Ultra magic 11x11 square

 

The key to construct an ultra magic 11x11 square is 0 - 10 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9

 

The second grid is a reflection (rotated by a quarter and mirrored) of the first grid.

 

 

Take 1x digit from the first grid +1

0 10 1 2 3 4 5 6 7 8 9
8 9 0 10 1 2 3 4 5 6 7
6 7 8 9 0 10 1 2 3 4 5
4 5 6 7 8 9 0 10 1 2 3
2 3 4 5 6 7 8 9 0 10 1
10 1 2 3 4 5 6 7 8 9 0
9 0 10 1 2 3 4 5 6 7 8
7 8 9 0 10 1 2 3 4 5 6
5 6 7 8 9 0 10 1 2 3 4
3 4 5 6 7 8 9 0 10 1 2
1 2 3 4 5 6 7 8 9 0 10

 

 

+11x digit from the second grid

0 8 6 4 2 10 9 7 5 3 1
10 9 7 5 3 1 0 8 6 4 2
1 0 8 6 4 2 10 9 7 5 3
2 10 9 7 5 3 1 0 8 6 4
3 1 0 8 6 4 2 10 9 7 5
4 2 10 9 7 5 3 1 0 8 6
5 3 1 0 8 6 4 2 10 9 7
6 4 2 10 9 7 5 3 1 0 8
7 5 3 1 0 8 6 4 2 10 9
8 6 4 2 10 9 7 5 3 1 0
9 7 5 3 1 0 8 6 4 2 10

 

 

= Ultra magic 11x11 square

1 99 68 47 26 115 105 84 63 42 21
119 109 78 66 35 14 4 93 72 51 30
18 8 97 76 45 33 112 102 81 60 39
27 116 106 85 64 43 12 11 90 69 48
36 15 5 94 73 52 31 120 100 88 57
55 24 113 103 82 61 40 19 9 98 67
65 34 22 2 91 70 49 28 117 107 86
74 53 32 111 110 79 58 37 16 6 95
83 62 41 20 10 89 77 46 25 114 104
92 71 50 29 118 108 87 56 44 13 3
101 80 59 38 17 7 96 75 54 23 121

 

 

This 11x11 magic square is panmagic and symmetric.

 

Use this method to construct magic squares of odd order which are no multiple of 3 from 5x5 to infinite (= 5x5, 7x7, 11x11, 13x13, 17x17, ... magic squares).

 

 

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11x11, Ultra magic.xls
Microsoft Excel werkblad 42.5 KB