With the alternative method of Strachey we make 4 as proportional as possible 11x11 magic squares to construct the 22x22 magic square, and than we swap numbers to get the magic square valid.
To construct the 4 magic 11x11 squares, take the numbers 0 up to 10 as row coordinates and take the numbers 0 up to (11 x 4 -/- 1 = ) 43 as column coordinates.
Use the following table to get the column coordinates.
0 | 0 | 0 | 0 | 3 | 3 | 3 | 3 | 0 | 2 | 3 | 17 | 0 | 4 | 8 | 12 | 19 | 23 | 27 | 31 | 32 | 38 | 43 | 237 | |||
3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 3 | 0 | 1 | 16 | 3 | 7 | 11 | 15 | 16 | 20 | 24 | 28 | 35 | 36 | 41 | 236 | |||
1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 3 | 0 | 16 | 1 | 5 | 9 | 13 | 18 | 22 | 26 | 30 | 33 | 39 | 40 | 236 | |||
2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 17 | 2 | 6 | 10 | 14 | 17 | 21 | 25 | 29 | 34 | 37 | 42 | 237 |
11x column coordinate + row coordinate +1 = 11x11 magic square
2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | ||||||||||||||||||||||||||||
2673 | 2673 | |||||||||||||||||||||||||||||||||||||
0 | 4 | 8 | 12 | 19 | 23 | 27 | 31 | 32 | 38 | 43 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 2673 | 1 | 46 | 91 | 136 | 214 | 259 | 304 | 349 | 361 | 428 | 484 | |||||
8 | 12 | 19 | 23 | 27 | 31 | 32 | 38 | 43 | 0 | 4 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 2673 | 98 | 143 | 210 | 255 | 300 | 345 | 357 | 424 | 480 | 8 | 53 | 2673 | ||||
19 | 23 | 27 | 31 | 32 | 38 | 43 | 0 | 4 | 8 | 12 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 2673 | 217 | 262 | 307 | 352 | 353 | 420 | 476 | 4 | 49 | 94 | 139 | 2673 | ||||
27 | 31 | 32 | 38 | 43 | 0 | 4 | 8 | 12 | 19 | 23 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 2673 | 303 | 348 | 360 | 427 | 483 | 11 | 45 | 90 | 135 | 213 | 258 | 2673 | ||||
32 | 38 | 43 | 0 | 4 | 8 | 12 | 19 | 23 | 27 | 31 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 2673 | 356 | 423 | 479 | 7 | 52 | 97 | 142 | 220 | 254 | 299 | 344 | 2673 | ||||
43 | 0 | 4 | 8 | 12 | 19 | 23 | 27 | 31 | 32 | 38 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 2673 | 475 | 3 | 48 | 93 | 138 | 216 | 261 | 306 | 351 | 363 | 419 | 2673 | ||||
4 | 8 | 12 | 19 | 23 | 27 | 31 | 32 | 38 | 43 | 0 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2673 | 55 | 89 | 134 | 212 | 257 | 302 | 347 | 359 | 426 | 482 | 10 | 2673 | ||||
12 | 19 | 23 | 27 | 31 | 32 | 38 | 43 | 0 | 4 | 8 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 2673 | 141 | 219 | 264 | 298 | 343 | 355 | 422 | 478 | 6 | 51 | 96 | 2673 | ||||
23 | 27 | 31 | 32 | 38 | 43 | 0 | 4 | 8 | 12 | 19 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 2673 | 260 | 305 | 350 | 362 | 429 | 474 | 2 | 47 | 92 | 137 | 215 | 2673 | ||||
31 | 32 | 38 | 43 | 0 | 4 | 8 | 12 | 19 | 23 | 27 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 2673 | 346 | 358 | 425 | 481 | 9 | 54 | 99 | 133 | 211 | 256 | 301 | 2673 | ||||
38 | 43 | 0 | 4 | 8 | 12 | 19 | 23 | 27 | 31 | 32 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2673 | 421 | 477 | 5 | 50 | 95 | 140 | 218 | 263 | 308 | 342 | 354 | 2673 | ||||
2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | ||||||||||||||||||||||||||||
2662 | 2662 | |||||||||||||||||||||||||||||||||||||
3 | 7 | 11 | 15 | 16 | 20 | 24 | 28 | 35 | 36 | 41 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 2662 | 34 | 79 | 124 | 169 | 181 | 226 | 271 | 316 | 394 | 406 | 462 | |||||
11 | 15 | 16 | 20 | 24 | 28 | 35 | 36 | 41 | 3 | 7 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 2662 | 131 | 176 | 177 | 222 | 267 | 312 | 390 | 402 | 458 | 41 | 86 | 2662 | ||||
16 | 20 | 24 | 28 | 35 | 36 | 41 | 3 | 7 | 11 | 15 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 2662 | 184 | 229 | 274 | 319 | 386 | 398 | 454 | 37 | 82 | 127 | 172 | 2662 | ||||
24 | 28 | 35 | 36 | 41 | 3 | 7 | 11 | 15 | 16 | 20 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 2662 | 270 | 315 | 393 | 405 | 461 | 44 | 78 | 123 | 168 | 180 | 225 | 2662 | ||||
35 | 36 | 41 | 3 | 7 | 11 | 15 | 16 | 20 | 24 | 28 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 2662 | 389 | 401 | 457 | 40 | 85 | 130 | 175 | 187 | 221 | 266 | 311 | 2662 | ||||
41 | 3 | 7 | 11 | 15 | 16 | 20 | 24 | 28 | 35 | 36 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 2662 | 453 | 36 | 81 | 126 | 171 | 183 | 228 | 273 | 318 | 396 | 397 | 2662 | ||||
7 | 11 | 15 | 16 | 20 | 24 | 28 | 35 | 36 | 41 | 3 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2662 | 88 | 122 | 167 | 179 | 224 | 269 | 314 | 392 | 404 | 460 | 43 | 2662 | ||||
15 | 16 | 20 | 24 | 28 | 35 | 36 | 41 | 3 | 7 | 11 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 2662 | 174 | 186 | 231 | 265 | 310 | 388 | 400 | 456 | 39 | 84 | 129 | 2662 | ||||
20 | 24 | 28 | 35 | 36 | 41 | 3 | 7 | 11 | 15 | 16 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 2662 | 227 | 272 | 317 | 395 | 407 | 452 | 35 | 80 | 125 | 170 | 182 | 2662 | ||||
28 | 35 | 36 | 41 | 3 | 7 | 11 | 15 | 16 | 20 | 24 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 2662 | 313 | 391 | 403 | 459 | 42 | 87 | 132 | 166 | 178 | 223 | 268 | 2662 | ||||
36 | 41 | 3 | 7 | 11 | 15 | 16 | 20 | 24 | 28 | 35 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2662 | 399 | 455 | 38 | 83 | 128 | 173 | 185 | 230 | 275 | 309 | 387 | 2662 | ||||
2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | 2662 | ||||||||||||||||||||||||||||
2662 | 2662 | |||||||||||||||||||||||||||||||||||||
1 | 5 | 9 | 13 | 18 | 22 | 26 | 30 | 33 | 39 | 40 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 2662 | 12 | 57 | 102 | 147 | 203 | 248 | 293 | 338 | 372 | 439 | 451 | |||||
9 | 13 | 18 | 22 | 26 | 30 | 33 | 39 | 40 | 1 | 5 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 2662 | 109 | 154 | 199 | 244 | 289 | 334 | 368 | 435 | 447 | 19 | 64 | 2662 | ||||
18 | 22 | 26 | 30 | 33 | 39 | 40 | 1 | 5 | 9 | 13 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 2662 | 206 | 251 | 296 | 341 | 364 | 431 | 443 | 15 | 60 | 105 | 150 | 2662 | ||||
26 | 30 | 33 | 39 | 40 | 1 | 5 | 9 | 13 | 18 | 22 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 2662 | 292 | 337 | 371 | 438 | 450 | 22 | 56 | 101 | 146 | 202 | 247 | 2662 | ||||
33 | 39 | 40 | 1 | 5 | 9 | 13 | 18 | 22 | 26 | 30 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 2662 | 367 | 434 | 446 | 18 | 63 | 108 | 153 | 209 | 243 | 288 | 333 | 2662 | ||||
40 | 1 | 5 | 9 | 13 | 18 | 22 | 26 | 30 | 33 | 39 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 2662 | 442 | 14 | 59 | 104 | 149 | 205 | 250 | 295 | 340 | 374 | 430 | 2662 | ||||
5 | 9 | 13 | 18 | 22 | 26 | 30 | 33 | 39 | 40 | 1 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2662 | 66 | 100 | 145 | 201 | 246 | 291 | 336 | 370 | 437 | 449 | 21 | 2662 | ||||
13 | 18 | 22 | 26 | 30 | 33 | 39 | 40 | 1 | 5 | 9 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 2662 | 152 | 208 | 253 | 287 | 332 | 366 | 433 | 445 | 17 | 62 | 107 | 2662 | ||||
22 | 26 | 30 | 33 | 39 | 40 | 1 | 5 | 9 | 13 | 18 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 2662 | 249 | 294 | 339 | 373 | 440 | 441 | 13 | 58 | 103 | 148 | 204 | 2662 | ||||
30 | 33 | 39 | 40 | 1 | 5 | 9 | 13 | 18 | 22 | 26 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 2662 | 335 | 369 | 436 | 448 | 20 | 65 | 110 | 144 | 200 | 245 | 290 | 2662 | ||||
39 | 40 | 1 | 5 | 9 | 13 | 18 | 22 | 26 | 30 | 33 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2662 | 432 | 444 | 16 | 61 | 106 | 151 | 207 | 252 | 297 | 331 | 365 | 2662 | ||||
2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | 2673 | ||||||||||||||||||||||||||||
2673 | 2673 | |||||||||||||||||||||||||||||||||||||
2 | 6 | 10 | 14 | 17 | 21 | 25 | 29 | 34 | 37 | 42 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 2673 | 23 | 68 | 113 | 158 | 192 | 237 | 282 | 327 | 383 | 417 | 473 | |||||
10 | 14 | 17 | 21 | 25 | 29 | 34 | 37 | 42 | 2 | 6 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 2673 | 120 | 165 | 188 | 233 | 278 | 323 | 379 | 413 | 469 | 30 | 75 | 2673 | ||||
17 | 21 | 25 | 29 | 34 | 37 | 42 | 2 | 6 | 10 | 14 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 2673 | 195 | 240 | 285 | 330 | 375 | 409 | 465 | 26 | 71 | 116 | 161 | 2673 | ||||
25 | 29 | 34 | 37 | 42 | 2 | 6 | 10 | 14 | 17 | 21 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 2673 | 281 | 326 | 382 | 416 | 472 | 33 | 67 | 112 | 157 | 191 | 236 | 2673 | ||||
34 | 37 | 42 | 2 | 6 | 10 | 14 | 17 | 21 | 25 | 29 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 2673 | 378 | 412 | 468 | 29 | 74 | 119 | 164 | 198 | 232 | 277 | 322 | 2673 | ||||
42 | 2 | 6 | 10 | 14 | 17 | 21 | 25 | 29 | 34 | 37 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 2673 | 464 | 25 | 70 | 115 | 160 | 194 | 239 | 284 | 329 | 385 | 408 | 2673 | ||||
6 | 10 | 14 | 17 | 21 | 25 | 29 | 34 | 37 | 42 | 2 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2673 | 77 | 111 | 156 | 190 | 235 | 280 | 325 | 381 | 415 | 471 | 32 | 2673 | ||||
14 | 17 | 21 | 25 | 29 | 34 | 37 | 42 | 2 | 6 | 10 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 2673 | 163 | 197 | 242 | 276 | 321 | 377 | 411 | 467 | 28 | 73 | 118 | 2673 | ||||
21 | 25 | 29 | 34 | 37 | 42 | 2 | 6 | 10 | 14 | 17 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 2673 | 238 | 283 | 328 | 384 | 418 | 463 | 24 | 69 | 114 | 159 | 193 | 2673 | ||||
29 | 34 | 37 | 42 | 2 | 6 | 10 | 14 | 17 | 21 | 25 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2 | 3 | 2673 | 324 | 380 | 414 | 470 | 31 | 76 | 121 | 155 | 189 | 234 | 279 | 2673 | ||||
37 | 42 | 2 | 6 | 10 | 14 | 17 | 21 | 25 | 29 | 34 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 1 | 2673 | 410 | 466 | 27 | 72 | 117 | 162 | 196 | 241 | 286 | 320 | 376 | 2673 |
Put the 4 magic 11x11 squares together:
22x22 (semi)magic square to be corrected
5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | 5335 | |||
5346 | 5324 | |||||||||||||||||||||||
5335 | 1 | 46 | 91 | 136 | 214 | 259 | 304 | 349 | 361 | 428 | 484 | 34 | 79 | 124 | 169 | 181 | 226 | 271 | 316 | 394 | 406 | 462 | ||
5335 | 98 | 143 | 210 | 255 | 300 | 345 | 357 | 424 | 480 | 8 | 53 | 131 | 176 | 177 | 222 | 267 | 312 | 390 | 402 | 458 | 41 | 86 | ||
5335 | 217 | 262 | 307 | 352 | 353 | 420 | 476 | 4 | 49 | 94 | 139 | 184 | 229 | 274 | 319 | 386 | 398 | 454 | 37 | 82 | 127 | 172 | ||
5335 | 303 | 348 | 360 | 427 | 483 | 11 | 45 | 90 | 135 | 213 | 258 | 270 | 315 | 393 | 405 | 461 | 44 | 78 | 123 | 168 | 180 | 225 | ||
5335 | 356 | 423 | 479 | 7 | 52 | 97 | 142 | 220 | 254 | 299 | 344 | 389 | 401 | 457 | 40 | 85 | 130 | 175 | 187 | 221 | 266 | 311 | ||
5335 | 475 | 3 | 48 | 93 | 138 | 216 | 261 | 306 | 351 | 363 | 419 | 453 | 36 | 81 | 126 | 171 | 183 | 228 | 273 | 318 | 396 | 397 | ||
5335 | 55 | 89 | 134 | 212 | 257 | 302 | 347 | 359 | 426 | 482 | 10 | 88 | 122 | 167 | 179 | 224 | 269 | 314 | 392 | 404 | 460 | 43 | ||
5335 | 141 | 219 | 264 | 298 | 343 | 355 | 422 | 478 | 6 | 51 | 96 | 174 | 186 | 231 | 265 | 310 | 388 | 400 | 456 | 39 | 84 | 129 | ||
5335 | 260 | 305 | 350 | 362 | 429 | 474 | 2 | 47 | 92 | 137 | 215 | 227 | 272 | 317 | 395 | 407 | 452 | 35 | 80 | 125 | 170 | 182 | ||
5335 | 346 | 358 | 425 | 481 | 9 | 54 | 99 | 133 | 211 | 256 | 301 | 313 | 391 | 403 | 459 | 42 | 87 | 132 | 166 | 178 | 223 | 268 | ||
5335 | 421 | 477 | 5 | 50 | 95 | 140 | 218 | 263 | 308 | 342 | 354 | 399 | 455 | 38 | 83 | 128 | 173 | 185 | 230 | 275 | 309 | 387 | ||
5335 | 12 | 57 | 102 | 147 | 203 | 248 | 293 | 338 | 372 | 439 | 451 | 23 | 68 | 113 | 158 | 192 | 237 | 282 | 327 | 383 | 417 | 473 | ||