Je kunt het 16x16 magisch vierkant opbouwen uit 4 evenredige Franklin panmagische 8x8 vierkanten. Evenredig betekent dat alle 4 Franklin panmagische 8x8 vierkanten dezelfde magische som van (1/2 x 2056 = ) 1028 hebben. We gebruiken de basissleutel methode (8x8) voor het maken van de Franklin panmagische 8x8 vierkanten. Alleen gebruiken we nu als rijcoördinaten niet de getallen 0 t/m 7 maar 0 t/m (4x8 -/- 1 = ) 31 en we verdelen de rijcoördinaten evenredig over de 4 Franklin panmagische 8x8 vierkanten.
1x rijcoördinaat +32x kolomcoördinaat + 1 = Franklin panm. 8x8 vierkant
0 | 7 | 31 | 24 | 8 | 15 | 23 | 16 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 1 | 232 | 32 | 249 | 9 | 240 | 24 | 241 | ||
31 | 24 | 0 | 7 | 23 | 16 | 8 | 15 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 64 | 217 | 33 | 200 | 56 | 209 | 41 | 208 | ||
0 | 7 | 31 | 24 | 8 | 15 | 23 | 16 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 225 | 8 | 256 | 25 | 233 | 16 | 248 | 17 | ||
31 | 24 | 0 | 7 | 23 | 16 | 8 | 15 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 224 | 57 | 193 | 40 | 216 | 49 | 201 | 48 | ||
0 | 7 | 31 | 24 | 8 | 15 | 23 | 16 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 65 | 168 | 96 | 185 | 73 | 176 | 88 | 177 | ||
31 | 24 | 0 | 7 | 23 | 16 | 8 | 15 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 128 | 153 | 97 | 136 | 120 | 145 | 105 | 144 | ||
0 | 7 | 31 | 24 | 8 | 15 | 23 | 16 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 161 | 72 | 192 | 89 | 169 | 80 | 184 | 81 | ||
31 | 24 | 0 | 7 | 23 | 16 | 8 | 15 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 160 | 121 | 129 | 104 | 152 | 113 | 137 | 112 | ||
1 | 6 | 30 | 25 | 9 | 14 | 22 | 17 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 2 | 231 | 31 | 250 | 10 | 239 | 23 | 242 | ||
30 | 25 | 1 | 6 | 22 | 17 | 9 | 14 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 63 | 218 | 34 | 199 | 55 | 210 | 42 | 207 | ||
1 | 6 | 30 | 25 | 9 | 14 | 22 | 17 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 226 | 7 | 255 | 26 | 234 | 15 | 247 | 18 | ||
30 | 25 | 1 | 6 | 22 | 17 | 9 | 14 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 223 | 58 | 194 | 39 | 215 | 50 | 202 | 47 | ||
1 | 6 | 30 | 25 | 9 | 14 | 22 | 17 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 66 | 167 | 95 | 186 | 74 | 175 | 87 | 178 | ||
30 | 25 | 1 | 6 | 22 | 17 | 9 | 14 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 127 | 154 | 98 | 135 | 119 | 146 | 106 | 143 | ||
1 | 6 | 30 | 25 | 9 | 14 | 22 | 17 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 162 | 71 | 191 | 90 | 170 | 79 | 183 | 82 | ||
30 | 25 | 1 | 6 | 22 | 17 | 9 | 14 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 159 | 122 | 130 | 103 | 151 | 114 | 138 | 111 | ||
2 | 5 | 29 | 26 | 10 | 13 | 21 | 18 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 3 | 230 | 30 | 251 | 11 | 238 | 22 | 243 | ||
29 | 26 | 2 | 5 | 21 | 18 | 10 | 13 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 62 | 219 | 35 | 198 | 54 | 211 | 43 | 206 | ||
2 | 5 | 29 | 26 | 10 | 13 | 21 | 18 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 227 | 6 | 254 | 27 | 235 | 14 | 246 | 19 | ||
29 | 26 | 2 | 5 | 21 | 18 | 10 | 13 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 222 | 59 | 195 | 38 | 214 | 51 | 203 | 46 | ||
2 | 5 | 29 | 26 | 10 | 13 | 21 | 18 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 67 | 166 | 94 | 187 | 75 | 174 | 86 | 179 | ||
29 | 26 | 2 | 5 | 21 | 18 | 10 | 13 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 126 | 155 | 99 | 134 | 118 | 147 | 107 | 142 | ||
2 | 5 | 29 | 26 | 10 | 13 | 21 | 18 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 163 | 70 | 190 | 91 | 171 | 78 | 182 | 83 | ||
29 | 26 | 2 | 5 | 21 | 18 | 10 | 13 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 158 | 123 | 131 | 102 | 150 | 115 | 139 | 110 | ||
3 | 4 | 28 | 27 | 11 | 12 | 20 | 19 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 4 | 229 | 29 | 252 | 12 | 237 | 21 | 244 | ||
28 | 27 | 3 | 4 | 20 | 19 | 11 | 12 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 61 | 220 | 36 | 197 | 53 | 212 | 44 | 205 | ||
3 | 4 | 28 | 27 | 11 | 12 | 20 | 19 | 7 | 0 | 7 | 0 | 7 | 0 | 7 | 0 | 228 | 5 | 253 | 28 | 236 | 13 | 245 | 20 | ||
28 | 27 | 3 | 4 | 20 | 19 | 11 | 12 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 221 | 60 | 196 | 37 | 213 | 52 | 204 | 45 | ||
3 | 4 | 28 | 27 | 11 | 12 | 20 | 19 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 68 | 165 | 93 | 188 | 76 | 173 | 85 | 180 | ||
28 | 27 | 3 | 4 | 20 | 19 | 11 | 12 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 125 | 156 | 100 | 133 | 117 | 148 | 108 | 141 | ||
3 | 4 | 28 | 27 | 11 | 12 | 20 | 19 | 5 | 2 | 5 | 2 | 5 | 2 | 5 | 2 | 164 | 69 | 189 | 92 | 172 | 77 | 181 | 84 | ||
28 | 27 | 3 | 4 | 20 | 19 | 11 | 12 | 4 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 157 | 124 | 132 | 101 | 149 | 116 | 140 | 109 |
Voeg de 4 Franklin panmagische 8x8 vierkanten op volgorde samen.
16x16 magisch vierkant
1 | 232 | 32 | 249 | 9 | 240 | 24 | 241 | 2 | 231 | 31 | 250 | 10 | 239 | 23 | 242 |
64 | 217 | 33 | 200 | 56 | 209 | 41 | 208 | 63 | 218 | 34 | 199 | 55 | 210 | 42 | 207 |
225 | 8 | 256 | 25 | 233 | 16 | 248 | 17 | 226 | 7 | 255 | 26 | 234 | 15 | 247 | 18 |
224 | 57 | 193 | 40 | 216 | 49 | 201 | 48 | 223 | 58 | 194 | 39 | 215 | 50 | 202 | 47 |
65 | 168 | 96 | 185 | 73 | 176 | 88 | 177 | 66 | 167 | 95 | 186 | 74 | 175 | 87 | 178 |
128 | 153 | 97 | 136 | 120 | 145 | 105 | 144 | 127 | 154 | 98 | 135 | 119 | 146 | 106 | 143 |
161 | 72 | 192 | 89 | 169 | 80 | 184 | 81 | 162 | 71 | 191 | 90 | 170 | 79 | 183 | 82 |
160 | 121 | 129 | 104 | 152 | 113 | 137 | 112 | 159 | 122 | 130 | 103 | 151 | 114 | 138 | 111 |
3 | 230 | 30 | 251 | 11 | 238 | 22 | 243 | 4 | 229 | 29 | 252 | 12 | 237 | 21 | 244 |
62 | 219 | 35 | 198 | 54 | 211 | 43 | 206 | 61 | 220 | 36 | 197 | 53 | 212 | 44 | 205 |
227 | 6 | 254 | 27 | 235 | 14 | 246 | 19 | 228 | 5 | 253 | 28 | 236 | 13 | 245 | 20 |
222 | 59 | 195 | 38 | 214 | 51 | 203 | 46 | 221 | 60 | 196 | 37 | 213 | 52 | 204 | 45 |
67 | 166 | 94 | 187 | 75 | 174 | 86 | 179 | 68 | 165 | 93 | 188 | 76 | 173 | 85 | 180 |
126 | 155 | 99 | 134 | 118 | 147 | 107 | 142 | 125 | 156 | 100 | 133 | 117 | 148 | 108 | 141 |
163 | 70 | 190 | 91 | 171 | 78 | 182 | 83 | 164 | 69 | 189 | 92 | 172 | 77 | 181 | 84 |
158 | 123 | 131 | 102 | 150 | 115 | 139 | 110 | 157 | 124 | 132 | 101 | 149 | 116 | 140 | 109 |
Helaas is bovenstaand 16x16 magisch vierkant nog niet volledig 2x2 compact. We gebruiken de techniek van de Khajuraho methode om systematisch getallen om te wisselen.
Franklin panmagisch 16x16 vierkant
3 | 230 | 32 | 249 | 11 | 238 | 24 | 241 | 4 | 229 | 31 | 250 | 12 | 237 | 23 | 242 |
62 | 219 | 33 | 200 | 54 | 211 | 41 | 208 | 61 | 220 | 34 | 199 | 53 | 212 | 42 | 207 |
225 | 8 | 254 | 27 | 233 | 16 | 246 | 19 | 226 | 7 | 253 | 28 | 234 | 15 | 245 | 20 |
224 | 57 | 195 | 38 | 216 | 49 | 203 | 46 | 223 | 58 | 196 | 37 | 215 | 50 | 204 | 45 |
67 | 166 | 96 | 185 | 75 | 174 | 88 | 177 | 68 | 165 | 95 | 186 | 76 | 173 | 87 | 178 |
126 | 155 | 97 | 136 | 118 | 147 | 105 | 144 | 125 | 156 | 98 | 135 | 117 | 148 | 106 | 143 |
161 | 72 | 190 | 91 | 169 | 80 | 182 | 83 | 162 | 71 | 189 | 92 | 170 | 79 | 181 | 84 |
160 | 121 | 131 | 102 | 152 | 113 | 139 | 110 | 159 | 122 | 132 | 101 | 151 | 114 | 140 | 109 |
1 | 232 | 30 | 251 | 9 | 240 | 22 | 243 | 2 | 231 | 29 | 252 | 10 | 239 | 21 | 244 |
64 | 217 | 35 | 198 | 56 | 209 | 43 | 206 | 63 | 218 | 36 | 197 | 55 | 210 | 44 | 205 |
227 | 6 | 256 | 25 | 235 | 14 | 248 | 17 | 228 | 5 | 255 | 26 | 236 | 13 | 247 | 18 |
222 | 59 | 193 | 40 | 214 | 51 | 201 | 48 | 221 | 60 | 194 | 39 | 213 | 52 | 202 | 47 |
65 | 168 | 94 | 187 | 73 | 176 | 86 | 179 | 66 | 167 | 93 | 188 | 74 | 175 | 85 | 180 |
128 | 153 | 99 | 134 | 120 | 145 | 107 | 142 | 127 | 154 | 100 | 133 | 119 | 146 | 108 | 141 |
163 | 70 | 192 | 89 | 171 | 78 | 184 | 81 | 164 | 69 | 191 | 90 | 172 | 77 | 183 | 82 |
158 | 123 | 129 | 104 | 150 | 115 | 137 | 112 | 157 | 124 | 130 | 103 | 149 | 116 | 138 | 111 |
Dit 16x16 magisch vierkant is panmagisch, (volledig) 2x2 compact en kloppend voor 1/4 rij/kolom/ diagonaal.