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Magic squares (most perfect, [Franklin] panmagic & inlaid)
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Basic pattern method (1a)
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How to produce a most perfect (Franklin pan)magic square from a 4x4
panmagic square
 
 From each (pattern of a) 4x4 pan magic square you can produce an 8x8 most perfect (Franklin pan)magic
square. The 8x8 square contains the following digits from 1 to 64 (= 4 x 16 digits):
 
 
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
 
 
Select a random 4x4 panmagic square and split the square in two subsquares as follows:

 
16
3
10
5
 
 
16
 
 
5
 
 
 
3
10
 
2
13
8
11
 
 
 
13
8
 
 
 
2
 
 
11
7
12
1
14
 
 
 
12
1
 
 
 
7
 
 
14
9
6
15
4
 
 
9
 
 
4
 
 
 
6
15
 
 
 
Enter digits from the same sub-square in the empty cells crosswise:
 
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
 
 
Combine the 2 sub-squares and add the same 2 sub-squares to the bottom:
 
 
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
 
 
Substitute the digits for the digits with the right colour from the above mentioned table:
 
 
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
 
 

There are 6 options to split up a 4x4 panmagic square and to produce a basic pattern.
 
 
  1 split up panmagic 4x4                                 Produce basic pattern                           8x8 most perfect (Franklin pan)magic square
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 split up panmagic 4x4                                 Produce basic pattern                           8x8 most perfect (Franklin pan)magic square
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
 
 
 
 
 
 
 
 
 
 
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 split up panmagic 4x4                                 Produce basic pattern                           8x8 most perfect (Franklin pan)magic square
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
 
6
15
 
9
 
 
4
 
 
1
6
15
12
9
14
7
4
 
 
1
54
15
60
9
62
7
52
 
 
 
 
 
 
 
 
 
 
16
11
2
5
8
3
10
13
 
 
32
43
18
37
24
35
26
45
 
 
 
 
 
 
 
 
 
 
2
5
16
11
10
13
8
3
 
 
34
21
48
27
42
29
40
19
 
 
 
 
 
 
 
 
 
 
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 split up panmagic 4x4                                 Produce basic pattern                           8x8 most perfect (Franklin pan)magic square
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 splitup panmagic 4x4                                Produce basic pattern                            8x8 most perfect (Franklin pan)magic square
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