Ultra magic 13x13 square

 

The key to construct an ultra magic 13x13 square is 0 - 12 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11

 

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 12 1 2 3 4 5 6 7 8 9 10 11
10 11 0 12 1 2 3 4 5 6 7 8 9
8 9 10 11 0 12 1 2 3 4 5 6 7
6 7 8 9 10 11 0 12 1 2 3 4 5
4 5 6 7 8 9 10 11 0 12 1 2 3
2 3 4 5 6 7 8 9 10 11 0 12 1
12 1 2 3 4 5 6 7 8 9 10 11 0
11 0 12 1 2 3 4 5 6 7 8 9 10
9 10 11 0 12 1 2 3 4 5 6 7 8
7 8 9 10 11 0 12 1 2 3 4 5 6
5 6 7 8 9 10 11 0 12 1 2 3 4
3 4 5 6 7 8 9 10 11 0 12 1 2
1 2 3 4 5 6 7 8 9 10 11 0 12

 

 

 + 13x digit from second grid

0 10 8 6 4 2 12 11 9 7 5 3 1
12 11 9 7 5 3 1 0 10 8 6 4 2
1 0 10 8 6 4 2 12 11 9 7 5 3
2 12 11 9 7 5 3 1 0 10 8 6 4
3 1 0 10 8 6 4 2 12 11 9 7 5
4 2 12 11 9 7 5 3 1 0 10 8 6
5 3 1 0 10 8 6 4 2 12 11 9 7
6 4 2 12 11 9 7 5 3 1 0 10 8
7 5 3 1 0 10 8 6 4 2 12 11 9
8 6 4 2 12 11 9 7 5 3 1 0 10
9 7 5 3 1 0 10 8 6 4 2 12 11
10 8 6 4 2 12 11 9 7 5 3 1 0
11 9 7 5 3 1 0 10 8 6 4 2 12

 

 

 = Ultra magic 13x13 square

1 143 106 81 56 31 162 150 125 100 75 50 25
167 155 118 104 67 42 17 5 136 111 86 61 36
22 10 141 116 79 65 28 159 147 122 97 72 47
33 164 152 127 102 77 40 26 2 133 108 83 58
44 19 7 138 113 88 63 38 157 156 119 94 69
55 30 161 149 124 99 74 49 24 12 131 117 80
78 41 16 4 135 110 85 60 35 166 154 129 92
90 53 39 158 146 121 96 71 46 21 9 140 115
101 76 51 14 13 132 107 82 57 32 163 151 126
112 87 62 37 168 144 130 93 68 43 18 6 137
123 98 73 48 23 11 142 105 91 54 29 160 148
134 109 84 59 34 165 153 128 103 66 52 15 3
145 120 95 70 45 20 8 139 114 89 64 27 169

 

 

This 13x13 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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13x13, ultra magic.xls
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