Je kunt het 18x18 magisch vierkant opbouwen uit 9 evenredige magische 6x6 vierkanten. Evenredig betekent dat alle 9 magische 6x6 vierkanten dezelfde magische som van (1/3 x 2925 = ) 975 hebben. We gebruiken de methode met reflecterende patronen (6x6) voor het maken van de magische 6x6 vierkanten. Alleen gebruiken we nu als rijcoördinaten niet de getallen 0 t/m 5 maar 0 t/m (9x6 -/- 1 = ) 53 en we verdelen de rijcoördinaten evenredig over de 9 magische 6x6 vierkanten.
1x rijcoördinaat +54x kolomcoördinaat + 1 = magisch 6x6 vierkant
0 | 17 | 35 | 18 | 36 | 53 | 0 | 5 | 0 | 5 | 5 | 0 | 1 | 288 | 36 | 289 | 307 | 54 | ||
53 | 17 | 18 | 35 | 36 | 0 | 1 | 1 | 4 | 4 | 1 | 4 | 108 | 72 | 235 | 252 | 91 | 217 | ||
0 | 36 | 18 | 35 | 17 | 53 | 3 | 2 | 2 | 2 | 3 | 3 | 163 | 145 | 127 | 144 | 180 | 216 | ||
53 | 36 | 18 | 35 | 17 | 0 | 2 | 3 | 3 | 3 | 2 | 2 | 162 | 199 | 181 | 198 | 126 | 109 | ||
53 | 17 | 35 | 18 | 36 | 0 | 4 | 4 | 1 | 1 | 4 | 1 | 270 | 234 | 90 | 73 | 253 | 55 | ||
0 | 36 | 35 | 18 | 17 | 53 | 5 | 0 | 5 | 0 | 0 | 5 | 271 | 37 | 306 | 19 | 18 | 324 | ||
1 | 16 | 34 | 19 | 37 | 52 | 0 | 5 | 0 | 5 | 5 | 0 | 2 | 287 | 35 | 290 | 308 | 53 | ||
52 | 16 | 19 | 34 | 37 | 1 | 1 | 1 | 4 | 4 | 1 | 4 | 107 | 71 | 236 | 251 | 92 | 218 | ||
1 | 37 | 19 | 34 | 16 | 52 | 3 | 2 | 2 | 2 | 3 | 3 | 164 | 146 | 128 | 143 | 179 | 215 | ||
52 | 37 | 19 | 34 | 16 | 1 | 2 | 3 | 3 | 3 | 2 | 2 | 161 | 200 | 182 | 197 | 125 | 110 | ||
52 | 16 | 34 | 19 | 37 | 1 | 4 | 4 | 1 | 1 | 4 | 1 | 269 | 233 | 89 | 74 | 254 | 56 | ||
1 | 37 | 34 | 19 | 16 | 52 | 5 | 0 | 5 | 0 | 0 | 5 | 272 | 38 | 305 | 20 | 17 | 323 | ||
2 | 15 | 33 | 20 | 38 | 51 | 0 | 5 | 0 | 5 | 5 | 0 | 3 | 286 | 34 | 291 | 309 | 52 | ||
51 | 15 | 20 | 33 | 38 | 2 | 1 | 1 | 4 | 4 | 1 | 4 | 106 | 70 | 237 | 250 | 93 | 219 | ||
2 | 38 | 20 | 33 | 15 | 51 | 3 | 2 | 2 | 2 | 3 | 3 | 165 | 147 | 129 | 142 | 178 | 214 | ||
51 | 38 | 20 | 33 | 15 | 2 | 2 | 3 | 3 | 3 | 2 | 2 | 160 | 201 | 183 | 196 | 124 | 111 | ||
51 | 15 | 33 | 20 | 38 | 2 | 4 | 4 | 1 | 1 | 4 | 1 | 268 | 232 | 88 | 75 | 255 | 57 | ||
2 | 38 | 33 | 20 | 15 | 51 | 5 | 0 | 5 | 0 | 0 | 5 | 273 | 39 | 304 | 21 | 16 | 322 | ||
3 | 14 | 32 | 21 | 39 | 50 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 285 | 33 | 292 | 310 | 51 | ||
50 | 14 | 21 | 32 | 39 | 3 | 1 | 1 | 4 | 4 | 1 | 4 | 105 | 69 | 238 | 249 | 94 | 220 | ||
3 | 39 | 21 | 32 | 14 | 50 | 3 | 2 | 2 | 2 | 3 | 3 | 166 | 148 | 130 | 141 | 177 | 213 | ||
50 | 39 | 21 | 32 | 14 | 3 | 2 | 3 | 3 | 3 | 2 | 2 | 159 | 202 | 184 | 195 | 123 | 112 | ||
50 | 14 | 32 | 21 | 39 | 3 | 4 | 4 | 1 | 1 | 4 | 1 | 267 | 231 | 87 | 76 | 256 | 58 | ||
3 | 39 | 32 | 21 | 14 | 50 | 5 | 0 | 5 | 0 | 0 | 5 | 274 | 40 | 303 | 22 | 15 | 321 | ||
4 | 13 | 31 | 22 | 40 | 49 | 0 | 5 | 0 | 5 | 5 | 0 | 5 | 284 | 32 | 293 | 311 | 50 | ||
49 | 13 | 22 | 31 | 40 | 4 | 1 | 1 | 4 | 4 | 1 | 4 | 104 | 68 | 239 | 248 | 95 | 221 | ||
4 | 40 | 22 | 31 | 13 | 49 | 3 | 2 | 2 | 2 | 3 | 3 | 167 | 149 | 131 | 140 | 176 | 212 | ||
49 | 40 | 22 | 31 | 13 | 4 | 2 | 3 | 3 | 3 | 2 | 2 | 158 | 203 | 185 | 194 | 122 | 113 | ||
49 | 13 | 31 | 22 | 40 | 4 | 4 | 4 | 1 | 1 | 4 | 1 | 266 | 230 | 86 | 77 | 257 | 59 | ||
4 | 40 | 31 | 22 | 13 | 49 | 5 | 0 | 5 | 0 | 0 | 5 | 275 | 41 | 302 | 23 | 14 | 320 | ||
5 | 12 | 30 | 23 | 41 | 48 | 0 | 5 | 0 | 5 | 5 | 0 | 6 | 283 | 31 | 294 | 312 | 49 | ||
48 | 12 | 23 | 30 | 41 | 5 | 1 | 1 | 4 | 4 | 1 | 4 | 103 | 67 | 240 | 247 | 96 | 222 | ||
5 | 41 | 23 | 30 | 12 | 48 | 3 | 2 | 2 | 2 | 3 | 3 | 168 | 150 | 132 | 139 | 175 | 211 | ||
48 | 41 | 23 | 30 | 12 | 5 | 2 | 3 | 3 | 3 | 2 | 2 | 157 | 204 | 186 | 193 | 121 | 114 | ||
48 | 12 | 30 | 23 | 41 | 5 | 4 | 4 | 1 | 1 | 4 | 1 | 265 | 229 | 85 | 78 | 258 | 60 | ||
5 | 41 | 30 | 23 | 12 | 48 | 5 | 0 | 5 | 0 | 0 | 5 | 276 | 42 | 301 | 24 | 13 | 319 | ||
6 | 11 | 29 | 24 | 42 | 47 | 0 | 5 | 0 | 5 | 5 | 0 | 7 | 282 | 30 | 295 | 313 | 48 | ||
47 | 11 | 24 | 29 | 42 | 6 | 1 | 1 | 4 | 4 | 1 | 4 | 102 | 66 | 241 | 246 | 97 | 223 | ||
6 | 42 | 24 | 29 | 11 | 47 | 3 | 2 | 2 | 2 | 3 | 3 | 169 | 151 | 133 | 138 | 174 | 210 | ||
47 | 42 | 24 | 29 | 11 | 6 | 2 | 3 | 3 | 3 | 2 | 2 | 156 | 205 | 187 | 192 | 120 | 115 | ||
47 | 11 | 29 | 24 | 42 | 6 | 4 | 4 | 1 | 1 | 4 | 1 | 264 | 228 | 84 | 79 | 259 | 61 | ||
6 | 42 | 29 | 24 | 11 | 47 | 5 | 0 | 5 | 0 | 0 | 5 | 277 | 43 | 300 | 25 | 12 | 318 | ||
7 | 10 | 28 | 25 | 43 | 46 | 0 | 5 | 0 | 5 | 5 | 0 | 8 | 281 | 29 | 296 | 314 | 47 | ||
46 | 10 | 25 | 28 | 43 | 7 | 1 | 1 | 4 | 4 | 1 | 4 | 101 | 65 | 242 | 245 | 98 | 224 | ||
7 | 43 | 25 | 28 | 10 | 46 | 3 | 2 | 2 | 2 | 3 | 3 | 170 | 152 | 134 | 137 | 173 | 209 | ||
46 | 43 | 25 | 28 | 10 | 7 | 2 | 3 | 3 | 3 | 2 | 2 | 155 | 206 | 188 | 191 | 119 | 116 | ||
46 | 10 | 28 | 25 | 43 | 7 | 4 | 4 | 1 | 1 | 4 | 1 | 263 | 227 | 83 | 80 | 260 | 62 | ||
7 | 43 | 28 | 25 | 10 | 46 | 5 | 0 | 5 | 0 | 0 | 5 | 278 | 44 | 299 | 26 | 11 | 317 | ||
8 | 9 | 27 | 26 | 44 | 45 | 0 | 5 | 0 | 5 | 5 | 0 | 9 | 280 | 28 | 297 | 315 | 46 | ||
45 | 9 | 26 | 27 | 44 | 8 | 1 | 1 | 4 | 4 | 1 | 4 | 100 | 64 | 243 | 244 | 99 | 225 | ||
8 | 44 | 26 | 27 | 9 | 45 | 3 | 2 | 2 | 2 | 3 | 3 | 171 | 153 | 135 | 136 | 172 | 208 | ||
45 | 44 | 26 | 27 | 9 | 8 | 2 | 3 | 3 | 3 | 2 | 2 | 154 | 207 | 189 | 190 | 118 | 117 | ||
45 | 9 | 27 | 26 | 44 | 8 | 4 | 4 | 1 | 1 | 4 | 1 | 262 | 226 | 82 | 81 | 261 | 63 | ||
8 | 44 | 27 | 26 | 9 | 45 | 5 | 0 | 5 | 0 | 0 | 5 | 279 | 45 | 298 | 27 | 10 | 316 |
Voeg de 9 magische 6x6 vierkanten op volgorde samen.
18x18 magisch vierkant
1 | 288 | 36 | 289 | 307 | 54 | 2 | 287 | 35 | 290 | 308 | 53 | 3 | 286 | 34 | 291 | 309 | 52 |
108 | 72 | 235 | 252 | 91 | 217 | 107 | 71 | 236 | 251 | 92 | 218 | 106 | 70 | 237 | 250 | 93 | 219 |
163 | 145 | 127 | 144 | 180 | 216 | 164 | 146 | 128 | 143 | 179 | 215 | 165 | 147 | 129 | 142 | 178 | 214 |
162 | 199 | 181 | 198 | 126 | 109 | 161 | 200 | 182 | 197 | 125 | 110 | 160 | 201 | 183 | 196 | 124 | 111 |
270 | 234 | 90 | 73 | 253 | 55 | 269 | 233 | 89 | 74 | 254 | 56 | 268 | 232 | 88 | 75 | 255 | 57 |
271 | 37 | 306 | 19 | 18 | 324 | 272 | 38 | 305 | 20 | 17 | 323 | 273 | 39 | 304 | 21 | 16 | 322 |
4 | 285 | 33 | 292 | 310 | 51 | 5 | 284 | 32 | 293 | 311 | 50 | 6 | 283 | 31 | 294 | 312 | 49 |
105 | 69 | 238 | 249 | 94 | 220 | 104 | 68 | 239 | 248 | 95 | 221 | 103 | 67 | 240 | 247 | 96 | 222 |
166 | 148 | 130 | 141 | 177 | 213 | 167 | 149 | 131 | 140 | 176 | 212 | 168 | 150 | 132 | 139 | 175 | 211 |
159 | 202 | 184 | 195 | 123 | 112 | 158 | 203 | 185 | 194 | 122 | 113 | 157 | 204 | 186 | 193 | 121 | 114 |
267 | 231 | 87 | 76 | 256 | 58 | 266 | 230 | 86 | 77 | 257 | 59 | 265 | 229 | 85 | 78 | 258 | 60 |
274 | 40 | 303 | 22 | 15 | 321 | 275 | 41 | 302 | 23 | 14 | 320 | 276 | 42 | 301 | 24 | 13 | 319 |
7 | 282 | 30 | 295 | 313 | 48 | 8 | 281 | 29 | 296 | 314 | 47 | 9 | 280 | 28 | 297 | 315 | 46 |
102 | 66 | 241 | 246 | 97 | 223 | 101 | 65 | 242 | 245 | 98 | 224 | 100 | 64 | 243 | 244 | 99 | 225 |
169 | 151 | 133 | 138 | 174 | 210 | 170 | 152 | 134 | 137 | 173 | 209 | 171 | 153 | 135 | 136 | 172 | 208 |
156 | 205 | 187 | 192 | 120 | 115 | 155 | 206 | 188 | 191 | 119 | 116 | 154 | 207 | 189 | 190 | 118 | 117 |
264 | 228 | 84 | 79 | 259 | 61 | 263 | 227 | 83 | 80 | 260 | 62 | 262 | 226 | 82 | 81 | 261 | 63 |
277 | 43 | 300 | 25 | 12 | 318 | 278 | 44 | 299 | 26 | 11 | 317 | 279 | 45 | 298 | 27 | 10 | 316 |
Het 18x18 magisch vierkant is kloppend voor 1/3 rij/kolom/diagonaal en 6x6 compact. Zie ook hoe de getallen in strakke volgorde in het 18x18 magische vierkant zijn gerang-schikt als je door de 6x6 deelvierkanten en weer terug kijkt (toch een regelmatige struc-tuur in een dubbel oneven magisch vierkant gevonden, hoewel dat niet mogelijk zou zijn).