René Chrétien had noticed the 15x15 composite (4) magic square and showed me it is possible to use the method to construct magic squares of even orders as well.
Construct the 30x30 magic square by using 25 proportional 6x6 magic squares. The squares are proportional because all 25 magic 6x6 squares have the same magic sum of (1/5 x 13515 = ) 2703. We use the method with reflecting grids (6x6) to produce the magic 6x6 squares. As row coordinates don't use 0 up to 5 but use 0 up to (25x6 -/- 1 = ) 149 instead. Take care that the sum of the row coordinates in each 6x6 square is the same (0+49+99+50+100+149 = 1+48+98+51+101+148 = ... = 24+25+75+74+124+125 = 447) to get proportional squares.
1x row coordinate +150x column coordinate + 1 = magic 6x6 square
0 | 49 | 99 | 50 | 100 | 149 | 0 | 5 | 0 | 5 | 5 | 0 | 1 | 800 | 100 | 801 | 851 | 150 | ||
149 | 49 | 50 | 99 | 100 | 0 | 1 | 1 | 4 | 4 | 1 | 4 | 300 | 200 | 651 | 700 | 251 | 601 | ||
0 | 100 | 50 | 99 | 49 | 149 | 3 | 2 | 2 | 2 | 3 | 3 | 451 | 401 | 351 | 400 | 500 | 600 | ||
149 | 100 | 50 | 99 | 49 | 0 | 2 | 3 | 3 | 3 | 2 | 2 | 450 | 551 | 501 | 550 | 350 | 301 | ||
149 | 49 | 99 | 50 | 100 | 0 | 4 | 4 | 1 | 1 | 4 | 1 | 750 | 650 | 250 | 201 | 701 | 151 | ||
0 | 100 | 99 | 50 | 49 | 149 | 5 | 0 | 5 | 0 | 0 | 5 | 751 | 101 | 850 | 51 | 50 | 900 | ||
1 | 48 | 98 | 51 | 101 | 148 | 0 | 5 | 0 | 5 | 5 | 0 | 2 | 799 | 99 | 802 | 852 | 149 | ||
148 | 48 | 51 | 98 | 101 | 1 | 1 | 1 | 4 | 4 | 1 | 4 | 299 | 199 | 652 | 699 | 252 | 602 | ||
1 | 101 | 51 | 98 | 48 | 148 | 3 | 2 | 2 | 2 | 3 | 3 | 452 | 402 | 352 | 399 | 499 | 599 | ||
148 | 101 | 51 | 98 | 48 | 1 | 2 | 3 | 3 | 3 | 2 | 2 | 449 | 552 | 502 | 549 | 349 | 302 | ||
148 | 48 | 98 | 51 | 101 | 1 | 4 | 4 | 1 | 1 | 4 | 1 | 749 | 649 | 249 | 202 | 702 | 152 | ||
1 | 101 | 98 | 51 | 48 | 148 | 5 | 0 | 5 | 0 | 0 | 5 | 752 | 102 | 849 | 52 | 49 | 899 | ||
2 | 47 | 97 | 52 | 102 | 147 | 0 | 5 | 0 | 5 | 5 | 0 | 3 | 798 | 98 | 803 | 853 | 148 | ||
147 | 47 | 52 | 97 | 102 | 2 | 1 | 1 | 4 | 4 | 1 | 4 | 298 | 198 | 653 | 698 | 253 | 603 | ||
2 | 102 | 52 | 97 | 47 | 147 | 3 | 2 | 2 | 2 | 3 | 3 | 453 | 403 | 353 | 398 | 498 | 598 | ||
147 | 102 | 52 | 97 | 47 | 2 | 2 | 3 | 3 | 3 | 2 | 2 | 448 | 553 | 503 | 548 | 348 | 303 | ||
147 | 47 | 97 | 52 | 102 | 2 | 4 | 4 | 1 | 1 | 4 | 1 | 748 | 648 | 248 | 203 | 703 | 153 | ||
2 | 102 | 97 | 52 | 47 | 147 | 5 | 0 | 5 | 0 | 0 | 5 | 753 | 103 | 848 | 53 | 48 | 898 | ||
3 | 46 | 96 | 53 | 103 | 146 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 797 | 97 | 804 | 854 | 147 | ||
146 | 46 | 53 | 96 | 103 | 3 | 1 | 1 | 4 | 4 | 1 | 4 | 297 | 197 | 654 | 697 | 254 | 604 | ||
3 | 103 | 53 | 96 | 46 | 146 | 3 | 2 | 2 | 2 | 3 | 3 | 454 | 404 | 354 | 397 | 497 | 597 | ||
146 | 103 | 53 | 96 | 46 | 3 | 2 | 3 | 3 | 3 | 2 | 2 | 447 | 554 | 504 | 547 | 347 | 304 | ||
146 | 46 | 96 | 53 | 103 | 3 | 4 | 4 | 1 | 1 | 4 | 1 | 747 | 647 | 247 | 204 | 704 | 154 | ||
3 | 103 | 96 | 53 | 46 | 146 | 5 | 0 | 5 | 0 | 0 | 5 | 754 | 104 | 847 | 54 | 47 | 897 | ||
4 | 45 | 95 | 54 | 104 | 145 | 0 | 5 | 0 | 5 | 5 | 0 | 5 | 796 | 96 | 805 | 855 | 146 | ||
145 | 45 | 54 | 95 | 104 | 4 | 1 | 1 | 4 | 4 | 1 | 4 | 296 | 196 | 655 | 696 | 255 | 605 | ||
4 | 104 | 54 | 95 | 45 | 145 | 3 | 2 | 2 | 2 | 3 | 3 | 455 | 405 | 355 | 396 | 496 | 596 | ||
145 | 104 | 54 | 95 | 45 | 4 | 2 | 3 | 3 | 3 | 2 | 2 | 446 | 555 | 505 | 546 | 346 | 305 | ||
145 | 45 | 95 | 54 | 104 | 4 | 4 | 4 | 1 | 1 | 4 | 1 | 746 | 646 | 246 | 205 | 705 | 155 | ||
4 | 104 | 95 | 54 | 45 | 145 | 5 | 0 | 5 | 0 | 0 | 5 | 755 | 105 | 846 | 55 | 46 | 896 | ||
5 | 44 | 94 | 55 | 105 | 144 | 0 | 5 | 0 | 5 | 5 | 0 | 6 | 795 | 95 | 806 | 856 | 145 | ||
144 | 44 | 55 | 94 | 105 | 5 | 1 | 1 | 4 | 4 | 1 | 4 | 295 | 195 | 656 | 695 | 256 | 606 | ||
5 | 105 | 55 | 94 | 44 | 144 | 3 | 2 | 2 | 2 | 3 | 3 | 456 | 406 | 356 | 395 | 495 | 595 | ||
144 | 105 | 55 | 94 | 44 | 5 | 2 | 3 | 3 | 3 | 2 | 2 | 445 | 556 | 506 | 545 | 345 | 306 | ||
144 | 44 | 94 | 55 | 105 | 5 | 4 | 4 | 1 | 1 | 4 | 1 | 745 | 645 | 245 | 206 | 706 | 156 | ||
5 | 105 | 94 | 55 | 44 | 144 | 5 | 0 | 5 | 0 | 0 | 5 | 756 | 106 | 845 | 56 | 45 | 895 | ||
6 | 43 | 93 | 56 | 106 | 143 | 0 | 5 | 0 | 5 | 5 | 0 | 7 | 794 | 94 | 807 | 857 | 144 | ||
143 | 43 | 56 | 93 | 106 | 6 | 1 | 1 | 4 | 4 | 1 | 4 | 294 | 194 | 657 | 694 | 257 | 607 | ||
6 | 106 | 56 | 93 | 43 | 143 | 3 | 2 | 2 | 2 | 3 | 3 | 457 | 407 | 357 | 394 | 494 | 594 | ||
143 | 106 | 56 | 93 | 43 | 6 | 2 | 3 | 3 | 3 | 2 | 2 | 444 | 557 | 507 | 544 | 344 | 307 | ||
143 | 43 | 93 | 56 | 106 | 6 | 4 | 4 | 1 | 1 | 4 | 1 | 744 | 644 | 244 | 207 | 707 | 157 | ||
6 | 106 | 93 | 56 | 43 | 143 | 5 | 0 | 5 | 0 | 0 | 5 | 757 | 107 | 844 | 57 | 44 | 894 | ||
7 | 42 | 92 | 57 | 107 | 142 | 0 | 5 | 0 | 5 | 5 | 0 | 8 | 793 | 93 | 808 | 858 | 143 | ||
142 | 42 | 57 | 92 | 107 | 7 | 1 | 1 | 4 | 4 | 1 | 4 | 293 | 193 | 658 | 693 | 258 | 608 | ||
7 | 107 | 57 | 92 | 42 | 142 | 3 | 2 | 2 | 2 | 3 | 3 | 458 | 408 | 358 | 393 | 493 | 593 | ||
142 | 107 | 57 | 92 | 42 | 7 | 2 | 3 | 3 | 3 | 2 | 2 | 443 | 558 | 508 | 543 | 343 | 308 | ||
142 | 42 | 92 | 57 | 107 | 7 | 4 | 4 | 1 | 1 | 4 | 1 | 743 | 643 | 243 | 208 | 708 | 158 | ||
7 | 107 | 92 | 57 | 42 | 142 | 5 | 0 | 5 | 0 | 0 | 5 | 758 | 108 | 843 | 58 | 43 | 893 | ||
8 | 41 | 91 | 58 | 108 | 141 | 0 | 5 | 0 | 5 | 5 | 0 | 9 | 792 | 92 | 809 | 859 | 142 | ||
141 | 41 | 58 | 91 | 108 | 8 | 1 | 1 | 4 | 4 | 1 | 4 | 292 | 192 | 659 | 692 | 259 | 609 | ||
8 | 108 | 58 | 91 | 41 | 141 | 3 | 2 | 2 | 2 | 3 | 3 | 459 | 409 | 359 | 392 | 492 | 592 | ||
141 | 108 | 58 | 91 | 41 | 8 | 2 | 3 | 3 | 3 | 2 | 2 | 442 | 559 | 509 | 542 | 342 | 309 | ||
141 | 41 | 91 | 58 | 108 | 8 | 4 | 4 | 1 | 1 | 4 | 1 | 742 | 642 | 242 | 209 | 709 | 159 | ||
8 | 108 | 91 | 58 | 41 | 141 | 5 | 0 | 5 | 0 | 0 | 5 | 759 | 109 | 842 | 59 | 42 | 892 | ||
9 | 40 | 90 | 59 | 109 | 140 | 0 | 5 | 0 | 5 | 5 | 0 | 10 | 791 | 91 | 810 | 860 | 141 | ||
140 | 40 | 59 | 90 | 109 | 9 | 1 | 1 | 4 | 4 | 1 | 4 | 291 | 191 | 660 | 691 | 260 | 610 | ||
9 | 109 | 59 | 90 | 40 | 140 | 3 | 2 | 2 | 2 | 3 | 3 | 460 | 410 | 360 | 391 | 491 | 591 | ||
140 | 109 | 59 | 90 | 40 | 9 | 2 | 3 | 3 | 3 | 2 | 2 | 441 | 560 | 510 | 541 | 341 | 310 | ||
140 | 40 | 90 | 59 | 109 | 9 | 4 | 4 | 1 | 1 | 4 | 1 | 741 | 641 | 241 | 210 | 710 | 160 | ||
9 | 109 | 90 | 59 | 40 | 140 | 5 | 0 | 5 | 0 | 0 | 5 | 760 | 110 | 841 | 60 | 41 | 891 | ||
10 | 39 | 89 | 60 | 110 | 139 | 0 | 5 | 0 | 5 | 5 | 0 | 11 | 790 | 90 | 811 | 861 | 140 | ||
139 | 39 | 60 | 89 | 110 | 10 | 1 | 1 | 4 | 4 | 1 | 4 | 290 | 190 | 661 | 690 | 261 | 611 | ||
10 | 110 | 60 | 89 | 39 | 139 | 3 | 2 | 2 | 2 | 3 | 3 | 461 | 411 | 361 | 390 | 490 | 590 | ||
139 | 110 | 60 | 89 | 39 | 10 | 2 | 3 | 3 | 3 | 2 | 2 | 440 | 561 | 511 | 540 | 340 | 311 | ||
139 | 39 | 89 | 60 | 110 | 10 | 4 | 4 | 1 | 1 | 4 | 1 | 740 | 640 | 240 | 211 | 711 | 161 | ||
10 | 110 | 89 | 60 | 39 | 139 | 5 | 0 | 5 | 0 | 0 | 5 | 761 | 111 | 840 | 61 | 40 | 890 | ||
11 | 38 | 88 | 61 | 111 | 138 | 0 | 5 | 0 | 5 | 5 | 0 | 12 | 789 | 89 | 812 | 862 | 139 | ||
138 | 38 | 61 | 88 | 111 | 11 | 1 | 1 | 4 | 4 | 1 | 4 | 289 | 189 | 662 | 689 | 262 | 612 | ||
11 | 111 | 61 | 88 | 38 | 138 | 3 | 2 | 2 | 2 | 3 | 3 | 462 | 412 | 362 | 389 | 489 | 589 | ||
138 | 111 | 61 | 88 | 38 | 11 | 2 | 3 | 3 | 3 | 2 | 2 | 439 | 562 | 512 | 539 | 339 | 312 | ||
138 | 38 | 88 | 61 | 111 | 11 | 4 | 4 | 1 | 1 | 4 | 1 | 739 | 639 | 239 | 212 | 712 | 162 | ||
11 | 111 | 88 | 61 | 38 | 138 | 5 | 0 | 5 | 0 | 0 | 5 | 762 | 112 | 839 | 62 | 39 | 889 | ||
12 | 37 | 87 | 62 | 112 | 137 | 0 | 5 | 0 | 5 | 5 | 0 | 13 | 788 | 88 | 813 | 863 | 138 | ||
137 | 37 | 62 | 87 | 112 | 12 | 1 | 1 | 4 | 4 | 1 | 4 | 288 | 188 | 663 | 688 | 263 | 613 | ||
12 | 112 | 62 | 87 | 37 | 137 | 3 | 2 | 2 | 2 | 3 | 3 | 463 | 413 | 363 | 388 | 488 | 588 | ||
137 | 112 | 62 | 87 | 37 | 12 | 2 | 3 | 3 | 3 | 2 | 2 | 438 | 563 | 513 | 538 | 338 | 313 | ||
137 | 37 | 87 | 62 | 112 | 12 | 4 | 4 | 1 | 1 | 4 | 1 | 738 | 638 | 238 | 213 | 713 | 163 | ||
12 | 112 | 87 | 62 | 37 | 137 | 5 | 0 | 5 | 0 | 0 | 5 | 763 | 113 | 838 | 63 | 38 | 888 | ||
13 | 36 | 86 | 63 | 113 | 136 | 0 | 5 | 0 | 5 | 5 | 0 | 14 | 787 | 87 | 814 | 864 | 137 | ||
136 | 36 | 63 | 86 | 113 | 13 | 1 | 1 | 4 | 4 | 1 | 4 | 287 | 187 | 664 | 687 | 264 | 614 | ||
13 | 113 | 63 | 86 | 36 | 136 | 3 | 2 | 2 | 2 | 3 | 3 | 464 | 414 | 364 | 387 | 487 | 587 | ||
136 | 113 | 63 | 86 | 36 | 13 | 2 | 3 | 3 | 3 | 2 | 2 | 437 | 564 | 514 | 537 | 337 | 314 | ||
136 | 36 | 86 | 63 | 113 | 13 | 4 | 4 | 1 | 1 | 4 | 1 | 737 | 637 | 237 | 214 | 714 | 164 | ||
13 | 113 | 86 | 63 | 36 | 136 | 5 | 0 | 5 | 0 | 0 | 5 | 764 | 114 | 837 | 64 | 37 | 887 | ||
14 | 35 | 85 | 64 | 114 | 135 | 0 | 5 | 0 | 5 | 5 | 0 | 15 | 786 | 86 | 815 | 865 | 136 | ||
135 | 35 | 64 | 85 | 114 | 14 | 1 | 1 | 4 | 4 | 1 | 4 | 286 | 186 | 665 | 686 | 265 | 615 | ||
14 | 114 | 64 | 85 | 35 | 135 | 3 | 2 | 2 | 2 | 3 | 3 | 465 | 415 | 365 | 386 | 486 | 586 | ||
135 | 114 | 64 | 85 | 35 | 14 | 2 | 3 | 3 | 3 | 2 | 2 | 436 | 565 | 515 | 536 | 336 | 315 | ||
135 | 35 | 85 | 64 | 114 | 14 | 4 | 4 | 1 | 1 | 4 | 1 | 736 | 636 | 236 | 215 | 715 | 165 | ||
14 | 114 | 85 | 64 | 35 | 135 | 5 | 0 | 5 | 0 | 0 | 5 | 765 | 115 | 836 | 65 | 36 | 886 | ||
15 | 34 | 84 | 65 | 115 | 134 | 0 | 5 | 0 | 5 | 5 | 0 | 16 | 785 | 85 | 816 | 866 | 135 | ||
134 | 34 | 65 | 84 | 115 | 15 | 1 | 1 | 4 | 4 | 1 | 4 | 285 | 185 | 666 | 685 | 266 | 616 | ||
15 | 115 | 65 | 84 | 34 | 134 | 3 | 2 | 2 | 2 | 3 | 3 | 466 | 416 | 366 | 385 | 485 | 585 | ||
134 | 115 | 65 | 84 | 34 | 15 | 2 | 3 | 3 | 3 | 2 | 2 | 435 | 566 | 516 | 535 | 335 | 316 | ||
134 | 34 | 84 | 65 | 115 | 15 | 4 | 4 | 1 | 1 | 4 | 1 | 735 | 635 | 235 | 216 | 716 | 166 | ||
15 | 115 | 84 | 65 | 34 | 134 | 5 | 0 | 5 | 0 | 0 | 5 | 766 | 116 | 835 | 66 | 35 | 885 | ||
16 | 33 | 83 | 66 | 116 | 133 | 0 | 5 | 0 | 5 | 5 | 0 | 17 | 784 | 84 | 817 | 867 | 134 | ||
133 | 33 | 66 | 83 | 116 | 16 | 1 | 1 | 4 | 4 | 1 | 4 | 284 | 184 | 667 | 684 | 267 | 617 | ||
16 | 116 | 66 | 83 | 33 | 133 | 3 | 2 | 2 | 2 | 3 | 3 | 467 | 417 | 367 | 384 | 484 | 584 | ||
133 | 116 | 66 | 83 | 33 | 16 | 2 | 3 | 3 | 3 | 2 | 2 | 434 | 567 | 517 | 534 | 334 | 317 | ||
133 | 33 | 83 | 66 | 116 | 16 | 4 | 4 | 1 | 1 | 4 | 1 | 734 | 634 | 234 | 217 | 717 | 167 | ||
16 | 116 | 83 | 66 | 33 | 133 | 5 | 0 | 5 | 0 | 0 | 5 | 767 | 117 | 834 | 67 | 34 | 884 | ||
17 | 32 | 82 | 67 | 117 | 132 | 0 | 5 | 0 | 5 | 5 | 0 | 18 | 783 | 83 | 818 | 868 | 133 | ||
132 | 32 | 67 | 82 | 117 | 17 | 1 | 1 | 4 | 4 | 1 | 4 | 283 | 183 | 668 | 683 | 268 | 618 | ||
17 | 117 | 67 | 82 | 32 | 132 | 3 | 2 | 2 | 2 | 3 | 3 | 468 | 418 | 368 | 383 | 483 | 583 | ||
132 | 117 | 67 | 82 | 32 | 17 | 2 | 3 | 3 | 3 | 2 | 2 | 433 | 568 | 518 | 533 | 333 | 318 | ||
132 | 32 | 82 | 67 | 117 | 17 | 4 | 4 | 1 | 1 | 4 | 1 | 733 | 633 | 233 | 218 | 718 | 168 | ||
17 | 117 | 82 | 67 | 32 | 132 | 5 | 0 | 5 | 0 | 0 | 5 | 768 | 118 | 833 | 68 | 33 | 883 | ||
18 | 31 | 81 | 68 | 118 | 131 | 0 | 5 | 0 | 5 | 5 | 0 | 19 | 782 | 82 | 819 | 869 | 132 | ||
131 | 31 | 68 | 81 | 118 | 18 | 1 | 1 | 4 | 4 | 1 | 4 | 282 | 182 | 669 | 682 | 269 | 619 | ||
18 | 118 | 68 | 81 | 31 | 131 | 3 | 2 | 2 | 2 | 3 | 3 | 469 | 419 | 369 | 382 | 482 | 582 | ||
131 | 118 | 68 | 81 | 31 | 18 | 2 | 3 | 3 | 3 | 2 | 2 | 432 | 569 | 519 | 532 | 332 | 319 | ||
131 | 31 | 81 | 68 | 118 | 18 | 4 | 4 | 1 | 1 | 4 | 1 | 732 | 632 | 232 | 219 | 719 | 169 | ||
18 | 118 | 81 | 68 | 31 | 131 | 5 | 0 | 5 | 0 | 0 | 5 | 769 | 119 | 832 | 69 | 32 | 882 | ||
19 | 30 | 80 | 69 | 119 | 130 | 0 | 5 | 0 | 5 | 5 | 0 | 20 | 781 | 81 | 820 | 870 | 131 | ||
130 | 30 | 69 | 80 | 119 | 19 | 1 | 1 | 4 | 4 | 1 | 4 | 281 | 181 | 670 | 681 | 270 | 620 | ||
19 | 119 | 69 | 80 | 30 | 130 | 3 | 2 | 2 | 2 | 3 | 3 | 470 | 420 | 370 | 381 | 481 | 581 | ||
130 | 119 | 69 | 80 | 30 | 19 | 2 | 3 | 3 | 3 | 2 | 2 | 431 | 570 | 520 | 531 | 331 | 320 | ||
130 | 30 | 80 | 69 | 119 | 19 | 4 | 4 | 1 | 1 | 4 | 1 | 731 | 631 | 231 | 220 | 720 | 170 | ||
19 | 119 | 80 | 69 | 30 | 130 | 5 | 0 | 5 | 0 | 0 | 5 | 770 | 120 | 831 | 70 | 31 | 881 | ||
20 | 29 | 79 | 70 | 120 | 129 | 0 | 5 | 0 | 5 | 5 | 0 | 21 | 780 | 80 | 821 | 871 | 130 | ||
129 | 29 | 70 | 79 | 120 | 20 | 1 | 1 | 4 | 4 | 1 | 4 | 280 | 180 | 671 | 680 | 271 | 621 | ||
20 | 120 | 70 | 79 | 29 | 129 | 3 | 2 | 2 | 2 | 3 | 3 | 471 | 421 | 371 | 380 | 480 | 580 | ||
129 | 120 | 70 | 79 | 29 | 20 | 2 | 3 | 3 | 3 | 2 | 2 | 430 | 571 | 521 | 530 | 330 | 321 | ||
129 | 29 | 79 | 70 | 120 | 20 | 4 | 4 | 1 | 1 | 4 | 1 | 730 | 630 | 230 | 221 | 721 | 171 | ||
20 | 120 | 79 | 70 | 29 | 129 | 5 | 0 | 5 | 0 | 0 | 5 | 771 | 121 | 830 | 71 | 30 | 880 | ||
21 | 28 | 78 | 71 | 121 | 128 | 0 | 5 | 0 | 5 | 5 | 0 | 22 | 779 | 79 | 822 | 872 | 129 | ||
128 | 28 | 71 | 78 | 121 | 21 | 1 | 1 | 4 | 4 | 1 | 4 | 279 | 179 | 672 | 679 | 272 | 622 | ||
21 | 121 | 71 | 78 | 28 | 128 | 3 | 2 | 2 | 2 | 3 | 3 | 472 | 422 | 372 | 379 | 479 | 579 | ||
128 | 121 | 71 | 78 | 28 | 21 | 2 | 3 | 3 | 3 | 2 | 2 | 429 | 572 | 522 | 529 | 329 | 322 | ||
128 | 28 | 78 | 71 | 121 | 21 | 4 | 4 | 1 | 1 | 4 | 1 | 729 | 629 | 229 | 222 | 722 | 172 | ||
21 | 121 | 78 | 71 | 28 | 128 | 5 | 0 | 5 | 0 | 0 | 5 | 772 | 122 | 829 | 72 | 29 | 879 | ||
22 | 27 | 77 | 72 | 122 | 127 | 0 | 5 | 0 | 5 | 5 | 0 | 23 | 778 | 78 | 823 | 873 | 128 | ||
127 | 27 | 72 | 77 | 122 | 22 | 1 | 1 | 4 | 4 | 1 | 4 | 278 | 178 | 673 | 678 | 273 | 623 | ||
22 | 122 | 72 | 77 | 27 | 127 | 3 | 2 | 2 | 2 | 3 | 3 | 473 | 423 | 373 | 378 | 478 | 578 | ||
127 | 122 | 72 | 77 | 27 | 22 | 2 | 3 | 3 | 3 | 2 | 2 | 428 | 573 | 523 | 528 | 328 | 323 | ||
127 | 27 | 77 | 72 | 122 | 22 | 4 | 4 | 1 | 1 | 4 | 1 | 728 | 628 | 228 | 223 | 723 | 173 | ||
22 | 122 | 77 | 72 | 27 | 127 | 5 | 0 | 5 | 0 | 0 | 5 | 773 | 123 | 828 | 73 | 28 | 878 | ||
23 | 26 | 76 | 73 | 123 | 126 | 0 | 5 | 0 | 5 | 5 | 0 | 24 | 777 | 77 | 824 | 874 | 127 | ||
126 | 26 | 73 | 76 | 123 | 23 | 1 | 1 | 4 | 4 | 1 | 4 | 277 | 177 | 674 | 677 | 274 | 624 | ||
23 | 123 | 73 | 76 | 26 | 126 | 3 | 2 | 2 | 2 | 3 | 3 | 474 | 424 | 374 | 377 | 477 | 577 | ||
126 | 123 | 73 | 76 | 26 | 23 | 2 | 3 | 3 | 3 | 2 | 2 | 427 | 574 | 524 | 527 | 327 | 324 | ||
126 | 26 | 76 | 73 | 123 | 23 | 4 | 4 | 1 | 1 | 4 | 1 | 727 | 627 | 227 | 224 | 724 | 174 | ||
23 | 123 | 76 | 73 | 26 | 126 | 5 | 0 | 5 | 0 | 0 | 5 | 774 | 124 | 827 | 74 | 27 | 877 | ||
24 | 25 | 75 | 74 | 124 | 125 | 0 | 5 | 0 | 5 | 5 | 0 | 25 | 776 | 76 | 825 | 875 | 126 | ||
125 | 25 | 74 | 75 | 124 | 24 | 1 | 1 | 4 | 4 | 1 | 4 | 276 | 176 | 675 | 676 | 275 | 625 | ||
24 | 124 | 74 | 75 | 25 | 125 | 3 | 2 | 2 | 2 | 3 | 3 | 475 | 425 | 375 | 376 | 476 | 576 | ||
125 | 124 | 74 | 75 | 25 | 24 | 2 | 3 | 3 | 3 | 2 | 2 | 426 | 575 | 525 | 526 | 326 | 325 | ||
125 | 25 | 75 | 74 | 124 | 24 | 4 | 4 | 1 | 1 | 4 | 1 | 726 | 626 | 226 | 225 | 725 | 175 | ||
24 | 124 | 75 | 74 | 25 | 125 | 5 | 0 | 5 | 0 | 0 | 5 | 775 | 125 | 826 | 75 | 26 | 876 |
30x30 magic square
1 | 800 | 100 | 801 | 851 | 150 | 2 | 799 | 99 | 802 | 852 | 149 | 3 | 798 | 98 | 803 | 853 | 148 | 4 | 797 | 97 | 804 | 854 | 147 | 5 | 796 | 96 | 805 | 855 | 146 |
300 | 200 | 651 | 700 | 251 | 601 | 299 | 199 | 652 | 699 | 252 | 602 | 298 | 198 | 653 | 698 | 253 | 603 | 297 | 197 | 654 | 697 | 254 | 604 | 296 | 196 | 655 | 696 | 255 | 605 |
451 | 401 | 351 | 400 | 500 | 600 | 452 | 402 | 352 | 399 | 499 | 599 | 453 | 403 | 353 | 398 | 498 | 598 | 454 | 404 | 354 | 397 | 497 | 597 | 455 | 405 | 355 | 396 | 496 | 596 |
450 | 551 | 501 | 550 | 350 | 301 | 449 | 552 | 502 | 549 | 349 | 302 | 448 | 553 | 503 | 548 | 348 | 303 | 447 | 554 | 504 | 547 | 347 | 304 | 446 | 555 | 505 | 546 | 346 | 305 |
750 | 650 | 250 | 201 | 701 | 151 | 749 | 649 | 249 | 202 | 702 | 152 | 748 | 648 | 248 | 203 | 703 | 153 | 747 | 647 | 247 | 204 | 704 | 154 | 746 | 646 | 246 | 205 | 705 | 155 |
751 | 101 | 850 | 51 | 50 | 900 | 752 | 102 | 849 | 52 | 49 | 899 | 753 | 103 | 848 | 53 | 48 | 898 | 754 | 104 | 847 | 54 | 47 | 897 | 755 | 105 | 846 | 55 | 46 | 896 |
6 | 795 | 95 | 806 | 856 | 145 | 7 | 794 | 94 | 807 | 857 | 144 | 8 | 793 | 93 | 808 | 858 | 143 | 9 | 792 | 92 | 809 | 859 | 142 | 10 | 791 | 91 | 810 | 860 | 141 |
295 | 195 | 656 | 695 | 256 | 606 | 294 | 194 | 657 | 694 | 257 | 607 | 293 | 193 | 658 | 693 | 258 | 608 | 292 | 192 | 659 | 692 | 259 | 609 | 291 | 191 | 660 | 691 | 260 | 610 |
456 | 406 | 356 | 395 | 495 | 595 | 457 | 407 | 357 | 394 | 494 | 594 | 458 | 408 | 358 | 393 | 493 | 593 | 459 | 409 | 359 | 392 | 492 | 592 | 460 | 410 | 360 | 391 | 491 | 591 |
445 | 556 | 506 | 545 | 345 | 306 | 444 | 557 | 507 | 544 | 344 | 307 | 443 | 558 | 508 | 543 | 343 | 308 | 442 | 559 | 509 | 542 | 342 | 309 | 441 | 560 | 510 | 541 | 341 | 310 |
745 | 645 | 245 | 206 | 706 | 156 | 744 | 644 | 244 | 207 | 707 | 157 | 743 | 643 | 243 | 208 | 708 | 158 | 742 | 642 | 242 | 209 | 709 | 159 | 741 | 641 | 241 | 210 | 710 | 160 |
756 | 106 | 845 | 56 | 45 | 895 | 757 | 107 | 844 | 57 | 44 | 894 | 758 | 108 | 843 | 58 | 43 | 893 | 759 | 109 | 842 | 59 | 42 | 892 | 760 | 110 | 841 | 60 | 41 | 891 |
11 | 790 | 90 | 811 | 861 | 140 | 12 | 789 | 89 | 812 | 862 | 139 | 13 | 788 | 88 | 813 | 863 | 138 | 14 | 787 | 87 | 814 | 864 | 137 | 15 | 786 | 86 | 815 | 865 | 136 |
290 | 190 | 661 | 690 | 261 | 611 | 289 | 189 | 662 | 689 | 262 | 612 | 288 | 188 | 663 | 688 | 263 | 613 | 287 | 187 | 664 | 687 | 264 | 614 | 286 | 186 | 665 | 686 | 265 | 615 |
461 | 411 | 361 | 390 | 490 | 590 | 462 | 412 | 362 | 389 | 489 | 589 | 463 | 413 | 363 | 388 | 488 | 588 | 464 | 414 | 364 | 387 | 487 | 587 | 465 | 415 | 365 | 386 | 486 | 586 |
440 | 561 | 511 | 540 | 340 | 311 | 439 | 562 | 512 | 539 | 339 | 312 | 438 | 563 | 513 | 538 | 338 | 313 | 437 | 564 | 514 | 537 | 337 | 314 | 436 | 565 | 515 | 536 | 336 | 315 |
740 | 640 | 240 | 211 | 711 | 161 | 739 | 639 | 239 | 212 | 712 | 162 | 738 | 638 | 238 | 213 | 713 | 163 | 737 | 637 | 237 | 214 | 714 | 164 | 736 | 636 | 236 | 215 | 715 | 165 |
761 | 111 | 840 | 61 | 40 | 890 | 762 | 112 | 839 | 62 | 39 | 889 | 763 | 113 | 838 | 63 | 38 | 888 | 764 | 114 | 837 | 64 | 37 | 887 | 765 | 115 | 836 | 65 | 36 | 886 |
16 | 785 | 85 | 816 | 866 | 135 | 17 | 784 | 84 | 817 | 867 | 134 | 18 | 783 | 83 | 818 | 868 | 133 | 19 | 782 | 82 | 819 | 869 | 132 | 20 | 781 | 81 | 820 | 870 | 131 |
285 | 185 | 666 | 685 | 266 | 616 | 284 | 184 | 667 | 684 | 267 | 617 | 283 | 183 | 668 | 683 | 268 | 618 | 282 | 182 | 669 | 682 | 269 | 619 | 281 | 181 | 670 | 681 | 270 | 620 |
466 | 416 | 366 | 385 | 485 | 585 | 467 | 417 | 367 | 384 | 484 | 584 | 468 | 418 | 368 | 383 | 483 | 583 | 469 | 419 | 369 | 382 | 482 | 582 | 470 | 420 | 370 | 381 | 481 | 581 |
435 | 566 | 516 | 535 | 335 | 316 | 434 | 567 | 517 | 534 | 334 | 317 | 433 | 568 | 518 | 533 | 333 | 318 | 432 | 569 | 519 | 532 | 332 | 319 | 431 | 570 | 520 | 531 | 331 | 320 |
735 | 635 | 235 | 216 | 716 | 166 | 734 | 634 | 234 | 217 | 717 | 167 | 733 | 633 | 233 | 218 | 718 | 168 | 732 | 632 | 232 | 219 | 719 | 169 | 731 | 631 | 231 | 220 | 720 | 170 |
766 | 116 | 835 | 66 | 35 | 885 | 767 | 117 | 834 | 67 | 34 | 884 | 768 | 118 | 833 | 68 | 33 | 883 | 769 | 119 | 832 | 69 | 32 | 882 | 770 | 120 | 831 | 70 | 31 | 881 |
21 | 780 | 80 | 821 | 871 | 130 | 22 | 779 | 79 | 822 | 872 | 129 | 23 | 778 | 78 | 823 | 873 | 128 | 24 | 777 | 77 | 824 | 874 | 127 | 25 | 776 | 76 | 825 | 875 | 126 |
280 | 180 | 671 | 680 | 271 | 621 | 279 | 179 | 672 | 679 | 272 | 622 | 278 | 178 | 673 | 678 | 273 | 623 | 277 | 177 | 674 | 677 | 274 | 624 | 276 | 176 | 675 | 676 | 275 | 625 |
471 | 421 | 371 | 380 | 480 | 580 | 472 | 422 | 372 | 379 | 479 | 579 | 473 | 423 | 373 | 378 | 478 | 578 | 474 | 424 | 374 | 377 | 477 | 577 | 475 | 425 | 375 | 376 | 476 | 576 |
430 | 571 | 521 | 530 | 330 | 321 | 429 | 572 | 522 | 529 | 329 | 322 | 428 | 573 | 523 | 528 | 328 | 323 | 427 | 574 | 524 | 527 | 327 | 324 | 426 | 575 | 525 | 526 | 326 | 325 |
730 | 630 | 230 | 221 | 721 | 171 | 729 | 629 | 229 | 222 | 722 | 172 | 728 | 628 | 228 | 223 | 723 | 173 | 727 | 627 | 227 | 224 | 724 | 174 | 726 | 626 | 226 | 225 | 725 | 175 |
771 | 121 | 830 | 71 | 30 | 880 | 772 | 122 | 829 | 72 | 29 | 879 | 773 | 123 | 828 | 73 | 28 | 878 | 774 | 124 | 827 | 74 | 27 | 877 | 775 | 125 | 826 | 75 | 26 | 876 |
Each 1/5 row/column/diagonal gives 1/5 of the magic sum and the 30x30 magic square is 6x6 compact. The numbers are in sequence in the 30x30 magic square following the numbers in the 6x6 squares from top left to right and down and back.
I have used composite method, proportional (1) to construct
8x8, 9x9, 12x12a, 12x12b, 15x15a, 15x15b, 16x16a, 16x16b, 18x18, 20x20a, 20x20b, 21x21a, 21x21b, 24x24a, 24x24b, 24x24c, 27x27a, 27x27b, 28x28a, 28x28b, 30x30a, 30x30b,32x32a, 32x32b and 32x32c