Use the ultra magic 9x9 square and it's row grid to construct the fifth level of the pandiagonal & compact 9x9x9 cube. To construct
the remaining levels we use the diagonal shifted versions of the ultra magic 9x9 square and the diagonal shifted versions of it's row grid (in reversed order):
(1) shifted version 9x9 |
row grid (9) |
9x9x9 magic cube, level 1 |
||||||||||||||||||||||||||||
41 |
27 |
60 |
43 |
20 |
62 |
39 |
22 |
55 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
284 |
27 |
384 |
691 |
425 |
548 |
120 |
589 |
217 |
||||
75 |
31 |
10 |
77 |
36 |
15 |
79 |
29 |
17 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
156 |
598 |
172 |
320 |
36 |
339 |
727 |
434 |
503 |
||||
52 |
2 |
71 |
48 |
4 |
64 |
50 |
9 |
69 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
700 |
407 |
557 |
129 |
571 |
226 |
293 |
9 |
393 |
||||
59 |
45 |
24 |
61 |
38 |
26 |
57 |
40 |
19 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
302 |
45 |
348 |
709 |
443 |
512 |
138 |
607 |
181 |
||||
12 |
76 |
28 |
14 |
81 |
33 |
16 |
74 |
35 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
93 |
643 |
190 |
257 |
81 |
357 |
664 |
479 |
521 |
||||
70 |
47 |
8 |
66 |
49 |
1 |
68 |
54 |
6 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
718 |
452 |
494 |
147 |
616 |
163 |
311 |
54 |
330 |
||||
23 |
63 |
42 |
25 |
56 |
44 |
21 |
58 |
37 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
266 |
63 |
366 |
673 |
461 |
530 |
102 |
625 |
199 |
||||
30 |
13 |
73 |
32 |
18 |
78 |
34 |
11 |
80 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
111 |
580 |
235 |
275 |
18 |
402 |
682 |
416 |
566 |
||||
7 |
65 |
53 |
3 |
67 |
46 |
5 |
72 |
51 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
655 |
470 |
539 |
84 |
634 |
208 |
248 |
72 |
375 |
||||
(2) Shifted version 9x9 |
row grid (8) |
9x9x9 magic cube, level 2 |
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51 |
7 |
65 |
53 |
3 |
67 |
46 |
5 |
72 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
618 |
169 |
308 |
53 |
327 |
715 |
451 |
491 |
153 |
||||
55 |
41 |
27 |
60 |
43 |
20 |
62 |
39 |
22 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
460 |
527 |
108 |
627 |
205 |
263 |
62 |
363 |
670 |
||||
17 |
75 |
31 |
10 |
77 |
36 |
15 |
79 |
29 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
17 |
399 |
679 |
415 |
563 |
117 |
582 |
241 |
272 |
||||
69 |
52 |
2 |
71 |
48 |
4 |
64 |
50 |
9 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
636 |
214 |
245 |
71 |
372 |
652 |
469 |
536 |
90 |
||||
19 |
59 |
45 |
24 |
61 |
38 |
26 |
57 |
40 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
424 |
545 |
126 |
591 |
223 |
281 |
26 |
381 |
688 |
||||
35 |
12 |
76 |
28 |
14 |
81 |
33 |
16 |
74 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
35 |
336 |
724 |
433 |
500 |
162 |
600 |
178 |
317 |
||||
6 |
70 |
47 |
8 |
66 |
49 |
1 |
68 |
54 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
573 |
232 |
290 |
8 |
390 |
697 |
406 |
554 |
135 |
||||
37 |
23 |
63 |
42 |
25 |
56 |
44 |
21 |
58 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
442 |
509 |
144 |
609 |
187 |
299 |
44 |
345 |
706 |
||||
80 |
30 |
13 |
73 |
32 |
18 |
78 |
34 |
11 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
80 |
354 |
661 |
478 |
518 |
99 |
645 |
196 |
254 |
||||
(3) Shifted version 9x9 |
row grid (7) |
9x9x9 magic cube, level 3 |
||||||||||||||||||||||||||||
11 |
80 |
30 |
13 |
73 |
32 |
18 |
78 |
34 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
497 |
161 |
597 |
175 |
316 |
32 |
342 |
726 |
439 |
||||
72 |
51 |
7 |
65 |
53 |
3 |
67 |
46 |
5 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
396 |
699 |
412 |
551 |
134 |
570 |
229 |
289 |
5 |
||||
22 |
55 |
41 |
27 |
60 |
43 |
20 |
62 |
39 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
184 |
298 |
41 |
351 |
708 |
448 |
506 |
143 |
606 |
||||
29 |
17 |
75 |
31 |
10 |
77 |
36 |
15 |
79 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
515 |
98 |
642 |
193 |
253 |
77 |
360 |
663 |
484 |
||||
9 |
69 |
52 |
2 |
71 |
48 |
4 |
64 |
50 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
333 |
717 |
457 |
488 |
152 |
615 |
166 |
307 |
50 |
||||
40 |
19 |
59 |
45 |
24 |
61 |
38 |
26 |
57 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
202 |
262 |
59 |
369 |
672 |
466 |
524 |
107 |
624 |
||||
74 |
35 |
12 |
76 |
28 |
14 |
81 |
33 |
16 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
560 |
116 |
579 |
238 |
271 |
14 |
405 |
681 |
421 |
||||
54 |
6 |
70 |
47 |
8 |
66 |
49 |
1 |
68 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
378 |
654 |
475 |
533 |
89 |
633 |
211 |
244 |
68 |
||||
58 |
37 |
23 |
63 |
42 |
25 |
56 |
44 |
21 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
220 |
280 |
23 |
387 |
690 |
430 |
542 |
125 |
588 |
||||
|
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(4) Shifted version 9x9 |
row grid (6) |
9x9x9 magic cube, level 4 |
||||||||||||||||||||||||||||
21 |
58 |
37 |
23 |
63 |
42 |
25 |
56 |
44 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
669 |
463 |
523 |
104 |
630 |
204 |
268 |
56 |
368 |
||||
34 |
11 |
80 |
30 |
13 |
73 |
32 |
18 |
78 |
3 |
0 |
4 |
8 |
5 |
6 |
1 |
7 |
2 |
277 |
11 |
404 |
678 |
418 |
559 |
113 |
585 |
240 |
||||
5 |
72 |
51 |
7 |
65 |
53 |
3 |
67 |
46 |
1 |
7 |
2 |
3 |
0 |
4 |
8 |
5 |
6 |
86 |
639 |
213 |
250 |
65 |
377 |
651 |
472 |
532 |
||||
39 |
22 |
55 |
41 |
27 |
60 |
43 |
20 |
62 |
8 |
5 |
6 |
1 |
7 |
2 |
3 |
0 |
4 |
687 |
427 |
541 |
122 |
594 |
222 |
286 |
20 |
386 |
||||
79 |
29 |
17 |
75 |
31 |
10 |
77 |
36 |
15 |
3 |
0 |
4 |
8 |
5 |
6 |