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.
Zie methode samengesteld, proportioneel (1) op deze website uitgewerkt voor
8x8, 9x9, 12x12a, 12x12b, 15x15a, 15x15b, 16x16a, 16x16b, 18x18, 20x20a, 20x20b, 21x21a, 21x21b, 24x24a, 24x24b, 24x24c, 27x27a, 27x27b, 28x28a, 28x28b, 30x30a, 30x30b, 32x32a, 32x32b, 32x32c