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How to make perfect magic squares & cubes
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8x8 most perfect magic squares, binary
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How to produce most perfect magic 8x8 squares by using binary patterns?
  
On page ‘panmagic 4x4 square, binary’ I show that you can produce all possible panmagic 4x4 squares by
using binary patterns. On this page I show that it is also possible to use the same (but adapted) method to
produce most perfect magic 8x8 squares.
 


The binary 8x8 grids

Choose 6 binary grids wether from A or from B. That gives 2x2x2x2x2x2 is 64 possibilities.



 [A]
 
 
 
 
H11
 
 
 
 
 
 
 
   
H12
 
 
 
 
 
 
 
   
H13
 
 
 
 
 
 
 
    
H14
 
 
 
0
0
1
1
0
0
1
1
 
 
0
0
1
1
0
1
1
0
 
 
0
0
1
1
1
0
0
1
 
 
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
 
 
1
1
0
0
1
0
0
1
 
 
1
1
0
0
0
1
1
0
 
 
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
 
 
0
0
1
1
0
1
1
0
 
 
0
0
1
1
1
0
0
1
 
 
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
 
 
1
1
0
0
1
0
0
1
 
 
1
1
0
0
0
1
1
0
 
 
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
 
 
0
0
1
1
0
1
1
0
 
 
0
0
1
1
1
0
0
1
 
 
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
 
 
1
1
0
0
1
0
0
1
 
 
1
1
0
0
0
1
1
0
 
 
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
 
 
0
0
1
1
0
1
1
0
 
 
0
0
1
1
1
0
0
1
 
 
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
 
 
1
1
0
0
1
0
0
1
 
 
1
1
0
0
0
1
1
0
 
 
1
1
0
0
0
0
1
1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
H21
 
 
 
 
 
 
 
 
H22
 
 
 
 
 
 
 
 
H23
 
 
 
 
 
 
 
 
H24
 
 
 
0
1
1
0
0
0
1
1
 
 
0
1
1
0
0
1
1
0
 
 
0
1
1
0
1
0
0
1
 
 
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
 
 
1
0
0
1
1
0
0
1
 
 
1
0
0
1
0
1
1
0
 
 
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
 
 
0
1
1
0
0
1
1
0
 
 
0
1
1
0
1
0
0
1
 
 
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
 
 
1
0
0
1
1
0
0
1
 
 
1
0
0
1
0
1
1
0
 
 
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
 
 
0
1
1
0
0
1
1
0
 
 
0
1
1
0
1
0
0
1
 
 
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
 
 
1
0
0
1
1
0
0
1
 
 
1
0
0
1
0
1
1
0
 
 
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
 
 
0
1
1
0
0
1
1
0
 
 
0
1
1
0
1
0
0
1
 
 
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
 
 
1
0
0
1
1
0
0
1
 
 
1
0
0
1
0
1
1
0
 
 
1
0
0
1
0
0
1
1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
V11
 
 
 
 
 
 
 
 
V12
 
 
 
 
 
 
 
 
V13
 
 
 
 
 
 
 
 
V14
 
 
 
0
1
0
1
0
1
0
1
 
 
0
1
0
1
0
1
0
1
 
 
0
1
0
1
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1
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1
 
 
0
1
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0
1
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1
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1
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1
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1
 
 
0
1
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1
 
 
0
1
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1
 
 
0
1
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1
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1
0
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0
 
 
1
0
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0
 
 
1
0
1
0
1
0
1
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1
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1
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0
 
 
1
0
1
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0
 
 
1
0
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1
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1
0
 
 
1
0
1
0
1
0
1
0
0
1
0
1
0
1
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1
 
 
0
1
0
1
0
1
0
1
 
 
1
0
1
0
1
0
1
0
 
 
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
 
 
1
0
1
0
1
0
1
0
 
 
0
1
0
1
0
1
0
1
 
 
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
 
 
1
0
1
0
1
0
1
0
 
 
0
1
0
1
0
1
0
1
 
 
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
 
 
0
1
0
1
0
1
0
1
 
 
1
0
1
0
1
0
1
0
 
 
0
1
0
1
0
1
0
1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
V21
 
 
 
 
 
 
 
 
V22
 
 
 
 
 
 
 
 
V23