Basic key method (ultra magic)
See below the key to construct an ultra magic 8x8 square. Notify that the second grid is a reflection of the first grid.
1x number + 8x [number -/- 1] = Ultra magic 8x8 square
|
1 |
7 |
4 |
6 |
6 |
4 |
7 |
1 |
1 |
8 |
1 |
8 |
1 |
8 |
1 |
8 |
1 |
63 |
4 |
62 |
6 |
60 |
7 |
57 |
||||
|
8 |
2 |
5 |
3 |
3 |
5 |
2 |
8 |
7 |
2 |
7 |
2 |
7 |
2 |
7 |
2 |
56 |
10 |
53 |
11 |
51 |
13 |
50 |
16 |
||||
|
1 |
7 |
4 |
6 |
6 |
4 |
7 |
1 |
4 |
5 |
4 |
5 |
4 |
5 |
4 |
5 |
25 |
39 |
28 |
38 |
30 |
36 |
31 |
33 |
||||
|
8 |
2 |
5 |
3 |
3 |
5 |
2 |
8 |
6 |
3 |
6 |
3 |
6 |
3 |
6 |
3 |
48 |
18 |
45 |
19 |
43 |
21 |
42 |
24 |
||||
|
1 |
7 |
4 |
6 |
6 |
4 |
7 |
1 |
6 |
3 |
6 |
3 |
6 |
3 |
6 |
3 |
41 |
23 |
44 |
22 |
46 |
20 |
47 |
17 |
||||
|
8 |
2 |
5 |
3 |
3 |
5 |
2 |
8 |
4 |
5 |
4 |
5 |
4 |
5 |
4 |
5 |
32 |
34 |
29 |
35 |
27 |
37 |
26 |
40 |
||||
|
1 |
7 |
4 |
6 |
6 |
4 |
7 |
1 |
7 |
2 |
7 |
2 |
7 |
2 |
7 |
2 |
49 |
15 |
52 |
14 |
54 |
12 |
55 |
9 |
||||
|
8 |
2 |
5 |
3 |
3 |
5 |
2 |
8 |
1 |
8 |
1 |
8 |
1 |
8 |
1 |
8 |
8 |
58 |
5 |
59 |
3 |
61 |
2 |
64 |
This 8x8 magic square is panmagic, 2x2 compact, symmetric and each 1/2 row/column gives 1/2 of the magic sum.
You can use this key to construct magic squares which are a multiple of 4 from 8x8 to infinity. See 8x8, 12x12, 16x16, 20x20, 24x24, 28x28 and 32x32
