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8x8 Magic Square 2 Geometry and Binary Math
The number of 8x8 Magic Squares is very large. Excluding "reflection and rotation," there is only one way to form a 3x3 Magic Square, there are 880 ways to form a 4x4 Magic Square and there are 275,305,224 ways to form a 5x5 Magic Square.
There are different kinds of Magic Squares, the most rare are generally called "Most Perfect Magic Squares". In such Magic Squares, the rows, columns and long diagonals all add up to the same total. Until recently, calculating the number of possible 8x8 Most Perfect Magic Squares was thought to be next to impossible.

When the two Trigrams of each Hexagram are replaced with their corresponding numerical value, this pattern emerges.

When the two Trigrams of each Hexagram are replaced with their corresponding numerical value, this pattern emerges.


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Finally it has been done! There are 368,640 ways to form 8x8 Most Perfect Magic Squares. With so many 8x8 Magic Squares evidently possible, it might seem they would be easy to find without a computer. Alas, such is not the case, as a matter of fact, they're a bit elusive!
Here is an 8x8 Magic Square, independently discovered by this author (using only a calculator), treated in the same manner as Fu Hsi's Square and the Magic Square of Mercury were earlier.

Notice the eight numbers in each of the two Long Diagonals add up to 260, the same as those found in Fu Hsi's Square and in the Magic Square of Mercury, although they are different numbers. The Numbers in each row and column also add up to 260, just as they do in the Magic Square of Mercury.
When the Two Trigram Numbers in each Hexagram are added together, the following pattern arises. Notice the eight number 9's are in different places than they were in the first two squares. The eight numbers in each row, column and long diagonal all add up to 72, as they do in the Magic Square of Mercury.

When the Two Trigram Numbers in each Hexagram are subtracted, the following pattern arises. Notice the eight 0's are in different places than they were in the first two squares. The eight numbers in each row, column and long diagonal all add up to 0, as they do in the Magic Square of Mercury.


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8x8 Most Perfect Magic Square
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