Take a 9x9 magic square and construct the second, third and fourth 9x9 magic square by adding (9 x 9 =) 81, (2 x 81 = ) 162 respectively (3 x 81 = ) 243 to all numbers of the first 9x9 magic square. Put the first square in the top left corner, put the second square in the bottom right corner, put the third square in the top right corner and put the fourth square in the bottom left corner.

The columns and the diagonals give already the magic sum. To get the right sum in the rows, you must swap numbers, as follows. We split the 9x9 square in the top left corner and the 9x9 square in the bottom left corner in 'quarters' (marked by the blue numbers). The ‘quarters’ top left and bottom left of the 9x9 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 9x9 square in the bottom left corner. Also the (blue) numbers on the border between the two 'quarters’ from the second cell up to the crossing point must be swapped. Finally the numbers of the top half of the last column(s) must be swapped with the numbers of the bottom half of the last column(s). Because the numbers of the first four columns must be swapped, the numbers of the last (4 – 1 = ) 3 columns must be swapped. See below the result.

18x18 magic square

Use this method to construct double odd ( 6x6, 10x10, 14x14, 18x18, ...) magic squares.