Je kunt het 16x16 magisch vierkant opbouwen uit 16 evenredige panmagische 4x4 vierkanten. Evenredig betekent dat alle 16 panmagisch 4x4 vierkanten dezelfde magische som van (1/4 x 2056 = ) 514 hebben. We gebruiken de basissleutel methode (4x4) voor het maken van de panmagische 4x4 vierkanten. Alleen gebruiken we nu als rijcoördinaten niet de getallen 0 t/m 3 maar 0 t/m (16x4 -/- 1 = ) 63 en we verdelen de rijcoördinaten evenredig over de 16 panmagische 4x4 vierkanten.
1x rijcoördinaat +64x kolomcoördinaat + 1 = panmagisch 4x4 vierkant
0 | 31 | 32 | 63 | 0 | 3 | 1 | 2 | 1 | 224 | 97 | 192 | ||
32 | 63 | 0 | 31 | 3 | 0 | 2 | 1 | 225 | 64 | 129 | 96 | ||
31 | 0 | 63 | 32 | 2 | 1 | 3 | 0 | 160 | 65 | 256 | 33 | ||
63 | 32 | 31 | 0 | 1 | 2 | 0 | 3 | 128 | 161 | 32 | 193 | ||
1 | 30 | 33 | 62 | 0 | 3 | 1 | 2 | 2 | 223 | 98 | 191 | ||
33 | 62 | 1 | 30 | 3 | 0 | 2 | 1 | 226 | 63 | 130 | 95 | ||
30 | 1 | 62 | 33 | 2 | 1 | 3 | 0 | 159 | 66 | 255 | 34 | ||
62 | 33 | 30 | 1 | 1 | 2 | 0 | 3 | 127 | 162 | 31 | 194 | ||
2 | 29 | 34 | 61 | 0 | 3 | 1 | 2 | 3 | 222 | 99 | 190 | ||
34 | 61 | 2 | 29 | 3 | 0 | 2 | 1 | 227 | 62 | 131 | 94 | ||
29 | 2 | 61 | 34 | 2 | 1 | 3 | 0 | 158 | 67 | 254 | 35 | ||
61 | 34 | 29 | 2 | 1 | 2 | 0 | 3 | 126 | 163 | 30 | 195 | ||
3 | 28 | 35 | 60 | 0 | 3 | 1 | 2 | 4 | 221 | 100 | 189 | ||
35 | 60 | 3 | 28 | 3 | 0 | 2 | 1 | 228 | 61 | 132 | 93 | ||
28 | 3 | 60 | 35 | 2 | 1 | 3 | 0 | 157 | 68 | 253 | 36 | ||
60 | 35 | 28 | 3 | 1 | 2 | 0 | 3 | 125 | 164 | 29 | 196 | ||
4 | 27 | 36 | 59 | 0 | 3 | 1 | 2 | 5 | 220 | 101 | 188 | ||
36 | 59 | 4 | 27 | 3 | 0 | 2 | 1 | 229 | 60 | 133 | 92 | ||
27 | 4 | 59 | 36 | 2 | 1 | 3 | 0 | 156 | 69 | 252 | 37 | ||
59 | 36 | 27 | 4 | 1 | 2 | 0 | 3 | 124 | 165 | 28 | 197 | ||
5 | 26 | 37 | 58 | 0 | 3 | 1 | 2 | 6 | 219 | 102 | 187 | ||
37 | 58 | 5 | 26 | 3 | 0 | 2 | 1 | 230 | 59 | 134 | 91 | ||
26 | 5 | 58 | 37 | 2 | 1 | 3 | 0 | 155 | 70 | 251 | 38 | ||
58 | 37 | 26 | 5 | 1 | 2 | 0 | 3 | 123 | 166 | 27 | 198 | ||
6 | 25 | 38 | 57 | 0 | 3 | 1 | 2 | 7 | 218 | 103 | 186 | ||
38 | 57 | 6 | 25 | 3 | 0 | 2 | 1 | 231 | 58 | 135 | 90 | ||
25 | 6 | 57 | 38 | 2 | 1 | 3 | 0 | 154 | 71 | 250 | 39 | ||
57 | 38 | 25 | 6 | 1 | 2 | 0 | 3 | 122 | 167 | 26 | 199 | ||
7 | 24 | 39 | 56 | 0 | 3 | 1 | 2 | 8 | 217 | 104 | 185 | ||
39 | 56 | 7 | 24 | 3 | 0 | 2 | 1 | 232 | 57 | 136 | 89 | ||
24 | 7 | 56 | 39 | 2 | 1 | 3 | 0 | 153 | 72 | 249 | 40 | ||
56 | 39 | 24 | 7 | 1 | 2 | 0 | 3 | 121 | 168 | 25 | 200 | ||
8 | 23 | 40 | 55 | 0 | 3 | 1 | 2 | 9 | 216 | 105 | 184 | ||
40 | 55 | 8 | 23 | 3 | 0 | 2 | 1 | 233 | 56 | 137 | 88 | ||
23 | 8 | 55 | 40 | 2 | 1 | 3 | 0 | 152 | 73 | 248 | 41 | ||
55 | 40 | 23 | 8 | 1 | 2 | 0 | 3 | 120 | 169 | 24 | 201 | ||
9 | 22 | 41 | 54 | 0 | 3 | 1 | 2 | 10 | 215 | 106 | 183 | ||
41 | 54 | 9 | 22 | 3 | 0 | 2 | 1 | 234 | 55 | 138 | 87 | ||
22 | 9 | 54 | 41 | 2 | 1 | 3 | 0 | 151 | 74 | 247 | 42 | ||
54 | 41 | 22 | 9 | 1 | 2 | 0 | 3 | 119 | 170 | 23 | 202 | ||
10 | 21 | 42 | 53 | 0 | 3 | 1 | 2 | 11 | 214 | 107 | 182 | ||
42 | 53 | 10 | 21 | 3 | 0 | 2 | 1 | 235 | 54 | 139 | 86 | ||
21 | 10 | 53 | 42 | 2 | 1 | 3 | 0 | 150 | 75 | 246 | 43 | ||
53 | 42 | 21 | 10 | 1 | 2 | 0 | 3 | 118 | 171 | 22 | 203 | ||
11 | 20 | 43 | 52 | 0 | 3 | 1 | 2 | 12 | 213 | 108 | 181 | ||
43 | 52 | 11 | 20 | 3 | 0 | 2 | 1 | 236 | 53 | 140 | 85 | ||
20 | 11 | 52 | 43 | 2 | 1 | 3 | 0 | 149 | 76 | 245 | 44 | ||
52 | 43 | 20 | 11 | 1 | 2 | 0 | 3 | 117 | 172 | 21 | 204 | ||
12 | 19 | 44 | 51 | 0 | 3 | 1 | 2 | 13 | 212 | 109 | 180 | ||
44 | 51 | 12 | 19 | 3 | 0 | 2 | 1 | 237 | 52 | 141 | 84 | ||
19 | 12 | 51 | 44 | 2 | 1 | 3 | 0 | 148 | 77 | 244 | 45 | ||
51 | 44 | 19 | 12 | 1 | 2 | 0 | 3 | 116 | 173 | 20 | 205 | ||
13 | 18 | 45 | 50 | 0 | 3 | 1 | 2 | 14 | 211 | 110 | 179 | ||
45 | 50 | 13 | 18 | 3 | 0 | 2 | 1 | 238 | 51 | 142 | 83 | ||
18 | 13 | 50 | 45 | 2 | 1 | 3 | 0 | 147 | 78 | 243 | 46 | ||
50 | 45 | 18 | 13 | 1 | 2 | 0 | 3 | 115 | 174 | 19 | 206 | ||
14 | 17 | 46 | 49 | 0 | 3 | 1 | 2 | 15 | 210 | 111 | 178 | ||
46 | 49 | 14 | 17 | 3 | 0 | 2 | 1 | 239 | 50 | 143 | 82 | ||
17 | 14 | 49 | 46 | 2 | 1 | 3 | 0 | 146 | 79 | 242 | 47 | ||
49 | 46 | 17 | 14 | 1 | 2 | 0 | 3 | 114 | 175 | 18 | 207 | ||
15 | 16 | 47 | 48 | 0 | 3 | 1 | 2 | 16 | 209 | 112 | 177 | ||
47 | 48 | 15 | 16 | 3 | 0 | 2 | 1 | 240 | 49 | 144 | 81 | ||
16 | 15 | 48 | 47 | 2 | 1 | 3 | 0 | 145 | 80 | 241 | 48 | ||
48 | 47 | 16 | 15 | 1 | 2 | 0 | 3 | 113 | 176 | 17 | 208 |
Voeg de 16 panmagische 4x4 vierkanten op volgorde samen.
16x16 magisch vierkant
1 | 224 | 97 | 192 | 2 | 223 | 98 | 191 | 3 | 222 | 99 | 190 | 4 | 221 | 100 | 189 |
225 | 64 | 129 | 96 | 226 | 63 | 130 | 95 | 227 | 62 | 131 | 94 | 228 | 61 | 132 | 93 |
160 | 65 | 256 | 33 | 159 | 66 | 255 | 34 | 158 | 67 | 254 | 35 | 157 | 68 | 253 | 36 |
128 | 161 | 32 | 193 | 127 | 162 | 31 | 194 | 126 | 163 | 30 | 195 | 125 | 164 | 29 | 196 |
5 | 220 | 101 | 188 | 6 | 219 | 102 | 187 | 7 | 218 | 103 | 186 | 8 | 217 | 104 | 185 |
229 | 60 | 133 | 92 | 230 | 59 | 134 | 91 | 231 | 58 | 135 | 90 | 232 | 57 | 136 | 89 |
156 | 69 | 252 | 37 | 155 | 70 | 251 | 38 | 154 | 71 | 250 | 39 | 153 | 72 | 249 | 40 |
124 | 165 | 28 | 197 | 123 | 166 | 27 | 198 | 122 | 167 | 26 | 199 | 121 | 168 | 25 | 200 |
9 | 216 | 105 | 184 | 10 | 215 | 106 | 183 | 11 | 214 | 107 | 182 | 12 | 213 | 108 | 181 |
233 | 56 | 137 | 88 | 234 | 55 | 138 | 87 | 235 | 54 | 139 | 86 | 236 | 53 | 140 | 85 |
152 | 73 | 248 | 41 | 151 | 74 | 247 | 42 | 150 | 75 | 246 | 43 | 149 | 76 | 245 | 44 |
120 | 169 | 24 | 201 | 119 | 170 | 23 | 202 | 118 | 171 | 22 | 203 | 117 | 172 | 21 | 204 |
13 | 212 | 109 | 180 | 14 | 211 | 110 | 179 | 15 | 210 | 111 | 178 | 16 | 209 | 112 | 177 |
237 | 52 | 141 | 84 | 238 | 51 | 142 | 83 | 239 | 50 | 143 | 82 | 240 | 49 | 144 | 81 |
148 | 77 | 244 | 45 | 147 | 78 | 243 | 46 | 146 | 79 | 242 | 47 | 145 | 80 | 241 | 48 |
116 | 173 | 20 | 205 | 115 | 174 | 19 | 206 | 114 | 175 | 18 | 207 | 113 | 176 | 17 | 208 |
Helaas is bovenstaand 16x16 magisch vierkant niet volledig 2x2 compact. We gebruiken de techniek van de Khajuraho methode om systematisch getallen om te wisselen.
Franklin panmagisch 16x16 vierkant
4 | 224 | 97 | 189 | 3 | 223 | 98 | 190 | 2 | 222 | 99 | 191 | 1 | 221 | 100 | 192 |
225 | 61 | 132 | 96 | 226 | 62 | 131 | 95 | 227 | 63 | 130 | 94 | 228 | 64 | 129 | 93 |
160 | 68 | 253 | 33 | 159 | 67 | 254 | 34 | 158 | 66 | 255 | 35 | 157 | 65 | 256 | 36 |
125 | 161 | 32 | 196 | 126 | 162 | 31 | 195 | 127 | 163 | 30 | 194 | 128 | 164 | 29 | 193 |
8 | 220 | 101 | 185 | 7 | 219 | 102 | 186 | 6 | 218 | 103 | 187 | 5 | 217 | 104 | 188 |
229 | 57 | 136 | 92 | 230 | 58 | 135 | 91 | 231 | 59 | 134 | 90 | 232 | 60 | 133 | 89 |
156 | 72 | 249 | 37 | 155 | 71 | 250 | 38 | 154 | 70 | 251 | 39 | 153 | 69 | 252 | 40 |
121 | 165 | 28 | 200 | 122 | 166 | 27 | 199 | 123 | 167 | 26 | 198 | 124 | 168 | 25 | 197 |
12 | 216 | 105 | 181 | 11 | 215 | 106 | 182 | 10 | 214 | 107 | 183 | 9 | 213 | 108 | 184 |
233 | 53 | 140 | 88 | 234 | 54 | 139 | 87 | 235 | 55 | 138 | 86 | 236 | 56 | 137 | 85 |
152 | 76 | 245 | 41 | 151 | 75 | 246 | 42 | 150 | 74 | 247 | 43 | 149 | 73 | 248 | 44 |
117 | 169 | 24 | 204 | 118 | 170 | 23 | 203 | 119 | 171 | 22 | 202 | 120 | 172 | 21 | 201 |
16 | 212 | 109 | 177 | 15 | 211 | 110 | 178 | 14 | 210 | 111 | 179 | 13 | 209 | 112 | 180 |
237 | 49 | 144 | 84 | 238 | 50 | 143 | 83 | 239 | 51 | 142 | 82 | 240 | 52 | 141 | 81 |
148 | 80 | 241 | 45 | 147 | 79 | 242 | 46 | 146 | 78 | 243 | 47 | 145 | 77 | 244 | 48 |
113 | 173 | 20 | 208 | 114 | 174 | 19 | 207 | 115 | 175 | 18 | 206 | 116 | 176 | 17 | 205 |
Dit 16x16 magisch vierkant is panmagisch, 2x2 compact en kloppend voor 1/4 rij/kolom/ diagonaal.