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Magic squares (most perfect, [Franklin] panmagic & inlaid)
Detailed explanation about the structure and construction of magic squares
Basic pattern method (2)
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How to use a panmagic 4x4 square to produce a most perfect magic
12x12 square
 
 It is also possible to use (the pattern of) each random chosen panmagic 4x4 square to produce a
most perfect magic 12x12 square.
 
You need 9x the same panmagic 4x4 square (see page ‘panmagic 4x4 square’) and 2 fixed 12x12
grids.
 
 
1x digit from grid of 9x the same 4x4 panmagic square
15
6
12
1
15
6
12
1
15
6
12
1
 
 
4
9
7
14
4
9
7
14
4
9
7
14
 
 
5
16
2
11
5
16
2
11
5
16
2
11
 
 
10
3
13
8
10
3
13
8
10
3
13
8
 
 
15
6
12
1
15
6
12
1
15
6
12
1
 
 
4
9
7
14
4
9
7
14
4
9
7
14
 
 
5
16
2
11
5
16
2
11
5
16
2
11
 
 
10
3
13
8
10
3
13
8
10
3
13
8
 
 
15
6
12
1
15
6
12
1
15
6
12
1
 
 
4
9
7
14
4
9
7
14
4
9
7
14
 
 
5
16
2
11
5
16
2
11
5
16
2
11
 
 
10
3
13
8
10
3
13
8
10
3
13
8
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
+ 16x digit from fixed grid 1
 
 
 
 
 
 
0
2
2
0
2
0
0
2
1
1
1
1
 
 
2
0
0
2
0
2
2
0
1
1
1
1
 
 
0
2
2
0
2
0
0
2
1
1
1
1
 
 
2
0
0
2
0
2
2
0
1
1
1
1
 
 
0
2
2
0
2
0
0
2
1
1
1
1
 
 
2
0
0
2
0
2
2
0
1
1
1
1
 
 
0
2
2
0
2
0
0
2
1
1
1
1
 
 
2
0
0
2
0
2
2
0
1
1
1
1
 
 
0
2
2
0
2
0
0
2
1
1
1
1
 
 
2
0
0
2
0
2
2
0
1
1
1
1
 
 
0
2
2
0
2
0
0
2
1
1
1
1
 
 
2
0
0
2
0
2
2
0
1
1
1
1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
+ 48x digit from fixed grid 2
 
 
 
 
 
 
0
2
0
2
0
2
0
2
0
2
0
2
 
 
2
0
2
0
2
0
2
0
2
0
2
0
 
 
2
0
2
0
2
0
2
0
2
0
2
0
 
 
0
2
0
2
0
2
0
2
0
2
0
2
 
 
2
0
2
0
2
0
2
0
2
0
2
0
 
 
0
2
0
2
0
2
0
2
0
2
0
2
 
 
0
2
0
2
0
2
0
2
0
2
0
2
 
 
2
0
2
0
2
0
2
0
2
0
2
0
 
 
1
1
1
1
1
1
1
1
1
1
1
1
 
 
1
1
1
1
1
1
1
1
1
1
1
1
 
 
1
1
1
1
1
1
1
1
1
1
1
1
 
 
1
1
1
1
1
1
1
1
1
1
1
1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
= most perfect 12x12 magic square
 
 
 
 
 
 
 
15
134
44
97
47
102
12
129
31
118
28
113
 
 
132
9
103
46
100
41
135
14
116
25
119
30
 
 
101
48
130
11
133
16
98
43
117
32
114
27
 
 
42
99
13
136
10
131
45
104
26
115
29
120
 
 
111
38
140
1
143
6
108
33
127
22
124
17
 
 
36
105
7
142
4
137
39
110
20
121
23
126
 
 
5
144
34
107
37
112
2
139
21
128
18
123
 
 
138
3
109
40
106
35
141
8
122
19
125
24
 
 
63
86
92
49
95
54
60
81
79
70
76
65
 
 
84
57
55
94
52
89
87
62
68
73
71
78
 
 
53
96
82
59
85
64
50
91
69
80
66
75
 
 
90
51
61
88
58
83
93
56
74
67
77
72
 
 
 
 
Notify that the most perfect 12x12 magic square has the extra magic feature X
(discovered by Willem Barink; see page ‘most perfect magic square, explanation’).



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Magic squares|Contact / guestbook|Most magic square per order|3x3 magic square|3x3 magic square, explanation|Sudoku method (1)|Sudoku method (2)|Sudoku method (3)|Pan magic 4x4 square|Pan magic 4x4 square, explanation|Pan magic 4x4 square, binary|Dürer & Franklin transformation|Transformation method|Transformation method, analysis|[ultra] pan magic 5x5 square|Pan magic 5x5 square, explanation|6x6 magic square|Ultra (pan)magic 8x8 square|Most perfect magic squares, explanation|8x8 most perfect magic squares, binary|Khajuraho method|Khajuraho method, explanation|Basic pattern method (1a)|Basic pattern method (1b)|Basic pattern method (2)|Basic pattern method (3a)|Basic pattern method (3b)|Basic pattern method (3c)|Basic pattern method (4)|Basic pattern method (5)|Basic pattern method (6)|Basic pattern method (7a)|Basic pattern method (7b)|Analysis Franklin panm. 8x8 (1)|Analysis Franklin panm. 8x8 (2)|Basic key method (1)|Basic key method (2)|Quadrant method (Willem Barink)|Quadrant method group 1 up to 5|Quadrant method group 6 up to 10|Quadrant method group 11 up to 19|[ultra] pan magic 9x9 square (1)|pan magic 9x9 square (2)|pan magic 9x9 square (3)|3x extra magic 9x9 square|10x10 magic square|Composite 12x12 magic square|14x14 magic square|[Ultra] pan magic 15x15 square|3x extra magic 15x15 square|The perfect magic square|3x extra magic 18x18 square|Ultra pan magic 25x25 square|[ultra] pan magic 27x27 square|[ultra] pan magic 35x35 square|extra magic 35x35 square|Bordered squares|Inlaid square (1)|Inlaid square (2)|Each magic sum|Water retention challenge|Most magic 4x4x4 cube|Perfect (Nasik) magic 8x8x8 cube|[More than] perfect magic 9x9x9 cube|Trick with 8x8 bimagic square|Favorite Links