Composite Magic Squares

Composite magic sqaures are magic squares that exist out of other magic squares. As a 3 by 3 magic square is the smallest possible magic square, it would be a fair guess to think that an order 6 magic square could be a composite magic square, however, this is not the case. Consider a 3 by 3 magic square consisting of numers 1 through 9 and giving it the number 1, an order 3 magic square consisting of numbers 10 through 18 => 2, 19 through 27 => 3 and 28 through 36 => 4. Than from these numbers 1 through 4, it becomes impossible to create a magic square, as an order 2 magic square can not exist (only 4 digits to use). Therefore, the first possible composite magic square is of order 9, as 9 order 3 magic squares can exist inside of it. An order 12 magic square can be composite in two ways, it can consist out of 12 order 3 magic squares, or 9 order 4 magic squares.