Basic pattern method (1)
Use 9x the same panmagic 4x4 square and 2 fixed grids to construct a most perfect (Franklin pan)magic 12x12 square.
|
1x number from grid with 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 number 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 number from 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 this most perfect 12x12 magic square has the extra tight Willem Barink structure.
Use basic pattern method (1) to construct magic squares of order is multiple of 4 from 8x8 to infinity. See 8x8, 12x12, 16x16a, 16x16b, 16x16c, 20x20, 24x24a, 24x24b, 28x28, 32x32a, 32x32b, 32x32c and 32x32d
