Zie Frost's magische 9x9x9 kubus op www.magic-squares.net/c-t-htm/c_update-6.htm.
Het geheim van Frost's 9x9x9 is niet moeilijk. Basis van de 9x9x9 kubus is het volgende magische 9x9 vierkant, dat symmetrisch en panmagisch maar niet compact is:
60 |
76 |
52 |
37 |
29 |
5 |
26 |
18 |
66 |
54 |
39 |
33 |
4 |
25 |
10 |
65 |
59 |
80 |
32 |
8 |
27 |
12 |
69 |
58 |
79 |
46 |
38 |
19 |
11 |
68 |
62 |
81 |
48 |
42 |
31 |
7 |
67 |
61 |
73 |
47 |
41 |
35 |
9 |
21 |
15 |
75 |
51 |
40 |
34 |
1 |
20 |
14 |
71 |
63 |
44 |
36 |
3 |
24 |
13 |
70 |
55 |
74 |
50 |
2 |
23 |
17 |
72 |
57 |
78 |
49 |
43 |
28 |
16 |
64 |
56 |
77 |
53 |
45 |
30 |
6 |
22 |
In de de lagen 1 t/m 9 vind je [de horizontaal verschoven versies van] het 9x9 vierkant 2-4-6-8-1-3-5-7-9 (= vierkant met het getal 54, 19, 75, 2, 60, 32, 67, 44 respectievelijk 16 in de
linker bovenhoek) en de (omgekeerde) kolom (in plaats van rij) patronen 9 t/m 1. Je kunt met Frost's methode perfect magische kubussen voor orde is oneven veelvoud van 3 maken.
Neem 1x getal + 9x getal = laag van 9x9x9 magische kubus
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 135 | 606 | 519 | 652 | 430 | 334 | 308 | 59 | 242 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 518 | 656 | 432 | 336 | 312 | 58 | 241 | 127 | 605 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 424 | 335 | 311 | 62 | 243 | 129 | 609 | 517 | 655 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 310 | 61 | 235 | 128 | 608 | 521 | 657 | 426 | 339 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 237 | 132 | 607 | 520 | 649 | 425 | 338 | 314 | 63 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 611 | 522 | 651 | 429 | 337 | 313 | 55 | 236 | 131 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 650 | 428 | 341 | 315 | 57 | 240 | 130 | 610 | 514 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 340 | 307 | 56 | 239 | 134 | 612 | 516 | 654 | 427 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 60 | 238 | 133 | 604 | 515 | 653 | 431 | 342 | 309 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 343 | 254 | 68 | 224 | 162 | 615 | 528 | 679 | 412 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 67 | 223 | 154 | 614 | 527 | 683 | 414 | 345 | 258 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 156 | 618 | 526 | 682 | 406 | 344 | 257 | 71 | 225 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 530 | 684 | 408 | 348 | 256 | 70 | 217 | 155 | 617 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 407 | 347 | 260 | 72 | 219 | 159 | 616 | 529 | 676 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 259 | 64 | 218 | 158 | 620 | 531 | 678 | 411 | 346 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 222 | 157 | 619 | 523 | 677 | 410 | 350 | 261 | 66 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 621 | 525 | 681 | 409 | 349 | 253 | 65 | 221 | 161 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 680 | 413 | 351 | 255 | 69 | 220 | 160 | 613 | 524 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 642 | 537 | 688 | 439 | 325 | 263 | 14 | 233 | 144 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 692 | 441 | 327 | 267 | 13 | 232 | 136 | 641 | 536 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 326 | 266 | 17 | 234 | 138 | 645 | 535 | 691 | 433 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 16 | 226 | 137 | 644 | 539 | 693 | 435 | 330 | 265 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 141 | 643 | 538 | 685 | 434 | 329 | 269 | 18 | 228 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 540 | 687 | 438 | 328 | 268 | 10 | 227 | 140 | 647 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 437 | 332 | 270 | 12 | 231 | 139 | 646 | 532 | 686 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 262 | 11 | 230 | 143 | 648 | 534 | 690 | 436 | 331 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 229 | 142 | 640 | 533 | 689 | 440 | 333 | 264 | 15 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 245 | 23 | 179 | 153 | 624 | 564 | 697 | 448 | 352 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 178 | 145 | 623 | 563 | 701 | 450 | 354 | 249 | 22 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 627 | 562 | 700 | 442 | 353 | 248 | 26 | 180 | 147 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 702 | 444 | 357 | 247 | 25 | 172 | 146 | 626 | 566 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 356 | 251 | 27 | 174 | 150 | 625 | 565 | 694 | 443 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 19 | 173 | 149 | 629 | 567 | 696 | 447 | 355 | 250 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 148 | 628 | 559 | 695 | 446 | 359 | 252 | 21 | 177 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 561 | 699 | 445 | 358 | 244 | 20 | 176 | 152 | 630 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 449 | 360 | 246 | 24 | 175 | 151 | 622 | 560 | 698 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 546 | 724 | 457 | 361 | 272 | 5 | 188 | 99 | 633 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 459 | 363 | 276 | 4 | 187 | 91 | 632 | 545 | 728 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 275 | 8 | 189 | 93 | 636 | 544 | 727 | 451 | 362 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 181 | 92 | 635 | 548 | 729 | 453 | 366 | 274 | 7 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 634 | 547 | 721 | 452 | 365 | 278 | 9 | 183 | 96 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 723 | 456 | 364 | 277 | 1 | 182 | 95 | 638 | 549 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 368 | 279 | 3 | 186 | 94 | 637 | 541 | 722 | 455 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 2 | 185 | 98 | 639 | 543 | 726 | 454 | 367 | 271 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 97 | 631 | 542 | 725 | 458 | 369 | 273 | 6 | 184 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 32 | 170 | 108 | 579 | 555 | 706 | 484 | 370 | 281 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 100 | 578 | 554 | 710 | 486 | 372 | 285 | 31 | 169 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 553 | 709 | 478 | 371 | 284 | 35 | 171 | 102 | 582 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 480 | 375 | 283 | 34 | 163 | 101 | 581 | 557 | 711 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 287 | 36 | 165 | 105 | 580 | 556 | 703 | 479 | 374 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 164 | 104 | 584 | 558 | 705 | 483 | 373 | 286 | 28 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 583 | 550 | 704 | 482 | 377 | 288 | 30 | 168 | 103 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 708 | 481 | 376 | 280 | 29 | 167 | 107 | 585 | 552 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 378 | 282 | 33 | 166 | 106 | 577 | 551 | 707 | 485 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 715 | 466 | 397 | 290 | 41 | 197 | 90 | 588 | 501 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 399 | 294 | 40 | 196 | 82 | 587 | 500 | 719 | 468 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 44 | 198 | 84 | 591 | 499 | 718 | 460 | 398 | 293 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 83 | 590 | 503 | 720 | 462 | 402 | 292 | 43 | 190 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 502 | 712 | 461 | 401 | 296 | 45 | 192 | 87 | 589 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 465 | 400 | 295 | 37 | 191 | 86 | 593 | 504 | 714 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 297 | 39 | 195 | 85 | 592 | 496 | 713 | 464 | 404 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 194 | 89 | 594 | 498 | 717 | 463 | 403 | 289 | 38 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 586 | 497 | 716 | 467 | 405 | 291 | 42 | 193 | 88 | ||||
44 | 36 | 3 | 24 | 13 | 70 | 55 | 74 | 50 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 206 | 117 | 570 | 510 | 661 | 475 | 379 | 317 | 50 | ||||
2 | 23 | 17 | 72 | 57 | 78 | 49 | 43 | 28 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 569 | 509 | 665 | 477 | 381 | 321 | 49 | 205 | 109 | ||||
16 | 64 | 56 | 77 | 53 | 45 | 30 | 6 | 22 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 664 | 469 | 380 | 320 | 53 | 207 | 111 | 573 | 508 | ||||
60 | 76 | 52 | 37 | 29 | 5 | 26 | 18 | 66 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 384 | 319 | 52 | 199 | 110 | 572 | 512 | 666 | 471 | ||||
54 | 39 | 33 | 4 | 25 | 10 | 65 | 59 | 80 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 54 | 201 | 114 | 571 | 511 | 658 | 470 | 383 | 323 | ||||
32 | 8 | 27 | 12 | 69 | 58 | 79 | 46 | 38 | 1 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 113 | 575 | 513 | 660 | 474 | 382 | 322 | 46 | 200 | ||||
19 | 11 | 68 | 62 | 81 | 48 | 42 | 31 | 7 | 6 | 8 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 505 | 659 | 473 | 386 | 324 | 48 | 204 | 112 | 574 | ||||
67 | 61 | 73 | 47 | 41 | 35 | 9 | 21 | 15 | 5 | 4 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 472 | 385 | 316 | 47 | 203 | 116 | 576 | 507 | 663 | ||||
75 | 51 | 40 | 34 | 1 | 20 | 14 | 71 | 63 | 3 | 0 | 2 | 1 | 7 | 6 | 8 | 5 | 4 | 318 | 51 | 202 | 115 | 568 | 506 | 662 | 476 | 387 | ||||