Symmetrische transformatie
Marios Mamzeris laat ons zien hoe je in 2 stappen een oneven vierkant met opeenvolgende getallen kunt transformeren in een symmetrisch magisch vierkant (https://www.oddmagicsquares.com/):
Stap 1, horizontale omwisseling
| < | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
| < | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | |
| < | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | |
| < | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | |
| < | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | |
| < | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | |
| < | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | |
| < | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | |
| < | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | |
| 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 | ||
| 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 | 201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | > | |
| 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | > | |
| 229 | 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 | 241 | 242 | 243 | 244 | 245 | 246 | 247 | > | |
| 248 | 249 | 250 | 251 | 252 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 | 261 | 262 | 263 | 264 | 265 | 266 | > | |
| 267 | 268 | 269 | 270 | 271 | 272 | 273 | 274 | 275 | 276 | 277 | 278 | 279 | 280 | 281 | 282 | 283 | 284 | 285 | > | |
| 286 | 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 295 | 296 | 297 | 298 | 299 | 300 | 301 | 302 | 303 | 304 | > | |
| 305 | 306 | 307 | 308 | 309 | 310 | 311 | 312 | 313 | 314 | 315 | 316 | 317 | 318 | 319 | 320 | 321 | 322 | 323 | > | |
| 324 | 325 | 326 | 327 | 328 | 329 | 330 | 331 | 332 | 333 | 334 | 335 | 336 | 337 | 338 | 339 | 340 | 341 | 342 | > | |
| 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 | 351 | 352 | 353 | 354 | 355 | 356 | 357 | 358 | 359 | 360 | 361 | > |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1 | |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 20 | 21 | |
| 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 39 | 40 | 41 | |
| 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 58 | 59 | 60 | 61 | |
| 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 77 | 78 | 79 | 80 | 81 | |
| 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 96 | 97 | 98 | 99 | 100 | 101 | |
| 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | |
| 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | |
| 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 | |
| 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 | |
| 201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 | |
| 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | |
| 241 | 242 | 243 | 244 | 245 | 246 | 247 | 229 | 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 | |
| 261 | 262 | 263 | 264 | 265 | 266 | 248 | 249 | 250 | 251 | 252 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 | |
| 281 | 282 | 283 | 284 | 285 | 267 | 268 | 269 | 270 | 271 | 272 | 273 | 274 | 275 | 276 | 277 | 278 | 279 | 280 | |
| 301 | 302 | 303 | 304 | 286 | 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 295 | 296 | 297 | 298 | 299 | 300 | |
| 321 | 322 | 323 | 305 | 306 | 307 | 308 | 309 | 310 | 311 | 312 | 313 | 314 | 315 | 316 | 317 | 318 | 319 | 320 | |
| 341 | 342 | 324 | 325 | 326 | 327 | 328 | 329 | 330 | 331 | 332 | 333 | 334 | 335 | 336 | 337 | 338 | 339 | 340 | |
| 361 | 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 | 351 | 352 | 353 | 354 | 355 | 356 | 357 | 358 | 359 | 360 |
Stap 2, verticale omwisseling
| ^ | ^ | ^ | ^ | ^ | ^ | ^ | ^ | ^ | ||||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1 |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 20 | 21 |
| 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 39 | 40 | 41 |
| 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 58 | 59 | 60 | 61 |
| 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 77 | 78 | 79 | 80 | 81 |
| 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 96 | 97 | 98 | 99 | 100 | 101 |
| 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | 115 | 116 | 117 | 118 | 119 | 120 | 121 |
| 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 |
| 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 |
| 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 |
| 201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 |
| 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 |
| 241 | 242 | 243 | 244 | 245 | 246 | 247 | 229 | 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 |
| 261 | 262 | 263 | 264 | 265 | 266 | 248 | 249 | 250 | 251 | 252 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 |
| 281 | 282 | 283 | 284 | 285 | 267 | 268 | 269 | 270 | 271 | 272 | 273 | 274 | 275 | 276 | 277 | 278 | 279 | 280 |
| 301 | 302 | 303 | 304 | 286 | 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 295 | 296 | 297 | 298 | 299 | 300 |
| 321 | 322 | 323 | 305 | 306 | 307 | 308 | 309 | 310 | 311 | 312 | 313 | 314 | 315 | 316 | 317 | 318 | 319 | 320 |
| 341 | 342 | 324 | 325 | 326 | 327 | 328 | 329 | 330 | 331 | 332 | 333 | 334 | 335 | 336 | 337 | 338 | 339 | 340 |
| 361 | 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 | 351 | 352 | 353 | 354 | 355 | 356 | 357 | 358 | 359 | 360 |
| v | v | v | v | v | v | v | v | v |
| 22 | 43 | 64 | 85 | 106 | 127 | 148 | 169 | 180 | 11 | 192 | 213 | 234 | 255 | 276 | 297 | 318 | 339 | 360 |
| 42 | 63 | 84 | 105 | 126 | 147 | 168 | 179 | 209 | 31 | 212 | 233 | 254 | 275 | 296 | 317 | 338 | 359 | 1 |
| 62 | 83 | 104 | 125 | 146 | 167 | 178 | 208 | 210 | 51 | 232 | 253 | 274 | 295 | 316 | 337 | 358 | 19 | 21 |
| 82 | 103 | 124 | 145 | 166 | 177 | 207 | 228 | 230 | 71 | 252 | 273 | 294 | 315 | 336 | 357 | 18 | 20 | 41 |
| 102 | 123 | 144 | 165 | 176 | 206 | 227 | 229 | 250 | 91 | 272 | 293 | 314 | 335 | 356 | 17 | 38 | 40 | 61 |
| 122 | 143 | 164 | 175 | 205 | 226 | 247 | 249 | 270 | 111 | 292 | 313 | 334 | 355 | 16 | 37 | 39 | 60 | 81 |
| 142 | 163 | 174 | 204 | 225 | 246 | 248 | 269 | 290 | 131 | 312 | 333 | 354 | 15 | 36 | 57 | 59 | 80 | 101 |
| 162 | 173 | 203 | 224 | 245 | 266 | 268 | 289 | 310 | 151 | 332 | 353 | 14 | 35 | 56 | 58 | 79 | 100 | 121 |
| 172 | 202 | 223 | 244 | 265 | 267 | 288 | 309 | 330 | 171 | 352 | 13 | 34 | 55 | 76 | 78 | 99 | 120 | 141 |
| 201 | 222 | 243 | 264 | 285 | 287 | 308 | 329 | 350 | 181 | 12 | 33 | 54 | 75 | 77 | 98 | 119 | 140 | 161 |
| 221 | 242 | 263 | 284 | 286 | 307 | 328 | 349 | 10 | 191 | 32 | 53 | 74 | 95 | 97 | 118 | 139 | 160 | 190 |
| 241 | 262 | 283 | 304 | 306 | 327 | 348 | 9 | 30 | 211 | 52 | 73 | 94 | 96 | 117 | 138 | 159 | 189 | 200 |
| 261 | 282 | 303 | 305 | 326 | 347 | 8 | 29 | 50 | 231 | 72 | 93 | 114 | 116 | 137 | 158 | 188 | 199 | 220 |
| 281 | 302 | 323 | 325 | 346 | 7 | 28 | 49 | 70 | 251 | 92 | 113 | 115 | 136 | 157 | 187 | 198 | 219 | 240 |
| 301 | 322 | 324 | 345 | 6 | 27 | 48 | 69 | 90 | 271 | 112 | 133 | 135 | 156 | 186 | 197 | 218 | 239 | 260 |
| 321 | 342 | 344 | 5 | 26 | 47 | 68 | 89 | 110 | 291 | 132 | 134 | 155 | 185 | 196 | 217 | 238 | 259 | 280 |
| 341 | 343 | 4 | 25 | 46 | 67 | 88 | 109 | 130 | 311 | 152 | 154 | 184 | 195 | 216 | 237 | 258 | 279 | 300 |
| 361 | 3 | 24 | 45 | 66 | 87 | 108 | 129 | 150 | 331 | 153 | 183 | 194 | 215 | 236 | 257 | 278 | 299 | 320 |
| 2 | 23 | 44 | 65 | 86 | 107 | 128 | 149 | 170 | 351 | 182 | 193 | 214 | 235 | 256 | 277 | 298 | 319 | 340 |
Deze methode werk voor alle oneven magische vierkanten van 3x3 tot oneindig. Zie uitgewerkt voor 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29, 31x31
