Explanation 18x18 magic square

The 18x18 magic square is double odd (2x9). Double odd magic squares have an irregular structure. That's why a pure panmagic, symmetric and/or compact 18x18 magic square does not exist. But, 18=3x6 and you can composite the 18x18 magic square using the 3x3 and the 6x6 magic square. It is possible to construct a 18x18 magic square consisting of 3x3 proportional 6x6 magic squares. Each 1/3 row/column/diagonal gives 1/3 of the magic sum. Special 18x18 magic squares are the 18x18 inlaid magic (with 16x16 inlay) square and the 18x18 concentric magic square.

Construction methods

Methods to construct the 18x18 magic square are:

• Medjig method
• Method of Strachey
• Alternative method Strachey
• LUX method
• Reflection (1)
• Reflection (2)
• Composite, Simple
• Composite, Prop. (1)
• Composite, Prop. (2)
• Inlaid magic square
• Most perfect 16x16 in 18x18
• Concentric

N.B.: A pure 18x18 magic square which is 2x2 or 3x3 compact is not possible.                However, composite proportional (1) and composite proportional (2) give pure 18x18 magic squares which are 6x6 compact.