With the alternative method of Strachey we make 4 as proportional as possible 15x15 magic squares to construct the 30x30 magic square, and than we swap numbers to get the magic square valid.
To construct the 4 magic 15x15 squares, take the numbers 0 up to 14 as row coordinates and take the numbers 0 up to (15 x 4 -/- 1 = ) 59 as column coordinates.
Use the following table to get the column coordinates.
0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 3 | 3 | 3 | 3 | 0 | 2 | 3 | 23 | |
3 | 3 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 1 | 22 | |
1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 3 | 0 | 22 | |
2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 23 |
0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 443 | |
3 | 7 | 11 | 15 | 19 | 23 | 24 | 28 | 32 | 36 | 40 | 44 | 51 | 52 | 57 | 442 | |
1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 442 | |
2 | 6 | 10 | 14 | 18 | 22 | 25 | 29 | 33 | 37 | 41 | 45 | 50 | 53 | 58 | 443 |
Construct the 15x15 magic squares.
15x column coordinate
0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 |
16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 |
35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 |
48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 |
4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 |
20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 |
39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 |
54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 |
8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 |
27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 |
43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 |
59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 |
12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 |
31 | 35 | 39 | 43 | 47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 |
47 | 48 | 54 | 59 | 0 | 4 | 8 | 12 | 16 | 20 | 27 | 31 | 35 | 39 | 43 |
57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 |
40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 |
24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 |
11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 |
52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 |
36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 |
23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 |
7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 |
51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 |
32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 |
19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 |
3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 |
44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 |
28 | 24 | 23 | 19 | 15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 |
15 | 11 | 7 | 3 | 57 | 52 | 51 | 44 | 40 | 36 | 32 | 28 | 24 | 23 | 19 |
1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 |
17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 |
34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 |
49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 |
5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 |
21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 |
38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 |
55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 |
9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 |
26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 |
42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 |
56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 |
13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 |
30 | 34 | 38 | 42 | 46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 |
46 | 49 | 55 | 56 | 1 | 5 | 9 | 13 | 17 | 21 | 26 | 30 | 34 | 38 | 42 |
58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 |
41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 |
25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 |
10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 |
53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 |
37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 |
22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 |
6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 |
50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 |
33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 |
18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 |
2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 |
45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 |
29 | 25 | 22 | 18 | 14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 |
14 | 10 | 6 | 2 | 58 | 53 | 50 | 45 | 41 | 37 | 33 | 29 | 25 | 22 | 18 |
+ row coordinate +1
3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 |
6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 |
10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 |
2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 |
12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 |
13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 |
14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 |
4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 |
11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 |
9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 |
5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 |
1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 |
7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 |
8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 | 0 | 5 | 14 | 10 |
0 | 5 | 14 | 10 | 8 | 9 | 13 | 6 | 7 | 11 | 12 | 3 | 1 | 4 | 2 |
= 15x15 magic squares
6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | |||
4845 | 7725 | ||||||||||||||||
6765 | 4 | 62 | 125 | 183 | 241 | 306 | 420 | 476 | 534 | 595 | 659 | 712 | 728 | 822 | 898 | ||
6765 | 247 | 308 | 417 | 478 | 529 | 587 | 650 | 708 | 721 | 816 | 900 | 11 | 69 | 130 | 194 | ||
6765 | 536 | 594 | 655 | 719 | 727 | 818 | 897 | 13 | 64 | 122 | 185 | 243 | 301 | 411 | 480 | ||
6765 | 723 | 811 | 891 | 15 | 71 | 129 | 190 | 254 | 307 | 413 | 477 | 538 | 589 | 647 | 710 | ||
6765 | 73 | 124 | 182 | 245 | 303 | 406 | 471 | 540 | 596 | 654 | 715 | 734 | 817 | 893 | 12 | ||
6765 | 314 | 412 | 473 | 537 | 598 | 649 | 707 | 725 | 813 | 886 | 6 | 75 | 131 | 189 | 250 | ||
6765 | 600 | 656 | 714 | 730 | 824 | 892 | 8 | 72 | 133 | 184 | 242 | 305 | 408 | 466 | 531 | ||
6765 | 815 | 888 | 1 | 66 | 135 | 191 | 249 | 310 | 419 | 472 | 533 | 597 | 658 | 709 | 722 | ||
6765 | 132 | 193 | 244 | 302 | 410 | 468 | 526 | 591 | 660 | 716 | 729 | 820 | 899 | 7 | 68 | ||
6765 | 415 | 479 | 532 | 593 | 657 | 718 | 724 | 812 | 890 | 3 | 61 | 126 | 195 | 251 | 309 | ||
6765 | 651 | 720 | 731 | 819 | 895 | 14 | 67 | 128 | 192 | 253 | 304 | 407 | 470 | 528 | 586 | ||
6765 | 887 | 5 | 63 | 121 | 186 | 255 | 311 | 414 | 475 | 539 | 592 | 653 | 717 | 733 | 814 | ||
6765 | 188 | 252 | 313 | 409 | 467 | 530 | 588 | 646 | 711 | 735 | 821 | 894 | 10 | 74 | 127 | ||
6765 | 474 | 535 | 599 | 652 | 713 | 732 | 823 | 889 | 2 | 65 | 123 | 181 | 246 | 315 | 416 | ||
6765 | 706 | 726 | 825 | 896 | 9 | 70 | 134 | 187 | 248 | 312 | 418 | 469 | 527 | 590 | 648 | ||
6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | |||
8520 | 5925 | ||||||||||||||||
6750 | 859 | 782 | 770 | 663 | 601 | 546 | 495 | 431 | 369 | 355 | 299 | 232 | 173 | 117 | 58 | ||
6750 | 607 | 548 | 492 | 433 | 364 | 347 | 290 | 228 | 166 | 111 | 60 | 866 | 789 | 775 | 674 | ||
6750 | 371 | 354 | 295 | 239 | 172 | 113 | 57 | 868 | 784 | 767 | 665 | 603 | 541 | 486 | 435 | ||
6750 | 168 | 106 | 51 | 870 | 791 | 774 | 670 | 614 | 547 | 488 | 432 | 373 | 349 | 287 | 230 | ||
6750 | 793 | 769 | 662 | 605 | 543 | 481 | 426 | 375 | 356 | 294 | 235 | 179 | 112 | 53 | 867 | ||
6750 | 554 | 487 | 428 | 372 | 358 | 289 | 227 | 170 | 108 | 46 | 861 | 795 | 776 | 669 | 610 | ||
6750 | 360 | 296 | 234 | 175 | 119 | 52 | 863 | 792 | 778 | 664 | 602 | 545 | 483 | 421 | 366 | ||
6750 | 110 | 48 | 856 | 786 | 780 | 671 | 609 | 550 | 494 | 427 | 368 | 357 | 298 | 229 | 167 | ||
6750 | 777 | 673 | 604 | 542 | 485 | 423 | 361 | 351 | 300 | 236 | 174 | 115 | 59 | 862 | 788 | ||
6750 | 490 | 434 | 367 | 353 | 297 | 238 | 169 | 107 | 50 | 858 | 781 | 771 | 675 | 611 | 549 | ||
6750 | 291 | 240 | 176 | 114 | 55 | 869 | 787 | 773 | 672 | 613 | 544 | 482 | 425 | 363 | 346 | ||
6750 | 47 | 860 | 783 | 766 | 666 | 615 | 551 | 489 | 430 | 374 | 352 | 293 | 237 | 178 | 109 | ||
6750 | 668 | 612 | 553 | 484 | 422 | 365 | 348 | 286 | 231 | 180 | 116 | 54 | 865 | 794 | 772 | ||
6750 | 429 | 370 | 359 | 292 | 233 | 177 | 118 | 49 | 857 | 785 | 768 | 661 | 606 | 555 | 491 | ||
6750 | 226 | 171 | 120 | 56 | 864 | 790 | 779 | 667 | 608 | 552 | 493 | 424 | 362 | 350 | 288 | ||
6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | 6750 | |||
4920 | 7590 | ||||||||||||||||
6750 | 19 | 77 | 140 | 198 | 256 | 321 | 405 | 461 | 519 | 580 | 644 | 697 | 743 | 837 | 853 | ||
6750 | 262 | 323 | 402 | 463 | 514 | 572 | 635 | 693 | 736 | 831 | 855 | 26 | 84 | 145 | 209 | ||
6750 | 521 | 579 | 640 | 704 | 742 | 833 | 852 | 28 | 79 | 137 | 200 | 258 | 316 | 396 | 465 | ||
6750 | 738 | 826 | 846 | 30 | 86 | 144 | 205 | 269 | 322 | 398 | 462 | 523 | 574 | 632 | 695 | ||
6750 | 88 | 139 | 197 | 260 | 318 | 391 | 456 | 525 | 581 | 639 | 700 | 749 | 832 | 848 | 27 | ||
6750 | 329 | 397 | 458 | 522 | 583 | 634 | 692 | 740 | 828 | 841 | 21 | 90 | 146 | 204 | 265 | ||
6750 | 585 | 641 | 699 | 745 | 839 | 847 | 23 | 87 | 148 | 199 | 257 | 320 | 393 | 451 | 516 | ||
6750 | 830 | 843 | 16 | 81 | 150 | 206 | 264 | 325 | 404 | 457 | 518 | 582 | 643 | 694 | 737 | ||
6750 | 147 | 208 | 259 | 317 | 395 | 453 | 511 | 576 | 645 | 701 | 744 | 835 | 854 | 22 | 83 | ||
6750 | 400 | 464 | 517 | 578 | 642 | 703 | 739 | 827 | 845 | 18 | 76 | 141 | 210 | 266 | 324 | ||
6750 | 636 | 705 | 746 | 834 | 850 | 29 | 82 | 143 | 207 | 268 | 319 | 392 | 455 | 513 | 571 | ||
6750 | 842 | 20 | 78 | 136 | 201 | 270 | 326 | 399 | 460 | 524 | 577 | 638 | 702 | 748 | 829 | ||
6750 | 203 | 267 | 328 | 394 | 452 | 515 | 573 | 631 | 696 | 750 | 836 | 849 | 25 | 89 | 142 | ||
6750 | 459 | 520 | 584 | 637 | 698 | 747 | 838 | 844 | 17 | 80 | 138 | 196 | 261 | 330 | 401 | ||
6750 | 691 | 741 | 840 | 851 | 24 | 85 | 149 | 202 | 263 | 327 | 403 | 454 | 512 | 575 | 633 | ||
6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | 6765 | |||
8595 | 5880 | ||||||||||||||||
6765 | 874 | 797 | 755 | 678 | 616 | 561 | 510 | 446 | 384 | 340 | 284 | 217 | 158 | 102 | 43 | ||
6765 | 622 | 563 | 507 | 448 | 379 | 332 | 275 | 213 | 151 | 96 | 45 | 881 | 804 | 760 | 689 | ||
6765 | 386 | 339 | 280 | 224 | 157 | 98 | 42 | 883 | 799 | 752 | 680 | 618 | 556 | 501 | 450 | ||
6765 | 153 | 91 | 36 | 885 | 806 | 759 | 685 | 629 | 562 | 503 | 447 | 388 | 334 | 272 | 215 | ||
6765 | 808 | 754 | 677 | 620 | 558 | 496 | 441 | 390 | 341 | 279 | 220 | 164 | 97 | 38 | 882 | ||
6765 | 569 | 502 | 443 | 387 | 343 | 274 | 212 | 155 | 93 | 31 | 876 | 810 | 761 | 684 | 625 | ||
6765 | 345 | 281 | 219 | 160 | 104 | 37 | 878 | 807 | 763 | 679 | 617 | 560 | 498 | 436 | 381 | ||
6765 | 95 | 33 | 871 | 801 | 765 | 686 | 624 | 565 | 509 | 442 | 383 | 342 | 283 | 214 | 152 | ||
6765 | 762 | 688 | 619 | 557 | 500 | 438 | 376 | 336 | 285 | 221 | 159 | 100 | 44 | 877 | 803 | ||
6765 | 505 | 449 | 382 | 338 | 282 | 223 | 154 | 92 | 35 | 873 | 796 | 756 | 690 | 626 | 564 | ||
6765 | 276 | 225 | 161 | 99 | 40 | 884 | 802 | 758 | 687 | 628 | 559 | 497 | 440 | 378 | 331 | ||
6765 | 32 | 875 | 798 | 751 | 681 | 630 | 566 | 504 | 445 | 389 | 337 | 278 | 222 | 163 | 94 | ||
6765 | 683 | 627 | 568 | 499 | 437 | 380 | 333 | 271 | 216 | 165 | 101 | 39 | 880 | 809 | 757 | ||
6765 | 444 | 385 | 344 | 277 | 218 | 162 | 103 | 34 | 872 | 800 | 753 | 676 | 621 | 570 | 506 | ||
6765 | 211 | 156 | 105 | 41 | 879 | 805 | 764 | 682 | 623 | 567 | 508 | 439 | 377 | 335 | 273 |
Put the 15x15 magic squares together.
30x30 (semi-)magic square, to be corrected
13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | |||
13440 | 13515 | |||||||||||||||||||||||||||||||
13515 | 4 | 62 | 125 | 183 | 241 | 306 | 420 | 476 | 534 | 595 | 659 | 712 | 728 | 822 | 898 | 859 | 782 | 770 | 663 | 601 | 546 | 495 | 431 | 369 | 355 | 299 | 232 | 173 | 117 | 58 | ||
13515 | 247 | 308 | 417 | 478 | 529 | 587 | 650 | 708 | 721 | 816 | 900 | 11 | 69 | 130 | 194 | 607 | 548 | 492 | 433 | 364 | 347 | 290 | 228 | 166 | 111 | 60 | 866 | 789 | 775 | 674 | ||
13515 | 536 | 594 | 655 | 719 | 727 | 818 | 897 | 13 | 64 | 122 | 185 | 243 | 301 | 411 | 480 | 371 | 354 | 295 | 239 | 172 | 113 | 57 | 868 | 784 | 767 | 665 | 603 | 541 | 486 | 435 | ||
13515 | 723 | 811 | 891 | 15 | 71 | 129 | 190 | 254 | 307 | 413 | 477 | 538 | 589 | 647 | 710 | 168 | 106 | 51 | 870 | 791 | 774 | 670 | 614 | 547 | 488 | 432 | 373 | 349 | 287 | 230 | ||
13515 | 73 | 124 | 182 | 245 | 303 | 406 | 471 | 540 | 596 | 654 | 715 | 734 | 817 | 893 | 12 | 793 | 769 | 662 | 605 | 543 | 481 | 426 | 375 | 356 | 294 | 235 | 179 | 112 | 53 | 867 | ||
13515 | 314 | 412 | 473 | 537 | 598 | 649 | 707 | 725 | 813 | 886 | 6 | 75 | 131 | 189 | 250 | 554 | 487 | 428 | 372 | 358 | 289 | 227 | 170 | 108 | 46 | 861 | 795 | 776 | 669 | 610 | ||
13515 | 600 | 656 | 714 | 730 | 824 | 892 | 8 | 72 | 133 | 184 | 242 | 305 | 408 | 466 | 531 | 360 | 296 | 234 | 175 | 119 | 52 | 863 | 792 | 778 | 664 | 602 | 545 | 483 | 421 | 366 | ||
13515 | 815 | 888 | 1 | 66 | 135 | 191 | 249 | 310 | 419 | 472 | 533 | 597 | 658 | 709 | 722 | 110 | 48 | 856 | 786 | 780 | 671 | 609 | 550 | 494 | 427 | 368 | 357 | 298 | 229 | 167 | ||
13515 | 132 | 193 | 244 | 302 | 410 | 468 | 526 | 591 | 660 | 716 | 729 | 820 | 899 | 7 | 68 | 777 | 673 | 604 | 542 | 485 | 423 | 361 | 351 | 300 | 236 | 174 | 115 | 59 | 862 | 788 | ||
13515 | 415 | 479 | 532 | 593 | 657 | 718 | 724 | 812 | 890 | 3 | 61 | 126 | 195 | 251 | 309 | 490 | 434 | 367 | 353 | 297 | 238 | 169 | 107 | 50 | 858 | 781 | 771 | 675 | 611 | 549 | ||
13515 | 651 | 720 | 731 | 819 | 895 | 14 | 67 | 128 | 192 | 253 | 304 | 407 | 470 | 528 | 586 | 291 | 240 | 176 | 114 | 55 | 869 | 787 | 773 | 672 | 613 | 544 | 482 | 425 | 363 | 346 | ||
13515 | 887 | 5 | 63 | 121 | 186 | 255 | 311 | 414 | 475 | 539 | 592 | 653 | 717 | 733 | 814 | 47 | 860 | 783 | 766 | 666 | 615 | 551 | 489 | 430 | 374 | 352 | 293 | 237 | 178 | 109 | ||
13515 | 188 | 252 | 313 | 409 | 467 | 530 | 588 | 646 | 711 | 735 | 821 | 894 | 10 | 74 | 127 | 668 | 612 | 553 | 484 | 422 | 365 | 348 | 286 | 231 | 180 | 116 | 54 | 865 | 794 | 772 | ||
13515 | 474 | 535 | 599 | 652 | 713 | 732 | 823 | 889 | 2 | 65 | 123 | 181 | 246 | 315 | 416 | 429 | 370 | 359 | 292 | 233 | 177 | 118 | 49 | 857 | 785 | 768 | 661 | 606 | 555 | 491 | ||
13515 | 706 | 726 | 825 | 896 | 9 | 70 | 134 | 187 | 248 | 312 | 418 | 469 | 527 | 590 | 648 | 226 | 171 | 120 | 56 | 864 | 790 | 779 | 667 | 608 | 552 | 493 | 424 | 362 | 350 | 288 | ||
13515 | 19 | 77 | 140 | 198 | 256 | 321 | 405 | 461 | 519 | 580 | 644 | 697 | 743 | 837 | 853 | 874 | 797 | 755 | 678 | 616 | 561 | 510 | 446 | 384 | 340 | 284 | 217 | 158 | 102 | 43 | ||
13515 | 262 | 323 | 402 | 463 | 514 | 572 | 635 | 693 | 736 | 831 | 855 | 26 | 84 | 145 | 209 | 622 | 563 | 507 | 448 | 379 | 332 | 275 | 213 | 151 | 96 | 45 | 881 | 804 | 760 | 689 | ||
13515 | 521 | 579 | 640 | 704 | 742 | 833 | 852 | 28 | 79 | 137 | 200 | 258 | 316 | 396 | 465 | 386 | 339 | 280 | 224 | 157 | 98 | 42 | 883 | 799 | 752 | 680 | 618 | 556 | 501 | 450 | ||
13515 | 738 | 826 | 846 | 30 | 86 | 144 | 205 | 269 | 322 | 398 | 462 | 523 | 574 | 632 | 695 | 153 | 91 | 36 | 885 | 806 | 759 | 685 | 629 | 562 | 503 | 447 | 388 | 334 | 272 | 215 | ||
13515 | 88 | 139 | 197 | 260 | 318 | 391 | 456 | 525 | 581 | 639 | 700 | 749 | 832 | 848 | 27 | 808 | 754 | 677 | 620 | 558 | 496 | 441 | 390 | 341 | 279 | 220 | 164 | 97 | 38 | 882 | ||
13515 | 329 | 397 | 458 | 522 | 583 | 634 | 692 | 740 | 828 | 841 | 21 | 90 | 146 | 204 | 265 | 569 | 502 | 443 | 387 | 343 | 274 | 212 | 155 | 93 | 31 | 876 | 810 | 761 | 684 | 625 | ||
13515 | 585 | 641 | 699 | 745 | 839 | 847 | 23 | 87 | 148 | 199 | 257 | 320 | 393 | 451 | 516 | 345 | 281 | 219 | 160 | 104 | 37 | 878 | 807 | 763 | 679 | 617 | 560 | 498 | 436 | 381 | ||
13515 | 830 | 843 | 16 | 81 | 150 | 206 | 264 | 325 | 404 | 457 | 518 | 582 | 643 | 694 | 737 | 95 | 33 | 871 | 801 | 765 | 686 | 624 | 565 | 509 | 442 | 383 | 342 | 283 | 214 | 152 | ||
13515 | 147 | 208 | 259 | 317 | 395 | 453 | 511 | 576 | 645 | 701 | 744 | 835 | 854 | 22 | 83 | 762 | 688 | 619 | 557 | 500 | 438 | 376 | 336 | 285 | 221 | 159 | 100 | 44 | 877 | 803 | ||
13515 | 400 | 464 | 517 | 578 | 642 | 703 | 739 | 827 | 845 | 18 | 76 | 141 | 210 | 266 | 324 | 505 | 449 | 382 | 338 | 282 | 223 | 154 | 92 | 35 | 873 | 796 | 756 | 690 | 626 | 564 | ||
13515 | 636 | 705 | 746 | 834 | 850 | 29 | 82 | 143 | 207 | 268 | 319 | 392 | 455 | 513 | 571 | 276 | 225 | 161 | 99 | 40 | 884 | 802 | 758 | 687 | 628 | 559 | 497 | 440 | 378 | 331 | ||
13515 | 842 | 20 | 78 | 136 | 201 | 270 | 326 | 399 | 460 | 524 | 577 | 638 | 702 | 748 | 829 | 32 | 875 | 798 | 751 | 681 | 630 | 566 | 504 | 445 | 389 | 337 | 278 | 222 | 163 | 94 | ||
13515 | 203 | 267 | 328 | 394 | 452 | 515 | 573 | 631 | 696 | 750 | 836 | 849 | 25 | 89 | 142 | 683 | 627 | 568 | 499 | 437 | 380 | 333 | 271 | 216 | 165 | 101 | 39 | 880 | 809 | 757 | ||
13515 | 459 | 520 | 584 | 637 | 698 | 747 | 838 | 844 | 17 | 80 | 138 | 196 | 261 | 330 | 401 | 444 | 385 | 344 | 277 | 218 | 162 | 103 | 34 | 872 | 800 | 753 | 676 | 621 | 570 | 506 | ||
13515 | 691 | 741 | 840 | 851 | 24 | 85 | 149 | 202 | 263 | 327 | 403 | 454 | 512 | 575 | 633 | 211 | 156 | 105 | 41 | 879 | 805 | 764 | 682 | 623 | 567 | 508 | 439 | 377 | 335 | 273 |
This 30x30 magic square is semi-magic, because the (main) diagonal from top left to bottom right does not give the magic sum. Swap 10x10 (instead of 195x195 with the method of Strachey) numbers to get a (simple) 30x30 magic square.
30x30 magic square
13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | 13515 | |||
13515 | 13515 | |||||||||||||||||||||||||||||||
13515 | 19 | 62 | 125 | 183 | 241 | 306 | 405 | 476 | 534 | 595 | 659 | 712 | 728 | 822 | 898 | 859 | 782 | 770 | 663 | 601 | 546 | 495 | 431 | 369 | 355 | 299 | 232 | 173 | 117 | 58 | ||
13515 | 247 | 323 | 417 | 478 | 529 | 587 | 650 | 693 | 721 | 816 | 900 | 11 | 69 | 130 | 194 | 607 | 548 | 492 | 433 | 364 | 347 | 290 | 228 | 166 | 111 | 60 | 866 | 789 | 775 | 674 | ||
13515 | 536 | 594 | 655 | 719 | 727 | 818 | 897 | 13 | 64 | 122 | 185 | 243 | 301 | 411 | 480 | 371 | 354 | 295 | 239 | 172 | 113 | 57 | 868 | 784 | 767 | 665 | 603 | 541 | 486 | 435 | ||
13515 | 723 | 811 | 891 | 30 | 71 | 129 | 190 | 254 | 307 | 398 | 477 | 538 | 589 | 647 | 710 | 168 | 106 | 51 | 870 | 791 | 774 | 670 | 614 | 547 | 488 | 432 | 373 | 349 | 287 | 230 | ||
13515 | 73 | 124 | 182 | 245 | 318 | 391 | 471 | 540 | 596 | 654 | 715 | 734 | 817 | 893 | 12 | 793 | 769 | 662 | 605 | 543 | 481 | 426 | 375 | 356 | 294 | 235 | 179 | 112 | 53 | 867 | ||
13515 | 314 | 412 | 473 | 537 | 598 | 649 | 707 | 725 | 813 | 886 | 6 | 75 | 131 | 189 | 250 | 554 | 487 | 428 | 372 | 358 | 289 | 227 | 170 | 108 | 46 | 861 | 795 | 776 | 669 | 610 | ||
13515 | 600 | 656 | 714 | 730 | 824 | 892 | 23 | 72 | 133 | 184 | 242 | 305 | 393 | 466 | 531 | 360 | 296 | 234 | 175 | 119 | 52 | 863 | 792 | 778 | 664 | 602 | 545 | 483 | 421 | 366 | ||
13515 | 815 | 888 | 1 | 66 | 135 | 191 | 249 | 310 | 419 | 472 | 533 | 597 | 658 | 709 | 722 | 110 | 48 | 856 | 786 | 780 | 671 | 609 | 550 | 494 | 427 | 368 | 357 | 298 | 229 | 167 | ||
13515 | 132 | 193 | 244 | 302 | 410 | 468 | 526 | 591 | 660 | 716 | 729 | 820 | 899 | 7 | 68 | 777 | 673 | 604 | 542 | 485 | 423 | 361 | 351 | 300 | 236 | 174 | 115 | 59 | 862 | 788 | ||
13515 | 415 | 479 | 532 | 593 | 657 | 718 | 724 | 812 | 890 | 3 | 61 | 126 | 195 | 251 | 309 | 490 | 434 | 367 | 353 | 297 | 238 | 169 | 107 | 50 | 858 | 781 | 771 | 675 | 611 | 549 | ||
13515 | 651 | 720 | 731 | 819 | 895 | 14 | 67 | 128 | 192 | 253 | 304 | 407 | 470 | 528 | 586 | 291 | 240 | 176 | 114 | 55 | 869 | 787 | 773 | 672 | 613 | 544 | 482 | 425 | 363 | 346 | ||
13515 | 887 | 5 | 63 | 121 | 186 | 255 | 311 | 414 | 475 | 539 | 592 | 653 | 717 | 733 | 814 | 47 | 860 | 783 | 766 | 666 | 615 | 551 | 489 | 430 | 374 | 352 | 293 | 237 | 178 | 109 | ||
13515 | 188 | 252 | 313 | 409 | 467 | 530 | 588 | 646 | 711 | 735 | 821 | 894 | 10 | 74 | 127 | 668 | 612 | 553 | 484 | 422 | 365 | 348 | 286 | 231 | 180 | 116 | 54 | 865 | 794 | 772 | ||
13515 | 474 | 535 | 599 | 652 | 713 | 732 | 823 | 889 | 2 | 65 | 123 | 181 | 246 | 315 | 416 | 429 | 370 | 359 | 292 | 233 | 177 | 118 | 49 | 857 | 785 | 768 | 661 | 606 | 555 | 491 | ||
13515 | 706 | 726 | 825 | 896 | 9 | 70 | 134 | 187 | 248 | 312 | 418 | 469 | 527 | 590 | 648 | 226 | 171 | 120 | 56 | 864 | 790 | 779 | 667 | 608 | 552 | 493 | 424 | 362 | 350 | 288 | ||
13515 | 4 | 77 | 140 | 198 | 256 | 321 | 420 | 461 | 519 | 580 | 644 | 697 | 743 | 837 | 853 | 874 | 797 | 755 | 678 | 616 | 561 | 510 | 446 | 384 | 340 | 284 | 217 | 158 | 102 | 43 | ||
13515 | 262 | 308 | 402 | 463 | 514 | 572 | 635 | 708 | 736 | 831 | 855 | 26 | 84 | 145 | 209 | 622 | 563 | 507 | 448 | 379 | 332 | 275 | 213 | 151 | 96 | 45 | 881 | 804 | 760 | 689 | ||
13515 | 521 | 579 | 640 | 704 | 742 | 833 | 852 | 28 | 79 | 137 | 200 | 258 | 316 | 396 | 465 | 386 | 339 | 280 | 224 | 157 | 98 | 42 | 883 | 799 | 752 | 680 | 618 | 556 | 501 | 450 | ||
13515 | 738 | 826 | 846 | 15 | 86 | 144 | 205 | 269 | 322 | 413 | 462 | 523 | 574 | 632 | 695 | 153 | 91 | 36 | 885 | 806 | 759 | 685 | 629 | 562 | 503 | 447 | 388 | 334 | 272 | 215 | ||
13515 | 88 | 139 | 197 | 260 | 303 | 406 | 456 | 525 | 581 | 639 | 700 | 749 | 832 | 848 | 27 | 808 | 754 | 677 | 620 | 558 | 496 | 441 | 390 | 341 | 279 | 220 | 164 | 97 | 38 | 882 | ||
13515 | 329 | 397 | 458 | 522 | 583 | 634 | 692 | 740 | 828 | 841 | 21 | 90 | 146 | 204 | 265 | 569 | 502 | 443 | 387 | 343 | 274 | 212 | 155 | 93 | 31 | 876 | 810 | 761 | 684 | 625 | ||
13515 | 585 | 641 | 699 | 745 | 839 | 847 | 8 | 87 | 148 | 199 | 257 | 320 | 408 | 451 | 516 | 345 | 281 | 219 | 160 | 104 | 37 | 878 | 807 | 763 | 679 | 617 | 560 | 498 | 436 | 381 | ||
13515 | 830 | 843 | 16 | 81 | 150 | 206 | 264 | 325 | 404 | 457 | 518 | 582 | 643 | 694 | 737 | 95 | 33 | 871 | 801 | 765 | 686 | 624 | 565 | 509 | 442 | 383 | 342 | 283 | 214 | 152 | ||
13515 | 147 | 208 | 259 | 317 | 395 | 453 | 511 | 576 | 645 | 701 | 744 | 835 | 854 | 22 | 83 | 762 | 688 | 619 | 557 | 500 | 438 | 376 | 336 | 285 | 221 | 159 | 100 | 44 | 877 | 803 | ||
13515 | 400 | 464 | 517 | 578 | 642 | 703 | 739 | 827 | 845 | 18 | 76 | 141 | 210 | 266 | 324 | 505 | 449 | 382 | 338 | 282 | 223 | 154 | 92 | 35 | 873 | 796 | 756 | 690 | 626 | 564 | ||
13515 | 636 | 705 | 746 | 834 | 850 | 29 | 82 | 143 | 207 | 268 | 319 | 392 | 455 | 513 | 571 | 276 | 225 | 161 | 99 | 40 | 884 | 802 | 758 | 687 | 628 | 559 | 497 | 440 | 378 | 331 | ||
13515 | 842 | 20 | 78 | 136 | 201 | 270 | 326 | 399 | 460 | 524 | 577 | 638 | 702 | 748 | 829 | 32 | 875 | 798 | 751 | 681 | 630 | 566 | 504 | 445 | 389 | 337 | 278 | 222 | 163 | 94 | ||
13515 | 203 | 267 | 328 | 394 | 452 | 515 | 573 | 631 | 696 | 750 | 836 | 849 | 25 | 89 | 142 | 683 | 627 | 568 | 499 | 437 | 380 | 333 | 271 | 216 | 165 | 101 | 39 | 880 | 809 | 757 | ||
13515 | 459 | 520 | 584 | 637 | 698 | 747 | 838 | 844 | 17 | 80 | 138 | 196 | 261 | 330 | 401 | 444 | 385 | 344 | 277 | 218 | 162 | 103 | 34 | 872 | 800 | 753 | 676 | 621 | 570 | 506 | ||
13515 | 691 | 741 | 840 | 851 | 24 | 85 | 149 | 202 | 263 | 327 | 403 | 454 | 512 | 575 | 633 | 211 | 156 | 105 | 41 | 879 | 805 | 764 | 682 | 623 | 567 | 508 | 439 | 377 | 335 | 273 |
Use the alternative method of Strachey to construct magic squares of order is double odd. See 6x6, 10x10, 14x14, 18x18, 22x22, 26x26 en 30x30