13x13 magic square

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 number 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 number 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.

 

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

 

Download
13x13, ultra magic.xls
Microsoft Excel werkblad 49.0 KB
Download
13x13 magic square