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Composite 12x12 magic square
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How to produce a composite 12x12 magic square?
 
Learn how to produce the composite magic 12x12 square from "Scripta Mathematica" of Royal Vale
Heath of 1938.
 
Take as first grid a 3x3 'blown up' panmagic 4x4 square. Take as second grid 8x a magic 3x3 square
(see yellow marked) and 8x the same magic 3x3 square turned up site down (see red marked). Take
finally 1x digit from the first grid and add [digit minus 1] x 16 from the same cell of the second grid. 
 
 
 1x digit from grid with 3x3 'blown up' panmagic 4x4 square
1
1
1
8
8
8
13
13
13
12
12
12
1
1
1
8
8
8
13
13
13
12
12
12
1
1
1
8
8
8
13
13
13
12
12
12
14
14
14
11
11
11
2
2
2
7
7
7
14
14
14
11
11
11
2
2
2
7
7
7
14
14
14
11
11
11
2
2
2
7
7
7
4
4
4
5
5
5
16
16
16
9
9
9
4
4
4
5
5
5
16
16
16
9
9
9
4
4
4
5
5
5
16
16
16
9
9
9
15
15
15
10
10
10
3
3
3
6
6
6
15
15
15
10
10
10
3
3
3
6
6
6
15
15
15
10
10
10
3
3
3
6
6
6
 
 
 
 + [digit minus 1] x 16 from grid with 3x3 (and upsite down) magic square
6
1
8
4
9
2
6
1
8
4
9
2
7
5
3
3
5
7
7
5
3
3
5
7
2
9
4
8
1
6
2
9
4
8
1
6
4
9
2
6
1
8
4
9
2
6
1
8
3
5
7
7
5
3
3
5
7
7
5
3
8
1
6
2
9
4
8
1
6
2
9
4
4
9
2
6
1
8
4
9
2
6
1
8
3
5
7
7
5
3
3
5
7
7
5
3
8
1
6
2
9
4
8
1
6
2
9
4
6
1
8
4
9
2
6
1
8
4
9
2
7
5
3
3
5
7
7
5
3
3
5
7
2
9
4
8
1
6
2
9
4
8
1
6
 
 
 = panmagic 12x12 square (consisting of 16 magic 3x3 squares)
81
1
113
56
136
24
93
13
125
60
140
28
97
65
33
40
72
104
109
77
45
44
76
108
17
129
49
120
8
88
29
141
61
124
12
92
62
142
30
91
11
123
50
130
18
87
7
119
46
78
110
107
75
43
34
66
98
103
71
39
126
14
94
27
139
59
114
2
82
23
135
55
52
132
20
85
5
117
64
144
32
89
9
121
36
68
100
101
69
37
48
80
112
105
73
41
116
4
84
21
133
53
128
16
96
25
137
57
95
15
127
58
138
26
83
3
115
54
134
22
111
79
47
42
74
106
99
67
35
38
70
102
31
143
63
122
10
90
19
131
51
118
6
86
 
 
 
What are the special magic features of this 12x12 magic square?
 

(1st) The 12x12 square is panmagic and consists of 16 (disproportional) magic 3x3 squares;
 

(2nd) It is possible to get 9 (proportional) panmagic 4x4 squares from the 12x12 magic square;
see below.
 
 
 12x12 magic square  -->  9x panmagic 4x4 square
81
1
113
56
136
24
93
13
125
60
140
28
97
65
33
40
72
104
109
77
45
44
76
108
17
129
49
120
8
88
29
141
61
124
12
92
62
142
30
91
11
123
50
130
18
87
7
119
46
78
110
107
75
43
34
66
98
103
71
39
126
14
94
27
139
59
114
2
82
23
135
55
52
132
20
85
5
117
64
144
32
89
9
121
36
68
100
101
69
37
48
80
112
105
73
41
116
4
84
21
133
53
128
16
96
25
137
57
95
15
127
58
138
26
83
3
115
54
134
22
111
79
47
42
74
106
99
67
35
38
70
102
31
143
63
122
10
90
19
131
51
118
6
86
 
 
Put for example all yellow marked digits together.
 
 
one of the 9 panmagic 4x4 squares:
 
 
 
290
290
290
290
 
 
 
 
290
 
 
 
 
290
 
 
290
 
81
56
93
60
 
 
 
290
 
62
91
50
87
 
290
290
290
 
52
85
64
89
 
290
290
290
 
95
58
83
54
 
290
290
 
 
 
(3rd) It is possible to get 27 (proportional) panmagic 8x8 squares from the 12x12 magic square.
Take from each of the 16 squares the same 2 digits of the 1st and 2nd ór 1st and 3rd ór 2nd and
3rd column ; see below.
 
 
 
01
 
 
 
 
02
 
 
 
 
03
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
04
 
 
 
 
05
 
 
 
 
06
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
07
 
 
 
 
08
 
 
 
 
09
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10
 
 
 
 
11
 
 
 
 
12
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
13
 
 
 
 
14
 
 
 
 
15
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
16
 
 
 
 
17
 
 
 
 
18
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
19
 
 
 
 
20
 
 
 
 
21
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
22
 
 
 
 
23
 
 
 
 
24
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
25
 
 
 
 
26
 
 
 
 
27
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

For example 12 gives the following panmagic 8x8 square.
 
 
one of the 27 panmagic 8x8 squares:
 
 
 
580
580
580
580
580
580
580
580
 
 
 
 
580
 
 
 
 
 
 
 
 
580
 
 
580
 
81
33
56
104
93
45
60
108
 
 
 
580
 
17
49
120
88
29
61
124
92
 
580