Analyse Franklin panmagisch 8x8 vierkant in 4x4 panma-gisch vierkant & Sudoku patroon
Inleiding
Exclusief draaiingen en/of spiegelingen zijn er 368.640 Franklin panmagische 8x8 vierkanten. In elk van de Franklin panmagische 8x8 vierkanten zit het panmagisch 4x4 vierkant 'verstopt'. Ik heb ontdekt dat je via splitsing van het 8x8 Franklin panmagisch vierkant in een 4x4 panmagisch vierkant patroon en in een Sudoku patroon, 6 verschillende groepen kunt onderscheiden.
Groep I [4x hetzelfde panmagisch 4x4 vierkant als basispatroon = Sudoku methode 3]
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 hetzelfde panmagische 4x4 vierkant als basispatroon]
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 verschillend panmagisch 4x4 vierkant als basispatroon]
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 gesplitst panmagisch 4x4 vierkant als basispatroon = Basis patroon methode (2)]
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 |
Basispatronen 1, 2, 3 en 4 kunnen ook het volgende afwijkende Sudokupatroon hebben (zie bijvoorbeeld):
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 gesplitst panmagisch 4x4 vierkant als basispatroon]
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 |
óf
Meest perfect magisch 8x8 Basispatroon Sudokupatroon
|
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 verschillend basispatroon = Sudoku methode 2]
Meest perfect magisch 8x8 Basispatroon 4x4 Sudokupatroon
|
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 |
Slotopmerking
De 6 groepen zijn niet altijd vanuit analyse in één keer herkenbaar. De groepen zijn namelijk gecorrigeerd voor de mogelijke omwisseling van rij 1&3 en/of rij 2&4 en/of rij 5&7 en/of rij 6&8 en/of kolom 1&3 en/of kolom 2&4 en/of kolom 5&7 en/of kolom 6&8.
