73 Posts 
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 ebooks 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.
Click here to view attached image. 

Michael Daniels Inner circle Isle of Man 1550 Posts 
Nice
Mike 

Jimso New user 73 Posts 
In answer to question, it was buried deep on page 5 of the thread, but here it is again.


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