Composite 9x9 magic square

 

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

 

 

1x digit

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 (digit -/- 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 digits of each 3x3 sub-square:

 

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

 

Download
9x9, composite magic square.xls
Microsoft Excel werkblad 38.5 KB