24x24x24 magic square

Diagonal 24x24x24 magic cube (Composite 5)

 

Use three grids to construct a 24x24x24 diagonal magic cube. The first grid consists of 64x diagonal 6x6x6 magic cube. The second grid consists of the 6x6 'blown up' 4x4 magic square (half of the levels consists of the inverse 4x4 magic square). The third grid consists of the numbers 0 up to 3. Take 1x number from first grid + 216x (number -/- 1) from second grid + 216x16x number from third grid. See below the grids and the result of the first level.

 

 

Take 1x number from first grid with 64x diagonal 6x6x6 magic cube [level 1]

109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107

 

 

+216x (number -/- 1) from second grid with 6x6 'blown up' 4x4 [level 1]

1 1 1 1 1 1 8 8 8 8 8 8 13 13 13 13 13 13 12 12 12 12 12 12
1 1 1 1 1 1 8 8 8 8 8 8 13 13 13 13 13 13 12 12 12 12 12 12
1 1 1 1 1 1 8 8 8 8 8 8 13 13 13 13 13 13 12 12 12 12 12 12
1 1 1 1 1 1 8 8 8 8 8 8 13 13 13 13 13 13 12 12 12 12 12 12
1 1 1 1 1 1 8 8 8 8 8 8 13 13 13 13 13 13 12 12 12 12 12 12
1 1 1 1 1 1 8 8 8 8 8 8 13 13 13 13 13 13 12 12 12 12 12 12
15 15 15 15 15 15 10 10 10 10 10 10 3 3 3 3 3 3 6 6 6 6 6 6
15 15 15 15 15 15 10 10 10 10 10 10 3 3 3 3 3 3 6 6 6 6 6 6
15 15 15 15 15 15 10 10 10 10 10 10 3 3 3 3 3 3 6 6 6 6 6 6
15 15 15 15 15 15 10 10 10 10 10 10 3 3 3 3 3 3 6 6 6 6 6 6
15 15 15 15 15 15 10 10 10 10 10 10 3 3 3 3 3 3 6 6 6 6 6 6
15 15 15 15 15 15 10 10 10 10 10 10 3 3 3 3 3 3 6 6 6 6 6 6
4 4 4 4 4 4 5 5 5 5 5 5 16 16 16 16 16 16 9 9 9 9 9 9
4 4 4 4 4 4 5 5 5 5 5 5 16 16 16 16 16 16 9 9 9 9 9 9
4 4 4 4 4 4 5 5 5 5 5 5 16 16 16 16 16 16 9 9 9 9 9 9
4 4 4 4 4 4 5 5 5 5 5 5 16 16 16 16 16 16 9 9 9 9 9 9
4 4 4 4 4 4 5 5 5 5 5 5 16 16 16 16 16 16 9 9 9 9 9 9
4 4 4 4 4 4 5 5 5 5 5 5 16 16 16 16 16 16 9 9 9 9 9 9
14 14 14 14 14 14 11 11 11 11 11 11 2 2 2 2 2 2 7 7 7 7 7 7
14 14 14 14 14 14 11 11 11 11 11 11 2 2 2 2 2 2 7 7 7 7 7 7
14 14 14 14 14 14 11 11 11 11 11 11 2 2 2 2 2 2 7 7 7 7 7 7
14 14 14 14 14 14 11 11 11 11 11 11 2 2 2 2 2 2 7 7 7 7 7 7
14 14 14 14 14 14 11 11 11 11 11 11 2 2 2 2 2 2 7 7 7 7 7 7
14 14 14 14 14 14 11 11 11 11 11 11 2 2 2 2 2 2 7 7 7 7 7 7

 

 

+216x16x number from third grid with numbers 0 up to 3 [level 1]

0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0

 

 

= 24x24x24 diagonal magic cube [level 1]

109 143 76 123 88 112 1621 1655 1588 1635 1600 1624 13069 13103 13036 13083 13048 13072 12853 12887 12820 12867 12832 12856
87 156 49 170 63 126 1599 1668 1561 1682 1575 1638 13047 13116 13009 13130 13023 13086 12831 12900 12793 12914 12807 12870
140 174 52 150 53 82 1652 1686 1564 1662 1565 1594 13100 13134 13012 13110 13013 13042 12884 12918 12796 12894 12797 12826
75 66 182 51 139 138 1587 1578 1694 1563 1651 1650 13035 13026 13142 13011 13099 13098 12819 12810 12926 12795 12883 12882
136 40 148 65 176 86 1648 1552 1660 1577 1688 1598 13096 13000 13108 13025 13136 13046 12880 12784 12892 12809 12920 12830
104 72 144 92 132 107 1616 1584 1656 1604 1644 1619 13064 13032 13104 13052 13092 13067 12848 12816 12888 12836 12876 12851
13501 13535 13468 13515 13480 13504 12421 12455 12388 12435 12400 12424 541 575 508 555 520 544 1189 1223 1156 1203 1168 1192
13479 13548 13441 13562 13455 13518 12399 12468 12361 12482 12375 12438 519 588 481 602 495 558 1167 1236 1129 1250 1143 1206
13532 13566 13444 13542 13445 13474 12452 12486 12364 12462 12365 12394 572 606 484 582 485 514 1220 1254 1132 1230 1133 1162
13467 13458 13574 13443 13531 13530 12387 12378 12494 12363 12451 12450 507 498 614 483 571 570 1155 1146 1262 1131 1219 1218
13528 13432 13540 13457 13568 13478 12448 12352 12460 12377 12488 12398 568 472 580 497 608 518 1216 1120 1228 1145 1256 1166
13496 13464 13536 13484 13524 13499 12416 12384 12456 12404 12444 12419 536 504 576 524 564 539 1184 1152 1224 1172 1212 1187
757 791 724 771 736 760 973 1007 940 987 952 976 13717 13751 13684 13731 13696 13720 12205 12239 12172 12219 12184 12208
735 804 697 818 711 774 951 1020 913 1034 927 990 13695 13764 13657 13778 13671 13734 12183 12252 12145 12266 12159 12222
788 822 700 798 701 730 1004 1038 916 1014 917 946 13748 13782 13660 13758 13661 13690 12236 12270 12148 12246 12149 12178
723 714 830 699 787 786 939 930 1046 915 1003 1002 13683 13674 13790 13659 13747 13746 12171 12162 12278 12147 12235 12234
784 688 796 713 824 734 1000 904 1012 929 1040 950 13744 13648 13756 13673 13784 13694 12232 12136 12244 12161 12272 12182
752 720 792 740 780 755 968 936 1008 956 996 971 13712 13680 13752 13700 13740 13715 12200 12168 12240 12188 12228 12203
13285 13319 13252 13299 13264 13288 12637 12671 12604 12651 12616 12640 325 359 292 339 304 328 1405 1439 1372 1419 1384 1408
13263 13332 13225 13346 13239 13302 12615 12684 12577 12698 12591 12654 303 372 265 386 279 342 1383 1452 1345 1466 1359 1422
13316 13350 13228 13326 13229 13258 12668 12702 12580 12678 12581 12610 356 390 268 366 269 298 1436 1470 1348 1446 1349 1378
13251 13242 13358 13227 13315 13314 12603 12594 12710 12579 12667 12666 291 282 398 267 355 354 1371 1362 1478 1347 1435 1434
13312 13216 13324 13241 13352 13262 12664 12568 12676 12593 12704 12614 352 256 364 281 392 302 1432 1336 1444 1361 1472 1382
13280 13248 13320 13268 13308 13283 12632 12600 12672 12620 12660 12635 320 288 360 308 348 323 1400 1368 1440 1388 1428 1403

 

 

The rows/columns/diagonals in each level give the magic sum and 1/4 pillars, 1/4 diagonals and 1/4 (main) triagonals through the levels give 1/4 of the magic sum.

 

See for all levels and check of all numbers are in the magic cube and addition of the numbers give the right magic sum, the download below.

 

With method composite 5 you use a magic cube of order A and a magic square of order B to construct a magic cube of order AxB. See on this website the construction of:

20x20x20 (pantriagonal), 24x24x24 (diagonal), 24x24x24 (pantriagonal),

28x28x28 (pantriagonal), 30x30x30, (diagonal) and 30x30x30 (pantriagonal)

 

Download
24x24x24, diagonal (C5).xlsx
Microsoft Excel werkblad 1.1 MB
Download
24x24x24 magic cube