You can transform a 8x8 square with consecutive numbers into a Franklin panmagic 8x8 square in the following 5 steps. Swap each time 'yellow' and 'red':
# |
* |
* |
# |
||||||||||||||||||||||||
1 |
9 |
17 |
25 |
33 |
41 |
49 |
57 |
1 |
9 |
57 |
49 |
33 |
41 |
25 |
17 |
1 |
9 |
57 |
49 |
33 |
41 |
25 |
17 |
||||
2 |
10 |
18 |
26 |
34 |
42 |
50 |
58 |
2 |
10 |
58 |
50 |
34 |
42 |
26 |
18 |
2 |
10 |
58 |
50 |
34 |
42 |
26 |
18 |
||||
3 |
11 |
19 |
27 |
35 |
43 |
51 |
59 |
# |
3 |
11 |
59 |
51 |
35 |
43 |
27 |
19 |
8 |
16 |
64 |
56 |
40 |
48 |
32 |
24 |
|||
4 |
12 |
20 |
28 |
36 |
44 |
52 |
60 |
* |
4 |
12 |
60 |
52 |
36 |
44 |
28 |
20 |
7 |
15 |
63 |
55 |
39 |
47 |
31 |
23 |
|||
5 |
13 |
21 |
29 |
37 |
45 |
53 |
61 |
5 |
13 |
61 |
53 |
37 |
45 |
29 |
21 |
5 |
13 |
61 |
53 |
37 |
45 |
29 |
21 |
||||
6 |
14 |
22 |
30 |
38 |
46 |
54 |
62 |
6 |
14 |
62 |
54 |
38 |
46 |
30 |
22 |
6 |
14 |
62 |
54 |
38 |
46 |
30 |
22 |
||||
7 |
15 |
23 |
31 |
39 |
47 |
55 |
63 |
* |
7 |
15 |
63 |
55 |
39 |
47 |
31 |
23 |
4 |
12 |
60 |
52 |
36 |
44 |
28 |
20 |
|||
8 |
16 |
24 |
32 |
40 |
48 |
56 |
64 |
# |
8 |
16 |
64 |
56 |
40 |
48 |
32 |
24 |
3 |
11 |
59 |
51 |
35 |
43 |
27 |
19 |
|||
1 |
16 |
57 |
56 |
33 |
48 |
25 |
24 |
1 |
16 |
57 |
56 |
33 |
48 |
25 |
24 |
1 |
16 |
57 |
56 |
33 |
48 |
25 |
24 |
||||
2 |
10 |
58 |
50 |
34 |
42 |
26 |
18 |
58 |
50 |
2 |
10 |
26 |
18 |
34 |
42 |
63 |
50 |
7 |
10 |
31 |
18 |
39 |
42 |
||||
8 |
9 |
64 |
49 |
40 |
41 |
32 |
17 |
8 |
9 |
64 |
49 |
40 |
41 |
32 |
17 |
8 |
9 |
64 |
49 |
40 |
41 |
32 |
17 |
||||
7 |
15 |
63 |
55 |
39 |
47 |
31 |
23 |
63 |
55 |
7 |
15 |
31 |
23 |
39 |
47 |
58 |
55 |
2 |
15 |
26 |
23 |
34 |
47 |
||||
5 |
12 |
61 |
52 |
37 |
44 |
29 |
20 |
5 |
12 |
61 |
52 |
37 |
44 |
29 |
20 |
5 |
12 |
61 |
52 |
37 |
44 |
29 |
20 |
||||
6 |
14 |
62 |
54 |
38 |
46 |
30 |
22 |
62 |
54 |
6 |
14 |
30 |
22 |
38 |
46 |
59 |
54 |
3 |
14 |
27 |
22 |
35 |
46 |
||||
4 |
13 |
60 |
53 |
36 |
45 |
28 |
21 |
4 |
13 |
60 |
53 |
36 |
45 |
28 |
21 |
4 |
13 |
60 |
53 |
36 |
45 |
28 |
21 |
||||
3 |
11 |
59 |
51 |
35 |
43 |
27 |
19 |
59 |
51 |
3 |
11 |
27 |
19 |
35 |
43 |
62 |
51 |
6 |
11 |
30 |
19 |
38 |
43 |
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