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How to make perfect magic squares & cubes
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Basic pattern method (4)
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How to use a panmagic 4x4 square to produce a most perfect magic
20x20 square
 
It is also possible to use (the pattern of) each random chosen panmagic 4x4 square to produce a
most perfect magic 20x20 square.
 
You need 25x the same panmagic 4x4 square (see page ‘panmagic 4x4 square’) and 2 fixed 20x20
grids.
 
 
1x digit from 20x20 grid of 25x the same panmagic 4x4 square
 
 
 
 
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
15
6
12
1
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
4
9
7
14
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
5
16
2
11
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
10
3
13
8
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
+ 16x digit from fixed grid1
 
 
 
 
 
 
 
 
 
 
 
 
 
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
0
4
4
0
4
0
0
4
1
3
3
1
3
1
1
3
2
2
2
2
4
0
0
4
0
4
4
0
3
1
1
3
1
3
3
1
2
2
2
2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
+ 80x digit from fixed grid2
 
 
 
 
 
 
 
 
 
 
 
 
 
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
3
1
3
1
3
1
3
1
3
1