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How to make perfect magic squares & cubes
The sky is the limit!!!
pan magic 9x9 square (2)
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How to produce a panmagic 9x9 square?

On the previous web page I have already presented a method to produce panmagic 9x9 squares.
These squares have the extra magic feature that each random chosen 3x3 sub-square gives also
the magic sum. Disadvantage of the previous method is that there are only a few possibilities. Look
at the following method.


Choose four grids from the grids below and choose one odd V, one even V, one odd H and one even
H (n.b.: 1, 3, 5, 7, 9 and 11 is odd and 2, 4, 6, 8, 10 and 12 is even).


V1                     V2                       H1                     H2                  
  0 1 2 0 1 2 0 1 2     0 1 2 0 1 2 0 1 2       0 0 0 1 1 1 2 2 2     0 0 0 2 2 2 1 1 1
  0 1 2 0 1 2 0 1 2     0 1 2 0 1 2 0 1 2       1 1 1 2 2 2 0 0 0     1 1 1 0 0 0 2 2 2
  0 1 2 0 1 2 0 1 2     0 1 2 0 1 2 0 1 2       2 2 2 0 0 0 1 1 1     2 2 2 1 1 1 0 0 0
  1 2 0 1 2 0 1 2 0     2 0 1 2 0 1 2 0 1       0 0 0 1 1 1 2 2 2     0 0 0 2 2 2 1 1 1
  1 2 0 1 2 0 1 2 0     2 0 1 2 0 1 2 0 1       1 1 1 2 2 2 0 0 0     1 1 1 0 0 0 2 2 2
  1 2 0 1 2 0 1 2 0     2 0 1 2 0 1 2 0 1       2 2 2 0 0 0 1 1 1     2 2 2 1 1 1 0 0 0
  2 0 1 2 0 1 2 0 1     1 2 0 1 2 0 1 2 0       0 0 0 1 1 1 2 2 2     0 0 0 2 2 2 1 1 1
  2 0 1 2 0 1 2 0 1     1 2 0 1 2 0 1 2 0       1 1 1 2 2 2 0 0 0     1 1 1 0 0 0 2 2 2
  2 0 1 2 0 1 2 0 1     1 2 0 1 2 0 1 2 0       2 2 2 0 0 0 1 1 1     2 2 2 1 1 1 0 0 0
                                                                                       
V3                     V4                       H3                     H4                  
  0 2 1 0 2 1 0 2 1     0 2 1 0 2 1 0 2 1       0 0 0 2 2 2 1 1 1     0 0 0 1 1 1 2 2 2
  0 2 1 0 2 1 0 2 1     0 2 1 0 2 1 0 2 1       2 2 2 1 1 1 0 0 0     2 2 2 0 0 0 1 1 1
  0 2 1 0 2 1 0 2 1     0 2 1 0 2 1 0 2 1       1 1 1 0 0 0 2 2 2     1 1 1 2 2 2 0 0 0
  2 1 0 2 1 0 2 1 0     1 0 2 1 0 2 1 0 2       0 0 0 2 2 2 1 1 1     0 0 0 1 1 1 2 2 2
  2 1 0 2 1 0 2 1 0     1 0 2 1 0 2 1 0 2       2 2 2 1 1 1 0 0 0     2 2 2 0 0 0 1 1 1
  2 1 0 2 1 0 2 1 0     1 0 2 1 0 2 1 0 2       1 1 1 0 0 0 2 2 2     1 1 1 2 2 2 0 0 0
  1 0 2 1 0 2 1 0 2     2 1 0 2 1 0 2 1 0       0 0 0 2 2 2 1 1 1     0 0 0 1 1 1 2 2 2
  1 0 2 1 0 2 1 0 2     2 1 0 2 1 0 2 1 0       2 2 2 1 1 1 0 0 0     2 2 2 0 0 0 1 1 1
  1 0 2 1 0 2 1 0 2     2 1 0 2 1 0 2 1 0       1 1 1 0 0 0 2 2 2     1 1 1 2 2 2 0 0 0
                                                                                       
V5                     V6                       H5                     H6                  
  1 0 2 1 0 2 1 0 2     1 0 2 1 0 2 1 0 2       1 1 1 0 0 0 2 2 2     1 1 1 2 2 2 0 0 0
  1 0 2 1 0 2 1 0 2     1 0 2 1 0 2 1 0 2       0 0 0 2 2 2 1 1 1     0 0 0 1 1 1 2 2 2
  1 0 2 1 0 2 1 0 2     1 0 2 1 0 2 1 0 2       2 2 2 1 1 1 0 0 0     2 2 2 0 0 0 1 1 1
  0 2 1 0 2 1 0 2 1     2 1 0 2 1 0 2 1 0       1 1 1 0 0 0 2 2 2     1 1 1 2 2 2 0 0 0
  0 2 1 0 2 1 0 2 1     2 1 0 2 1 0 2 1 0       0 0 0 2 2 2 1 1 1     0 0 0 1 1 1 2 2 2
  0 2 1 0 2 1 0 2 1     2 1 0 2 1 0 2 1 0       2 2 2 1 1 1 0 0 0     2 2 2 0 0 0 1 1 1
  2 1 0 2 1 0 2 1 0     0 2 1 0 2 1 0 2 1       1 1 1 0 0 0 2 2 2     1 1 1 2 2 2 0 0 0
  2 1 0 2 1 0 2 1 0     0 2 1 0 2 1 0 2 1       0 0 0 2 2 2 1 1 1     0 0 0 1 1 1 2 2 2
  2 1 0 2 1 0 2 1 0     0 2 1 0 2 1 0 2 1       2 2 2 1 1 1 0 0 0     2 2 2 0 0 0 1 1 1
                                                                                       
V7                     V8                       H7                     H8                  
  1 2 0 1 2 0 1 2 0     1 2 0 1 2 0 1 2 0       1 1 1 2 2 2 0 0 0     1 1 1 0 0 0 2 2 2
  1 2 0 1 2 0 1 2 0     1 2 0 1 2 0 1 2 0       2 2 2 0 0 0 1 1 1     2 2 2 1 1 1 0 0 0
  1 2 0 1 2 0 1 2 0     1 2 0 1 2 0 1 2 0       0 0 0 1 1 1 2 2 2     0 0 0 2 2 2 1 1 1
  2 0 1 2 0 1 2 0 1     0 1 2 0 1 2 0 1 2       1 1 1 2 2 2 0 0 0     1 1 1 0 0 0 2 2 2
  2 0 1 2 0 1 2 0 1     0 1 2 0 1 2 0 1 2       2 2 2 0 0 0 1 1 1     2 2 2 1 1 1 0 0 0
  2 0 1 2 0 1 2 0 1     0 1 2 0 1 2 0 1 2       0 0 0 1 1 1 2 2 2     0 0 0 2 2 2 1 1 1
  0 1 2 0 1 2 0 1 2     2 0 1 2 0 1 2 0 1       1 1 1 2 2 2 0 0 0     1 1 1 0 0 0 2 2 2
  0 1 2 0 1 2 0 1 2     2 0 1 2 0 1 2 0 1       2 2 2 0 0 0 1 1 1     2 2 2 1 1 1 0 0 0
  0 1 2 0 1 2 0 1 2     2 0 1 2 0 1 2 0 1       0 0 0 1 1 1 2 2 2     0 0