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How to make perfect magic squares & cubes
The sky is the limit!!!
Basic pattern method (7a)
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How to use a panmagic 4x4 square to produce a most perfect magic
32x32 square
 
It is also possible to use a panmagic 4x4 square to produce a most perfect (Franklin pan)magic
32x32 square.
 
You need a panmagic 4x4 square (see page ‘panmagic 4x4 square’) and 2 fixed patterns.
 
 
1x digit from carpet of 8x8 the same panmagic 4x4 square
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8
3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13 3 6 12 13
16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2 16 9 7 2
5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11 5 4 14 11
10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8 10 15 1 8


+ 16x digit from fixed pattern 1
0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7
1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6
7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0
6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5
3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4
5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2
4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3
1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6
0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7
6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0
3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4
2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5
4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3
5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2
7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0
6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7
1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6
5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2
4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3
2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5
3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4
6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0
1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6
0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7