De sleutel voor het ultramagisch 13x13 vierkant is 0 - 12 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11
Het tweede patroon is een reflectie (kwartslag gedraaid en gespiegeld) van het eerste patroon
Neem 1x getal uit 1e patroon +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 getal uit 2e patroon
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 magisch 13x13 vierkant
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 |
Dit 13x13 magisch vierkant is panmagisch en symmetrisch.
Deze methode werkt voor grootte is oneven maar geen veelvoud van 3 van 5x5 tot oneindig.