Explanation 9x9 magic square

The 9x9 magic square is odd and not only a multiple of 3, but 3x3 (= 3 squared). So the construction method differ from the 5x5 and 7x7 magic square. You can use the shift method, but with boundary conditions and less posibilities. Construction with ternary grids (with 0, 1 and 2) gives many more possibilities. The ultramagic 9x9 square is not only panmagic and symmetric, but also 3x3 compact and each 1/3 row/column gives 1/3 of the magic sum.

Construction methods

The construction methods of the 9x9 magic square are:

• Composite, Simple
• Composite, Prop. (1)
• Diagonal method
• Siamese method
• Knight movement method
• Symmetric transformation
• Lozenge method
• Shift method (1)
• Shift method (2)
• Grids (1)
• Grids (2)
• Grids (3)
• Baselines
• Swapping
• Ultra magic
• Pan 7x7 in 9x9 (1)
• Pan 7x7 in 9x9 (2)
• Concentric
• Concentric with diamond
• Bimagic

Use composite simple, diagonal method, Siamese method, knight movement method, symmetric transformation and Lozenge method to construct simple, symmetric 9x9 magic squares.

Use composite proportional (1), pan 7x7 in 9x9, concentric [with diamond] and bimagic to construct special 9x9 magic squares.

With the remaining methods you can construct panmagic 9x9 squares, which are sometimes 3x3 compact and/or symmetric too.

Only the ultramagic square is panmagic, symmetric, 3x3 compact and each 1/3 row/column gives 1/3 of the magic sum.