### Composite 9x9 magic square (1)

It is possible to use one 3x3 magic square to produce a (simple) 9x9 magic square.

The first grid consists of 3x3 the same 3x3 magic square.

The second grid consists of the '3x3 blown up' version of the 3x3 magic square.

Take a number from a cell of the fist grid and add 9 x (number -/- 1) from the same cell of the second grid.

1x number

 2 9 4 2 9 4 2 9 4 7 5 3 7 5 3 7 5 3 6 1 8 6 1 8 6 1 8 2 9 4 2 9 4 2 9 4 7 5 3 7 5 3 7 5 3 6 1 8 6 1 8 6 1 8 2 9 4 2 9 4 2 9 4 7 5 3 7 5 3 7 5 3 6 1 8 6 1 8 6 1 8

+ 9 x (number -/- 1)

 2 2 2 9 9 9 4 4 4 2 2 2 9 9 9 4 4 4 2 2 2 9 9 9 4 4 4 7 7 7 5 5 5 3 3 3 7 7 7 5 5 5 3 3 3 7 7 7 5 5 5 3 3 3 6 6 6 1 1 1 8 8 8 6 6 6 1 1 1 8 8 8 6 6 6 1 1 1 8 8 8

= (simple) 9x9 magic square

 11 18 13 74 81 76 29 36 31 16 14 12 79 77 75 34 32 30 15 10 17 78 73 80 33 28 35 56 63 58 38 45 40 20 27 22 61 59 57 43 41 39 25 23 21 60 55 62 42 37 44 24 19 26 47 54 49 2 9 4 65 72 67 52 50 48 7 5 3 70 68 66 51 46 53 6 1 8 69 64 71

Thanks to Mallesh K S, who pointed me that I was forgotten to present this method on my website. And he showed me that you can produce the following (not pure) 3x3 magic square by using the sum of the numbers of each 3x3 sub-square:

 1107 1107 1107 1107 1107 1107 126 693 288 1107 531 369 207 1107 450 45 612

9x9, composite magic square.xls