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 | 362 | 363 | 364 | 365 | 366 | 367 | 368 | 369 | 370 | 371 | 372 | 373 | 374 | 375 | 376 | 377 | 378 | > | |
| 379 | 380 | 381 | 382 | 383 | 384 | 385 | 386 | 387 | 388 | 389 | 390 | 391 | 392 | 393 | 394 | 395 | 396 | 397 | 398 | 399 | > | |
| 400 | 401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 | 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 | 419 | 420 | > | |
| 421 | 422 | 423 | 424 | 425 | 426 | 427 | 428 | 429 | 430 | 431 | 432 | 433 | 434 | 435 | 436 | 437 | 438 | 439 | 440 | 441 | > |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 1 | |
| 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 22 | 23 | |
| 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 43 | 44 | 45 | |
| 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 64 | 65 | 66 | 67 | |
| 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 85 | 86 | 87 | 88 | 89 | |
| 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 106 | 107 | 108 | 109 | 110 | 111 | |
| 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | |
| 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 148 | 149 | 150 | 151 | 152 | 153 | 154 | 155 | |
| 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 169 | 170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 | |
| 200 | 201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | 210 | 190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | |
| 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | 229 | 230 | 231 | |
| 243 | 244 | 245 | 246 | 247 | 248 | 249 | 250 | 251 | 252 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 | 241 | 242 | |
| 265 | 266 | 267 | 268 | 269 | 270 | 271 | 272 | 273 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 | 261 | 262 | 263 | 264 | |
| 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 274 | 275 | 276 | 277 | 278 | 279 | 280 | 281 | 282 | 283 | 284 | 285 | 286 | |
| 309 | 310 | 311 | 312 | 313 | 314 | 315 | 295 | 296 | 297 | 298 | 299 | 300 | 301 | 302 | 303 | 304 | 305 | 306 | 307 | 308 | |
| 331 | 332 | 333 | 334 | 335 | 336 | 316 | 317 | 318 | 319 | 320 | 321 | 322 | 323 | 324 | 325 | 326 | 327 | 328 | 329 | 330 | |
| 353 | 354 | 355 | 356 | 357 | 337 | 338 | 339 | 340 | 341 | 342 | 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 | 351 | 352 | |
| 375 | 376 | 377 | 378 | 358 | 359 | 360 | 361 | 362 | 363 | 364 | 365 | 366 | 367 | 368 | 369 | 370 | 371 | 372 | 373 | 374 | |
| 397 | 398 | 399 | 379 | 380 | 381 | 382 | 383 | 384 | 385 | 386 | 387 | 388 | 389 | 390 | 391 | 392 | 393 | 394 | 395 | 396 | |
| 419 | 420 | 400 | 401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 | 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 | |
| 441 | 421 | 422 | 423 | 424 | 425 | 426 | 427 | 428 | 429 | 430 | 431 | 432 | 433 | 434 | 435 | 436 | 437 | 438 | 439 | 440 |
Stap 2, verticale omwisseling
| ^ | ^ | ^ | ^ | ^ | ^ | ^ | ^ | ^ | ^ | |||||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 1 |
| 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 22 | 23 |
| 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 43 | 44 | 45 |
| 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 64 | 65 | 66 | 67 |
| 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 85 | 86 | 87 | 88 | 89 |
| 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 106 | 107 | 108 | 109 | 110 | 111 |
| 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 127 | 128 | 129 | 130 | 131 | 132 | 133 |
| 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 148 | 149 | 150 | 151 | 152 | 153 | 154 | 155 |
| 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 169 | 170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 |
| 200 | 201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | 210 | 190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 |
| 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | 229 | 230 | 231 |
| 243 | 244 | 245 | 246 | 247 | 248 | 249 | 250 | 251 | 252 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 | 241 | 242 |
| 265 | 266 | 267 | 268 | 269 | 270 | 271 | 272 | 273 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 | 261 | 262 | 263 | 264 |
| 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 274 | 275 | 276 | 277 | 278 | 279 | 280 | 281 | 282 | 283 | 284 | 285 | 286 |
| 309 | 310 | 311 | 312 | 313 | 314 | 315 | 295 | 296 | 297 | 298 | 299 | 300 | 301 | 302 | 303 | 304 | 305 | 306 | 307 | 308 |
| 331 | 332 | 333 | 334 | 335 | 336 | 316 | 317 | 318 | 319 | 320 | 321 | 322 | 323 | 324 | 325 | 326 | 327 | 328 | 329 | 330 |
| 353 | 354 | 355 | 356 | 357 | 337 | 338 | 339 | 340 | 341 | 342 | 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 | 351 | 352 |
| 375 | 376 | 377 | 378 | 358 | 359 | 360 | 361 | 362 | 363 | 364 | 365 | 366 | 367 | 368 | 369 | 370 | 371 | 372 | 373 | 374 |
| 397 | 398 | 399 | 379 | 380 | 381 | 382 | 383 | 384 | 385 | 386 | 387 | 388 | 389 | 390 | 391 | 392 | 393 | 394 | 395 | 396 |
| 419 | 420 | 400 | 401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 | 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 |
| 441 | 421 | 422 | 423 | 424 | 425 | 426 | 427 | 428 | 429 | 430 | 431 | 432 | 433 | 434 | 435 | 436 | 437 | 438 | 439 | 440 |
| v | v | v | v | v | v | v | v | v | v |
| 24 | 47 | 70 | 93 | 116 | 139 | 162 | 185 | 208 | 220 | 12 | 233 | 256 | 279 | 302 | 325 | 348 | 371 | 394 | 417 | 440 |
| 46 | 69 | 92 | 115 | 138 | 161 | 184 | 207 | 219 | 252 | 34 | 255 | 278 | 301 | 324 | 347 | 370 | 393 | 416 | 439 | 1 |
| 68 | 91 | 114 | 137 | 160 | 183 | 206 | 218 | 251 | 253 | 56 | 277 | 300 | 323 | 346 | 369 | 392 | 415 | 438 | 21 | 23 |
| 90 | 113 | 136 | 159 | 182 | 205 | 217 | 250 | 273 | 275 | 78 | 299 | 322 | 345 | 368 | 391 | 414 | 437 | 20 | 22 | 45 |
| 112 | 135 | 158 | 181 | 204 | 216 | 249 | 272 | 274 | 297 | 100 | 321 | 344 | 367 | 390 | 413 | 436 | 19 | 42 | 44 | 67 |
| 134 | 157 | 180 | 203 | 215 | 248 | 271 | 294 | 296 | 319 | 122 | 343 | 366 | 389 | 412 | 435 | 18 | 41 | 43 | 66 | 89 |
| 156 | 179 | 202 | 214 | 247 | 270 | 293 | 295 | 318 | 341 | 144 | 365 | 388 | 411 | 434 | 17 | 40 | 63 | 65 | 88 | 111 |
| 178 | 201 | 213 | 246 | 269 | 292 | 315 | 317 | 340 | 363 | 166 | 387 | 410 | 433 | 16 | 39 | 62 | 64 | 87 | 110 | 133 |
| 200 | 212 | 245 | 268 | 291 | 314 | 316 | 339 | 362 | 385 | 188 | 409 | 432 | 15 | 38 | 61 | 84 | 86 | 109 | 132 | 155 |
| 211 | 244 | 267 | 290 | 313 | 336 | 338 | 361 | 384 | 407 | 210 | 431 | 14 | 37 | 60 | 83 | 85 | 108 | 131 | 154 | 177 |
| 243 | 266 | 289 | 312 | 335 | 337 | 360 | 383 | 406 | 429 | 221 | 13 | 36 | 59 | 82 | 105 | 107 | 130 | 153 | 176 | 199 |
| 265 | 288 | 311 | 334 | 357 | 359 | 382 | 405 | 428 | 11 | 232 | 35 | 58 | 81 | 104 | 106 | 129 | 152 | 175 | 198 | 231 |
| 287 | 310 | 333 | 356 | 358 | 381 | 404 | 427 | 10 | 33 | 254 | 57 | 80 | 103 | 126 | 128 | 151 | 174 | 197 | 230 | 242 |
| 309 | 332 | 355 | 378 | 380 | 403 | 426 | 9 | 32 | 55 | 276 | 79 | 102 | 125 | 127 | 150 | 173 | 196 | 229 | 241 | 264 |
| 331 | 354 | 377 | 379 | 402 | 425 | 8 | 31 | 54 | 77 | 298 | 101 | 124 | 147 | 149 | 172 | 195 | 228 | 240 | 263 | 286 |
| 353 | 376 | 399 | 401 | 424 | 7 | 30 | 53 | 76 | 99 | 320 | 123 | 146 | 148 | 171 | 194 | 227 | 239 | 262 | 285 | 308 |
| 375 | 398 | 400 | 423 | 6 | 29 | 52 | 75 | 98 | 121 | 342 | 145 | 168 | 170 | 193 | 226 | 238 | 261 | 284 | 307 | 330 |
| 397 | 420 | 422 | 5 | 28 | 51 | 74 | 97 | 120 | 143 | 364 | 167 | 169 | 192 | 225 | 237 | 260 | 283 | 306 | 329 | 352 |
| 419 | 421 | 4 | 27 | 50 | 73 | 96 | 119 | 142 | 165 | 386 | 189 | 191 | 224 | 236 | 259 | 282 | 305 | 328 | 351 | 374 |
| 441 | 3 | 26 | 49 | 72 | 95 | 118 | 141 | 164 | 187 | 408 | 190 | 223 | 235 | 258 | 281 | 304 | 327 | 350 | 373 | 396 |
| 2 | 25 | 48 | 71 | 94 | 117 | 140 | 163 | 186 | 209 | 430 | 222 | 234 | 257 | 280 | 303 | 326 | 349 | 372 | 395 | 418 |
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
