Most perfect transformation
It takes 5 steps to transform a 4x4 square with consecutive numbers into the 3 basic panmagic 4x4 squares. Swap each time the numbers from 'yellow' and 'red' with each other.
3x panmagic 4x4
|
1 |
5 |
9 |
13 |
1 |
5 |
13 |
9 |
1 |
5 |
13 |
9 |
1 |
8 |
13 |
12 |
1 |
8 |
13 |
12 |
1 |
8 |
13 |
12 |
|||||
|
2 |
6 |
10 |
14 |
2 |
6 |
14 |
10 |
2 |
6 |
14 |
10 |
2 |
6 |
14 |
10 |
14 |
10 |
2 |
6 |
15 |
10 |
3 |
6 |
|||||
|
3 |
7 |
11 |
15 |
3 |
7 |
15 |
11 |
4 |
8 |
16 |
12 |
4 |
5 |
16 |
9 |
4 |
5 |
16 |
12 |
4 |
5 |
16 |
9 |
|||||
|
4 |
8 |
12 |
16 |
4 |
8 |
16 |
12 |
3 |
7 |
15 |
11 |
3 |
7 |
15 |
11 |
15 |
11 |
3 |
7 |
14 |
11 |
2 |
7 |
|||||
|
1 |
3 |
9 |
11 |
1 |
3 |
11 |
9 |
1 |
3 |
11 |
9 |
1 |
8 |
11 |
14 |
1 |
8 |
11 |
14 |
1 |
8 |
11 |
14 |
|||||
|
2 |
4 |
10 |
12 |
2 |
4 |
12 |
10 |
2 |
4 |
12 |
10 |
2 |
4 |
12 |
10 |
12 |
10 |
2 |
4 |
15 |
10 |
5 |
4 |
|||||
|
5 |
7 |
13 |
15 |
5 |
7 |
15 |
13 |
6 |
8 |
16 |
14 |
6 |
3 |
16 |
9 |
6 |
3 |
16 |
9 |
6 |
3 |
16 |
9 |
|||||
|
6 |
8 |
14 |
16 |
6 |
8 |
16 |
14 |
5 |
7 |
15 |
13 |
5 |
7 |
15 |
13 |
15 |
13 |
5 |
7 |
12 |
13 |
2 |
7 |
|||||
|
1 |
2 |
9 |
10 |
1 |
2 |
10 |
9 |
1 |
2 |
10 |
9 |
1 |
8 |
10 |
15 |
1 |
8 |
10 |
15 |
1 |
8 |
10 |
15 |
|||||
|
3 |
4 |
11 |
12 |
3 |
4 |
12 |
11 |
3 |
4 |
12 |
11 |
3 |
4 |
12 |
11 |
12 |
11 |
3 |
4 |
14 |
11 |
5 |
4 |
|||||
|
5 |
6 |
13 |
14 |
5 |
6 |
14 |
13 |
7 |
8 |
16 |
15 |
7 |
2 |
16 |
9 |
7 |
2 |
16 |
9 |
7 |
2 |
16 |
9 |
|||||
|
7 |
8 |
15 |
16 |
7 |
8 |
16 |
15 |
5 |
6 |
14 |
13 |
5 |
6 |
14 |
13 |
14 |
13 |
5 |
6 |
12 |
13 |
3 |
6 |
Use this method to construct magic squares of order is multiple of 4 from 4x4 to infinity. See 4x4, 8x8, 12x12, 16x16, 20x20, 24x24, 28x28, 32x32
