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Magic squares (most perfect, [Franklin] panmagic & inlaid)
Detailed explanation about the structure and construction of magic squares
Sudoku method (2)
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How to produce most perfect magic squares from a 4x4 Sudoku
  
It is also possible to produce squares that are odd multiples of 4, for example the 12x12 square. You need
the following 2 Sudoku patterns:
 
● The first pattern of the 12x12 square is a 3x3 carpet of the second (don’t split it up!)  pattern of the 4x4
panmagic square [see page ‘Sudoku method (1)’].
 
● The second pattern of the 12x12 square is a fixed pattern.
 
 
 1x digit from the first pattern
2
1
3
0
2
1
3
0
2
1
3
0
3
0
2
1
3
0
2
1
3
0
2
1
0
3
1
2
0
3
1
2
0
3
1
2
1
2
0
3
1
2
0
3
1
2
0
3
2
1
3
0
2
1
3
0
2
1
3
0
3
0
2
1
3
0
2
1
3
0
2
1
0
3
1
2
0
3
1
2
0
3
1
2
1
2
0
3
1
2
0
3
1
2
0
3
2
1
3
0
2
1
3
0
2
1
3
0
3
0
2
1
3
0
2
1
3
0
2
1
0
3
1
2
0
3
1
2
0
3
1
2
1
2
0
3
1
2
0
3
1
2
0
3
 
 
 4x digit from the second (fixed) pattern
35
5
30
0
34
4
31
1
33
3
32
2
0
30
5
35
1
31
4
34
2
32
3
33
5
35
0
30
4
34
1
31
3
33
2
32
30
0
35
5
31
1
34
4
32
2
33
3
29
11
24
6
28
10
25
7
27
9
26
8
6
24
11
29
7
25
10
28
8
26
9
27
11
29
6
24
10
28
7
25
9
27
8
26
24
6
29
11
25
7
28
10
26
8
27
9
23
17
18
12
22
16
19
13
21
15
20
14
12
18
17
23
13
19
16
22
14
20
15
21
17
23
12
18
16
22
13
19
15
21
14
20
18
12
23
17
19
13
22
16
20
14
21
15
 
 
Add 1 to each digit and you produce the following magic square:
 
 
 Most magic 12x12 square
143
22
124
1
139
18
128
5
135
14
132
9
4
121
23
142
8
125
19
138
12
129
15
134
21
144
2
123
17
140
6
127
13
136
10
131
122
3
141
24
126
7
137
20
130
11
133
16
119
46
100
25
115
42
104
29
111
38
108
33
28
97
47
118
32
101
43
114
36
105
39
110
45
120
26
99
41
116
30
103
37
112
34
107
98
27
117
48
102
31
113
44
106
35
109
40
95
70
76
49
91
66
80
53
87
62
84
57
52
73
71
94
56
77
67
90
60
81
63
86
69
96
50
75
65
92
54
79
61
88
58
83
74
51
93
72
78
55
89
68
82
59
85
64
 
 
See on page ‘Basic key method (2) option a and b of the 12x12 most magic square and note that the 12x12
square mentioned above has different magic features. The above mentioned 12x12 square is a most perfect
magic square.
 
 

Take 1x digit from 2x2, 3x3, 4x4, 5x5, 6x6, ... the 4x4 Sudoku pattern

You can use the method mentioned above for each multiple of 4 to produce most perfect (for each multiple of
8 also Franklin pan)magic squares. You need the (2x2, 3x3, 4x4, …) carpet of the 4x4 Sudoku pattern and a
fixed (8x8, 12x12, 16x16, …) pattern.
 
 
 1x digit
2
1
3
0
3
0
2
1
0
3
1
2
1
2
0
3
 
 
 
Add 4x digit from the fixed 8x8, 12x12, 16x16, 20x20, 24x24, ... grid
 
 
 4x digit from fixed 8x8 pattern
15
3
12
0
14
2
13
1
0
12
3
15
1
13
2
14
3
15
0
12
2
14
1
13
12
0
15
3
13
1
14
2
11
7
8
4
10
6
9
5
4
8
7
11
5
9
6
10
7
11
4
8
6
10
5
9
8
4
11
7
9
5
10
6
 
 
 or
 
 
 4x digit from fixed 12x12 pattern
35
5
30
0
34
4
31
1
33
3
32
2
0
30
5
35
1
31
4
34
2
32
3
33
5
35
0
30
4
34
1
31
3
33
2
32
30
0
35
5
31
1
34
4
32
2
33
3
29
11
24
6
28
10
25
7
27
9
26
8
6
24
11
29
7
25
10
28
8
26
9
27
11
29
6
24
10
28
7
25
9
27
8
26
24
6
29
11
25
7
28
10
26
8
27
9
23
17
18
12
22
16
19
13
21
15
20
14
12
18
17
23
13
19
16
22
14
20
15
21
17
23
12
18
16
22
13
19
15
21
14
20
18
12
23
17
19
13
22
16
20
14
21
15
 
 
 or
 
 
 4x digit from fixed 16x16 pattern
63
7
56
0
62
6
57
1
61
5
58
2
60
4
59
3
0
56
7
63
1
57
6
62
2
58
5
61
3
59
4
60
7
63
0
56
6
62
1
57
5
61
2
58
4
60
3
59
56
0
63
7
57
1
62
6
58
2
61
5
59
3
60
4
55
15
48
8
54
14
49
9
53
13
50
10
52
12
51
11
8
48
15
55
9
49
14
54
10
50
13
53
11
51
12
52
15
55
8
48
14
54
9
49
13
53
10
50
12
52
11
51
48
8
55
15
49
9
54
14
50
10
53
13
51
11
52
12
47
23
40
16
46
22
41
17
45
21
42
18
44
20
43
19
16
40
23
47
17
41
22
46
18
42
21
45
19
43
20
44
23
47
16
40
22
46
17
41
21
45
18
42
20
44
19
43
40
16
47
23
41
17
46
22
42
18
45
21
43
19
44
20
39
31
32
24
38
30
33
25
37
29
34
26
36
28
35
27
24
32
31
39
25
33
30
38
26
34
29
37
27
35
28
36
31
39
24
32
30
38
25
33
29
37
26
34
28
36
27
35
32
24
39
31
33
25
38
30
34
26
37
29
35
27
36
28
 
 
 or
 
 
 4x digit from fixed 20x20 pattern
99
9
90
0
98
8
91
1
97
7
92
2
96
6
93
3
95
5
94
4
0
90
9
99
1
91
8
98
2
92
7
97
3
93
6
96
4
94
5
95
9
99
0
90
8
98
1
91
7
97
2
92
6
96
3
93
5
95
4
94
90
0
99
9
91
1
98
8
92
2
97
7
93
3
96
6
94
4
95
5
89
19
80
10
88
18
81
11
87
17
82
12
86
16
83
13
85
15
84
14
10
80
19
89
11
81
18
88
12
82
17
87
13
83
16
86
14
84
15
85
19
89
10
80
18
88
11
81
17
87
12
82
16
86
13
83
15
85
14
84
80
10
89
19
81
11
88
18
82
12
87
17
83
13
86
16
84
14
85
15
79
29
70
20
78
28
71
21
77
27
72
22
76
26
73
23
75
25
74
24
20
70
29
79
21
71
28
78
22
72
27
77
23
73
26
76
24
74
25
75
29
79
20
70
28
78
21
71
27
77
22
72
26
76
23
73
25
75
24
74
70
20
79
29
71
21
78
28
72
22
77
27
73
23
76
26
74
24
75
25
69
39
60
30
68
38
61
31
67
37
62
32
66
36
63
33
65
35
64
34
30
60
39
69
31
61
38
68
32
62
37
67
33
63
36
66
34
64
35
65