See below how to use a 4x4 panmagic square to construct a most perfect 4x4x4 magic cube:
1x number |
+ 4x number |
= |
first level 4x4x4 cube |
|||||||||||||
1 |
8 |
13 |
12 |
1 |
0 |
3 |
2 |
17 |
8 |
61 |
44 |
|||||
15 |
10 |
3 |
6 |
0 |
2 |
1 |
3 |
15 |
42 |
19 |
54 |
|||||
4 |
5 |
16 |
9 |
3 |
1 |
2 |
0 |
52 |
21 |
48 |
9 |
|||||
14 |
11 |
2 |
7 |
2 |
3 |
0 |
1 |
46 |
59 |
2 |
23 |
|||||
1x number |
+ 4x number |
= |
second level 4x4x4 cube |
|||||||||||||
10 |
15 |
6 |
3 |
0 |
2 |
1 |
3 |
10 |
47 |
22 |
51 |
|||||
8 |
1 |
12 |
13 |
2 |
3 |
0 |
1 |
40 |
49 |
12 |
29 |
|||||
11 |
14 |
7 |
2 |
1 |
0 |
3 |
2 |
27 |
14 |
55 |
34 |
|||||
5 |
4 |
9 |
16 |
3 |
1 |
2 |
0 |
53 |
20 |
41 |
16 |
|||||
1x number |
+ 4x number |
= |
third level 4x4x4 cube |
|||||||||||||
16 |
9 |
4 |
5 |
3 |
1 |
2 |
0 |
64 |
25 |
36 |
5 |
|||||
2 |
7 |
14 |
11 |
1 |
0 |
3 |
2 |
18 |
7 |
62 |
43 |
|||||
13 |
12 |
1 |
8 |
2 |
3 |
0 |
1 |
45 |
60 |
1 |
24 |
|||||
3 |
6 |
15 |
10 |
0 |
2 |
1 |
3 |
3 |
38 |
31 |
58 |
|||||
1x number |
+ 4x number |
= |
fourth level 4x4x4 cube |
|||||||||||||
7 |
2 |
11 |
14 |
2 |
3 |
0 |
1 |
39 |
50 |
11 |
30 |
|||||
9 |
16 |
5 |
4 |
3 |
1 |
2 |
0 |
57 |
32 |
37 |
4 |
|||||
6 |
3 |
10 |
15 |
0 |
2 |
1 |
3 |
6 |
35 |
26 |
63 |
|||||
12 |
13 |
8 |
1 |
1 |
0 |
3 |
2 |
28 |
13 |
56 |
33 |
Use instead of a panmagic 4x4 square (= group 1) a symmetric 4x4 square (= group 3; Dürer magic) or the vertical oriented magic
4x4 squares from group 6 to construct a most perfect 4x4x4 magic cube; see download below.