Grids (2)
It is possible to take the shifted versions of grids (1) to construct more panmagic 9x9 squares.
|
Take 1x number from H2' |
Take 1x number from H2'' |
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|
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
||
|
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
||
|
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
||
|
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
||
|
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
||
|
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
||
|
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
||
|
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
||
|
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
||
|
+3x number, from V4' |
+3x number from V4'' |
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|
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
||
|
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
||
|
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
||
|
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
||
|
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
||
|
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
||
|
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
||
|
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
||
|
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
2 |
1 |
0 |
||
|
+ 9x number from V1' |
+ 9x number from V1'' |
||||||||||||||||||
|
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
||
|
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
||
|
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
||
|
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
||
|
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
||
|
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
||
|
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
||
|
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
||
|
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
||
|
+ 27x number from H3' +1 |
+ 27x number from H3'' +1 |
||||||||||||||||||
|
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
||
|
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
||
|
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
||
|
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
||
|
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
||
|
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
||
|
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
||
|
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
||
|
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
1 |
||
|
= panmagic 9x9 ' |
= panmagic 9x9 '' |
||||||||||||||||||
|
25 |
4 |
66 |
81 |
60 |
38 |
53 |
32 |
10 |
25 |
60 |
66 |
81 |
32 |
38 |
53 |
4 |
10 |
||
|
56 |
71 |
49 |
28 |
43 |
24 |
3 |
18 |
77 |
80 |
31 |
37 |
52 |
6 |
12 |
27 |
59 |
65 |
||
|
30 |
45 |
23 |
2 |
17 |
76 |
55 |
70 |
51 |
30 |
17 |
23 |
2 |
70 |
76 |
55 |
45 |
51 |
||
|
1 |
16 |
78 |
57 |
72 |
50 |
29 |
44 |
22 |
1 |
72 |
78 |
57 |
44 |
50 |
29 |
16 |
22 |
||
|
68 |
74 |
34 |
40 |
46 |
9 |
15 |
21 |
62 |
56 |
43 |
49 |
28 |
18 |
24 |
3 |
71 |
77 |
||
|
42 |
48 |
8 |
14 |
20 |
61 |
67 |
73 |
36 |
42 |
20 |
8 |
14 |
73 |
61 |
67 |
48 |
36 |
||
|
13 |
19 |
63 |
69 |
75 |
35 |
41 |
47 |
7 |
13 |
75 |
63 |
69 |
47 |
35 |
41 |
19 |
7 |
||
|
80 |
59 |
37 |
52 |
31 |
12 |
27 |
6 |
65 |
68 |
46 |
34 |
40 |
21 |
9 |
15 |
74 |
62 |
||
|
54 |
33 |
11 |
26 |
5 |
64 |
79 |
58 |
39 |
54 |
5 |
11 |
26 |
58 |
64 |
79 |
33 |
39 |
||
It is possible to combine the original grids with the [double] shifted versions of the grids to construct many more panmagic 9x9 squares.
