11x11 magic square

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 number 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 number 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.

 

You can use this method to construct ultra magic squares of order is prime number from 5x5 to infinity. See 5x5, 7x7, 11x11, 13x13, 17x17, 19x19, 23x23, 29x29, 31x31

 

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11x11, Ultra magic.xls
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11x11 magic square