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How to make perfect magic squares & cubes
The sky is the limit!!!
extra magic 35x35 square
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How to produce an extra magic 35x35 square


Put the digits 0 up to 34 in the first row of the first as well as the second grid. Take care that each 1/7
row gives the sum of 85 (see rectangle 7x5).


  Rectangle 7x5
0
7
24
20
34
85
1
8
16
27
33
85
2
23
19
9
32
85
3
26
15
10
31
85
4
22
18
11
30
85
5
12
14
25
29
85
6
21
13
17
28
85


Produce the first five rows of the first as well as the second grid. Shift the digits of row 2 up to 5 of the
first grid two places to the right. Shift the digits of row 2 up to 5 of the second grid two places to the left
(see method on page 'panmagic 5x5 square').


The first five rows of the first grid (shift the digits of the first row each time two places to the right)
0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28
20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13
7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6
34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17
24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21



The first five rows of the second grid (shift the digits of the first row each time two places to the left)
0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28
24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21
34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17
7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6
20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13


Finish the two grids by shifting the top seven 5x5 squares. Shift the top seven 5x5 squares of the first grid
to the left. Shift the top seven 5x5 squares of the second grid to the right (see colours).


 +1x digit+1 from the first grid
0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28
20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13
7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6
34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17
24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21
1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34
27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24
8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0
33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20
16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7
2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33
9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16
23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1
32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27
19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8
3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32
10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19
26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2
31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9
15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23
4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31
11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15
22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3
30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10
18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26
5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30
25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18
12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4
29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11
14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22
6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29
17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14
21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5
28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25
13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12



+35x digit from the second grid
0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28
24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21
34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17
7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6
20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13
6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29
13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12
28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25
21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5
17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14
5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30
14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22
29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11
12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4
25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18
4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32 3 26 15 10 31
18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23 15 10 31 3 26
30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9 31 3 26 15 10
22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2 26 15 10 31 3
11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19 10 31 3 26 15
3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33 2 23 19 9 32
15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8 19 9 32 2 23
31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27 32 2 23 19 9
26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1 23 19 9 32 2
10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16 9 32 2 23 19
2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34 1 8 16 27 33
19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7 16 27 33 1 8
32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20 33 1 8 16 27
23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0 8 16 27 33 1
9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24 27 33 1 8 16
1 8 16 27 33 2 23 19 9 32 3 26 15 10 31 4 22 18 11 30 5 12 14 25 29 6 21 13 17 28 0 7 24 20 34
16 27 33 1 8 19 9 32 2 23 15 10 31 3 26 18 11 30 4 22 14 25 29 5 12 13 17 28 6 21 24 20 34 0 7
33 1 8 16 27 32 2 23 19 9 31 3 26 15 10 30 4 22 18 11 29 5 12 14 25 28 6 21 13 17 34 0 7 24 20
8 16 27 33 1 23 19 9 32 2 26 15 10 31 3 22 18 11 30 4 12 14 25 29 5 21 13 17 28 6 7 24 20 34 0
27 33 1 8 16 9 32 2 23 19 10 31 3 26 15 11 30 4 22 18 25 29 5 12 14 17 28 6 21 13 20 34 0 7 24



= Extra magic 35x35 square
1 253 865 721 1225 37 289 577 973 1189 73 829 685 325 1153 109 937 541 361 1117 145 793 649 397 1081 181 433 505 901 1045 217 757 469 613 1009
861 735 1191 8 270 588 979 1157 44 297 675 348 1123 94 825 536 382 1089 132 926 642 416 1055 163 789 516 905 1021 188 435 473 624 987 232 749
1198 25 266 875 701 1164 52 308 594 947 1144 90 815 698 318 1112 121 921 557 354 1073 159 782 661 390 1028 190 446 520 881 1002 224 753 484 602
280 841 708 1215 21 314 562 954 1172 63 838 668 339 1140 80 942 529 377 1101 116 801 635 408 1069 152 450 496 888 1030 201 764 462 617 994 228
725 1211 35 246 848 962 1183 69 282 569 335 1130 103 808 689 366 1096 137 914 552 404 1062 171 775 653 890 1041 205 426 503 609 998 239 742 477
212 744 472 623 1014 3 269 860 710 1223 39 307 576 956 1187 75 828 684 327 1151 111 923 540 376 1115 147 792 644 403 1079 176 428 515 896 1050
483 629 982 219 752 850 733 1193 24 265 571 977 1159 62 296 677 346 1125 93 824 551 380 1091 118 925 648 414 1057 162 784 511 910 1016 183 445
989 227 763 489 597 1214 20 255 873 703 1182 51 291 592 949 1143 89 817 696 320 1098 120 936 555 356 1072 154 788 659 392 1023 200 441 525 876
769 457 604 997 238 278 843 724 1210 10 312 564 972 1171 46 836 670 338 1139 82 940 531 363 1100 131 799 637 407 1064 158 455 491 883 1040 196
612 1008 244 737 464 720 1200 33 248 864 961 1166 67 284 587 334 1132 101 810 688 365 1111 135 916 538 399 1068 169 777 652 900 1036 210 421 498
178 444 510 885 1048 214 762 471 606 1012 5 268 859 712 1221 41 293 575 971 1185 77 827 679 333 1149 106 918 550 371 1120 142 779 647 413 1084
500 908 1018 199 440 466 627 984 237 751 852 731 1195 23 264 586 975 1161 48 295 683 344 1127 92 819 546 385 1086 113 935 658 419 1052 149 787
1039 195 430 523 878 1007 226 746 487 599 1213 19 257 871 705 1168 50 306 590 951 1142 84 823 694 322 1093 130 931 560 351 1059 157 798 664 387
453 493 899 1035 185 767 459 622 996 221 276 845 723 1209 12 310 566 958 1170 61 834 672 337 1134 88 945 526 358 1110 126 804 632 394 1067 168
895 1025 208 423 514 611 991 242 739 482 719 1202 31 250 863 960 1181 65 286 573 329 1138 99 812 687 375 1106 140 911 533 402 1078 174 772 639
144 797 646 396 1082 180 443 509 887 1046 216 748 470 621 1010 7 267 854 718 1219 36 288 585 966 1190 72 814 682 343 1154 108 934 545 360 1118
641 417 1054 167 786 502 906 1020 198 439 481 625 986 223 750 858 729 1197 22 259 581 980 1156 43 305 693 349 1122 79 822 535 383 1088 129 930
1077 156 781 662 389 1038 194 432 521 880 993 225 761 485 601 1212 14 263 869 707 1163 60 301 595 946 1129 87 833 699 317 1109 125 920 558 353
802 634 412 1066 151 451 495 898 1034 187 765 461 608 995 236 274 847 722 1204 18 315 561 953 1180 56 839 667 324 1137 98 943 528 374 1105 115
401 1061 172 774 657 894 1027 206 425 513 610 1006 240 741 468 714 1208 29 252 862 970 1176 70 281 568 332 1148 104 807 674 370 1095 138 913 549
110 933 544 362 1116 146 783 645 411 1080 182 442 504 893 1044 211 743 480 616 1015 2 254 857 728 1224 38 304 580 955 1188 74 832 681 326 1152
537 381 1090 128 929 656 415 1056 153 785 508 904 1022 197 434 476 630 981 218 760 868 734 1192 9 262 570 978 1158 59 300 676 347 1124 97 821
1108 124 922 556 355 1063 155 796 660 391 1037 189 438 519 882 988 235 756 490 596 1199 17 273 874 702 1179 55 290 593 948 1147 86 816 697 319
941 530 373 1104 117 800 636 398 1065 166 449 497 897 1029 193 770 456 603 1005 231 279 842 709 1207 28 313 563 969 1175 45 837 669 342 1136 81
369 1097 136 915 548 400 1076 170 776 643 889 1033 204 427 512 620 1001 245 736 463 717 1218 34 247 849 965 1165 68 283 584 331 1131 102 809 692
76 818 680 341 1150 112 932 539 368 1114 141 778 655 406 1085 177 429 507 903 1049 213 759 475 605 1013 4 272 856 711 1222 40 303 579 957 1186
691 345 1126 83 820 543 379 1092 127 924 651 420 1051 148 795 518 909 1017 184 437 465 628 983 234 755 851 732 1194 27 261 572 976 1160 58 299
1133 85 831 695 321 1107 119 928 554 357 1058 165 791 665 386 1024 192 448 524 877 1004 230 745 488 598 1217 16 256 872 704 1178 54 292 591 950
835 671 328 1135 96 939 532 372 1099 123 805 631 393 1075 161 454 492 884 1032 203 768 458 619 1000 220 277 844 727 1206 11 311 565 968 1174 47
330 1146 100 811 678 364 1103 134 917 547 410 1071 175 771 638 892 1043 209 422 499 615 990 243 738 479 716 1201 32 249 867 964 1167 66 285 583
42 302 574 963 1184 71 813 690 336 1155 107 919 542 378 1119 143 794 650 395 1083 179 447 506 886 1047 215 758 474 607 1011 6 258 855 726 1220
578 974 1162 57 294 686 350 1121 78 830 553 384 1087 114 927 640 418 1053 164 790 501 907 1019 202 436 467 626 985 233 754 866 730 1196 13 260
1177 49 298 589 952 1128 95 826 700 316 1094 122 938 559 352 1074 160 780 663 388 1042 191 431 522 879 1003 229 747 486 600 1203 15 271 870 706
309 567 967 1169 53 840 666 323 1145 91 944 527 359 1102 133 803 633 409 1070 150 452 494 902 1031 186 766 460 618 999 222 275 846 713 1205 26
959 1173 64 287 582 340 1141 105 806 673 367 1113 139 912 534 405 1060 173 773 654 891 1026 207 424 517 614 992 241 740 478 715 1216 30 251 853



Notify that each 1/7 row, 1/7 column and 1/7 diagonal gives 1/7 of the magic sum.


Download for analysis and construction in EXCEL:  extra magic 35x35 square



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Magic squares and cubes|Contact / guestbook|Most magic square per order|3x3 magic square|3x3 magic square, explanation|Sudoku method (1)|Sudoku method (2)|Sudoku method (3)|Pan magic 4x4 square|Pan magic 4x4 square, explanation|Pan magic 4x4 square, binary|Dürer & Franklin transformation|Transformation method|Transformation method, analysis|[ultra] pan magic 5x5 square|Pan magic 5x5 square, explanation|6x6 magic square|Ultra (pan)magic 8x8 square|Most perfect magic squares, explanation|8x8 most perfect magic squares, binary|Khajuraho method|Khajuraho method, explanation|Basic pattern method (1a)|Basic pattern method (1b)|Basic pattern method (2)|Basic pattern method (3a)|Basic pattern method (3b)|Basic pattern method (3c)|Basic pattern method (4)|Basic pattern method (5)|Basic pattern method (6)|Basic pattern method (7a)|Basic pattern method (7b)|Analysis Franklin panm. 8x8 (1)|Analysis Franklin panm. 8x8 (2)|Basic key method (1)|Basic key method (2)|Quadrant method (Willem Barink)|Quadrant method group 1 up to 5|Quadrant method group 6 up to 10|Quadrant method group 11 up to 19|[ultra] pan magic 9x9 square (1)|pan magic 9x9 square (2)|pan magic 9x9 square (3)|3x extra magic 9x9 square|bimagic 9x9 square|10x10 magic square|Composite 12x12 magic square|14x14 magic square|[Ultra] pan magic 15x15 square|3x extra magic 15x15 square|The perfect magic square|3x extra magic 18x18 square|Composite 24x24 magic square|Ultra pan magic 25x25 square (1)|Ultra pan magic 25x25 square (2)|Ultra bimagic 25x25 square|[ultra] pan magic 27x27 square|[ultra] pan magic 35x35 square|extra magic 35x35 square|Bordered squares|Inlaid square (1)|Inlaid square (2)|Each magic sum|Water retention challenge|Most magic cube per order|Most magic 4x4x4 cube|symmetric & semi (pan)magic 5x5x5 cube|Symmetric & panmagic 7x7x7 cube|Perfect (Nasik) & compact 8x8x8 cube|[More than] perfect magic 9x9x9 cube|Perfect (Nasik) magic 11x11x11 cube|Perfect (Nasik) magic 15x15x15 cube|Trick with 8x8 bimagic square|Perfect (Nasik) 16x16x16, step 1&2|Perfect (Nasik) 16x16x16, step 3&4|Perfect (Nasik) 16x16x16, result|Favorite Links