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