6 groups of Franklin panmagic 8x8 squares
Introduction
Excluding rotating and/or mirroring there are 368.640 Franklin panmagic 8x8 squares. In each of the Franklin panmagic 8x8 squares you can find the panmagic 4x4 square. You can distinguish 6 different groups.
Group I [4x the same panmagic 4x4 square = Sudoku method 3]
Franklin panmagic 8x8 square 4x same 4x4 panmagic square Sudoku grid
|
63 |
17 |
40 |
10 |
47 |
1 |
56 |
26 |
15 |
1 |
8 |
10 |
15 |
1 |
8 |
10 |
3 |
1 |
2 |
0 |
2 |
0 |
3 |
1 |
||||
|
6 |
44 |
29 |
51 |
22 |
60 |
13 |
35 |
6 |
12 |
13 |
3 |
6 |
12 |
13 |
3 |
0 |
2 |
1 |
3 |
1 |
3 |
0 |
2 |
||||
|
25 |
55 |
2 |
48 |
9 |
39 |
18 |
64 |
9 |
7 |
2 |
16 |
9 |
7 |
2 |
16 |
1 |
3 |
0 |
2 |
0 |
2 |
1 |
3 |
||||
|
36 |
14 |
59 |
21 |
52 |
30 |
43 |
5 |
4 |
14 |
11 |
5 |
4 |
14 |
11 |
5 |
2 |
0 |
3 |
1 |
3 |
1 |
2 |
0 |
||||
|
31 |
49 |
8 |
42 |
15 |
33 |
24 |
58 |
15 |
1 |
8 |
10 |
15 |
1 |
8 |
10 |
1 |
3 |
0 |
2 |
0 |
2 |
1 |
3 |
||||
|
38 |
12 |
61 |
19 |
54 |
28 |
45 |
3 |
6 |
12 |
13 |
3 |
6 |
12 |
13 |
3 |
2 |
0 |
3 |
1 |
3 |
1 |
2 |
0 |
||||
|
57 |
23 |
34 |
16 |
41 |
7 |
50 |
32 |
9 |
7 |
2 |
16 |
9 |
7 |
2 |
16 |
3 |
1 |
2 |
0 |
2 |
0 |
3 |
1 |
||||
|
4 |
46 |
27 |
53 |
20 |
62 |
11 |
37 |
4 |
14 |
11 |
5 |
4 |
14 |
11 |
5 |
0 |
2 |
1 |
3 |
1 |
3 |
0 |
2 |
Groep II [2x2 the same panmagic 4x4 square]
Franklin panmagic 8x8 square 2x2 same 4x4 panmagic square Sudoku grid
|
63 |
33 |
24 |
10 |
31 |
1 |
56 |
42 |
15 |
1 |
8 |
10 |
15 |
1 |
8 |
10 |
3 |
2 |
1 |
0 |
1 |
0 |
3 |
2 |
||||
|
6 |
28 |
45 |
51 |
38 |
60 |
13 |
19 |
6 |
12 |
13 |
3 |
6 |
12 |
13 |
3 |
0 |
1 |
2 |
3 |
2 |
3 |
0 |
1 |
||||
|
41 |
55 |
2 |
32 |
9 |
23 |
34 |
64 |
9 |
7 |
2 |
16 |
9 |
7 |
2 |
16 |
2 |
3 |
0 |
1 |
0 |
1 |
2 |
3 |
||||
|
20 |
14 |
59 |
37 |
52 |
46 |
27 |
5 |
4 |
14 |
11 |
5 |
4 |
14 |
11 |
5 |
1 |
0 |
3 |
2 |
3 |
2 |
1 |
0 |
||||
|
43 |
53 |
4 |
30 |
11 |
21 |
36 |
62 |
11 |
5 |
4 |
14 |
11 |
5 |
4 |
14 |
2 |
3 |
0 |
1 |
0 |
1 |
2 |
3 |
||||
|
18 |
16 |
57 |
39 |
50 |
48 |
25 |
7 |
2 |
16 |
9 |
7 |
2 |
16 |
9 |
7 |
1 |
0 |
3 |
2 |
3 |
2 |
1 |
0 |
||||
|
61 |
35 |
22 |
12 |
29 |
3 |
54 |
44 |
13 |
3 |
6 |
12 |
13 |
3 |
6 |
12 |
3 |
2 |
1 |
0 |
1 |
0 |
3 |
2 |
||||
|
8 |
26 |
47 |
49 |
40 |
58 |
15 |
17 |
8 |
10 |
15 |
1 |
8 |
10 |
15 |
1 |
0 |
1 |
2 |
3 |
2 |
3 |
0 |
1 |
Groep III [4x different panmagic 4x4 square]
Franklin panmagic 8x8 square 4 different 4x4 panmagic squares Sudoku grid
|
63 |
33 |
28 |
6 |
64 |
34 |
27 |
5 |
15 |
1 |
12 |
6 |
16 |
2 |
11 |
5 |
3 |
2 |
1 |
0 |
3 |
2 |
1 |
0 |
||||
|
26 |
8 |
61 |
35 |
25 |
7 |
62 |
36 |
10 |
8 |
13 |
3 |
9 |
7 |
14 |
4 |
1 |
0 |
3 |
2 |
1 |
0 |
3 |
2 |
||||
|
37 |
59 |
2 |
32 |
38 |
60 |
1 |
31 |
5 |
11 |
2 |
16 |
6 |
12 |
1 |
15 |
2 |
3 |
0 |
1 |
2 |
3 |
0 |
1 |
||||
|
4 |
30 |
39 |
57 |
3 |
29 |
40 |
58 |
4 |
14 |
7 |
9 |
3 |
13 |
8 |
10 |
0 |
1 |
2 |
3 |
0 |
1 |
2 |
3 |
||||
|
55 |
41 |
20 |
14 |
56 |
42 |
19 |
13 |
7 |
9 |
4 |
14 |
8 |
10 |
3 |
13 |
3 |
2 |
1 |
0 |
3 |
2 |
1 |
0 |
||||
|
18 |
16 |
53 |
43 |
17 |
15 |
54 |
44 |
2 |
16 |
5 |
11 |
1 |
15 |
6 |
12 |
1 |
0 |
3 |
2 |
1 |
0 |
3 |
2 |
||||
|
45 |
51 |
10 |
24 |
46 |
52 |
9 |
23 |
13 |
3 |
10 |
8 |
14 |
4 |
9 |
7 |
2 |
3 |
0 |
1 |
2 |
3 |
0 |
1 |
||||
|
12 |
22 |
47 |
49 |
11 |
21 |
48 |
50 |
12 |
6 |
15 |
1 |
11 |
5 |
16 |
2 |
0 |
1 |
2 |
3 |
0 |
1 |
2 |
3 |
Groep IV [1x splitted panmagic 4x4 square = Basis pattern method (1)]
Franklin panmagic 8x8 square 1x splitted panmagic 4x4 square Sudoku grid
|
63 |
3 |
54 |
10 |
61 |
1 |
56 |
12 |
15 |
3 |
6 |
10 |
13 |
1 |
8 |
12 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
||||
|
50 |
14 |
59 |
7 |
52 |
16 |
57 |
5 |
2 |
14 |
11 |
7 |
4 |
16 |
9 |
5 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
||||
|
11 |
55 |
2 |
62 |
9 |
53 |
4 |
64 |
11 |
7 |
2 |
14 |
9 |
5 |
4 |
16 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
||||
|
6 |
58 |
15 |
51 |
8 |
60 |
13 |
49 |
6 |
10 |
15 |
3 |
8 |
12 |
13 |
1 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
||||
|
31 |
35 |
22 |
42 |
29 |
33 |
24 |
44 |
15 |
3 |
6 |
10 |
13 |
12 |
8 |
1 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
||||
|
18 |
46 |
27 |
39 |
20 |
48 |
25 |
37 |
2 |
14 |
11 |
7 |
4 |
5 |
9 |
16 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
||||
|
43 |
23 |
34 |
30 |
41 |
21 |
36 |
32 |
11 |
7 |
2 |
14 |
9 |
16 |
4 |
5 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
||||
|
38 |
26 |
47 |
19 |
40 |
28 |
45 |
17 |
6 |
10 |
15 |
3 |
8 |
1 |
13 |
12 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
Sudoku grid can also be:
Franklin panmagic 8x8 square 1x splitted 4x4 panmagic square Sudoku grid
|
63 |
8 |
58 |
1 |
59 |
4 |
62 |
5 |
15 |
8 |
10 |
1 |
11 |
4 |
14 |
5 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
||||
|
18 |
41 |
23 |
48 |
22 |
45 |
19 |
44 |
2 |
9 |
7 |
16 |
6 |
13 |
3 |
12 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
||||
|
7 |
64 |
2 |
57 |
3 |
60 |
6 |
61 |
7 |
16 |
2 |
9 |
3 |
12 |
6 |
13 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
||||
|
42 |
17 |
47 |
24 |
46 |
21 |
43 |
20 |
10 |
1 |
15 |
8 |
14 |
5 |
11 |
4 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
||||
|
15 |
56 |
10 |
49 |
11 |
52 |
14 |
53 |
15 |
8 |
10 |
1 |
11 |
4 |
14 |
5 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
||||
|
34 |
25 |
39 |
32 |
38 |
29 |
35 |
28 |
2 |
9 |
7 |
16 |
6 |
13 |
3 |
12 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
||||
|
55 |
16 |
50 |
9 |
51 |
12 |
54 |
13 |
7 |
16 |
2 |
9 |
3 |
12 |
6 |
13 |
3 |
0 |
3 |
0 |
3 |
0 |
3 |
0 |
||||
|
26 |
33 |
31 |
40 |
30 |
37 |
27 |
36 |
10 |
1 |
15 |
8 |
14 |
5 |
11 |
4 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
Groep V [2x splitted panmagic 4x4 square]
Franklin panmagic 8x8 square 2x splitted 4x4 panmagic square Sudoku grid
|
63 |
8 |
25 |
34 |
59 |
4 |
29 |
38 |
15 |
8 |
9 |
2 |
11 |
4 |
13 |
6 |
3 |
0 |
1 |
2 |
3 |
0 |
1 |
2 |
||||
|
26 |
33 |
64 |
7 |
30 |
37 |
60 |
3 |
10 |
1 |
16 |
7 |
14 |
5 |
12 |
3 |
1 |
2 |
3 |
0 |
1 |
2 |
3 |
0 |
||||
|
40 |
31 |
2 |
57 |
36 |
27 |
6 |
61 |
8 |
15 |
2 |
9 |
4 |
11 |
6 |
13 |
2 |
1 |
0 |
3 |
2 |
1 |
0 |
3 |
||||
|
1 |
58 |
39 |
32 |
5 |
62 |
35 |
28 |
1 |
10 |
7 |
16 |
5 |
14 |
3 |
12 |
0 |
3 |
2 |
1 |
0 |
3 |
2 |
1 |
||||
|
55 |
16 |
17 |
42 |
51 |
12 |
21 |
46 |
7 |
16 |
1 |
10 |
3 |
12 |
5 |
14 |
3 |
0 |
1 |
2 |
3 |
0 |
1 |
2 |
||||
|
18 |
41 |
56 |
15 |
22 |
45 |
52 |
11 |
2 |
9 |
8 |
15 |
6 |
13 |
4 |
11 |
1 |
2 |
3 |
0 |
1 |
2 |
3 |
0 |
||||
|
48 |
23 |
10 |
49 |
44 |
19 |
14 |
53 |
16 |
7 |
10 |
1 |
12 |
3 |
14 |
5 |
2 |
1 |
0 |
3 |
2 |
1 |
0 |
3 |
||||
|
9 |
50 |
47 |
24 |
13 |
54 |
43 |
20 |
9 |
2 |
15 |
8 |
13 |
6 |
11 |
4 |
0 |
3 |
2 |
1 |
0 |
3 |
2 |
1 |
ór
Franklin panmagic 8x8 square 2x splitted 4x4 panmagic square Sudoku grid
|
63 |
22 |
44 |
1 |
60 |
17 |
47 |
6 |
15 |
6 |
12 |
1 |
12 |
1 |
15 |
6 |
3 |
1 |
2 |
0 |
3 |
1 |
2 |
0 |
||||
|
12 |
33 |
31 |
54 |
15 |
38 |
28 |
49 |
12 |
1 |
15 |
6 |
15 |
6 |
12 |
1 |
0 |
2 |
1 |
3 |
0 |
2 |
1 |
3 |
||||
|
21 |
64 |
2 |
43 |
18 |
59 |
5 |
48 |
5 |
16 |
2 |
11 |
2 |
11 |
5 |
16 |
1 |
3 |
0 |
2 |
1 |
3 |
0 |
2 |
||||
|
34 |
11 |
53 |
32 |
37 |
16 |
50 |
27 |
2 |
11 |
5 |
16 |
5 |
16 |
2 |
11 |
2 |
0 |
3 |
1 |
2 |
0 |
3 |
1 |
||||
|
55 |
30 |
36 |
9 |
52 |
25 |
39 |
14 |
7 |
14 |
4 |
9 |
4 |
9 |
7 |
14 |
3 |
1 |
2 |
0 |
3 |
1 |
2 |
0 |
||||
|
4 |
41 |
23 |
62 |
7 |
46 |
20 |
57 |
4 |
9 |
7 |
14 |
7 |
14 |
4 |
9 |
0 |
2 |
1 |
3 |
0 |
2 |
1 |
3 |
||||
|
29 |
56 |
10 |
35 |
26 |
51 |
13 |
40 |
13 |
8 |
10 |
3 |
10 |
3 |
13 |
8 |
1 |
3 |
0 |
2 |
1 |
3 |
0 |
2 |
||||
|
42 |
3 |
61 |
24 |
45 |
8 |
58 |
19 |
10 |
3 |
13 |
8 |
13 |
8 |
10 |
3 |
2 |
0 |
3 |
1 |
2 |
0 |
3 |
1 |
Groep VI [4x splitted 4x4 panmagic square (= Sudoku method 2)]
Franklin panmagic 8x8 square 4x splitted 4x4 panmagic square Sudo grid
|
63 |
14 |
35 |
18 |
55 |
6 |
43 |
26 |
15 |
14 |
3 |
2 |
7 |
6 |
11 |
10 |
3 |
0 |
2 |
1 |
3 |
0 |
2 |
1 |
||||
|
34 |
19 |
62 |
15 |
42 |
27 |
54 |
7 |
2 |
3 |
14 |
15 |
10 |
11 |
6 |
7 |
2 |
1 |
3 |
0 |
2 |
1 |
3 |
0 |
||||
|
30 |
47 |
2 |
51 |
22 |
39 |
10 |
59 |
14 |
15 |
2 |
3 |
6 |
7 |
10 |
11 |
1 |
2 |
0 |
3 |
1 |
2 |
0 |
3 |
||||
|
3 |
50 |
31 |
46 |
11 |
58 |
23 |
38 |
3 |
2 |
15 |
14 |
11 |
10 |
7 |
6 |
0 |
3 |
1 |
2 |
0 |
3 |
1 |
2 |
||||
|
61 |
16 |
33 |
20 |
53 |
8 |
41 |
28 |
13 |
16 |
1 |
4 |
5 |
8 |
9 |
12 |
3 |
0 |
2 |
1 |
3 |
0 |
2 |
1 |
||||
|
36 |
17 |
64 |
13 |
44 |
25 |
56 |
5 |
4 |
1 |
16 |
13 |
12 |
9 |
8 |
5 |
2 |
1 |
3 |
0 |
2 |
1 |
3 |
0 |
||||
|
32 |
45 |
4 |
49 |
24 |
37 |
12 |
57 |
16 |
13 |
4 |
1 |
8 |
5 |
12 |
9 |
1 |
2 |
0 |
3 |
1 |
2 |
0 |
3 |
||||
|
1 |
52 |
29 |
48 |
9 |
60 |
21 |
40 |
1 |
4 |
13 |
16 |
9 |
12 |
5 |
8 |
0 |
3 |
1 |
2 |
0 |
3 |
1 |
2 |
Final remark
You can not always recognize the 6 groups very clearly. The groups are corrected for swap row 1&3 and/or row 2&4 and/or row 5&7 and/or row 6&8 and/or column 1&3 and/or column 2&4 and/or column 5&7 and/or column 6&8.
