Ultra magic 7x7 square

 

The key to construct an ultra magic (= symmetric and panmagic) 7x7 square is: 0 - 6 - 1 - 2 - 3 - 4 - 5

 

 

1x digit from shift 2 to the right   +   7x digit from reflection 1st grid+1 =   7x7 ultra magic square

0 6 1 2 3 4 5   0 4 2 6 5 3 1   1 35 16 45 39 26 13
4 5 0 6 1 2 3   6 5 3 1 0 4 2   47 41 22 14 2 31 18
2 3 4 5 0 6 1   1 0 4 2 6 5 3   10 4 33 20 43 42 23
6 1 2 3 4 5 0   2 6 5 3 1 0 4   21 44 38 25 12 6 29
5 0 6 1 2 3 4   3 1 0 4 2 6 5   27 8 7 30 17 46 40
3 4 5 0 6 1 2   4 2 6 5 3 1 0   32 19 48 36 28 9 3
1 2 3 4 5 0 6   5 3 1 0 4 2 6   37 24 11 5 34 15 49

 

 

You can use his method to construct magic squares of odd order which are no multiple of from 5x5 to infinite (= 5x5, 7x7, 11x11, 13x13, ... magic squares).

 

 

Download
7x7, Ultra magic.xls
Microsoft Excel werkblad 31.5 KB