Je kunt een 4x4 panmagisch vierkant uitbreiden naar een 8x8 Franklin panmagisch vierkant. In het 8x8 vierkant komen de volgende (4x16= ) 64 getallen te staan:
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
50 |
51 |
52 |
53 |
54 |
55 |
56 |
57 |
58 |
59 |
60 |
61 |
62 |
63 |
64 |
Kies een 4x4 panmagisch vierkant en splits deze als volgt:
16 |
3 |
10 |
5 |
16 |
5 |
3 |
10 |
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2 |
13 |
8 |
11 |
13 |
8 |
2 |
11 |
||||||||
7 |
12 |
1 |
14 |
12 |
1 |
7 |
14 |
||||||||
9 |
6 |
15 |
4 |
9 |
4 |
6 |
15 |
Vul de
lege vakjes kruiselings op met getallen uit het zelfde vierkant:
16 |
4 |
9 |
5 |
15 |
3 |
10 |
6 |
||
1 |
13 |
8 |
12 |
2 |
14 |
7 |
11 |
||
8 |
12 |
1 |
13 |
7 |
11 |
2 |
14 |
||
9 |
5 |
16 |
4 |
10 |
6 |
15 |
3 |
Voeg de
2 vierkanten samen en voeg nog 2 dezelfde vierkanten onderaan toe:
16 |
4 |
9 |
5 |
15 |
3 |
10 |
6 |
1 |
13 |
8 |
12 |
2 |
14 |
7 |
11 |
8 |
12 |
1 |
13 |
7 |
11 |
2 |
14 |
9 |
5 |
16 |
4 |
10 |
6 |
15 |
3 |
16 |
4 |
9 |
5 |
15 |
3 |
10 |
6 |
1 |
13 |
8 |
12 |
2 |
14 |
7 |
11 |
8 |
12 |
1 |
13 |
7 |
11 |
2 |
14 |
9 |
5 |
16 |
4 |
10 |
6 |
15 |
3 |
Vul ten
slotte de bij de kleuren passende getallen (zie boven) in:
16 |
52 |
9 |
53 |
15 |
51 |
10 |
54 |
1 |
61 |
8 |
60 |
2 |
62 |
7 |
59 |
56 |
12 |
49 |
13 |
55 |
11 |
50 |
14 |
57 |
5 |
64 |
4 |
58 |
6 |
63 |
3 |
32 |
36 |
25 |
37 |
31 |
35 |
26 |
38 |
17 |
45 |
24 |
44 |
18 |
46 |
23 |
43 |
40 |
28 |
33 |
29 |
39 |
27 |
34 |
30 |
41 |
21 |
48 |
20 |
42 |
22 |
47 |
19 |
Er zijn in totaal 6 manieren om een panmagisch 4x4 vierkant uit te splitsen en hiervan een basispatroon te maken:
1 splitsen panmagisch 4x4 Opvullen en verdubbelen = Franklin panmagisch 8x8
16 |
5 |
3 |
10 |
16 |
4 |
9 |
5 |
15 |
3 |
10 |
6 |
16 |
52 |
9 |
53 |
15 |
51 |
10 |
54 |
||||||||
13 |
8 |
2 |
11 |
1 |
13 |
8 |
12 |
2 |
14 |
7 |
11 |
1 |
61 |
8 |
60 |
2 |
62 |
7 |
59 |
||||||||
12 |
1 |
7 |
14 |
8 |
12 |
1 |
13 |
7 |
11 |
2 |
14 |
56 |
12 |
49 |
13 |
55 |
11 |
50 |
14 |
||||||||
9 |
4 |
6 |
15 |
9 |
5 |
16 |
4 |
10 |
6 |
15 |
3 |
57 |
5 |
64 |
4 |
58 |
6 |
63 |
3 |
||||||||
16 |
4 |
9 |
5 |
15 |
3 |
10 |
6 |
32 |
36 |
25 |
37 |
31 |
35 |
26 |
38 |
||||||||||||
1 |
13 |
8 |
12 |
2 |
14 |
7 |
11 |
17 |
45 |
24 |
44 |
18 |
46 |
23 |
43 |
||||||||||||
8 |
12 |
1 |
13 |
7 |
11 |
2 |
14 |
40 |
28 |
33 |
29 |
39 |
27 |
34 |
30 |
||||||||||||
9 |
5 |
16 |
4 |
10 |
6 |
15 |
3 |
41 |
21 |
48 |
20 |
42 |
22 |
47 |
19 |
2 splitsen panmagisch 4x4 Opvullen en verdubbelen = Franklin panmagisch 8x8
16 |
3 |
10 |
5 |
16 |
3 |
9 |
6 |
15 |
4 |
10 |
5 |
16 |
51 |
9 |
54 |
15 |
52 |
10 |
53 |
||||||||
8 |
11 |
2 |
13 |
1 |
14 |
8 |
11 |
2 |
13 |
7 |
12 |
1 |
62 |
8 |
59 |
2 |
61 |
7 |
60 |
||||||||
1 |
14 |
7 |
12 |
8 |
11 |
1 |
14 |
7 |
12 |
2 |
13 |
56 |
11 |
49 |
14 |
55 |
12 |
50 |
13 |
||||||||
9 |
6 |
15 |
4 |
9 |
6 |
16 |
3 |
10 |
5 |
15 |
4 |
57 |
6 |
64 |
3 |
58 |
5 |
63 |
4 |
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16 |
3 |
9 |
6 |
15 |
4 |
10 |
5 |
32 |
35 |
25 |
38 |
31 |
36 |
26 |
37 |
||||||||||||
1 |
14 |
8 |
11 |
2 |
13 |
7 |
12 |
17 |
46 |
24 |
43 |
18 |
45 |
23 |
44 |
||||||||||||
8 |
11 |
1 |
14 |
7 |
12 |
2 |
13 |
40 |
27 |
33 |
30 |
39 |
28 |
34 |
29 |
||||||||||||
9 |
6 |
16 |
3 |
10 |
5 |
15 |
4 |
41 |
22 |
48 |
19 |
42 |
21 |
47 |
20 |
3 splitsen panmagisch 4x4 Opvullen en verdubbelen = Franklin panmagisch 8x8
16 |
5 |
3 |
10 |
16 |
11 |
2 |
5 |
8 |
3 |
10 |
13 |
16 |
59 |
2 |
53 |
8 |
51 |
10 |
61 |
||||||||
2 |
11 |
13 |
8 |
2 |
5 |
16 |
11 |
10 |
13 |
8 |
3 |
50 |
5 |
64 |
11 |
58 |
13 |
56 |
3 |
||||||||
12 |
1 |
7 |
14 |
15 |
12 |
1 |
6 |
7 |
4 |
9 |
14 |
63 |
12 |
49 |
6 |
55 |
4 |
57 |
14 |
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6 |
15 |
9 |
4 |
1 |
6 |
15 |
12 |
9 |
14 |
7 |
4 |
1 |
54 |
15 |
60 |
9 |
62 |
7 |
52 |
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16 |
11 |
2 |
5 |
8 |
3 |
10 |
13 |
32 |
43 |
18 |
37 |
24 |
35 |
26 |
45 |
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2 |
5 |
16 |
11 |
10 |
13 |
8 |
3 |
34 |
21 |
48 |
27 |
42 |
29 |
40 |
19 |
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15 |
12 |
1 |
6 |
7 |
4 |
9 |
14 |
47 |
28 |
33 |
22 |
39 |
20 |
41 |
30 |
||||||||||||
1 |
6 |
15 |
12 |
9 |
14 |
7 |
4 |
17 |
38 |
31 |
44 |
25 |
46 |
23 |
36 |
4 splitsen panmagisch 4x4 Opvullen en verdubbelen = Franklin panmagisch 8x8
16 |
3 |
10 |
5 |
16 |
3 |
2 |
13 |
8 |
11 |
10 |
5 |
16 |
51 |
2 |
61 |
8 |
59 |
10 |
53 |
||||||||
2 |
13 |
8 |
11 |
2 |
13 |
16 |
3 |
10 |
5 |
8 |
11 |
50 |
13 |
64 |
3 |
58 |
5 |
56 |
11 |
||||||||
1 |
14 |
7 |
12 |
15 |
4 |
1 |
14 |
7 |
12 |
9 |
6 |
63 |
4 |
49 |
14 |
55 |
12 |
57 |
6 |
||||||||
15 |
4 |
9 |
6 |
1 |
14 |
15 |
4 |
9 |
6 |
7 |
12 |
1 |
62 |
15 |
52 |
9 |
54 |
7 |
60 |
||||||||
16 |
3 |
2 |
13 |
8 |
11 |
10 |
5 |
32 |
35 |
18 |
45 |
24 |
43 |
26 |
37 |
||||||||||||
2 |
13 |
16 |
3 |
10 |
5 |
8 |
11 |
34 |
29 |
48 |
19 |
42 |
21 |
40 |
27 |
||||||||||||
15 |
4 |
1 |
14 |
7 |
12 |
9 |
6 |
47 |
20 |
33 |
30 |
39 |
28 |
41 |
22 |
||||||||||||
1 |
14 |
15 |
4 |
9 |
6 |
7 |
12 |
17 |
46 |
31 |
36 |
25 |
38 |
23 |
44 |
5 splitsen panmagisch 4x4 Opvullen en verdubbelen = Franklin panmagisch 8x8
16 |
10 |
3 |
5 |
16 |
7 |
10 |
1 |
12 |
3 |
14 |
5 |
48 |
23 |
58 |
1 |
60 |
3 |
46 |
21 |
||||||||
2 |
8 |
13 |
11 |
2 |
9 |
8 |
15 |
6 |
13 |
4 |
11 |
18 |
41 |
8 |
63 |
6 |
61 |
20 |
43 |
||||||||
7 |
1 |
12 |
14 |
7 |
16 |
1 |
10 |
3 |
12 |
5 |
14 |
7 |
64 |
17 |
42 |
19 |
44 |
5 |
62 |
||||||||
9 |
15 |
6 |
4 |
9 |
2 |
15 |
8 |
13 |
6 |
11 |
4 |
57 |
2 |
47 |
24 |
45 |
22 |
59 |
4 |
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