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Put only in one Integer
in a and d. |
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Create your own bimagic
square n9 |
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Bimagic Square n9:1.1a |
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MS Matrix n9:1.1b |
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BiMagic Square n9:B.1a |
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Euler Matrix n9:B.1b |
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Put only in Integer from a bimagic square of order 9 |
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| a = |
1 |
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a = 0,1,2,3…… |
[-∞ < a <
∞] |
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22 |
3 |
81 |
42 |
34 |
47 |
17 |
59 |
64 |
20049 |
|
C4 |
A3 |
I9 |
E6 |
D7 |
F2 |
B8 |
G5 |
H1 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
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A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
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2 |
31 |
63 |
25 |
48 |
77 |
15 |
44 |
64 |
20049 |
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37 |
54 |
15 |
71 |
76 |
57 |
32 |
20 |
7 |
20049 |
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E1 |
F9 |
B6 |
H8 |
I4 |
G3 |
D5 |
C2 |
A7 |
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53 |
31 |
39 |
78 |
56 |
70 |
19 |
9 |
14 |
20049 |
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F8 |
D4 |
E3 |
I6 |
G2 |
H7 |
C1 |
A9 |
B5 |
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68 |
16 |
39 |
55 |
6 |
35 |
81 |
20 |
49 |
20049 |
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| d = |
1 |
|
d = 1,2,3,4…… |
num: [d ≠ 0] |
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33 |
38 |
8 |
55 |
72 |
77 |
52 |
13 |
21 |
20049 |
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D6 |
E2 |
A8 |
G1 |
H9 |
I5 |
F7 |
B4 |
C3 |
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68 |
73 |
63 |
12 |
26 |
4 |
43 |
51 |
29 |
20049 |
|
H5 |
I1 |
G9 |
B3 |
C8 |
A4 |
E7 |
F6 |
D2 |
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53 |
73 |
24 |
40 |
72 |
11 |
30 |
59 |
7 |
20049 |
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68 |
73 |
43 |
12 |
26 |
4 |
63 |
51 |
29 |
20049 |
|
H5 |
I1 |
E7 |
B3 |
C8 |
A4 |
G9 |
F6 |
D2 |
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75 |
62 |
67 |
25 |
6 |
11 |
50 |
28 |
45 |
20049 |
|
I3 |
G8 |
H4 |
C7 |
A6 |
B2 |
F5 |
D1 |
E9 |
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37 |
69 |
17 |
36 |
56 |
4 |
50 |
79 |
21 |
20049 |
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| Σ = |
369 |
|
Σy = sum(A1:I9) /n |
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2 |
16 |
58 |
46 |
41 |
36 |
24 |
66 |
80 |
20049 |
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A2 |
B7 |
G4 |
F1 |
E5 |
D9 |
C6 |
H3 |
I8 |
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18 |
23 |
1 |
40 |
48 |
35 |
65 |
79 |
60 |
20049 |
|
B9 |
C5 |
A1 |
E4 |
F3 |
D8 |
H2 |
I7 |
G6 |
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22 |
54 |
74 |
12 |
41 |
70 |
8 |
28 |
60 |
20049 |
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MS DataBase© |
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53 |
31 |
19 |
78 |
56 |
70 |
39 |
9 |
14 |
20049 |
|
F8 |
D4 |
C1 |
I6 |
G2 |
H7 |
E3 |
A9 |
B5 |
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33 |
38 |
52 |
55 |
72 |
77 |
8 |
13 |
21 |
20049 |
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D6 |
E2 |
F7 |
G1 |
H9 |
I5 |
A8 |
B4 |
C3 |
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61 |
3 |
32 |
78 |
26 |
46 |
65 |
13 |
45 |
20049 |
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|
Create your own bimagic square |
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| Σ = |
369 |
|
Σ(n:a,d) = ½·n·[2·a
+ d·(n^2 -1)] |
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61 |
69 |
30 |
5 |
10 |
27 |
74 |
44 |
49 |
20049 |
|
G7 |
H6 |
D3 |
A5 |
B1 |
C9 |
I2 |
E8 |
F4 |
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37 |
54 |
32 |
71 |
76 |
57 |
15 |
20 |
7 |
20049 |
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E1 |
F9 |
D5 |
H8 |
I4 |
G3 |
B6 |
C2 |
A7 |
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75 |
23 |
52 |
71 |
10 |
42 |
58 |
9 |
29 |
20049 |
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[Hunter and Madachy
1975] |
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75 |
62 |
50 |
25 |
6 |
11 |
67 |
28 |
45 |
20049 |
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I3 |
G8 |
F5 |
C7 |
A6 |
B2 |
H4 |
D1 |
E9 |
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61 |
69 |
74 |
5 |
10 |
27 |
30 |
44 |
49 |
20049 |
|
G7 |
H6 |
I2 |
A5 |
B1 |
C9 |
D3 |
E8 |
F4 |
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33 |
62 |
1 |
47 |
76 |
27 |
43 |
66 |
14 |
20049 |
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| |
MS order n = |
9 |
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18 |
23 |
65 |
35 |
48 |
40 |
1 |
79 |
60 |
20049 |
|
B9 |
C5 |
H2 |
D8 |
F3 |
E4 |
A1 |
I7 |
G6 |
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22 |
3 |
17 |
47 |
34 |
42 |
81 |
59 |
64 |
20049 |
|
C4 |
A3 |
B8 |
F2 |
D7 |
E6 |
I9 |
G5 |
H1 |
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18 |
38 |
67 |
5 |
34 |
57 |
19 |
51 |
80 |
20049 |
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The Key |
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369 |
369 |
369 |
369 |
1225449 |
369 |
369 |
369 |
369 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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A1 |
= |
1 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C4[1] |
F9 |
A8 |
B3 |
E5 |
H7 |
I2 |
D1 |
G6 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A2 |
D4 |
G9 |
C7 |
F3 |
I5 |
B6 |
E8 |
H1 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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A2 |
= |
2 |
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B9 |
G8 |
D3 |
I6 |
E5 |
A4 |
F7 |
C2 |
H1 |
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C4 |
H6 |
D5 |
G1 |
F3 |
B2 |
E7 |
A9 |
I8 |
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A3 |
= |
3 |
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[2] |
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A4 |
= |
4 |
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A5 |
= |
5 |
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| |
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A6 |
= |
6 |
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|
Bimagic Square n9:1.2a |
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|
Euler´s Matrix n9:1.2b |
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BiMagic Square n9:B.2a |
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Euler Matrix n9:B.2b |
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New One Bimagic Square n9 |
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| |
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A7 |
= |
7 |
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24 |
7 |
73 |
53 |
30 |
40 |
11 |
59 |
72 |
20049 |
|
C6 |
A7 |
I1 |
F8 |
D3 |
E4 |
B2 |
G5 |
H9 |
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|
8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
|
A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
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2 |
39 |
73 |
50 |
60 |
13 |
71 |
27 |
34 |
20049 |
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| |
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A8 |
= |
8 |
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45 |
46 |
13 |
65 |
78 |
61 |
32 |
26 |
3 |
20049 |
|
E9 |
F1 |
B4 |
H2 |
I6 |
G7 |
D5 |
C8 |
A3 |
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|
47 |
33 |
43 |
76 |
62 |
66 |
27 |
1 |
14 |
20049 |
|
F2 |
D6 |
E7 |
I4 |
G8 |
H3 |
C9 |
A1 |
B5 |
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63 |
16 |
53 |
21 |
28 |
65 |
42 |
76 |
5 |
20049 |
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| |
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A9 |
= |
9 |
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31 |
44 |
2 |
63 |
64 |
77 |
48 |
15 |
25 |
20049 |
|
D4 |
E8 |
A2 |
G9 |
H1 |
I5 |
F3 |
B6 |
C7 |
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|
68 |
81 |
55 |
16 |
20 |
6 |
39 |
49 |
35 |
20049 |
|
H5 |
I9 |
G1 |
B7 |
C2 |
A6 |
E3 |
F4 |
D8 |
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31 |
68 |
24 |
79 |
8 |
45 |
10 |
47 |
57 |
20049 |
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| |
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B1 |
= |
10 |
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|
68 |
81 |
39 |
16 |
20 |
6 |
55 |
49 |
35 |
20049 |
|
H5 |
I9 |
E3 |
B7 |
C2 |
A6 |
G1 |
F4 |
D8 |
|
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|
|
|
79 |
56 |
69 |
21 |
4 |
17 |
50 |
36 |
37 |
20049 |
|
I7 |
G2 |
H6 |
C3 |
A4 |
B8 |
F5 |
D9 |
E1 |
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15 |
49 |
59 |
36 |
70 |
26 |
75 |
1 |
38 |
20049 |
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| |
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|
B2 |
= |
11 |
|
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|
8 |
12 |
60 |
28 |
41 |
54 |
22 |
70 |
74 |
20049 |
|
A8 |
B3 |
G6 |
D1 |
E5 |
F9 |
C4 |
H7 |
I2 |
|
|
|
|
|
10 |
23 |
9 |
42 |
52 |
29 |
71 |
75 |
58 |
20049 |
|
B1 |
C5 |
A9 |
E6 |
F7 |
D2 |
H8 |
I3 |
G4 |
|
|
|
|
|
64 |
20 |
30 |
4 |
41 |
78 |
52 |
62 |
18 |
20049 |
|
|
|
|
|
|
|
MS DataBase© |
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| |
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|
B3 |
= |
12 |
|
|
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|
47 |
33 |
27 |
76 |
62 |
66 |
43 |
1 |
14 |
20049 |
|
F2 |
D6 |
C9 |
I4 |
G8 |
H3 |
E7 |
A1 |
B5 |
|
|
|
|
|
31 |
44 |
48 |
63 |
64 |
77 |
2 |
15 |
25 |
20049 |
|
D4 |
E8 |
F3 |
G9 |
H1 |
I5 |
A2 |
B6 |
C7 |
|
|
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|
44 |
81 |
7 |
56 |
12 |
46 |
23 |
33 |
67 |
20049 |
|
|
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|
|
|
Create your own bimagic square |
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| |
|
|
B4 |
= |
13 |
|
|
|
|
57 |
67 |
34 |
5 |
18 |
19 |
80 |
38 |
51 |
20049 |
|
G3 |
H4 |
D7 |
A5 |
B9 |
C1 |
I8 |
E2 |
F6 |
|
|
|
|
|
45 |
46 |
32 |
65 |
78 |
61 |
13 |
26 |
3 |
20049 |
|
E9 |
F1 |
D5 |
H2 |
I6 |
G7 |
B4 |
C8 |
A3 |
|
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25 |
35 |
72 |
37 |
74 |
3 |
58 |
14 |
51 |
20049 |
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| |
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|
B5 |
= |
14 |
|
|
|
|
79 |
56 |
50 |
21 |
4 |
17 |
69 |
36 |
37 |
20049 |
|
I7 |
G2 |
F5 |
C3 |
A4 |
B8 |
H6 |
D9 |
E1 |
|
|
|
|
|
57 |
67 |
80 |
5 |
18 |
19 |
34 |
38 |
51 |
20049 |
|
G3 |
H4 |
I8 |
A5 |
B9 |
C1 |
D7 |
E2 |
F6 |
|
|
|
|
|
77 |
6 |
40 |
17 |
54 |
61 |
29 |
66 |
19 |
20049 |
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| |
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|
B6 |
= |
15 |
|
|
|
|
10 |
23 |
71 |
42 |
52 |
29 |
9 |
75 |
58 |
20049 |
|
B1 |
C5 |
H8 |
E6 |
F7 |
D2 |
A9 |
I3 |
G4 |
|
|
|
|
|
24 |
7 |
11 |
53 |
30 |
40 |
73 |
59 |
72 |
20049 |
|
C6 |
A7 |
B2 |
F8 |
D3 |
E4 |
I1 |
G5 |
H9 |
|
|
|
|
|
48 |
55 |
11 |
69 |
22 |
32 |
9 |
43 |
80 |
20049 |
|
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| |
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|
B7 |
= |
16 |
|
|
|
|
369 |
369 |
369 |
369 |
1225449 |
369 |
369 |
369 |
369 |
1225449 |
|
|
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|
|
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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| |
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B8 |
= |
17 |
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C6[3] |
F1 |
A2 |
B7 |
E5 |
H3 |
I8 |
D9 |
G4 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A8 |
D6 |
G1 |
C3 |
F7 |
I5 |
B4 |
E2 |
H9 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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| |
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B9 |
= |
18 |
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|
B1 |
G2 |
D7 |
I4 |
E5 |
A6 |
F3 |
C8 |
H9 |
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|
C6 |
H4 |
D5 |
G9 |
F7 |
B8 |
E3 |
A1 |
I2 |
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| |
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C1 |
= |
19 |
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[4] |
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MS DataBase© |
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| |
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C2 |
= |
20 |
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| |
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C3 |
= |
21 |
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| |
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C4 |
= |
22 |
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|
Bimagic Square n9:1.3a |
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Euler´s Matrix n9:1.3b |
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BiMagic Square n9:B.3a |
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Euler Matrix n9:B.3b |
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New Two Bimagic Square n9 |
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| |
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C5 |
= |
23 |
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|
20 |
7 |
81 |
49 |
30 |
44 |
15 |
59 |
64 |
20049 |
|
C2 |
A7 |
I9 |
F4 |
D3 |
E8 |
B6 |
G5 |
H1 |
|
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|
4 |
18 |
20 |
30 |
41 |
52 |
62 |
64 |
78 |
20049 |
|
A4 |
B9 |
C2 |
D3 |
E5 |
F7 |
G8 |
H1 |
I6 |
|
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2 |
53 |
68 |
75 |
18 |
33 |
37 |
61 |
22 |
20049 |
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| |
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C6 |
= |
24 |
|
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|
37 |
54 |
17 |
69 |
74 |
61 |
32 |
22 |
3 |
20049 |
|
E1 |
F9 |
B8 |
H6 |
I2 |
G7 |
D5 |
C4 |
A3 |
|
|
|
|
|
51 |
35 |
37 |
74 |
58 |
72 |
25 |
3 |
14 |
20049 |
|
F6 |
D8 |
E1 |
I2 |
G4 |
H9 |
C7 |
A3 |
B5 |
|
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|
|
73 |
16 |
31 |
38 |
62 |
23 |
3 |
54 |
69 |
20049 |
|
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| |
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C7 |
= |
25 |
|
|
|
|
35 |
40 |
6 |
55 |
72 |
77 |
48 |
11 |
25 |
20049 |
|
D8 |
E4 |
A6 |
G1 |
H9 |
I5 |
F3 |
B2 |
C7 |
|
|
|
|
|
68 |
79 |
57 |
10 |
24 |
8 |
45 |
47 |
31 |
20049 |
|
H5 |
I7 |
G3 |
B1 |
C6 |
A8 |
E9 |
F2 |
D4 |
|
|
|
|
|
39 |
63 |
24 |
1 |
52 |
67 |
74 |
17 |
32 |
20049 |
|
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| |
|
|
C8 |
= |
26 |
|
|
|
|
68 |
73 |
39 |
16 |
24 |
2 |
63 |
53 |
31 |
20049 |
|
H5 |
I1 |
E3 |
B7 |
C6 |
A2 |
G9 |
F8 |
D4 |
|
|
|
|
|
73 |
60 |
71 |
27 |
2 |
13 |
50 |
34 |
39 |
20049 |
|
I1 |
G6 |
H8 |
C9 |
A2 |
B4 |
F5 |
D7 |
E3 |
|
|
|
|
|
71 |
5 |
47 |
36 |
78 |
12 |
25 |
40 |
55 |
20049 |
|
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| |
|
|
C9 |
= |
27 |
|
|
|
|
4 |
12 |
56 |
36 |
41 |
46 |
26 |
70 |
78 |
20049 |
|
A4 |
B3 |
G2 |
D9 |
E5 |
F1 |
C8 |
H7 |
I6 |
|
|
|
|
|
12 |
23 |
7 |
44 |
46 |
33 |
67 |
81 |
56 |
20049 |
|
B3 |
C5 |
A7 |
E8 |
F1 |
D6 |
H4 |
I9 |
G2 |
|
|
|
|
|
34 |
76 |
10 |
26 |
41 |
56 |
72 |
6 |
48 |
20049 |
|
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|
MS DataBase© |
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| |
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D1 |
= |
28 |
|
|
|
|
51 |
29 |
19 |
80 |
58 |
66 |
43 |
9 |
14 |
20049 |
|
F6 |
D2 |
C1 |
I8 |
G4 |
H3 |
E7 |
A9 |
B5 |
|
|
|
|
|
29 |
40 |
54 |
61 |
66 |
77 |
6 |
17 |
19 |
20049 |
|
D2 |
E4 |
F9 |
G7 |
H3 |
I5 |
A6 |
B8 |
C1 |
|
|
|
|
|
27 |
42 |
57 |
70 |
4 |
46 |
35 |
77 |
11 |
20049 |
|
|
|
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|
|
Create your own bimagic square |
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| |
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D2 |
= |
29 |
|
|
|
|
57 |
71 |
34 |
5 |
10 |
27 |
76 |
42 |
47 |
20049 |
|
G3 |
H8 |
D7 |
A5 |
B1 |
C9 |
I4 |
E6 |
F2 |
|
|
|
|
|
43 |
48 |
32 |
69 |
80 |
55 |
11 |
22 |
9 |
20049 |
|
E7 |
F3 |
D5 |
H6 |
I8 |
G1 |
B2 |
C4 |
A9 |
|
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|
50 |
65 |
8 |
15 |
30 |
81 |
58 |
19 |
43 |
20049 |
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| |
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D3 |
= |
30 |
|
|
|
|
79 |
60 |
50 |
21 |
8 |
13 |
65 |
28 |
45 |
20049 |
|
I7 |
G6 |
F5 |
C3 |
A8 |
B4 |
H2 |
D1 |
E9 |
|
|
|
|
|
63 |
65 |
76 |
5 |
16 |
21 |
28 |
42 |
53 |
20049 |
|
G9 |
H2 |
I4 |
A5 |
B7 |
C3 |
D1 |
E6 |
F8 |
|
|
|
|
|
13 |
28 |
79 |
59 |
20 |
44 |
51 |
66 |
9 |
20049 |
|
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| |
|
|
D4 |
= |
31 |
|
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|
|
18 |
23 |
67 |
38 |
52 |
33 |
1 |
75 |
62 |
20049 |
|
B9 |
C5 |
H4 |
E2 |
F7 |
D6 |
A1 |
I3 |
G8 |
|
|
|
|
|
26 |
1 |
15 |
49 |
36 |
38 |
75 |
59 |
70 |
20049 |
|
C8 |
A1 |
B6 |
F4 |
D9 |
E2 |
I3 |
G5 |
H7 |
|
|
|
|
|
60 |
21 |
45 |
49 |
64 |
7 |
14 |
29 |
80 |
20049 |
|
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|
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|
|
|
|
|
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| |
|
|
D5 |
= |
32 |
|
|
|
|
369 |
369 |
369 |
369 |
1225449 |
369 |
369 |
369 |
369 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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|
|
|
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|
| |
|
|
D6 |
= |
33 |
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C2[5] |
F9 |
A6 |
B7 |
E5 |
H3 |
I4 |
D1 |
G8 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A4 |
D8 |
G3 |
C9 |
F1 |
I5 |
B2 |
E6 |
H7 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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| |
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D7 |
= |
34 |
|
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|
B9 |
G6 |
D7 |
I8 |
E5 |
A2 |
F3 |
C4 |
H1 |
|
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|
C8 |
H2 |
D5 |
G7 |
F1 |
B4 |
E9 |
A3 |
I6 |
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| |
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D8 |
= |
35 |
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|
[6] |
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|
|
MS DataBase© |
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|
| |
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|
D9 |
= |
36 |
|
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| |
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E1 |
= |
37 |
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|
Create your own bimagic
square n9 |
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|
| |
|
|
E2 |
= |
38 |
|
|
|
|
|
|
|
|
Bimagic Square n9:1.4a |
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|
|
|
|
|
|
|
Euler´s Matrix n9:1.4b |
|
|
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|
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|
|
|
|
|
|
BiMagic Square n9:B.4a |
|
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|
|
Euler Matrix n9:B.4b |
|
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|
|
Put only in Integer from a bimagic square of order 9 |
|
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| |
|
|
E3 |
= |
39 |
|
|
|
|
26 |
3 |
73 |
51 |
34 |
38 |
13 |
59 |
72 |
20049 |
|
C8 |
A3 |
I1 |
F6 |
D7 |
E2 |
B4 |
G5 |
H9 |
|
|
|
|
|
6 |
10 |
26 |
34 |
41 |
48 |
56 |
72 |
76 |
20049 |
|
A6 |
B1 |
C8 |
D7 |
E5 |
F3 |
G2 |
H9 |
I4 |
|
|
|
|
|
2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
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|
|
|
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|
|
|
|
|
|
| |
|
|
E4 |
= |
40 |
|
|
|
|
45 |
46 |
11 |
67 |
80 |
57 |
32 |
24 |
7 |
20049 |
|
E9 |
F1 |
B2 |
H4 |
I8 |
G3 |
D5 |
C6 |
A7 |
|
|
|
|
|
49 |
29 |
45 |
80 |
60 |
64 |
21 |
7 |
14 |
20049 |
|
F4 |
D2 |
E9 |
I8 |
G6 |
H1 |
C3 |
A7 |
B5 |
|
|
|
|
|
31 |
39 |
53 |
56 |
70 |
78 |
9 |
14 |
19 |
20049 |
|
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|
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|
| |
|
|
E5 |
= |
41 |
|
|
|
|
29 |
42 |
4 |
63 |
64 |
77 |
52 |
17 |
21 |
20049 |
|
D2 |
E6 |
A4 |
G9 |
H1 |
I5 |
F7 |
B8 |
C3 |
|
|
|
|
|
68 |
75 |
61 |
18 |
22 |
2 |
37 |
53 |
33 |
20049 |
|
H5 |
I3 |
G7 |
B9 |
C4 |
A2 |
E1 |
F8 |
D6 |
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|
63 |
68 |
73 |
4 |
12 |
26 |
29 |
43 |
51 |
20049 |
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| |
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E6 |
= |
42 |
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68 |
81 |
43 |
12 |
22 |
8 |
55 |
47 |
33 |
20049 |
|
H5 |
I9 |
E7 |
B3 |
C4 |
A8 |
G1 |
F2 |
D6 |
|
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|
81 |
58 |
65 |
19 |
8 |
15 |
50 |
30 |
43 |
20049 |
|
I9 |
G4 |
H2 |
C1 |
A8 |
B6 |
F5 |
D3 |
E7 |
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25 |
6 |
11 |
50 |
28 |
45 |
75 |
62 |
67 |
20049 |
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| |
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E7 |
= |
43 |
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6 |
16 |
62 |
28 |
41 |
54 |
20 |
66 |
76 |
20049 |
|
A6 |
B7 |
G8 |
D1 |
E5 |
F9 |
C2 |
H3 |
I4 |
|
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|
|
16 |
23 |
3 |
38 |
54 |
31 |
69 |
73 |
62 |
20049 |
|
B7 |
C5 |
A3 |
E2 |
F9 |
D4 |
H6 |
I1 |
G8 |
|
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|
48 |
35 |
40 |
79 |
60 |
65 |
23 |
1 |
18 |
20049 |
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|
MS DataBase© |
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| |
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E8 |
= |
44 |
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49 |
35 |
27 |
74 |
60 |
70 |
39 |
1 |
14 |
20049 |
|
F4 |
D8 |
C9 |
I2 |
G6 |
H7 |
E3 |
A1 |
B5 |
|
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|
35 |
42 |
46 |
57 |
70 |
77 |
4 |
11 |
27 |
20049 |
|
D8 |
E6 |
F1 |
G3 |
H7 |
I5 |
A4 |
B2 |
C9 |
|
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|
77 |
55 |
72 |
21 |
8 |
13 |
52 |
33 |
38 |
20049 |
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Create your own bimagic square |
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| |
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E9 |
= |
45 |
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|
61 |
65 |
30 |
5 |
18 |
19 |
78 |
40 |
53 |
20049 |
|
G7 |
H2 |
D3 |
A5 |
B9 |
C1 |
I6 |
E4 |
F8 |
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|
39 |
52 |
32 |
67 |
74 |
63 |
17 |
24 |
1 |
20049 |
|
E3 |
F7 |
D5 |
H4 |
I2 |
G9 |
B8 |
C6 |
A1 |
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15 |
20 |
7 |
37 |
54 |
32 |
71 |
76 |
57 |
20049 |
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| |
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F1 |
= |
46 |
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|
75 |
58 |
50 |
25 |
2 |
15 |
71 |
36 |
37 |
20049 |
|
I3 |
G4 |
F5 |
C7 |
A2 |
B6 |
H8 |
D9 |
E1 |
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|
55 |
71 |
78 |
5 |
12 |
25 |
36 |
40 |
47 |
20049 |
|
G1 |
H8 |
I6 |
A5 |
B3 |
C7 |
D9 |
E4 |
F2 |
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44 |
49 |
30 |
69 |
74 |
61 |
10 |
27 |
5 |
20049 |
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A1-A8, B1-B8, C1-C8 |
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| |
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F2 |
= |
47 |
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10 |
23 |
69 |
44 |
48 |
31 |
9 |
79 |
56 |
20049 |
|
B1 |
C5 |
H6 |
E8 |
F3 |
D4 |
A9 |
I7 |
G2 |
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20 |
9 |
13 |
51 |
28 |
44 |
79 |
59 |
66 |
20049 |
|
C2 |
A9 |
B4 |
F6 |
D1 |
E8 |
I7 |
G5 |
H3 |
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|
64 |
81 |
59 |
17 |
22 |
3 |
42 |
47 |
34 |
20049 |
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| |
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F3 |
= |
48 |
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|
369 |
369 |
369 |
369 |
1225449 |
369 |
369 |
369 |
369 |
1225449 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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| |
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F4 |
= |
49 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C8[7] |
F1 |
A4 |
B3 |
E5 |
H7 |
I6 |
D9 |
G3 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A6 |
D2 |
G7 |
C1 |
F9 |
I5 |
B8 |
E4 |
H3 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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| |
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F5 |
= |
50 |
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B1 |
G4 |
D3 |
I2 |
E5 |
A8 |
F7 |
C6 |
H9 |
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C2 |
H8 |
D5 |
G3 |
F9 |
B6 |
E1 |
A7 |
I4 |
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| |
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F6 |
= |
51 |
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[8] |
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| |
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F7 |
= |
52 |
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| |
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F8 |
= |
53 |
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| |
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F9 |
= |
54 |
|
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|
Bimagic Square n9:2.1a |
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MS Matrix n9:2.1b |
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BiMagic Square n9:B.5a |
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Euler Matrix n9:B.5b |
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New One Bimagic Square n9 |
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| |
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G1 |
= |
55 |
|
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|
64 |
59 |
17 |
40 |
48 |
35 |
81 |
3 |
22 |
20049 |
|
H1 |
G5 |
B8 |
E4 |
F3 |
D8 |
I9 |
A3 |
C4 |
|
|
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|
|
2 |
18 |
22 |
34 |
41 |
48 |
60 |
64 |
80 |
20049 |
|
A2 |
B9 |
C4 |
D7 |
E5 |
F3 |
G6 |
H1 |
I8 |
|
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|
2 |
24 |
16 |
58 |
80 |
66 |
36 |
46 |
41 |
20049 |
|
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| |
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G2 |
= |
56 |
|
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|
7 |
20 |
67 |
57 |
6 |
71 |
50 |
54 |
37 |
20049 |
|
A7 |
C2 |
H4 |
G3 |
A6 |
H8 |
F5 |
F9 |
E1 |
|
|
|
|
|
53 |
33 |
37 |
76 |
56 |
72 |
21 |
7 |
14 |
20049 |
|
F8 |
D6 |
E1 |
I4 |
G2 |
H9 |
C3 |
A7 |
B5 |
|
|
|
|
|
53 |
39 |
31 |
19 |
14 |
9 |
78 |
70 |
56 |
20049 |
|
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| |
|
|
G3 |
= |
57 |
|
|
|
|
21 |
38 |
52 |
77 |
72 |
55 |
8 |
13 |
33 |
20049 |
|
C3 |
E2 |
F7 |
I5 |
H9 |
G1 |
A8 |
B4 |
D6 |
|
|
|
|
|
68 |
75 |
61 |
10 |
26 |
6 |
45 |
49 |
29 |
20049 |
|
H5 |
I3 |
G7 |
B1 |
C8 |
A6 |
E9 |
F4 |
D2 |
|
|
|
|
|
68 |
63 |
73 |
43 |
29 |
51 |
12 |
4 |
26 |
20049 |
|
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|
|
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|
| |
|
|
G4 |
= |
58 |
|
|
|
|
53 |
51 |
63 |
4 |
56 |
12 |
43 |
73 |
14 |
20049 |
|
F8 |
F6 |
G9 |
A4 |
G2 |
B3 |
E7 |
I1 |
B5 |
|
|
|
|
|
73 |
62 |
69 |
27 |
4 |
11 |
50 |
30 |
43 |
20049 |
|
I1 |
G8 |
H6 |
C9 |
A4 |
B2 |
F5 |
D3 |
E7 |
|
|
|
|
|
75 |
67 |
62 |
50 |
45 |
28 |
25 |
11 |
6 |
20049 |
|
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| |
|
|
G5 |
= |
59 |
|
|
|
|
2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
|
|
|
|
|
16 |
23 |
3 |
42 |
46 |
35 |
65 |
81 |
58 |
20049 |
|
B7 |
C5 |
A3 |
E6 |
F1 |
D8 |
H2 |
I9 |
G4 |
|
|
|
|
|
18 |
1 |
23 |
65 |
60 |
79 |
40 |
35 |
48 |
20049 |
|
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|
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|
|
MS DataBase© |
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| |
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G6 |
= |
60 |
|
|
|
|
68 |
9 |
39 |
70 |
26 |
78 |
19 |
31 |
29 |
20049 |
|
H5 |
A9 |
E3 |
H7 |
C8 |
I6 |
C1 |
D4 |
D2 |
|
|
|
|
|
31 |
38 |
54 |
57 |
70 |
77 |
8 |
15 |
19 |
20049 |
|
D4 |
E2 |
F9 |
G3 |
H7 |
I5 |
A8 |
B6 |
C1 |
|
|
|
|
|
33 |
52 |
38 |
8 |
21 |
13 |
55 |
77 |
72 |
20049 |
|
|
|
|
|
|
|
Create your own bimagic square |
|
|
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| |
|
|
G7 |
= |
61 |
|
|
|
|
49 |
69 |
74 |
27 |
10 |
5 |
30 |
44 |
61 |
20049 |
|
F4 |
H6 |
I2 |
C9 |
B1 |
A5 |
D3 |
E8 |
G7 |
|
|
|
|
|
39 |
52 |
32 |
71 |
78 |
55 |
13 |
20 |
9 |
20049 |
|
E3 |
F7 |
D5 |
H8 |
I6 |
G1 |
B4 |
C2 |
A9 |
|
|
|
|
|
37 |
32 |
54 |
15 |
7 |
20 |
71 |
57 |
76 |
20049 |
|
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|
| |
|
|
G8 |
= |
62 |
|
|
|
|
45 |
28 |
32 |
11 |
76 |
25 |
15 |
62 |
75 |
20049 |
|
E9 |
D1 |
D5 |
B2 |
I4 |
C7 |
B6 |
G8 |
I3 |
|
|
|
|
|
63 |
67 |
74 |
5 |
12 |
25 |
28 |
44 |
51 |
20049 |
|
G9 |
H4 |
I2 |
A5 |
B3 |
C7 |
D1 |
E8 |
F6 |
|
|
|
|
|
61 |
74 |
69 |
30 |
49 |
44 |
5 |
27 |
10 |
20049 |
|
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|
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|
| |
|
|
G9 |
= |
63 |
|
|
|
|
60 |
79 |
1 |
47 |
34 |
42 |
65 |
23 |
18 |
20049 |
|
G6 |
I7 |
A1 |
F2 |
D7 |
E6 |
H2 |
C5 |
B9 |
|
|
|
|
|
24 |
1 |
17 |
47 |
36 |
40 |
79 |
59 |
66 |
20049 |
|
C6 |
A1 |
B8 |
F2 |
D9 |
E4 |
I7 |
G5 |
H3 |
|
|
|
|
|
22 |
17 |
3 |
81 |
64 |
59 |
47 |
42 |
34 |
20049 |
|
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|
| |
|
|
H1 |
= |
64 |
|
|
|
|
369 |
369 |
369 |
20049 |
20049 |
20049 |
369 |
369 |
369 |
1225449 |
|
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|
|
|
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|
|
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|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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|
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|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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| |
|
|
H2 |
= |
65 |
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
H1[9] |
C2 |
F7 |
A4 |
E5 |
I6 |
D3 |
G8 |
B9 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A2 |
D6 |
G7 |
C9 |
F1 |
I5 |
B4 |
E8 |
H3 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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| |
|
|
H3 |
= |
66 |
|
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|
G6 |
D1 |
I2 |
H7 |
E5 |
B3 |
A8 |
F9 |
C4 |
|
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C6 |
H4 |
D5 |
G3 |
F1 |
B2 |
E9 |
A7 |
I8 |
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| |
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H4 |
= |
67 |
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|
MS DataBase© |
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| |
|
|
H5 |
= |
68 |
|
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H6 |
= |
69 |
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Create your own bimagic
square n9 |
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H7 |
= |
70 |
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Bimagic Square n9:2.2a |
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MS Matrix n9:2.2b |
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BiMagic Square n9:B.6a |
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Euler Matrix n9:B.6b |
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Put only in Integer from a bimagic square of order 9 |
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H8 |
= |
71 |
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72 |
59 |
11 |
42 |
52 |
29 |
73 |
7 |
24 |
20049 |
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H9 |
G5 |
B2 |
E6 |
F7 |
D2 |
I1 |
A7 |
C6 |
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8 |
10 |
24 |
30 |
41 |
52 |
58 |
72 |
74 |
20049 |
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A8 |
B1 |
C6 |
D3 |
E5 |
F7 |
G4 |
H9 |
I2 |
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2 |
31 |
63 |
25 |
48 |
77 |
15 |
44 |
64 |
20049 |
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H9 |
= |
72 |
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3 |
26 |
69 |
61 |
4 |
65 |
50 |
46 |
45 |
20049 |
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A3 |
C8 |
H6 |
G7 |
A4 |
H2 |
F5 |
F1 |
E9 |
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47 |
31 |
45 |
78 |
62 |
64 |
25 |
3 |
14 |
20049 |
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F2 |
D4 |
E9 |
I6 |
G8 |
H1 |
C7 |
A3 |
B5 |
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68 |
16 |
39 |
55 |
6 |
35 |
81 |
20 |
49 |
20049 |
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I1 |
= |
73 |
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25 |
44 |
48 |
77 |
64 |
63 |
2 |
15 |
31 |
20049 |
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C7 |
E8 |
F3 |
I5 |
H1 |
G9 |
A2 |
B6 |
D4 |
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68 |
79 |
57 |
18 |
20 |
4 |
37 |
51 |
35 |
20049 |
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H5 |
I7 |
G3 |
B9 |
C2 |
A4 |
E1 |
F6 |
D8 |
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53 |
73 |
24 |
40 |
72 |
11 |
30 |
59 |
7 |
20049 |
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I2 |
= |
74 |
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47 |
49 |
55 |
6 |
62 |
16 |
39 |
81 |
14 |
20049 |
|
F2 |
F4 |
G1 |
A6 |
G8 |
B7 |
E3 |
I9 |
B5 |
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81 |
56 |
67 |
19 |
6 |
17 |
50 |
34 |
39 |
20049 |
|
I9 |
G2 |
H4 |
C1 |
A6 |
B8 |
F5 |
D7 |
E3 |
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37 |
69 |
17 |
36 |
56 |
4 |
50 |
79 |
21 |
20049 |
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I3 |
= |
75 |
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8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
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A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
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12 |
23 |
7 |
40 |
54 |
29 |
71 |
73 |
60 |
20049 |
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B3 |
C5 |
A7 |
E4 |
F9 |
D2 |
H8 |
I1 |
G6 |
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22 |
54 |
74 |
12 |
41 |
70 |
8 |
28 |
60 |
20049 |
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MS DataBase© |
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I4 |
= |
76 |
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68 |
1 |
43 |
66 |
20 |
76 |
27 |
33 |
35 |
20049 |
|
H5 |
A1 |
E7 |
H3 |
C2 |
I4 |
C9 |
D6 |
D8 |
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33 |
44 |
46 |
61 |
66 |
77 |
2 |
13 |
27 |
20049 |
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D6 |
E8 |
F1 |
G7 |
H3 |
I5 |
A2 |
B4 |
C9 |
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61 |
3 |
32 |
78 |
26 |
46 |
65 |
13 |
45 |
20049 |
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Create your own bimagic square |
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I5 |
= |
77 |
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51 |
67 |
80 |
19 |
18 |
5 |
34 |
38 |
57 |
20049 |
|
F6 |
H4 |
I8 |
C1 |
B9 |
A5 |
D7 |
E2 |
G3 |
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43 |
48 |
32 |
65 |
76 |
63 |
15 |
26 |
1 |
20049 |
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E7 |
F3 |
D5 |
H2 |
I4 |
G9 |
B6 |
C8 |
A1 |
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75 |
23 |
52 |
71 |
10 |
42 |
58 |
9 |
29 |
20049 |
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I6 |
= |
78 |
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37 |
36 |
32 |
17 |
78 |
21 |
13 |
56 |
79 |
20049 |
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E1 |
D9 |
D5 |
B8 |
I6 |
C3 |
B4 |
G2 |
I7 |
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55 |
69 |
80 |
5 |
16 |
21 |
36 |
38 |
49 |
20049 |
|
G1 |
H6 |
I8 |
A5 |
B7 |
C3 |
D9 |
E2 |
F4 |
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33 |
62 |
1 |
47 |
76 |
27 |
43 |
66 |
14 |
20049 |
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| |
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I7 |
= |
79 |
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58 |
75 |
9 |
53 |
30 |
40 |
71 |
23 |
10 |
20049 |
|
G4 |
I3 |
A9 |
F8 |
D3 |
E4 |
H8 |
C5 |
B1 |
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22 |
9 |
11 |
53 |
28 |
42 |
75 |
59 |
70 |
20049 |
|
C4 |
A9 |
B2 |
F8 |
D1 |
E6 |
I3 |
G5 |
H7 |
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18 |
38 |
67 |
5 |
34 |
57 |
19 |
51 |
80 |
20049 |
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| |
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I8 |
= |
80 |
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369 |
369 |
369 |
20049 |
20049 |
20049 |
369 |
369 |
369 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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| |
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I9 |
= |
81 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
H9 |
C8 |
F3 |
A6 |
E5 |
I4 |
D7 |
G2 |
B1 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A8 |
D4 |
G3 |
C1 |
F9 |
I5 |
B6 |
E2 |
H7 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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G4 |
D9 |
I8 |
H3 |
E5 |
B7 |
A2 |
F1 |
C6 |
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C4 |
H6 |
D5 |
G7 |
F9 |
B8 |
E1 |
A3 |
I2 |
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MQM copy right © 2019 |
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Bimagic Square n9:3.1a |
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Euler Matrix n9:3.1b |
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BiMagic Square n9:B.7a |
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Euler Matrix n9:B.7b |
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New One Bimagic Square n9 |
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22 |
3 |
17 |
47 |
34 |
42 |
81 |
59 |
64 |
20049 |
|
C4 |
A3 |
B8 |
F2 |
D7 |
E6 |
I9 |
G5 |
H1 |
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4 |
12 |
26 |
36 |
41 |
46 |
56 |
70 |
78 |
20049 |
|
A4 |
B3 |
C8 |
D9 |
E5 |
F1 |
G2 |
H7 |
I6 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
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37 |
54 |
32 |
71 |
76 |
57 |
15 |
20 |
7 |
20049 |
|
E1 |
F9 |
D5 |
H8 |
I4 |
G3 |
B6 |
C2 |
A7 |
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51 |
29 |
43 |
80 |
58 |
66 |
19 |
9 |
14 |
20049 |
|
F6 |
D2 |
E7 |
I8 |
G4 |
H3 |
C1 |
A9 |
B5 |
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63 |
68 |
73 |
4 |
12 |
26 |
29 |
43 |
51 |
20049 |
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61 |
69 |
74 |
5 |
10 |
27 |
30 |
44 |
49 |
20049 |
|
G7 |
H6 |
I2 |
A5 |
B1 |
C9 |
D3 |
E8 |
F4 |
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68 |
73 |
63 |
16 |
24 |
2 |
39 |
53 |
31 |
20049 |
|
H5 |
I1 |
G9 |
B7 |
C6 |
A2 |
E3 |
F8 |
D4 |
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31 |
39 |
53 |
56 |
70 |
78 |
9 |
14 |
19 |
20049 |
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68 |
73 |
63 |
12 |
26 |
4 |
43 |
51 |
29 |
20049 |
|
H5 |
I1 |
G9 |
B3 |
C8 |
A4 |
E7 |
F6 |
D2 |
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79 |
60 |
65 |
21 |
8 |
13 |
50 |
28 |
45 |
20049 |
|
I7 |
G6 |
H2 |
C3 |
A8 |
B4 |
F5 |
D1 |
E9 |
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15 |
20 |
7 |
37 |
54 |
32 |
71 |
76 |
57 |
20049 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
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18 |
23 |
1 |
38 |
52 |
33 |
67 |
75 |
62 |
20049 |
|
B9 |
C5 |
A1 |
E2 |
F7 |
D6 |
H4 |
I3 |
G8 |
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64 |
81 |
59 |
17 |
22 |
3 |
42 |
47 |
34 |
20049 |
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MS DataBase© |
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53 |
31 |
39 |
78 |
56 |
70 |
19 |
9 |
14 |
20049 |
|
F8 |
D4 |
E3 |
I6 |
G2 |
H7 |
C1 |
A9 |
B5 |
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35 |
40 |
48 |
55 |
72 |
77 |
6 |
11 |
25 |
20049 |
|
D8 |
E4 |
F3 |
G1 |
H9 |
I5 |
A6 |
B2 |
C7 |
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44 |
49 |
30 |
69 |
74 |
61 |
10 |
27 |
5 |
20049 |
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Create your own bimagic square |
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33 |
38 |
52 |
55 |
72 |
77 |
8 |
13 |
21 |
20049 |
|
D6 |
E2 |
F7 |
G1 |
H9 |
I5 |
A8 |
B4 |
C3 |
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37 |
54 |
32 |
69 |
74 |
61 |
17 |
22 |
3 |
20049 |
|
E1 |
F9 |
D5 |
H6 |
I2 |
G7 |
B8 |
C4 |
A3 |
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25 |
6 |
11 |
50 |
28 |
45 |
75 |
62 |
67 |
20049 |
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75 |
62 |
67 |
25 |
6 |
11 |
50 |
28 |
45 |
20049 |
|
I3 |
G8 |
H4 |
C7 |
A6 |
B2 |
F5 |
D1 |
E9 |
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57 |
71 |
76 |
5 |
10 |
27 |
34 |
42 |
47 |
20049 |
|
G3 |
H8 |
I4 |
A5 |
B1 |
C9 |
D7 |
E6 |
F2 |
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77 |
55 |
72 |
21 |
8 |
13 |
52 |
33 |
38 |
20049 |
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18 |
23 |
1 |
40 |
48 |
35 |
65 |
79 |
60 |
20049 |
|
B9 |
C5 |
A1 |
E4 |
F3 |
D8 |
H2 |
I7 |
G6 |
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20 |
7 |
15 |
49 |
30 |
44 |
81 |
59 |
64 |
20049 |
|
C2 |
A7 |
B6 |
F4 |
D3 |
E8 |
I9 |
G5 |
H1 |
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48 |
35 |
40 |
79 |
60 |
65 |
23 |
1 |
18 |
20049 |
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20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C4[10] |
F9 |
I2 |
B3 |
E5 |
H7 |
A8 |
D1 |
G6 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A4 |
D2 |
G9 |
C3 |
F7 |
I5 |
B8 |
E6 |
H1 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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B9 |
G8 |
F7 |
I6 |
E5 |
A4 |
D3 |
C2 |
H1 |
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C2 |
H8 |
D5 |
G1 |
F7 |
B4 |
E3 |
A9 |
I6 |
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MS DataBase© |
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Bimagic Square n9:3.2a |
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Euler Matrix n9:3.2b |
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BiMagic Square n9:B.8a |
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Euler Matrix n9:B.8b |
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New Two Bimagic Square n9 |
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24 |
7 |
11 |
53 |
30 |
40 |
73 |
59 |
72 |
20049 |
|
C6 |
A7 |
B2 |
F8 |
D3 |
E4 |
I1 |
G5 |
H9 |
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6 |
16 |
20 |
28 |
41 |
54 |
62 |
66 |
76 |
20049 |
|
A6 |
B7 |
C2 |
D1 |
E5 |
F9 |
G8 |
H3 |
I4 |
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2 |
24 |
16 |
58 |
80 |
66 |
36 |
46 |
41 |
20049 |
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45 |
46 |
32 |
65 |
78 |
61 |
13 |
26 |
3 |
20049 |
|
E9 |
F1 |
D5 |
H2 |
I6 |
G7 |
B4 |
C8 |
A3 |
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49 |
35 |
39 |
74 |
60 |
70 |
27 |
1 |
14 |
20049 |
|
F4 |
D8 |
E3 |
I2 |
G6 |
H7 |
C9 |
A1 |
B5 |
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73 |
68 |
63 |
51 |
43 |
29 |
26 |
12 |
4 |
20049 |
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57 |
67 |
80 |
5 |
18 |
19 |
34 |
38 |
51 |
20049 |
|
G3 |
H4 |
I8 |
A5 |
B9 |
C1 |
D7 |
E2 |
F6 |
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68 |
81 |
55 |
12 |
22 |
8 |
43 |
47 |
33 |
20049 |
|
H5 |
I9 |
G1 |
B3 |
C4 |
A8 |
E7 |
F2 |
D6 |
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39 |
31 |
53 |
14 |
9 |
19 |
70 |
56 |
78 |
20049 |
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68 |
81 |
55 |
16 |
20 |
6 |
39 |
49 |
35 |
20049 |
|
H5 |
I9 |
G1 |
B7 |
C2 |
A6 |
E3 |
F4 |
D8 |
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75 |
58 |
71 |
25 |
2 |
15 |
50 |
36 |
37 |
20049 |
|
I3 |
G4 |
H8 |
C7 |
A2 |
B6 |
F5 |
D9 |
E1 |
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71 |
57 |
76 |
37 |
32 |
54 |
15 |
7 |
20 |
20049 |
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8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
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A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
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10 |
23 |
9 |
44 |
48 |
31 |
69 |
79 |
56 |
20049 |
|
B1 |
C5 |
A9 |
E8 |
F3 |
D4 |
H6 |
I7 |
G2 |
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34 |
47 |
42 |
3 |
22 |
17 |
59 |
81 |
64 |
20049 |
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MS DataBase© |
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47 |
33 |
43 |
76 |
62 |
66 |
27 |
1 |
14 |
20049 |
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F2 |
D6 |
E7 |
I4 |
G8 |
H3 |
C9 |
A1 |
B5 |
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29 |
42 |
52 |
63 |
64 |
77 |
4 |
17 |
21 |
20049 |
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D2 |
E6 |
F7 |
G9 |
H1 |
I5 |
A4 |
B8 |
C3 |
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27 |
10 |
5 |
74 |
69 |
61 |
49 |
44 |
30 |
20049 |
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Create your own bimagic square |
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31 |
44 |
48 |
63 |
64 |
77 |
2 |
15 |
25 |
20049 |
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D4 |
E8 |
F3 |
G9 |
H1 |
I5 |
A2 |
B6 |
C7 |
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45 |
46 |
32 |
67 |
80 |
57 |
11 |
24 |
7 |
20049 |
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E9 |
F1 |
D5 |
H4 |
I8 |
G3 |
B2 |
C6 |
A7 |
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50 |
45 |
28 |
25 |
11 |
6 |
75 |
67 |
62 |
20049 |
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79 |
56 |
69 |
21 |
4 |
17 |
50 |
36 |
37 |
20049 |
|
I7 |
G2 |
H6 |
C3 |
A4 |
B8 |
F5 |
D9 |
E1 |
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61 |
65 |
78 |
5 |
18 |
19 |
30 |
40 |
53 |
20049 |
|
G7 |
H2 |
I6 |
A5 |
B9 |
C1 |
D3 |
E4 |
F8 |
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13 |
8 |
21 |
72 |
55 |
77 |
38 |
33 |
52 |
20049 |
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10 |
23 |
9 |
42 |
52 |
29 |
71 |
75 |
58 |
20049 |
|
B1 |
C5 |
A9 |
E6 |
F7 |
D2 |
H8 |
I3 |
G4 |
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26 |
3 |
13 |
51 |
34 |
38 |
73 |
59 |
72 |
20049 |
|
C8 |
A3 |
B4 |
F6 |
D7 |
E2 |
I1 |
G5 |
H9 |
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60 |
79 |
65 |
35 |
48 |
40 |
1 |
23 |
18 |
20049 |
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20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C6[11] |
F1 |
I8 |
B7 |
E5 |
H3 |
A2 |
D9 |
G4 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A6 |
D8 |
G1 |
C7 |
F3 |
I5 |
B2 |
E4 |
H9 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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B1 |
G2 |
F3 |
I4 |
E5 |
A6 |
D7 |
C8 |
H9 |
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C8 |
H2 |
D5 |
G8 |
F3 |
B6 |
E7 |
A1 |
I4 |
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MS DataBase© |
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Create your own bimagic
square n9 |
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|
Bimagic Square n9:4.1a |
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|
Euler Matrix n9:4.1b |
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|
BiMagic Square n9:C.1a |
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|
Euler Matrix n9:C.1b |
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Put only in Integer from a bimagic square of order 9 |
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20 |
9 |
13 |
51 |
28 |
44 |
79 |
59 |
66 |
20049 |
|
C2 |
A9 |
B4 |
F6 |
D1 |
E8 |
I7 |
G5 |
H3 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
|
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64 |
81 |
59 |
17 |
22 |
3 |
42 |
47 |
34 |
20049 |
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39 |
52 |
32 |
67 |
74 |
63 |
17 |
24 |
1 |
20049 |
|
E3 |
F7 |
D5 |
H4 |
I2 |
G9 |
B8 |
C6 |
A1 |
|
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39 |
53 |
31 |
70 |
78 |
56 |
14 |
19 |
9 |
20049 |
|
E3 |
F8 |
D4 |
H7 |
I6 |
G2 |
B5 |
C1 |
A9 |
|
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15 |
20 |
7 |
37 |
54 |
32 |
71 |
76 |
57 |
20049 |
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55 |
71 |
78 |
5 |
12 |
25 |
36 |
40 |
47 |
20049 |
|
G1 |
H8 |
I6 |
A5 |
B3 |
C7 |
D9 |
E4 |
F2 |
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73 |
63 |
68 |
26 |
4 |
12 |
51 |
29 |
43 |
20049 |
|
I1 |
G9 |
H5 |
C8 |
A4 |
B3 |
F6 |
D2 |
E7 |
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44 |
49 |
30 |
69 |
74 |
61 |
10 |
27 |
5 |
20049 |
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68 |
75 |
61 |
18 |
22 |
2 |
37 |
53 |
33 |
20049 |
|
H5 |
I3 |
G7 |
B9 |
C4 |
A2 |
E1 |
F8 |
D6 |
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50 |
28 |
45 |
75 |
62 |
67 |
25 |
6 |
11 |
20049 |
|
F5 |
D1 |
E9 |
I3 |
G8 |
H4 |
C7 |
A6 |
B2 |
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63 |
68 |
73 |
4 |
12 |
26 |
29 |
43 |
51 |
20049 |
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6 |
10 |
26 |
34 |
41 |
48 |
56 |
72 |
76 |
20049 |
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A6 |
B1 |
C8 |
D7 |
E5 |
F3 |
G2 |
H9 |
I4 |
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|
60 |
65 |
79 |
1 |
18 |
23 |
35 |
40 |
48 |
20049 |
|
G6 |
H2 |
I7 |
A1 |
B9 |
C5 |
D8 |
E4 |
F3 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
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MS DataBase© |
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49 |
29 |
45 |
80 |
60 |
64 |
21 |
7 |
14 |
20049 |
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F4 |
D2 |
E9 |
I8 |
G6 |
H1 |
C3 |
A7 |
B5 |
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13 |
21 |
8 |
38 |
52 |
33 |
72 |
77 |
55 |
20049 |
|
B4 |
C3 |
A8 |
E2 |
F7 |
D6 |
H9 |
I5 |
G1 |
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31 |
39 |
53 |
56 |
70 |
78 |
9 |
14 |
19 |
20049 |
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Create your own bimagic square |
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35 |
42 |
46 |
57 |
70 |
77 |
4 |
11 |
27 |
20049 |
|
D8 |
E6 |
F1 |
G3 |
H7 |
I5 |
A4 |
B2 |
C9 |
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|
71 |
76 |
57 |
15 |
20 |
7 |
37 |
54 |
32 |
20049 |
|
H8 |
I4 |
G3 |
B6 |
C2 |
A7 |
E1 |
F9 |
D5 |
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77 |
55 |
72 |
21 |
8 |
13 |
52 |
33 |
38 |
20049 |
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81 |
58 |
65 |
19 |
8 |
15 |
50 |
30 |
43 |
20049 |
|
I9 |
G4 |
H2 |
C1 |
A8 |
B6 |
F5 |
D3 |
E7 |
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27 |
5 |
10 |
49 |
30 |
44 |
74 |
61 |
69 |
20049 |
|
C9 |
A5 |
B1 |
F4 |
D3 |
E8 |
I2 |
G7 |
H6 |
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25 |
6 |
11 |
50 |
28 |
45 |
75 |
62 |
67 |
20049 |
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16 |
23 |
3 |
38 |
54 |
31 |
69 |
73 |
62 |
20049 |
|
B7 |
C5 |
A3 |
E2 |
F9 |
D4 |
H6 |
I1 |
G8 |
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34 |
42 |
47 |
59 |
64 |
81 |
3 |
17 |
22 |
20049 |
|
D7 |
E6 |
F2 |
G5 |
H1 |
I9 |
A3 |
B8 |
C4 |
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48 |
35 |
40 |
79 |
60 |
65 |
23 |
1 |
18 |
20049 |
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20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C2[12] |
F7 |
I6 |
B9 |
E5 |
H1 |
A4 |
D3 |
G8 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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A2 |
F8 |
H5 |
I3 |
B9 |
D6 |
E1 |
G7 |
C4 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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B7 |
G4 |
F1 |
I8 |
E5 |
A2 |
D9 |
C6 |
H3 |
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D7 |
A5 |
G3 |
E2 |
B9 |
H4 |
F6 |
C1 |
I8 |
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[13] |
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Bimagic Square n9:4.2a |
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Euler Matrix n9:4.2b |
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BiMagic Square n9:C.2a |
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Euler Matrix n9:C.2b |
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New One Bimagic Square n9 |
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26 |
1 |
15 |
49 |
36 |
38 |
75 |
59 |
70 |
20049 |
|
C8 |
A1 |
B6 |
F4 |
D9 |
E2 |
I3 |
G5 |
H7 |
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8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
|
A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
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34 |
42 |
47 |
59 |
64 |
81 |
3 |
17 |
22 |
20049 |
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43 |
48 |
32 |
69 |
80 |
55 |
11 |
22 |
9 |
20049 |
|
E7 |
F3 |
D5 |
H6 |
I8 |
G1 |
B2 |
C4 |
A9 |
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43 |
47 |
33 |
66 |
76 |
62 |
14 |
27 |
1 |
20049 |
|
E7 |
F2 |
D6 |
H3 |
I4 |
G8 |
B5 |
C9 |
A1 |
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71 |
76 |
57 |
15 |
20 |
7 |
37 |
54 |
32 |
20049 |
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63 |
65 |
76 |
5 |
16 |
21 |
28 |
42 |
53 |
20049 |
|
G9 |
H2 |
I4 |
A5 |
B7 |
C3 |
D1 |
E6 |
F8 |
|
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|
81 |
55 |
68 |
20 |
6 |
16 |
49 |
35 |
39 |
20049 |
|
I9 |
G1 |
H5 |
C2 |
A6 |
B7 |
F4 |
D8 |
E3 |
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27 |
5 |
10 |
49 |
30 |
44 |
74 |
61 |
69 |
20049 |
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68 |
79 |
57 |
10 |
24 |
8 |
45 |
47 |
31 |
20049 |
|
H5 |
I7 |
G3 |
B1 |
C6 |
A8 |
E9 |
F2 |
D4 |
|
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50 |
36 |
37 |
79 |
56 |
69 |
21 |
4 |
17 |
20049 |
|
F5 |
D9 |
E1 |
I7 |
G2 |
H6 |
C3 |
A4 |
B8 |
|
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73 |
63 |
68 |
26 |
4 |
12 |
51 |
29 |
43 |
20049 |
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4 |
18 |
20 |
30 |
41 |
52 |
62 |
64 |
78 |
20049 |
|
A4 |
B9 |
C2 |
D3 |
E5 |
F7 |
G8 |
H1 |
I6 |
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|
58 |
71 |
75 |
9 |
10 |
23 |
29 |
42 |
52 |
20049 |
|
G4 |
H8 |
I3 |
A9 |
B1 |
C5 |
D2 |
E6 |
F7 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
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MS DataBase© |
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51 |
35 |
37 |
74 |
58 |
72 |
25 |
3 |
14 |
20049 |
|
F6 |
D8 |
E1 |
I2 |
G4 |
H9 |
C7 |
A3 |
B5 |
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15 |
25 |
2 |
44 |
48 |
31 |
64 |
77 |
63 |
20049 |
|
B6 |
C7 |
A2 |
E8 |
F3 |
D4 |
H1 |
I5 |
G9 |
|
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39 |
53 |
31 |
70 |
78 |
56 |
14 |
19 |
9 |
20049 |
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|
Create your own bimagic square |
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29 |
40 |
54 |
61 |
66 |
77 |
6 |
17 |
19 |
20049 |
|
D2 |
E4 |
F9 |
G7 |
H3 |
I5 |
A6 |
B8 |
C1 |
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|
65 |
78 |
61 |
13 |
26 |
3 |
45 |
46 |
32 |
20049 |
|
H2 |
I6 |
G7 |
B4 |
C8 |
A3 |
E9 |
F1 |
D5 |
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13 |
21 |
8 |
38 |
52 |
33 |
72 |
77 |
55 |
20049 |
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73 |
60 |
71 |
27 |
2 |
13 |
50 |
34 |
39 |
20049 |
|
I1 |
G6 |
H8 |
C9 |
A2 |
B4 |
F5 |
D7 |
E3 |
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19 |
5 |
18 |
51 |
34 |
38 |
80 |
57 |
67 |
20049 |
|
C1 |
A5 |
B9 |
F6 |
D7 |
E2 |
I8 |
G3 |
H4 |
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50 |
28 |
45 |
75 |
62 |
67 |
25 |
6 |
11 |
20049 |
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12 |
23 |
7 |
44 |
46 |
33 |
67 |
81 |
56 |
20049 |
|
B3 |
C5 |
A7 |
E8 |
F1 |
D6 |
H4 |
I9 |
G2 |
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30 |
40 |
53 |
59 |
72 |
73 |
7 |
11 |
24 |
20049 |
|
D3 |
E4 |
F8 |
G5 |
H9 |
I1 |
A7 |
B2 |
C6 |
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60 |
65 |
79 |
1 |
18 |
23 |
35 |
40 |
48 |
20049 |
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20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C8[14] |
F3 |
I4 |
B1 |
E5 |
H9 |
A6 |
D7 |
G2 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A8 |
F2 |
H5 |
I7 |
B1 |
D4 |
E9 |
G3 |
C6 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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B3 |
G6 |
F9 |
I2 |
E5 |
A8 |
D1 |
C4 |
H7 |
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D3 |
A5 |
G7 |
E8 |
B1 |
H6 |
F4 |
C9 |
I2 |
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MS DataBase© |
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Bimagic Square n9:5.1a |
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Euler Matrix n9:5.1b |
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BiMagic Square n9:C.3a |
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Euler Matrix n9:C.3b |
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New Two Bimagic Square n9 |
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22 |
9 |
11 |
53 |
28 |
42 |
75 |
59 |
70 |
20049 |
|
C4 |
A9 |
B2 |
F8 |
D1 |
E6 |
I3 |
G5 |
H7 |
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4 |
18 |
20 |
30 |
41 |
52 |
62 |
64 |
78 |
20049 |
|
A4 |
B9 |
C2 |
D3 |
E5 |
F7 |
G8 |
H1 |
I6 |
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22 |
3 |
17 |
47 |
34 |
42 |
81 |
59 |
64 |
20049 |
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43 |
48 |
32 |
65 |
76 |
63 |
15 |
26 |
1 |
20049 |
|
E7 |
F3 |
D5 |
H2 |
I4 |
G9 |
B6 |
C8 |
A1 |
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37 |
51 |
35 |
72 |
74 |
58 |
14 |
25 |
3 |
20049 |
|
E1 |
F6 |
D8 |
H9 |
I2 |
G4 |
B5 |
C7 |
A3 |
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37 |
54 |
32 |
71 |
76 |
57 |
15 |
20 |
7 |
20049 |
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55 |
69 |
80 |
5 |
16 |
21 |
36 |
38 |
49 |
20049 |
|
G1 |
H6 |
I8 |
A5 |
B7 |
C3 |
D9 |
E2 |
F4 |
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|
79 |
57 |
68 |
24 |
8 |
10 |
47 |
31 |
45 |
20049 |
|
I7 |
G3 |
H5 |
C6 |
A8 |
B1 |
F2 |
D4 |
E9 |
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61 |
69 |
74 |
5 |
10 |
27 |
30 |
44 |
49 |
20049 |
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68 |
79 |
57 |
18 |
20 |
4 |
37 |
51 |
35 |
20049 |
|
H5 |
I7 |
G3 |
B9 |
C2 |
A4 |
E1 |
F6 |
D8 |
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50 |
34 |
39 |
73 |
60 |
71 |
27 |
2 |
13 |
20049 |
|
F5 |
D7 |
E3 |
I1 |
G6 |
H8 |
C9 |
A2 |
B4 |
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68 |
73 |
63 |
12 |
26 |
4 |
43 |
51 |
29 |
20049 |
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8 |
10 |
24 |
30 |
41 |
52 |
58 |
72 |
74 |
20049 |
|
A8 |
B1 |
C6 |
D3 |
E5 |
F7 |
G4 |
H9 |
I2 |
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56 |
67 |
81 |
7 |
12 |
23 |
33 |
44 |
46 |
20049 |
|
G2 |
H4 |
I9 |
A7 |
B3 |
C5 |
D6 |
E8 |
F1 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
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MS DataBase© |
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47 |
31 |
45 |
78 |
62 |
64 |
25 |
3 |
14 |
20049 |
|
F2 |
D4 |
E9 |
I6 |
G8 |
H1 |
C7 |
A3 |
B5 |
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17 |
19 |
6 |
40 |
54 |
29 |
66 |
77 |
61 |
20049 |
|
B8 |
C1 |
A6 |
E4 |
F9 |
D2 |
H3 |
I5 |
G7 |
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53 |
31 |
39 |
78 |
56 |
70 |
19 |
9 |
14 |
20049 |
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Create your own bimagic square |
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33 |
44 |
46 |
61 |
66 |
77 |
2 |
13 |
27 |
20049 |
|
D6 |
E8 |
F1 |
G7 |
H3 |
I5 |
A2 |
B4 |
C9 |
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69 |
80 |
55 |
11 |
22 |
9 |
43 |
48 |
32 |
20049 |
|
H6 |
I8 |
G1 |
B2 |
C4 |
A9 |
E7 |
F3 |
D5 |
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33 |
38 |
52 |
55 |
72 |
77 |
8 |
13 |
21 |
20049 |
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81 |
56 |
67 |
19 |
6 |
17 |
50 |
34 |
39 |
20049 |
|
I9 |
G2 |
H4 |
C1 |
A6 |
B8 |
F5 |
D7 |
E3 |
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21 |
5 |
16 |
53 |
28 |
42 |
76 |
63 |
65 |
20049 |
|
C3 |
A5 |
B7 |
F8 |
D1 |
E6 |
I4 |
G9 |
H2 |
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75 |
62 |
67 |
25 |
6 |
11 |
50 |
28 |
45 |
20049 |
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12 |
23 |
7 |
40 |
54 |
29 |
71 |
73 |
60 |
20049 |
|
B3 |
C5 |
A7 |
E4 |
F9 |
D2 |
H8 |
I1 |
G6 |
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36 |
38 |
49 |
59 |
70 |
75 |
1 |
15 |
26 |
20049 |
|
D9 |
E2 |
F4 |
G5 |
H7 |
I3 |
A1 |
B6 |
C8 |
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18 |
23 |
1 |
40 |
48 |
35 |
65 |
79 |
60 |
20049 |
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20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C4[15] |
F3 |
I8 |
B9 |
E5 |
H1 |
A2 |
D7 |
G6 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A4 |
F6 |
H5 |
I1 |
B3 |
D2 |
E7 |
G9 |
C8 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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B3 |
G2 |
F1 |
I6 |
E5 |
A4 |
D9 |
C8 |
H7 |
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D9 |
A5 |
G1 |
E4 |
B3 |
H8 |
F2 |
C7 |
I6 |
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MS DataBase© |
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|
Bimagic Square n9:5.2a |
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|
Euler Matrix n9:5.2b |
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BiMagic Square n9:C.4a |
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Euler Matrix n9:C.4b |
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24 |
1 |
17 |
47 |
36 |
40 |
79 |
59 |
66 |
20049 |
|
C6 |
A1 |
B8 |
F2 |
D9 |
E4 |
I7 |
G5 |
H3 |
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6 |
10 |
26 |
34 |
41 |
48 |
56 |
72 |
76 |
20049 |
|
A6 |
B1 |
C8 |
D7 |
E5 |
F3 |
G2 |
H9 |
I4 |
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39 |
52 |
32 |
71 |
78 |
55 |
13 |
20 |
9 |
20049 |
|
E3 |
F7 |
D5 |
H8 |
I6 |
G1 |
B4 |
C2 |
A9 |
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45 |
49 |
29 |
64 |
80 |
60 |
14 |
21 |
7 |
20049 |
|
E9 |
F4 |
D2 |
H1 |
I8 |
G6 |
B5 |
C3 |
A7 |
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63 |
67 |
74 |
5 |
12 |
25 |
28 |
44 |
51 |
20049 |
|
G9 |
H4 |
I2 |
A5 |
B3 |
C7 |
D1 |
E8 |
F6 |
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|
75 |
61 |
68 |
22 |
2 |
18 |
53 |
33 |
37 |
20049 |
|
I3 |
G7 |
H5 |
C4 |
A2 |
B9 |
F8 |
D6 |
E1 |
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68 |
75 |
61 |
10 |
26 |
6 |
45 |
49 |
29 |
20049 |
|
H5 |
I3 |
G7 |
B1 |
C8 |
A6 |
E9 |
F4 |
D2 |
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50 |
30 |
43 |
81 |
58 |
65 |
19 |
8 |
15 |
20049 |
|
F5 |
D3 |
E7 |
I9 |
G4 |
H2 |
C1 |
A8 |
B6 |
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2 |
18 |
22 |
34 |
41 |
48 |
60 |
64 |
80 |
20049 |
|
A2 |
B9 |
C4 |
D7 |
E5 |
F3 |
G6 |
H1 |
I8 |
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62 |
69 |
73 |
3 |
16 |
23 |
31 |
38 |
54 |
20049 |
|
G8 |
H6 |
I1 |
A3 |
B7 |
C5 |
D4 |
E2 |
F9 |
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53 |
33 |
37 |
76 |
56 |
72 |
21 |
7 |
14 |
20049 |
|
F8 |
D6 |
E1 |
I4 |
G2 |
H9 |
C3 |
A7 |
B5 |
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11 |
27 |
4 |
42 |
46 |
35 |
70 |
77 |
57 |
20049 |
|
B2 |
C9 |
A4 |
E6 |
F1 |
D8 |
H7 |
I5 |
G3 |
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31 |
38 |
54 |
57 |
70 |
77 |
8 |
15 |
19 |
20049 |
|
D4 |
E2 |
F9 |
G3 |
H7 |
I5 |
A8 |
B6 |
C1 |
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|
67 |
74 |
63 |
17 |
24 |
1 |
39 |
52 |
32 |
20049 |
|
H4 |
I2 |
G9 |
B8 |
C6 |
A1 |
E3 |
F7 |
D5 |
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73 |
62 |
69 |
27 |
4 |
11 |
50 |
30 |
43 |
20049 |
|
I1 |
G8 |
H6 |
C9 |
A4 |
B2 |
F5 |
D3 |
E7 |
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25 |
5 |
12 |
47 |
36 |
40 |
78 |
55 |
71 |
20049 |
|
C7 |
A5 |
B3 |
F2 |
D9 |
E4 |
I6 |
G1 |
H8 |
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16 |
23 |
3 |
42 |
46 |
35 |
65 |
81 |
58 |
20049 |
|
B7 |
C5 |
A3 |
E6 |
F1 |
D8 |
H2 |
I9 |
G4 |
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28 |
44 |
51 |
59 |
66 |
79 |
9 |
13 |
20 |
20049 |
|
D1 |
E8 |
F6 |
G5 |
H3 |
I7 |
A9 |
B4 |
C2 |
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20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C6[16] |
F7 |
I2 |
B1 |
E5 |
H9 |
A8 |
D3 |
G4 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A6 |
F4 |
H5 |
I9 |
B7 |
D8 |
E3 |
G1 |
C2 |
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|
B7 |
G8 |
F9 |
I4 |
E5 |
A6 |
D1 |
C2 |
H3 |
|
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|
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|
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|
|
|
|
D1 |
A5 |
G9 |
E6 |
B7 |
H2 |
F8 |
C3 |
I4 |
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|
Bimagic Square n9:6.1a |
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|
Euler Matrix n9:6.1b |
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BiMagic Square n9:C.5a |
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Euler Matrix n9:C.5b |
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|
|
26 |
3 |
13 |
51 |
34 |
38 |
73 |
59 |
72 |
20049 |
|
C8 |
A3 |
B4 |
F6 |
D7 |
E2 |
I1 |
G5 |
H9 |
|
|
|
|
|
2 |
18 |
22 |
34 |
41 |
48 |
60 |
64 |
80 |
20049 |
|
A2 |
B9 |
C4 |
D7 |
E5 |
F3 |
G6 |
H1 |
I8 |
|
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|
|
|
|
|
|
|
45 |
46 |
32 |
67 |
80 |
57 |
11 |
24 |
7 |
20049 |
|
E9 |
F1 |
D5 |
H4 |
I8 |
G3 |
B2 |
C6 |
A7 |
|
|
|
|
|
37 |
53 |
33 |
72 |
76 |
56 |
14 |
21 |
7 |
20049 |
|
E1 |
F8 |
D6 |
H9 |
I4 |
G2 |
B5 |
C3 |
A7 |
|
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|
|
|
|
|
|
|
|
61 |
65 |
78 |
5 |
18 |
19 |
30 |
40 |
53 |
20049 |
|
G7 |
H2 |
I6 |
A5 |
B9 |
C1 |
D3 |
E4 |
F8 |
|
|
|
|
|
75 |
61 |
68 |
26 |
6 |
10 |
49 |
29 |
45 |
20049 |
|
I3 |
G7 |
H5 |
C8 |
A6 |
B1 |
F4 |
D2 |
E9 |
|
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|
|
|
|
|
|
|
|
68 |
81 |
55 |
12 |
22 |
8 |
43 |
47 |
33 |
20049 |
|
H5 |
I9 |
G1 |
B3 |
C4 |
A8 |
E7 |
F2 |
D6 |
|
|
|
|
|
50 |
30 |
43 |
73 |
62 |
69 |
27 |
4 |
11 |
20049 |
|
F5 |
D3 |
E7 |
I1 |
G8 |
H6 |
C9 |
A4 |
B2 |
|
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|
|
|
|
|
|
|
|
6 |
16 |
20 |
28 |
41 |
54 |
62 |
66 |
76 |
20049 |
|
A6 |
B7 |
C2 |
D1 |
E5 |
F9 |
G8 |
H3 |
I4 |
|
|
|
|
|
58 |
65 |
81 |
3 |
16 |
23 |
35 |
42 |
46 |
20049 |
|
G4 |
H2 |
I9 |
A3 |
B7 |
C5 |
D8 |
E6 |
F1 |
|
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|
|
|
|
|
|
|
49 |
35 |
39 |
74 |
60 |
70 |
27 |
1 |
14 |
20049 |
|
F4 |
D8 |
E3 |
I2 |
G6 |
H7 |
C9 |
A1 |
B5 |
|
|
|
|
|
15 |
19 |
8 |
38 |
54 |
31 |
70 |
77 |
57 |
20049 |
|
B6 |
C1 |
A8 |
E2 |
F9 |
D4 |
H7 |
I5 |
G3 |
|
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|
|
|
29 |
42 |
52 |
63 |
64 |
77 |
4 |
17 |
21 |
20049 |
|
D2 |
E6 |
F7 |
G9 |
H1 |
I5 |
A4 |
B8 |
C3 |
|
|
|
|
|
71 |
78 |
55 |
13 |
20 |
9 |
39 |
52 |
32 |
20049 |
|
H8 |
I6 |
G1 |
B4 |
C2 |
A9 |
E3 |
F7 |
D5 |
|
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|
|
|
|
|
|
|
|
|
75 |
58 |
71 |
25 |
2 |
15 |
50 |
36 |
37 |
20049 |
|
I3 |
G4 |
H8 |
C7 |
A2 |
B6 |
F5 |
D9 |
E1 |
|
|
|
|
|
25 |
5 |
12 |
51 |
28 |
44 |
74 |
63 |
67 |
20049 |
|
C7 |
A5 |
B3 |
F6 |
D1 |
E8 |
I2 |
G9 |
H4 |
|
|
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|
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|
|
|
|
|
|
|
|
|
10 |
23 |
9 |
44 |
48 |
31 |
69 |
79 |
56 |
20049 |
|
B1 |
C5 |
A9 |
E8 |
F3 |
D4 |
H6 |
I7 |
G2 |
|
|
|
|
|
36 |
40 |
47 |
59 |
66 |
79 |
1 |
17 |
24 |
20049 |
|
D9 |
E4 |
F2 |
G5 |
H3 |
I7 |
A1 |
B8 |
C6 |
|
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|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
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|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C8[17] |
F1 |
I6 |
B3 |
E5 |
H7 |
A4 |
D9 |
G2 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A2 |
F8 |
H5 |
I1 |
B7 |
D4 |
E3 |
G9 |
C6 |
|
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|
|
B1 |
G4 |
F7 |
I2 |
E5 |
A8 |
D3 |
C6 |
H9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D9 |
A5 |
G1 |
E2 |
B7 |
H6 |
F4 |
C3 |
I8 |
|
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|
|
|
|
|
Bimagic Square n9:6.2a |
|
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|
|
|
|
|
|
|
Euler Matrix n9:6.2b |
|
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|
|
|
|
|
|
|
|
|
|
BiMagic Square n9:C.6a |
|
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|
|
|
|
|
|
|
Euler Matrix n9:C.6b |
|
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|
|
|
|
|
|
|
|
|
|
|
20 |
7 |
15 |
49 |
30 |
44 |
81 |
59 |
64 |
20049 |
|
C2 |
A7 |
B6 |
F4 |
D3 |
E8 |
I9 |
G5 |
H1 |
|
|
|
|
|
8 |
10 |
24 |
30 |
41 |
52 |
58 |
72 |
74 |
20049 |
|
A8 |
B1 |
C6 |
D3 |
E5 |
F7 |
G4 |
H9 |
I2 |
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
37 |
54 |
32 |
69 |
74 |
61 |
17 |
22 |
3 |
20049 |
|
E1 |
F9 |
D5 |
H6 |
I2 |
G7 |
B8 |
C4 |
A3 |
|
|
|
|
|
45 |
47 |
31 |
64 |
78 |
62 |
14 |
25 |
3 |
20049 |
|
E9 |
F2 |
D4 |
H1 |
I6 |
G8 |
B5 |
C7 |
A3 |
|
|
|
|
|
|
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|
|
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|
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|
|
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|
|
|
|
|
|
|
|
|
57 |
71 |
76 |
5 |
10 |
27 |
34 |
42 |
47 |
20049 |
|
G3 |
H8 |
I4 |
A5 |
B1 |
C9 |
D7 |
E6 |
F2 |
|
|
|
|
|
79 |
57 |
68 |
20 |
4 |
18 |
51 |
35 |
37 |
20049 |
|
I7 |
G3 |
H5 |
C2 |
A4 |
B9 |
F6 |
D8 |
E1 |
|
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|
|
|
|
|
|
|
68 |
73 |
63 |
16 |
24 |
2 |
39 |
53 |
31 |
20049 |
|
H5 |
I1 |
G9 |
B7 |
C6 |
A2 |
E3 |
F8 |
D4 |
|
|
|
|
|
50 |
34 |
39 |
81 |
56 |
67 |
19 |
6 |
17 |
20049 |
|
F5 |
D7 |
E3 |
I9 |
G2 |
H4 |
C1 |
A6 |
B8 |
|
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|
|
|
|
|
|
|
4 |
12 |
26 |
36 |
41 |
46 |
56 |
70 |
78 |
20049 |
|
A4 |
B3 |
C8 |
D9 |
E5 |
F1 |
G2 |
H7 |
I6 |
|
|
|
|
|
60 |
71 |
73 |
7 |
12 |
23 |
29 |
40 |
54 |
20049 |
|
G6 |
H8 |
I1 |
A7 |
B3 |
C5 |
D2 |
E4 |
F9 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
51 |
29 |
43 |
80 |
58 |
66 |
19 |
9 |
14 |
20049 |
|
F6 |
D2 |
E7 |
I8 |
G4 |
H3 |
C1 |
A9 |
B5 |
|
|
|
|
|
13 |
27 |
2 |
44 |
46 |
33 |
66 |
77 |
61 |
20049 |
|
B4 |
C9 |
A2 |
E8 |
F1 |
D6 |
H3 |
I5 |
G7 |
|
|
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|
|
|
|
|
|
|
35 |
40 |
48 |
55 |
72 |
77 |
6 |
11 |
25 |
20049 |
|
D8 |
E4 |
F3 |
G1 |
H9 |
I5 |
A6 |
B2 |
C7 |
|
|
|
|
|
65 |
76 |
63 |
15 |
26 |
1 |
43 |
48 |
32 |
20049 |
|
H2 |
I4 |
G9 |
B6 |
C8 |
A1 |
E7 |
F3 |
D5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
79 |
60 |
65 |
21 |
8 |
13 |
50 |
28 |
45 |
20049 |
|
I7 |
G6 |
H2 |
C3 |
A8 |
B4 |
F5 |
D1 |
E9 |
|
|
|
|
|
21 |
5 |
16 |
49 |
36 |
38 |
80 |
55 |
69 |
20049 |
|
C3 |
A5 |
B7 |
F4 |
D9 |
E2 |
I8 |
G1 |
H6 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
18 |
23 |
1 |
38 |
52 |
33 |
67 |
75 |
62 |
20049 |
|
B9 |
C5 |
A1 |
E2 |
F7 |
D6 |
H4 |
I3 |
G8 |
|
|
|
|
|
28 |
42 |
53 |
59 |
70 |
75 |
9 |
11 |
22 |
20049 |
|
D1 |
E6 |
F8 |
G5 |
H7 |
I3 |
A9 |
B2 |
C4 |
|
|
|
|
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|
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|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
1225449 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
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|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C2[18] |
F9 |
I4 |
B7 |
E5 |
H3 |
A6 |
D1 |
G8 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A8 |
F2 |
H5 |
I9 |
B3 |
D6 |
E7 |
G1 |
C4 |
|
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|
|
|
|
|
B9 |
G6 |
F3 |
I8 |
E5 |
A2 |
D7 |
C4 |
H1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D1 |
A5 |
G9 |
E8 |
B3 |
H4 |
F6 |
C7 |
I2 |
|
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|
Bimagic Square n9:7.1a |
|
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|
|
|
Euler Matrix n9:7.1b |
|
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|
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|
|
BiMagic Square n9:C.7a |
|
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|
Euler Matrix n9:C.7b |
|
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|
|
|
|
|
|
|
73 |
68 |
63 |
2 |
16 |
24 |
53 |
39 |
31 |
20049 |
|
I1 |
H5 |
G9 |
A2 |
B7 |
C6 |
F8 |
E3 |
D4 |
|
|
|
|
|
4 |
12 |
26 |
36 |
41 |
46 |
56 |
70 |
78 |
20049 |
|
A4 |
B3 |
C8 |
D9 |
E5 |
F1 |
G2 |
H7 |
I6 |
|
|
|
|
|
|
|
|
|
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|
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|
|
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|
|
|
|
|
|
|
|
|
12 |
4 |
26 |
46 |
36 |
41 |
70 |
56 |
78 |
20049 |
|
B3 |
A4 |
C8 |
F1 |
D9 |
E5 |
H7 |
G2 |
I6 |
|
|
|
|
|
43 |
51 |
29 |
66 |
80 |
58 |
14 |
19 |
9 |
20049 |
|
E7 |
F6 |
D2 |
H3 |
I8 |
G4 |
B5 |
C1 |
A9 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
29 |
51 |
43 |
66 |
80 |
58 |
9 |
19 |
14 |
20049 |
|
D2 |
F6 |
E7 |
H3 |
I8 |
G4 |
A9 |
C1 |
B5 |
|
|
|
|
|
73 |
63 |
68 |
24 |
2 |
16 |
53 |
31 |
39 |
20049 |
|
I1 |
G9 |
H5 |
C6 |
A2 |
B7 |
F8 |
D4 |
E3 |
|
|
|
|
|
|
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|
|
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|
|
|
|
|
|
|
|
|
71 |
57 |
76 |
27 |
5 |
10 |
42 |
34 |
47 |
20049 |
|
H8 |
G3 |
I4 |
C9 |
A5 |
B1 |
E6 |
D7 |
F2 |
|
|
|
|
|
50 |
28 |
45 |
79 |
60 |
65 |
21 |
8 |
13 |
20049 |
|
F5 |
D1 |
E9 |
I7 |
G6 |
H2 |
C3 |
A8 |
B4 |
|
|
|
|
|
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
54 |
37 |
32 |
61 |
69 |
74 |
22 |
17 |
3 |
20049 |
|
F9 |
E1 |
D5 |
G7 |
H6 |
I2 |
C4 |
B8 |
A3 |
|
|
|
|
|
62 |
67 |
75 |
1 |
18 |
23 |
33 |
38 |
52 |
20049 |
|
G8 |
H4 |
I3 |
A1 |
B9 |
C5 |
D6 |
E2 |
F7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
20 |
15 |
44 |
49 |
30 |
59 |
81 |
64 |
20049 |
|
A7 |
C2 |
B6 |
E8 |
F4 |
D3 |
G5 |
I9 |
H1 |
|
|
|
|
|
11 |
25 |
6 |
40 |
48 |
35 |
72 |
77 |
55 |
20049 |
|
B2 |
C7 |
A6 |
E4 |
F3 |
D8 |
H9 |
I5 |
G1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
40 |
35 |
48 |
77 |
55 |
72 |
11 |
6 |
25 |
20049 |
|
E4 |
D8 |
F3 |
I5 |
G1 |
H9 |
B2 |
A6 |
C7 |
|
|
|
|
|
69 |
74 |
61 |
17 |
22 |
3 |
37 |
54 |
32 |
20049 |
|
H6 |
I2 |
G7 |
B8 |
C4 |
A3 |
E1 |
F9 |
D5 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
60 |
79 |
65 |
13 |
21 |
8 |
28 |
50 |
45 |
20049 |
|
G6 |
I7 |
H2 |
B4 |
C3 |
A8 |
D1 |
F5 |
E9 |
|
|
|
|
|
27 |
5 |
10 |
47 |
34 |
42 |
76 |
57 |
71 |
20049 |
|
C9 |
A5 |
B1 |
F2 |
D7 |
E6 |
I4 |
G3 |
H8 |
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
23 |
18 |
1 |
33 |
38 |
52 |
75 |
67 |
62 |
20049 |
|
C5 |
B9 |
A1 |
D6 |
E2 |
F7 |
I3 |
H4 |
G8 |
|
|
|
|
|
30 |
44 |
49 |
59 |
64 |
81 |
7 |
15 |
20 |
20049 |
|
D3 |
E8 |
F4 |
G5 |
H1 |
I9 |
A7 |
B6 |
C2 |
|
|
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|
|
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|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
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|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
I1[19] |
A4 |
E7 |
C9 |
H6 |
D3 |
B2 |
F5 |
G8 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A4 |
F6 |
H5 |
I7 |
B9 |
D8 |
E1 |
G3 |
C2 |
|
|
|
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|
|
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|
|
|
|
|
C5 |
I7 |
F3 |
E8 |
H6 |
B1 |
A9 |
G2 |
D4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D3 |
A5 |
G7 |
E4 |
B9 |
H2 |
F8 |
C1 |
I6 |
|
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|
|
|
|
|
|
|
|
Bimagic Square n9:7.2a |
|
|
|
|
|
|
|
|
|
|
Euler Matrix n9:7.2b |
|
|
|
|
|
|
|
|
|
|
|
|
|
BiMagic Square n9:C.8a |
|
|
|
|
|
|
|
|
|
|
Euler Matrix n9:C.8b |
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
81 |
68 |
55 |
8 |
12 |
22 |
47 |
43 |
33 |
20049 |
|
I9 |
H5 |
G1 |
A8 |
B3 |
C4 |
F2 |
E7 |
D6 |
|
|
|
|
|
6 |
16 |
20 |
28 |
41 |
54 |
62 |
66 |
76 |
20049 |
|
A6 |
B7 |
C2 |
D1 |
E5 |
F9 |
G8 |
H3 |
I4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
16 |
6 |
20 |
54 |
28 |
41 |
66 |
62 |
76 |
20049 |
|
B7 |
A6 |
C2 |
F9 |
D1 |
E5 |
H3 |
G8 |
I4 |
|
|
|
|
|
39 |
49 |
35 |
70 |
74 |
60 |
14 |
27 |
1 |
20049 |
|
E3 |
F4 |
D8 |
H7 |
I2 |
G6 |
B5 |
C9 |
A1 |
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
35 |
49 |
39 |
70 |
74 |
60 |
1 |
27 |
14 |
20049 |
|
D8 |
F4 |
E3 |
H7 |
I2 |
G6 |
A1 |
C9 |
B5 |
|
|
|
|
|
81 |
55 |
68 |
22 |
8 |
12 |
47 |
33 |
43 |
20049 |
|
I9 |
G1 |
H5 |
C4 |
A8 |
B3 |
F2 |
D6 |
E7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
65 |
61 |
78 |
19 |
5 |
18 |
40 |
30 |
53 |
20049 |
|
H2 |
G7 |
I6 |
C1 |
A5 |
B9 |
E4 |
D3 |
F8 |
|
|
|
|
|
50 |
36 |
37 |
75 |
58 |
71 |
25 |
2 |
15 |
20049 |
|
F5 |
D9 |
E1 |
I3 |
G4 |
H8 |
C7 |
A2 |
B6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
46 |
45 |
32 |
57 |
67 |
80 |
24 |
11 |
7 |
20049 |
|
F1 |
E9 |
D5 |
G3 |
H4 |
I8 |
C6 |
B2 |
A7 |
|
|
|
|
|
56 |
69 |
79 |
9 |
10 |
23 |
31 |
44 |
48 |
20049 |
|
G2 |
H6 |
I7 |
A9 |
B1 |
C5 |
D4 |
E8 |
F3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
26 |
13 |
38 |
51 |
34 |
59 |
73 |
72 |
20049 |
|
A3 |
C8 |
B4 |
E2 |
F6 |
D7 |
G5 |
I1 |
H9 |
|
|
|
|
|
17 |
21 |
4 |
42 |
52 |
29 |
64 |
77 |
63 |
20049 |
|
B8 |
C3 |
A4 |
E6 |
F7 |
D2 |
H1 |
I5 |
G9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
42 |
29 |
52 |
77 |
63 |
64 |
17 |
4 |
21 |
20049 |
|
E6 |
D2 |
F7 |
I5 |
G9 |
H1 |
B8 |
A4 |
C3 |
|
|
|
|
|
67 |
80 |
57 |
11 |
24 |
7 |
45 |
46 |
32 |
20049 |
|
H4 |
I8 |
G3 |
B2 |
C6 |
A7 |
E9 |
F1 |
D5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
58 |
75 |
71 |
15 |
25 |
2 |
36 |
50 |
37 |
20049 |
|
G4 |
I3 |
H8 |
B6 |
C7 |
A2 |
D9 |
F5 |
E1 |
|
|
|
|
|
19 |
5 |
18 |
53 |
30 |
40 |
78 |
61 |
65 |
20049 |
|
C1 |
A5 |
B9 |
F8 |
D3 |
E4 |
I6 |
G7 |
H2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
23 |
10 |
9 |
31 |
44 |
48 |
79 |
69 |
56 |
20049 |
|
C5 |
B1 |
A9 |
D4 |
E8 |
F3 |
I7 |
H6 |
G2 |
|
|
|
|
|
34 |
38 |
51 |
59 |
72 |
73 |
3 |
13 |
26 |
20049 |
|
D7 |
E2 |
F6 |
G5 |
H9 |
I1 |
A3 |
B4 |
C8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
|
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|
|
|
|
|
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|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
I9[20] |
A6 |
E3 |
C1 |
H4 |
D7 |
B8 |
F5 |
G2 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A6 |
F4 |
H5 |
I3 |
B1 |
D2 |
E9 |
G7 |
C8 |
|
|
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|
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|
|
|
|
|
|
|
|
C5 |
I3 |
F7 |
E2 |
H4 |
B9 |
A1 |
G8 |
D6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D7 |
A5 |
G3 |
E6 |
B1 |
H8 |
F2 |
C9 |
I4 |
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
|
|
|
|
|
|
Bimagic Square n9:8.1a |
|
|
|
|
|
|
|
|
|
|
Euler Matrix n9:8.1b |
|
|
|
|
|
|
|
|
|
|
|
|
|
Bimagic Square n9:10.1a |
|
|
|
|
|
|
|
|
|
|
Euler's Matrix n9:10.1b |
|
|
|
|
|
|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
74 |
72 |
58 |
8 |
10 |
24 |
52 |
41 |
30 |
20049 |
|
I2 |
H9 |
G4 |
A8 |
B1 |
C6 |
F7 |
E5 |
D3 |
|
|
|
|
|
70 |
77 |
57 |
15 |
19 |
8 |
38 |
54 |
31 |
20049 |
|
H7 |
I5 |
G3 |
B6 |
C1 |
A8 |
E2 |
F9 |
D4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
14 |
3 |
25 |
47 |
31 |
45 |
64 |
62 |
78 |
20049 |
|
B5 |
A3 |
C7 |
F2 |
D4 |
E9 |
H1 |
G8 |
I6 |
|
|
|
|
|
11 |
27 |
4 |
43 |
50 |
30 |
69 |
73 |
62 |
20049 |
|
B2 |
C9 |
A4 |
E7 |
F5 |
D3 |
H6 |
I1 |
G8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
35 |
51 |
37 |
68 |
79 |
57 |
4 |
20 |
18 |
20049 |
|
D8 |
F6 |
E1 |
H5 |
I7 |
G3 |
A4 |
C2 |
B9 |
|
|
|
|
|
42 |
46 |
35 |
65 |
81 |
58 |
16 |
23 |
3 |
20049 |
|
E6 |
F1 |
D8 |
H2 |
I9 |
G4 |
B7 |
C5 |
A3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
70 |
59 |
75 |
22 |
9 |
11 |
42 |
28 |
53 |
20049 |
|
H7 |
G5 |
I3 |
C4 |
A9 |
B2 |
E6 |
D1 |
F8 |
|
|
|
|
|
59 |
66 |
79 |
1 |
17 |
24 |
36 |
40 |
47 |
20049 |
|
G5 |
H3 |
I7 |
A1 |
B8 |
C6 |
D9 |
E4 |
F2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
49 |
38 |
36 |
55 |
69 |
80 |
21 |
16 |
5 |
20049 |
|
F4 |
E2 |
D9 |
G1 |
H6 |
I8 |
C3 |
B7 |
A5 |
|
|
|
|
|
9 |
13 |
20 |
32 |
39 |
52 |
55 |
71 |
78 |
20049 |
|
A9 |
B4 |
C2 |
D5 |
E3 |
F7 |
G1 |
H8 |
I6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
26 |
15 |
43 |
48 |
32 |
63 |
76 |
65 |
20049 |
|
A1 |
C8 |
B6 |
E7 |
F3 |
D5 |
G9 |
I4 |
H2 |
|
|
|
|
|
28 |
44 |
51 |
63 |
67 |
74 |
5 |
12 |
25 |
20049 |
|
D1 |
E8 |
F6 |
G9 |
H4 |
I2 |
A5 |
B3 |
C7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
39 |
34 |
50 |
81 |
56 |
67 |
17 |
6 |
19 |
20049 |
|
E3 |
D7 |
F5 |
I9 |
G2 |
H4 |
B8 |
A6 |
C1 |
|
|
|
|
|
75 |
61 |
68 |
26 |
6 |
10 |
49 |
29 |
45 |
20049 |
|
I3 |
G7 |
H5 |
C8 |
A6 |
B1 |
F4 |
D2 |
E9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
60 |
73 |
71 |
12 |
23 |
7 |
29 |
54 |
40 |
20049 |
|
G6 |
I1 |
H8 |
B3 |
C5 |
A7 |
D2 |
F9 |
E4 |
|
|
|
|
|
22 |
2 |
18 |
48 |
34 |
41 |
80 |
60 |
64 |
20049 |
|
C4 |
A2 |
B9 |
F3 |
D7 |
E5 |
I8 |
G6 |
H1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
27 |
13 |
2 |
33 |
44 |
46 |
77 |
66 |
61 |
20049 |
|
C9 |
B4 |
A2 |
D6 |
E8 |
F1 |
I5 |
H3 |
G7 |
|
|
|
|
|
53 |
33 |
37 |
76 |
56 |
72 |
21 |
7 |
14 |
20049 |
|
F8 |
D6 |
E1 |
I4 |
G2 |
H9 |
C3 |
A7 |
B5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
I2[21] |
A3 |
E1 |
C4 |
H6 |
D5 |
B8 |
F9 |
G7 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
H7[22] |
C9 |
D8 |
A1 |
E3 |
I2 |
F4 |
G6 |
B5 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
|
|
|
|
C9 |
I1 |
F5 |
E7 |
H6 |
B2 |
A4 |
G8 |
D3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
F8 |
A2 |
H5 |
G9 |
E3 |
C6 |
B7 |
I1 |
D4 |
|
|
|
|
|
|
|
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|
Bimagic Square n9:8.2a |
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|
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|
|
|
Euler Matrix n9:8.2b |
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|
Bimagic Square n9:10.2a |
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|
Euler's Matrix n9:10.2b |
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|
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|
|
|
|
|
|
|
|
|
80 |
64 |
60 |
2 |
18 |
22 |
48 |
41 |
34 |
20049 |
|
I8 |
H1 |
G6 |
A2 |
B9 |
C4 |
F3 |
E5 |
D7 |
|
|
|
|
|
66 |
77 |
61 |
13 |
27 |
2 |
44 |
46 |
33 |
20049 |
|
H3 |
I5 |
G7 |
B4 |
C9 |
A2 |
E8 |
F1 |
D6 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
14 |
7 |
21 |
53 |
33 |
37 |
72 |
56 |
76 |
20049 |
|
B5 |
A7 |
C3 |
F8 |
D6 |
E1 |
H9 |
G2 |
I4 |
|
|
|
|
|
17 |
19 |
6 |
39 |
50 |
34 |
67 |
81 |
56 |
20049 |
|
B8 |
C1 |
A6 |
E3 |
F5 |
D7 |
H4 |
I9 |
G2 |
|
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|
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|
|
|
|
|
|
|
|
29 |
49 |
45 |
68 |
75 |
61 |
6 |
26 |
10 |
20049 |
|
D2 |
F4 |
E9 |
H5 |
I3 |
G7 |
A6 |
C8 |
B1 |
|
|
|
|
|
40 |
54 |
29 |
71 |
73 |
60 |
12 |
23 |
7 |
20049 |
|
E4 |
F9 |
D2 |
H8 |
I1 |
G6 |
B3 |
C5 |
A7 |
|
|
|
|
|
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|
|
|
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|
|
|
66 |
59 |
79 |
24 |
1 |
17 |
40 |
36 |
47 |
20049 |
|
H3 |
G5 |
I7 |
C6 |
A1 |
B8 |
E4 |
D9 |
F2 |
|
|
|
|
|
59 |
70 |
75 |
9 |
11 |
22 |
28 |
42 |
53 |
20049 |
|
G5 |
H7 |
I3 |
A9 |
B2 |
C4 |
D1 |
E6 |
F8 |
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|
|
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|
|
|
51 |
44 |
28 |
63 |
67 |
74 |
25 |
12 |
5 |
20049 |
|
F6 |
E8 |
D1 |
G9 |
H4 |
I2 |
C7 |
B3 |
A5 |
|
|
|
|
|
1 |
15 |
26 |
32 |
43 |
48 |
63 |
65 |
76 |
20049 |
|
A1 |
B6 |
C8 |
D5 |
E7 |
F3 |
G9 |
H2 |
I4 |
|
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|
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|
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|
|
|
|
9 |
20 |
13 |
39 |
52 |
32 |
55 |
78 |
71 |
20049 |
|
A9 |
C2 |
B4 |
E3 |
F7 |
D5 |
G1 |
I6 |
H8 |
|
|
|
|
|
36 |
38 |
49 |
55 |
69 |
80 |
5 |
16 |
21 |
20049 |
|
D9 |
E2 |
F4 |
G1 |
H6 |
I8 |
A5 |
B7 |
C3 |
|
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|
|
|
|
|
|
|
|
43 |
30 |
50 |
73 |
62 |
69 |
11 |
4 |
27 |
20049 |
|
E7 |
D3 |
F5 |
I1 |
G8 |
H6 |
B2 |
A4 |
C9 |
|
|
|
|
|
79 |
57 |
68 |
20 |
4 |
18 |
51 |
35 |
37 |
20049 |
|
I7 |
G3 |
H5 |
C2 |
A4 |
B9 |
F6 |
D8 |
E1 |
|
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|
|
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|
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|
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|
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|
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|
|
|
|
|
|
|
|
58 |
81 |
65 |
16 |
23 |
3 |
35 |
46 |
42 |
20049 |
|
G4 |
I9 |
H2 |
B7 |
C5 |
A3 |
D8 |
F1 |
E6 |
|
|
|
|
|
24 |
8 |
10 |
52 |
30 |
41 |
74 |
58 |
72 |
20049 |
|
C6 |
A8 |
B1 |
F7 |
D3 |
E5 |
I2 |
G4 |
H9 |
|
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|
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|
|
|
|
|
|
|
|
19 |
15 |
8 |
31 |
38 |
54 |
77 |
70 |
57 |
20049 |
|
C1 |
B6 |
A8 |
D4 |
E2 |
F9 |
I5 |
H7 |
G3 |
|
|
|
|
|
47 |
31 |
45 |
78 |
62 |
64 |
25 |
3 |
14 |
20049 |
|
F2 |
D4 |
E9 |
I6 |
G8 |
H1 |
C7 |
A3 |
B5 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
I8[23] |
A7 |
E9 |
C6 |
H4 |
D5 |
B2 |
F1 |
G3 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
H3[24] |
C1 |
D2 |
A9 |
E7 |
I8 |
F6 |
G4 |
B5 |
|
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|
|
C1 |
I9 |
F5 |
E3 |
H4 |
B8 |
A6 |
G2 |
D7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
F2 |
A8 |
H5 |
G1 |
E7 |
C4 |
B3 |
I9 |
D6 |
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|
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|
|
Bimagic Square n9:9.1a |
|
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|
|
|
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|
|
Euler Matrix n9:9.1b |
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|
|
|
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|
|
|
|
|
Special Bimagic Square n9:1.1a |
|
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|
|
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|
|
Euler Matrix n9:1.1b |
|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
66 |
77 |
61 |
17 |
19 |
6 |
40 |
54 |
29 |
20049 |
|
H3 |
I5 |
G7 |
B8 |
C1 |
A6 |
E4 |
F9 |
D2 |
|
|
|
|
|
19 |
5 |
18 |
51 |
34 |
38 |
80 |
57 |
67 |
20049 |
|
C1 |
A5 |
B9 |
F6 |
D7 |
E2 |
I8 |
G3 |
H4 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
13 |
27 |
2 |
39 |
50 |
34 |
71 |
73 |
60 |
20049 |
|
B4 |
C9 |
A2 |
E3 |
F5 |
D7 |
H8 |
I1 |
G6 |
|
|
|
|
|
43 |
47 |
33 |
66 |
76 |
62 |
14 |
27 |
1 |
20049 |
|
E7 |
F2 |
D6 |
H3 |
I4 |
G8 |
B5 |
C9 |
A1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
44 |
46 |
33 |
67 |
81 |
56 |
12 |
23 |
7 |
20049 |
|
E8 |
F1 |
D6 |
H4 |
I9 |
G2 |
B3 |
C5 |
A7 |
|
|
|
|
|
58 |
71 |
75 |
9 |
10 |
23 |
29 |
42 |
52 |
20049 |
|
G4 |
H8 |
I3 |
A9 |
B1 |
C5 |
D2 |
E6 |
F7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
59 |
70 |
75 |
1 |
15 |
26 |
36 |
38 |
49 |
20049 |
|
G5 |
H7 |
I3 |
A1 |
B6 |
C8 |
D9 |
E2 |
F4 |
|
|
|
|
|
65 |
78 |
61 |
13 |
26 |
3 |
45 |
46 |
32 |
20049 |
|
H2 |
I6 |
G7 |
B4 |
C8 |
A3 |
E9 |
F1 |
D5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
11 |
22 |
32 |
43 |
48 |
55 |
69 |
80 |
20049 |
|
A9 |
B2 |
C4 |
D5 |
E7 |
F3 |
G1 |
H6 |
I8 |
|
|
|
|
|
8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
|
A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
28 |
42 |
53 |
63 |
65 |
76 |
5 |
16 |
21 |
20049 |
|
D1 |
E6 |
F8 |
G9 |
H2 |
I4 |
A5 |
B7 |
C3 |
|
|
|
|
|
50 |
36 |
37 |
79 |
56 |
69 |
21 |
4 |
17 |
20049 |
|
F5 |
D9 |
E1 |
I7 |
G2 |
H6 |
C3 |
A4 |
B8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
79 |
57 |
68 |
24 |
8 |
10 |
47 |
31 |
45 |
20049 |
|
I7 |
G3 |
H5 |
C6 |
A8 |
B1 |
F2 |
D4 |
E9 |
|
|
|
|
|
30 |
40 |
53 |
59 |
72 |
73 |
7 |
11 |
24 |
20049 |
|
D3 |
E4 |
F8 |
G5 |
H9 |
I1 |
A7 |
B2 |
C6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20 |
4 |
18 |
52 |
30 |
41 |
78 |
62 |
64 |
20049 |
|
C2 |
A4 |
B9 |
F7 |
D3 |
E5 |
I6 |
G8 |
H1 |
|
|
|
|
|
81 |
55 |
68 |
20 |
6 |
16 |
49 |
35 |
39 |
20049 |
|
I9 |
G1 |
H5 |
C2 |
A6 |
B7 |
F4 |
D8 |
E3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
51 |
35 |
37 |
74 |
58 |
72 |
25 |
3 |
14 |
20049 |
|
F6 |
D8 |
E1 |
I2 |
G4 |
H9 |
C7 |
A3 |
B5 |
|
|
|
|
|
15 |
25 |
2 |
44 |
48 |
31 |
64 |
77 |
63 |
20049 |
|
B6 |
C7 |
A2 |
E8 |
F3 |
D4 |
H1 |
I5 |
G9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
H3[25] |
C9 |
D6 |
A1 |
E7 |
I4 |
F2 |
G8 |
B5 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C1 |
F2 |
I3 |
B4 |
E5 |
H6 |
A7 |
D8 |
G9 |
|
|
|
|
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|
|
|
|
|
F6 |
A4 |
H5 |
G9 |
E7 |
C8 |
B3 |
I1 |
D2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
B6 |
G1 |
F8 |
I7 |
E5 |
A3 |
D2 |
C9 |
H4 |
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|
Bimagic Square n9:9.2a |
|
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|
|
|
|
|
Euler Matrix n9:9.2b |
|
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|
Special Bimagic Square n9:1.2a |
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|
MS Matrix n9:1.2b |
|
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|
|
|
|
|
|
|
|
70 |
77 |
57 |
11 |
27 |
4 |
42 |
46 |
35 |
20049 |
|
H7 |
I5 |
G3 |
B2 |
C9 |
A4 |
E6 |
F1 |
D8 |
|
|
|
|
|
19 |
5 |
18 |
44 |
48 |
31 |
80 |
57 |
67 |
20049 |
|
C1 |
A5 |
B9 |
E8 |
F3 |
D4 |
I8 |
G3 |
H4 |
|
|
|
|
|
|
|
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|
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|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
|
15 |
19 |
8 |
43 |
50 |
30 |
65 |
81 |
58 |
20049 |
|
B6 |
C1 |
A8 |
E7 |
F5 |
D3 |
H2 |
I9 |
G4 |
|
|
|
|
|
43 |
47 |
33 |
66 |
76 |
62 |
14 |
27 |
1 |
20049 |
|
E7 |
F2 |
D6 |
H3 |
I4 |
G8 |
B5 |
C9 |
A1 |
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
38 |
54 |
31 |
69 |
73 |
62 |
16 |
23 |
3 |
20049 |
|
E2 |
F9 |
D4 |
H6 |
I1 |
G8 |
B7 |
C5 |
A3 |
|
|
|
|
|
58 |
71 |
75 |
9 |
10 |
23 |
29 |
42 |
52 |
20049 |
|
G4 |
H8 |
I3 |
A9 |
B1 |
C5 |
D2 |
E6 |
F7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
59 |
66 |
79 |
9 |
13 |
20 |
28 |
44 |
51 |
20049 |
|
G5 |
H3 |
I7 |
A9 |
B4 |
C2 |
D1 |
E8 |
F6 |
|
|
|
|
|
65 |
78 |
61 |
13 |
26 |
3 |
45 |
46 |
32 |
20049 |
|
H2 |
I6 |
G7 |
B4 |
C8 |
A3 |
E9 |
F1 |
D5 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
17 |
24 |
32 |
39 |
52 |
63 |
67 |
74 |
20049 |
|
A1 |
B8 |
C6 |
D5 |
E3 |
F7 |
G9 |
H4 |
I2 |
|
|
|
|
|
8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
|
A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
36 |
40 |
47 |
55 |
71 |
78 |
5 |
12 |
25 |
20049 |
|
D9 |
E4 |
F2 |
G1 |
H8 |
I6 |
A5 |
B3 |
C7 |
|
|
|
|
|
50 |
36 |
37 |
79 |
56 |
69 |
21 |
4 |
17 |
20049 |
|
F5 |
D9 |
E1 |
I7 |
G2 |
H6 |
C3 |
A4 |
B8 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
75 |
61 |
68 |
22 |
2 |
18 |
53 |
33 |
37 |
20049 |
|
I3 |
G7 |
H5 |
C4 |
A2 |
B9 |
F8 |
D6 |
E1 |
|
|
|
|
|
30 |
40 |
53 |
59 |
72 |
73 |
7 |
11 |
24 |
20049 |
|
D3 |
E4 |
F8 |
G5 |
H9 |
I1 |
A7 |
B2 |
C6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
26 |
6 |
10 |
48 |
34 |
41 |
76 |
56 |
72 |
20049 |
|
C8 |
A6 |
B1 |
F3 |
D7 |
E5 |
I4 |
G2 |
H9 |
|
|
|
|
|
81 |
55 |
68 |
20 |
6 |
16 |
49 |
35 |
39 |
20049 |
|
I9 |
G1 |
H5 |
C2 |
A6 |
B7 |
F4 |
D8 |
E3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
49 |
29 |
45 |
80 |
60 |
64 |
21 |
7 |
14 |
20049 |
|
F4 |
D2 |
E9 |
I8 |
G6 |
H1 |
C3 |
A7 |
B5 |
|
|
|
|
|
15 |
25 |
2 |
51 |
34 |
38 |
64 |
77 |
63 |
20049 |
|
B6 |
C7 |
A2 |
F6 |
D7 |
E2 |
H1 |
I5 |
G9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
H7[26] |
C1 |
D4 |
A9 |
E3 |
I6 |
F8 |
G2 |
B5 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C1 |
F2 |
I3 |
B4 |
E5 |
H6 |
A7 |
D8 |
G9 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
|
|
|
|
|
|
|
|
F4 |
A6 |
H5 |
G1 |
E3 |
C2 |
B7 |
I9 |
D8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
B6 |
G1 |
F8 |
I7 |
E5 |
A3 |
D2 |
C9 |
H4 |
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
BiMagic Square n9:A.1a |
|
|
|
|
|
|
|
|
|
|
Euler Matrix n9:A.1b |
|
|
|
|
|
|
|
|
|
|
|
|
|
Special Bimagic Square n9:2.1a |
|
|
|
|
|
|
|
|
|
|
Euler Matrix n9:2.1b |
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
|
|
|
|
|
27 |
5 |
10 |
49 |
30 |
44 |
74 |
61 |
69 |
20049 |
|
C9 |
A5 |
B1 |
F4 |
D3 |
E8 |
I2 |
G7 |
H6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
31 |
39 |
53 |
56 |
70 |
78 |
9 |
14 |
19 |
20049 |
|
D4 |
E3 |
F8 |
G2 |
H7 |
I6 |
A9 |
B5 |
C1 |
|
|
|
|
|
39 |
53 |
31 |
70 |
78 |
56 |
14 |
19 |
9 |
20049 |
|
E3 |
F8 |
D4 |
H7 |
I6 |
G2 |
B5 |
C1 |
A9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
63 |
68 |
73 |
4 |
12 |
26 |
29 |
43 |
51 |
20049 |
|
G9 |
H5 |
I1 |
A4 |
B3 |
C8 |
D2 |
E7 |
F6 |
|
|
|
|
|
60 |
65 |
79 |
1 |
18 |
23 |
35 |
40 |
48 |
20049 |
|
G6 |
H2 |
I7 |
A1 |
B9 |
C5 |
D8 |
E4 |
F3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
25 |
6 |
11 |
50 |
28 |
45 |
75 |
62 |
67 |
20049 |
|
C7 |
A6 |
B2 |
F5 |
D1 |
E9 |
I3 |
G8 |
H4 |
|
|
|
|
|
71 |
76 |
57 |
15 |
20 |
7 |
37 |
54 |
32 |
20049 |
|
H8 |
I4 |
G3 |
B6 |
C2 |
A7 |
E1 |
F9 |
D5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
48 |
35 |
40 |
79 |
60 |
65 |
23 |
1 |
18 |
20049 |
|
F3 |
D8 |
E4 |
I7 |
G6 |
H2 |
C5 |
A1 |
B9 |
|
|
|
|
|
2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
77 |
55 |
72 |
21 |
8 |
13 |
52 |
33 |
38 |
20049 |
|
I5 |
G1 |
H9 |
C3 |
A8 |
B4 |
F7 |
D6 |
E2 |
|
|
|
|
|
50 |
28 |
45 |
75 |
62 |
67 |
25 |
6 |
11 |
20049 |
|
F5 |
D1 |
E9 |
I3 |
G8 |
H4 |
C7 |
A6 |
B2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
15 |
20 |
7 |
37 |
54 |
32 |
71 |
76 |
57 |
20049 |
|
B6 |
C2 |
A7 |
E1 |
F9 |
D5 |
H8 |
I4 |
G3 |
|
|
|
|
|
34 |
42 |
47 |
59 |
64 |
81 |
3 |
17 |
22 |
20049 |
|
D7 |
E6 |
F2 |
G5 |
H1 |
I9 |
A3 |
B8 |
C4 |
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
44 |
49 |
30 |
69 |
74 |
61 |
10 |
27 |
5 |
20049 |
|
E8 |
F4 |
D3 |
H6 |
I2 |
G7 |
B1 |
C9 |
A5 |
|
|
|
|
|
73 |
63 |
68 |
26 |
4 |
12 |
51 |
29 |
43 |
20049 |
|
I1 |
G9 |
H5 |
C8 |
A4 |
B3 |
F6 |
D2 |
E7 |
|
|
|
|
|
|
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|
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|
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|
|
|
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|
|
|
|
|
|
|
|
64 |
81 |
59 |
17 |
22 |
3 |
42 |
47 |
34 |
20049 |
|
H1 |
I9 |
G5 |
B8 |
C4 |
A3 |
E6 |
F2 |
D7 |
|
|
|
|
|
13 |
21 |
8 |
38 |
52 |
33 |
72 |
77 |
55 |
20049 |
|
B4 |
C3 |
A8 |
E2 |
F7 |
D6 |
H9 |
I5 |
G1 |
|
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
|
|
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A2 |
E3 |
I1 |
F5 |
G6 |
B4 |
H8 |
C9 |
D7 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C9 |
F8 |
I7 |
B6 |
E5 |
H4 |
A3 |
D2 |
G1 |
|
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|
H1 |
F4 |
A7 |
C3 |
G6 |
E9 |
D2 |
B5 |
I8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
B4 |
G9 |
F2 |
I3 |
E5 |
A7 |
D8 |
C1 |
H6 |
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|
BiMagic Square n9:A.2a |
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|
|
Euler Matrix n9:A.2b |
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|
Special Bimagic Square n9:2.2a |
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|
MS Matrix n9:2.2b |
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|
|
|
8 |
12 |
22 |
28 |
41 |
54 |
60 |
70 |
74 |
20049 |
|
A8 |
B3 |
C4 |
D1 |
E5 |
F9 |
G6 |
H7 |
I2 |
|
|
|
|
|
27 |
5 |
10 |
38 |
52 |
33 |
74 |
61 |
69 |
20049 |
|
C9 |
A5 |
B1 |
E2 |
F7 |
D6 |
I2 |
G7 |
H6 |
|
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|
|
|
|
|
|
|
33 |
43 |
47 |
62 |
66 |
76 |
1 |
14 |
27 |
20049 |
|
D6 |
E7 |
F2 |
G8 |
H3 |
I4 |
A1 |
B5 |
C9 |
|
|
|
|
|
39 |
53 |
31 |
70 |
78 |
56 |
14 |
19 |
9 |
20049 |
|
E3 |
F8 |
D4 |
H7 |
I6 |
G2 |
B5 |
C1 |
A9 |
|
|
|
|
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|
|
|
|
|
|
|
|
55 |
68 |
81 |
6 |
16 |
20 |
35 |
39 |
49 |
20049 |
|
G1 |
H5 |
I9 |
A6 |
B7 |
C2 |
D8 |
E3 |
F4 |
|
|
|
|
|
60 |
65 |
79 |
1 |
18 |
23 |
35 |
40 |
48 |
20049 |
|
G6 |
H2 |
I7 |
A1 |
B9 |
C5 |
D8 |
E4 |
F3 |
|
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|
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|
|
|
|
|
|
|
21 |
4 |
17 |
50 |
36 |
37 |
79 |
56 |
69 |
20049 |
|
C3 |
A4 |
B8 |
F5 |
D9 |
E1 |
I7 |
G2 |
H6 |
|
|
|
|
|
71 |
76 |
57 |
15 |
20 |
7 |
37 |
54 |
32 |
20049 |
|
H8 |
I4 |
G3 |
B6 |
C2 |
A7 |
E1 |
F9 |
D5 |
|
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|
|
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|
|
|
|
|
|
|
|
|
|
52 |
29 |
42 |
75 |
58 |
71 |
23 |
9 |
10 |
20049 |
|
F7 |
D2 |
E6 |
I3 |
G4 |
H8 |
C5 |
A9 |
B1 |
|
|
|
|
|
2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
77 |
63 |
64 |
25 |
2 |
15 |
48 |
31 |
44 |
20049 |
|
I5 |
G9 |
H1 |
C7 |
A2 |
B6 |
F3 |
D4 |
E8 |
|
|
|
|
|
50 |
28 |
45 |
75 |
62 |
67 |
25 |
6 |
11 |
20049 |
|
F5 |
D1 |
E9 |
I3 |
G8 |
H4 |
C7 |
A6 |
B2 |
|
|
|
|
|
|
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|
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|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
13 |
26 |
3 |
45 |
46 |
32 |
65 |
78 |
61 |
20049 |
|
B4 |
C8 |
A3 |
E9 |
F1 |
D5 |
H2 |
I6 |
G7 |
|
|
|
|
|
34 |
42 |
47 |
59 |
64 |
81 |
3 |
17 |
22 |
20049 |
|
D7 |
E6 |
F2 |
G5 |
H1 |
I9 |
A3 |
B8 |
C4 |
|
|
|
|
|
|
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|
|
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|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
38 |
51 |
34 |
67 |
80 |
57 |
18 |
19 |
5 |
20049 |
|
E2 |
F6 |
D7 |
H4 |
I8 |
G3 |
B9 |
C1 |
A5 |
|
|
|
|
|
73 |
63 |
68 |
26 |
4 |
12 |
51 |
29 |
43 |
20049 |
|
I1 |
G9 |
H5 |
C8 |
A4 |
B3 |
F6 |
D2 |
E7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
72 |
73 |
59 |
11 |
24 |
7 |
40 |
53 |
30 |
20049 |
|
H9 |
I1 |
G5 |
B2 |
C6 |
A7 |
E4 |
F8 |
D3 |
|
|
|
|
|
13 |
21 |
8 |
49 |
30 |
44 |
72 |
77 |
55 |
20049 |
|
B4 |
C3 |
A8 |
F4 |
D3 |
E8 |
H9 |
I5 |
G1 |
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A8 |
E7 |
I9 |
F5 |
G4 |
B6 |
H2 |
C1 |
D3 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
C9 |
F8 |
I7 |
B6 |
E5 |
H4 |
A3 |
D2 |
G1 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
H9 |
F6 |
A3 |
C7 |
G4 |
E1 |
D8 |
B5 |
I2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
B4 |
G9 |
F2 |
I3 |
E5 |
A7 |
D8 |
C1 |
H6 |
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
BiMagic Square n9:A.3a |
|
|
|
|
|
|
|
|
|
|
Euler's Matrix n9:A.3b |
|
|
|
|
|
|
|
|
|
|
|
|
|
Special Bimagic Square n9:3.1a |
|
|
|
|
|
|
|
|
|
|
Euler Matrix n9:3.1b |
|
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|
|
|
|
|
|
|
|
|
|
|
4 |
18 |
20 |
30 |
41 |
52 |
62 |
64 |
78 |
20049 |
|
A4 |
B9 |
C2 |
D3 |
E5 |
F7 |
G8 |
H1 |
I6 |
|
|
|
|
|
29 |
40 |
54 |
61 |
66 |
77 |
6 |
17 |
19 |
20049 |
|
D2 |
E4 |
F9 |
G7 |
H3 |
I5 |
A6 |
B8 |
C1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
35 |
37 |
51 |
58 |
72 |
74 |
3 |
14 |
25 |
20049 |
|
D8 |
E1 |
F6 |
G4 |
H9 |
I2 |
A3 |
B5 |
C7 |
|
|
|
|
|
68 |
79 |
57 |
10 |
24 |
8 |
45 |
47 |
31 |
20049 |
|
H5 |
I7 |
G3 |
B1 |
C6 |
A8 |
E9 |
F2 |
D4 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
57 |
68 |
79 |
8 |
10 |
24 |
31 |
45 |
47 |
20049 |
|
G3 |
H5 |
I7 |
A8 |
B1 |
C6 |
D4 |
E9 |
F2 |
|
|
|
|
|
26 |
1 |
15 |
49 |
36 |
38 |
75 |
59 |
70 |
20049 |
|
C8 |
A1 |
B6 |
F4 |
D9 |
E2 |
I3 |
G5 |
H7 |
|
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|
27 |
2 |
13 |
50 |
34 |
39 |
73 |
60 |
71 |
20049 |
|
C9 |
A2 |
B4 |
F5 |
D7 |
E3 |
I1 |
G6 |
H8 |
|
|
|
|
|
73 |
60 |
71 |
27 |
2 |
13 |
50 |
34 |
39 |
20049 |
|
I1 |
G6 |
H8 |
C9 |
A2 |
B4 |
F5 |
D7 |
E3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
46 |
33 |
44 |
81 |
56 |
67 |
23 |
7 |
12 |
20049 |
|
F1 |
D6 |
E8 |
I9 |
G2 |
H4 |
C5 |
A7 |
B3 |
|
|
|
|
|
4 |
18 |
20 |
30 |
41 |
52 |
62 |
64 |
78 |
20049 |
|
A4 |
B9 |
C2 |
D3 |
E5 |
F7 |
G8 |
H1 |
I6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
77 |
61 |
66 |
19 |
6 |
17 |
54 |
29 |
40 |
20049 |
|
I5 |
G7 |
H3 |
C1 |
A6 |
B8 |
F9 |
D2 |
E4 |
|
|
|
|
|
43 |
48 |
32 |
69 |
80 |
55 |
11 |
22 |
9 |
20049 |
|
E7 |
F3 |
D5 |
H6 |
I8 |
G1 |
B2 |
C4 |
A9 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
11 |
22 |
9 |
43 |
48 |
32 |
69 |
80 |
55 |
20049 |
|
B2 |
C4 |
A9 |
E7 |
F3 |
D5 |
H6 |
I8 |
G1 |
|
|
|
|
|
12 |
23 |
7 |
44 |
46 |
33 |
67 |
81 |
56 |
20049 |
|
B3 |
C5 |
A7 |
E8 |
F1 |
D6 |
H4 |
I9 |
G2 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
42 |
53 |
28 |
65 |
76 |
63 |
16 |
21 |
5 |
20049 |
|
E6 |
F8 |
D1 |
H2 |
I4 |
G9 |
B7 |
C3 |
A5 |
|
|
|
|
|
51 |
35 |
37 |
74 |
58 |
72 |
25 |
3 |
14 |
20049 |
|
F6 |
D8 |
E1 |
I2 |
G4 |
H9 |
C7 |
A3 |
B5 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
70 |
75 |
59 |
15 |
26 |
1 |
38 |
49 |
36 |
20049 |
|
H7 |
I3 |
G5 |
B6 |
C8 |
A1 |
E2 |
F4 |
D9 |
|
|
|
|
|
63 |
65 |
76 |
5 |
16 |
21 |
28 |
42 |
53 |
20049 |
|
G9 |
H2 |
I4 |
A5 |
B7 |
C3 |
D1 |
E6 |
F8 |
|
|
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|
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|
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|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
|
|
|
|
|
|
|
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A4 |
E1 |
I7 |
F5 |
G2 |
B8 |
H6 |
C3 |
D9 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
D2 |
I7 |
B6 |
C9 |
E5 |
G1 |
H4 |
A3 |
F8 |
|
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|
|
H7 |
F8 |
A9 |
C1 |
G2 |
E3 |
D4 |
B5 |
I6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
G9 |
D8 |
A7 |
H6 |
E5 |
B4 |
I3 |
F2 |
C1 |
|
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|
BiMagic Square n9:A.4a |
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|
|
Euler's Matrix n9:A.4 |
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|
Special Bimagic Square n9:3.2a |
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|
MS Matrix n9:3.2b |
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|
|
|
|
|
|
|
6 |
10 |
26 |
34 |
41 |
48 |
56 |
72 |
76 |
20049 |
|
A6 |
B1 |
C8 |
D7 |
E5 |
F3 |
G2 |
H9 |
I4 |
|
|
|
|
|
29 |
40 |
54 |
61 |
66 |
77 |
6 |
17 |
19 |
20049 |
|
D2 |
E4 |
F9 |
G7 |
H3 |
I5 |
A6 |
B8 |
C1 |
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
29 |
45 |
49 |
60 |
64 |
80 |
7 |
14 |
21 |
20049 |
|
D2 |
E9 |
F4 |
G6 |
H1 |
I8 |
A7 |
B5 |
C3 |
|
|
|
|
|
68 |
79 |
57 |
10 |
24 |
8 |
45 |
47 |
31 |
20049 |
|
H5 |
I7 |
G3 |
B1 |
C6 |
A8 |
E9 |
F2 |
D4 |
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
61 |
68 |
75 |
2 |
18 |
22 |
33 |
37 |
53 |
20049 |
|
G7 |
H5 |
I3 |
A2 |
B9 |
C4 |
D6 |
E1 |
F8 |
|
|
|
|
|
26 |
1 |
15 |
44 |
46 |
33 |
75 |
59 |
70 |
20049 |
|
C8 |
A1 |
B6 |
E8 |
F1 |
D6 |
I3 |
G5 |
H7 |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
19 |
8 |
15 |
50 |
30 |
43 |
81 |
58 |
65 |
20049 |
|
C1 |
A8 |
B6 |
F5 |
D3 |
E7 |
I9 |
G4 |
H2 |
|
|
|
|
|
73 |
60 |
71 |
27 |
2 |
13 |
50 |
34 |
39 |
20049 |
|
I1 |
G6 |
H8 |
C9 |
A2 |
B4 |
F5 |
D7 |
E3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
54 |
31 |
38 |
73 |
62 |
69 |
23 |
3 |
16 |
20049 |
|
F9 |
D4 |
E2 |
I1 |
G8 |
H6 |
C5 |
A3 |
B7 |
|
|
|
|
|
4 |
18 |
20 |
30 |
41 |
52 |
62 |
64 |
78 |
20049 |
|
A4 |
B9 |
C2 |
D3 |
E5 |
F7 |
G8 |
H1 |
I6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
77 |
57 |
70 |
27 |
4 |
11 |
46 |
35 |
42 |
20049 |
|
I5 |
G3 |
H7 |
C9 |
A4 |
B2 |
F1 |
D8 |
E6 |
|
|
|
|
|
43 |
48 |
32 |
69 |
80 |
55 |
11 |
22 |
9 |
20049 |
|
E7 |
F3 |
D5 |
H6 |
I8 |
G1 |
B2 |
C4 |
A9 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
17 |
24 |
1 |
39 |
52 |
32 |
67 |
74 |
63 |
20049 |
|
B8 |
C6 |
A1 |
E3 |
F7 |
D5 |
H4 |
I2 |
G9 |
|
|
|
|
|
12 |
23 |
7 |
49 |
36 |
38 |
67 |
81 |
56 |
20049 |
|
B3 |
C5 |
A7 |
F4 |
D9 |
E2 |
H4 |
I9 |
G2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
40 |
47 |
36 |
71 |
78 |
55 |
12 |
25 |
5 |
20049 |
|
E4 |
F2 |
D9 |
H8 |
I6 |
G1 |
B3 |
C7 |
A5 |
|
|
|
|
|
51 |
35 |
37 |
74 |
58 |
72 |
25 |
3 |
14 |
20049 |
|
F6 |
D8 |
E1 |
I2 |
G4 |
H9 |
C7 |
A3 |
B5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
66 |
79 |
59 |
13 |
20 |
9 |
44 |
51 |
28 |
20049 |
|
H3 |
I7 |
G5 |
B4 |
C2 |
A9 |
E8 |
F6 |
D1 |
|
|
|
|
|
63 |
65 |
76 |
5 |
16 |
21 |
28 |
42 |
53 |
20049 |
|
G9 |
H2 |
I4 |
A5 |
B7 |
C3 |
D1 |
E6 |
F8 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
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|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A6 |
E9 |
I3 |
F5 |
G8 |
B2 |
H4 |
C7 |
D1 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
D2 |
I7 |
B6 |
C9 |
E5 |
G1 |
H4 |
A3 |
F8 |
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
H3 |
F2 |
A1 |
C9 |
G8 |
E7 |
D6 |
B5 |
I4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
G9 |
D8 |
A7 |
H6 |
E5 |
B4 |
I3 |
F2 |
C1 |
|
|
|
|
|
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|
|
|
|
|
|
|
BiMagic Square n9:A.5a |
|
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|
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|
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|
|
Euler's Matrix n9:A.5b |
|
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|
Special Bimagic Square n9:4.1a |
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Euler Matrix n9:4.1b |
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2 |
18 |
22 |
34 |
41 |
48 |
60 |
64 |
80 |
20049 |
|
A2 |
B9 |
C4 |
D7 |
E5 |
F3 |
G6 |
H1 |
I8 |
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35 |
42 |
46 |
57 |
70 |
77 |
4 |
11 |
27 |
20049 |
|
D8 |
E6 |
F1 |
G3 |
H7 |
I5 |
A4 |
B2 |
C9 |
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33 |
37 |
53 |
56 |
72 |
76 |
7 |
14 |
21 |
20049 |
|
D6 |
E1 |
F8 |
G2 |
H9 |
I4 |
A7 |
B5 |
C3 |
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|
68 |
75 |
61 |
18 |
22 |
2 |
37 |
53 |
33 |
20049 |
|
H5 |
I3 |
G7 |
B9 |
C4 |
A2 |
E1 |
F8 |
D6 |
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61 |
68 |
75 |
6 |
10 |
26 |
29 |
45 |
49 |
20049 |
|
G7 |
H5 |
I3 |
A6 |
B1 |
C8 |
D2 |
E9 |
F4 |
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20 |
9 |
13 |
51 |
28 |
44 |
79 |
59 |
66 |
20049 |
|
C2 |
A9 |
B4 |
F6 |
D1 |
E8 |
I7 |
G5 |
H3 |
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27 |
4 |
11 |
50 |
30 |
43 |
73 |
62 |
69 |
20049 |
|
C9 |
A4 |
B2 |
F5 |
D3 |
E7 |
I1 |
G8 |
H6 |
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81 |
58 |
65 |
19 |
8 |
15 |
50 |
30 |
43 |
20049 |
|
I9 |
G4 |
H2 |
C1 |
A8 |
B6 |
F5 |
D3 |
E7 |
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46 |
35 |
42 |
81 |
58 |
65 |
23 |
3 |
16 |
20049 |
|
F1 |
D8 |
E6 |
I9 |
G4 |
H2 |
C5 |
A3 |
B7 |
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6 |
10 |
26 |
34 |
41 |
48 |
56 |
72 |
76 |
20049 |
|
A6 |
B1 |
C8 |
D7 |
E5 |
F3 |
G2 |
H9 |
I4 |
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77 |
57 |
70 |
19 |
8 |
15 |
54 |
31 |
38 |
20049 |
|
I5 |
G3 |
H7 |
C1 |
A8 |
B6 |
F9 |
D4 |
E2 |
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39 |
52 |
32 |
67 |
74 |
63 |
17 |
24 |
1 |
20049 |
|
E3 |
F7 |
D5 |
H4 |
I2 |
G9 |
B8 |
C6 |
A1 |
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13 |
20 |
9 |
39 |
52 |
32 |
71 |
78 |
55 |
20049 |
|
B4 |
C2 |
A9 |
E3 |
F7 |
D5 |
H8 |
I6 |
G1 |
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16 |
23 |
3 |
38 |
54 |
31 |
69 |
73 |
62 |
20049 |
|
B7 |
C5 |
A3 |
E2 |
F9 |
D4 |
H6 |
I1 |
G8 |
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44 |
51 |
28 |
67 |
74 |
63 |
12 |
25 |
5 |
20049 |
|
E8 |
F6 |
D1 |
H4 |
I2 |
G9 |
B3 |
C7 |
A5 |
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49 |
29 |
45 |
80 |
60 |
64 |
21 |
7 |
14 |
20049 |
|
F4 |
D2 |
E9 |
I8 |
G6 |
H1 |
C3 |
A7 |
B5 |
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66 |
79 |
59 |
17 |
24 |
1 |
40 |
47 |
36 |
20049 |
|
H3 |
I7 |
G5 |
B8 |
C6 |
A1 |
E4 |
F2 |
D9 |
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55 |
71 |
78 |
5 |
12 |
25 |
36 |
40 |
47 |
20049 |
|
G1 |
H8 |
I6 |
A5 |
B3 |
C7 |
D9 |
E4 |
F2 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A2 |
E1 |
I3 |
F5 |
G4 |
B6 |
H8 |
C7 |
D9 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
D8 |
I3 |
B4 |
C1 |
E5 |
G9 |
H6 |
A7 |
F2 |
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H3 |
F6 |
A9 |
C1 |
G4 |
E7 |
D2 |
B5 |
I8 |
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G1 |
D2 |
A3 |
H4 |
E5 |
B6 |
I7 |
F8 |
C9 |
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BiMagic Square n9:A.6a |
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Euler's Matrix n9:A.6b |
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Special Bimagic Square n9:4.2a |
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MS Matrix n9:4.2b |
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8 |
10 |
24 |
30 |
41 |
52 |
58 |
72 |
74 |
20049 |
|
A8 |
B1 |
C6 |
D3 |
E5 |
F7 |
G4 |
H9 |
I2 |
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|
35 |
42 |
46 |
57 |
70 |
77 |
4 |
11 |
27 |
20049 |
|
D8 |
E6 |
F1 |
G3 |
H7 |
I5 |
A4 |
B2 |
C9 |
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31 |
45 |
47 |
62 |
64 |
78 |
3 |
14 |
25 |
20049 |
|
D4 |
E9 |
F2 |
G8 |
H1 |
I6 |
A3 |
B5 |
C7 |
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|
68 |
75 |
61 |
18 |
22 |
2 |
37 |
53 |
33 |
20049 |
|
H5 |
I3 |
G7 |
B9 |
C4 |
A2 |
E1 |
F8 |
D6 |
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57 |
68 |
79 |
4 |
18 |
20 |
35 |
37 |
51 |
20049 |
|
G3 |
H5 |
I7 |
A4 |
B9 |
C2 |
D8 |
E1 |
F6 |
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|
20 |
9 |
13 |
38 |
54 |
31 |
79 |
59 |
66 |
20049 |
|
C2 |
A9 |
B4 |
E2 |
F9 |
D4 |
I7 |
G5 |
H3 |
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19 |
6 |
17 |
50 |
34 |
39 |
81 |
56 |
67 |
20049 |
|
C1 |
A6 |
B8 |
F5 |
D7 |
E3 |
I9 |
G2 |
H4 |
|
|
|
|
|
81 |
58 |
65 |
19 |
8 |
15 |
50 |
30 |
43 |
20049 |
|
I9 |
G4 |
H2 |
C1 |
A8 |
B6 |
F5 |
D3 |
E7 |
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54 |
29 |
40 |
73 |
60 |
71 |
23 |
7 |
12 |
20049 |
|
F9 |
D2 |
E4 |
I1 |
G6 |
H8 |
C5 |
A7 |
B3 |
|
|
|
|
|
6 |
10 |
26 |
34 |
41 |
48 |
56 |
72 |
76 |
20049 |
|
A6 |
B1 |
C8 |
D7 |
E5 |
F3 |
G2 |
H9 |
I4 |
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77 |
61 |
66 |
27 |
2 |
13 |
46 |
33 |
44 |
20049 |
|
I5 |
G7 |
H3 |
C9 |
A2 |
B4 |
F1 |
D6 |
E8 |
|
|
|
|
|
39 |
52 |
32 |
67 |
74 |
63 |
17 |
24 |
1 |
20049 |
|
E3 |
F7 |
D5 |
H4 |
I2 |
G9 |
B8 |
C6 |
A1 |
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15 |
26 |
1 |
43 |
48 |
32 |
65 |
76 |
63 |
20049 |
|
B6 |
C8 |
A1 |
E7 |
F3 |
D5 |
H2 |
I4 |
G9 |
|
|
|
|
|
16 |
23 |
3 |
51 |
28 |
44 |
69 |
73 |
62 |
20049 |
|
B7 |
C5 |
A3 |
F6 |
D1 |
E8 |
H6 |
I1 |
G8 |
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|
38 |
49 |
36 |
69 |
80 |
55 |
16 |
21 |
5 |
20049 |
|
E2 |
F4 |
D9 |
H6 |
I8 |
G1 |
B7 |
C3 |
A5 |
|
|
|
|
|
49 |
29 |
45 |
80 |
60 |
64 |
21 |
7 |
14 |
20049 |
|
F4 |
D2 |
E9 |
I8 |
G6 |
H1 |
C3 |
A7 |
B5 |
|
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|
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|
|
|
70 |
75 |
59 |
11 |
22 |
9 |
42 |
53 |
28 |
20049 |
|
H7 |
I3 |
G5 |
B2 |
C4 |
A9 |
E6 |
F8 |
D1 |
|
|
|
|
|
55 |
71 |
78 |
5 |
12 |
25 |
36 |
40 |
47 |
20049 |
|
G1 |
H8 |
I6 |
A5 |
B3 |
C7 |
D9 |
E4 |
F2 |
|
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
369 |
1225449 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A8 |
E9 |
I7 |
F5 |
G6 |
B4 |
H2 |
C3 |
D1 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
1225449 |
|
D8 |
I3 |
B4 |
C1 |
E5 |
G9 |
H6 |
A7 |
F2 |
|
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H7 |
F4 |
A1 |
C9 |
G6 |
E3 |
D8 |
B5 |
I2 |
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G1 |
D2 |
A3 |
H4 |
E5 |
B6 |
I7 |
F8 |
C9 |
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BiMagic Square n9:A.7a |
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Euler's Matrix n9:A.7b |
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Rotation Square n9:1a |
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Euler Matrix n9:1b |
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4 |
12 |
26 |
36 |
41 |
46 |
56 |
70 |
78 |
20049 |
|
A4 |
B3 |
C8 |
D9 |
E5 |
F1 |
G2 |
H7 |
I6 |
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64 |
81 |
59 |
17 |
22 |
3 |
42 |
47 |
34 |
20049 |
|
H1 |
I9 |
G5 |
B8 |
C4 |
A3 |
E6 |
F2 |
D7 |
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29 |
43 |
51 |
58 |
66 |
80 |
9 |
14 |
19 |
20049 |
|
D2 |
E7 |
F6 |
G4 |
H3 |
I8 |
A9 |
B5 |
C1 |
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15 |
20 |
7 |
37 |
54 |
32 |
71 |
76 |
57 |
20049 |
|
B6 |
C2 |
A7 |
E1 |
F9 |
D5 |
H8 |
I4 |
G3 |
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63 |
68 |
73 |
2 |
16 |
24 |
31 |
39 |
53 |
20049 |
|
G9 |
H5 |
I1 |
A2 |
B7 |
C6 |
D4 |
E3 |
F8 |
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44 |
49 |
30 |
69 |
74 |
61 |
10 |
27 |
5 |
20049 |
|
E8 |
F4 |
D3 |
H6 |
I2 |
G7 |
B1 |
C9 |
A5 |
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21 |
8 |
13 |
50 |
28 |
45 |
79 |
60 |
65 |
20049 |
|
C3 |
A8 |
B4 |
F5 |
D1 |
E9 |
I7 |
G6 |
H2 |
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63 |
68 |
73 |
4 |
12 |
26 |
29 |
43 |
51 |
20049 |
|
G9 |
H5 |
I1 |
A4 |
B3 |
C8 |
D2 |
E7 |
F6 |
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52 |
33 |
38 |
75 |
62 |
67 |
23 |
1 |
18 |
20049 |
|
F7 |
D6 |
E2 |
I3 |
G8 |
H4 |
C5 |
A1 |
B9 |
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2 |
16 |
24 |
36 |
41 |
46 |
58 |
66 |
80 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
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77 |
55 |
72 |
25 |
6 |
11 |
48 |
35 |
40 |
20049 |
|
I5 |
G1 |
H9 |
C7 |
A6 |
B2 |
F3 |
D8 |
E4 |
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31 |
39 |
53 |
56 |
70 |
78 |
9 |
14 |
19 |
20049 |
|
D4 |
E3 |
F8 |
G2 |
H7 |
I6 |
A9 |
B5 |
C1 |
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17 |
22 |
3 |
37 |
54 |
32 |
69 |
74 |
61 |
20049 |
|
B8 |
C4 |
A3 |
E1 |
F9 |
D5 |
H6 |
I2 |
G7 |
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|
77 |
55 |
72 |
21 |
8 |
13 |
52 |
33 |
38 |
20049 |
|
I5 |
G1 |
H9 |
C3 |
A8 |
B4 |
F7 |
D6 |
E2 |
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42 |
47 |
34 |
71 |
76 |
57 |
10 |
27 |
5 |
20049 |
|
E6 |
F2 |
D7 |
H8 |
I4 |
G3 |
B1 |
C9 |
A5 |
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25 |
6 |
11 |
50 |
28 |
45 |
75 |
62 |
67 |
20049 |
|
C7 |
A6 |
B2 |
F5 |
D1 |
E9 |
I3 |
G8 |
H4 |
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64 |
81 |
59 |
15 |
20 |
7 |
44 |
49 |
30 |
20049 |
|
H1 |
I9 |
G5 |
B6 |
C2 |
A7 |
E8 |
F4 |
D3 |
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48 |
35 |
40 |
79 |
60 |
65 |
23 |
1 |
18 |
20049 |
|
F3 |
D8 |
E4 |
I7 |
G6 |
H2 |
C5 |
A1 |
B9 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A4 |
E7 |
I1 |
F5 |
G8 |
B2 |
H6 |
C9 |
D3 |
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
H1 |
C2 |
D3 |
A4 |
E5 |
I6 |
F7 |
G8 |
B9 |
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H1 |
F2 |
A3 |
C7 |
G8 |
E9 |
D4 |
B5 |
I6 |
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|
F3 |
A6 |
H9 |
G2 |
E5 |
C8 |
B1 |
I4 |
D7 |
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BiMagic Square n9:A.8a |
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Euler's Matrix n9:A.8b |
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Rotation Square n9:2a |
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Euler Matrix n9:2b |
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6 |
16 |
20 |
28 |
41 |
54 |
62 |
66 |
76 |
20049 |
|
A6 |
B7 |
C2 |
D1 |
E5 |
F9 |
G8 |
H3 |
I4 |
|
|
|
|
|
2 |
53 |
39 |
15 |
64 |
81 |
32 |
61 |
22 |
369 |
|
A2 |
F8 |
E3 |
B6 |
H1 |
I9 |
D5 |
G7 |
C4 |
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35 |
39 |
49 |
60 |
70 |
74 |
1 |
14 |
27 |
20049 |
|
D8 |
E3 |
F4 |
G6 |
H7 |
I2 |
A1 |
B5 |
C9 |
|
|
|
|
|
73 |
16 |
31 |
44 |
20 |
59 |
3 |
54 |
69 |
20049 |
|
I1 |
B7 |
D4 |
E8 |
C2 |
G5 |
A3 |
F9 |
H6 |
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55 |
68 |
81 |
8 |
12 |
22 |
33 |
43 |
47 |
20049 |
|
G1 |
H5 |
I9 |
A8 |
B3 |
C4 |
D6 |
E7 |
F2 |
|
|
|
|
|
68 |
63 |
24 |
49 |
30 |
7 |
74 |
17 |
37 |
369 |
|
H5 |
G9 |
C6 |
F4 |
D3 |
A7 |
I2 |
B8 |
E1 |
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25 |
2 |
15 |
50 |
36 |
37 |
75 |
58 |
71 |
20049 |
|
C7 |
A2 |
B6 |
F5 |
D9 |
E1 |
I3 |
G4 |
H8 |
|
|
|
|
|
25 |
77 |
55 |
36 |
4 |
12 |
71 |
42 |
47 |
20049 |
|
C7 |
I5 |
G1 |
D9 |
A4 |
B3 |
H8 |
E6 |
F2 |
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48 |
31 |
44 |
79 |
56 |
69 |
23 |
9 |
10 |
20049 |
|
F3 |
D4 |
E8 |
I7 |
G2 |
H6 |
C5 |
A9 |
B1 |
|
|
|
|
|
48 |
6 |
72 |
56 |
41 |
26 |
10 |
76 |
34 |
20049 |
|
F3 |
A6 |
H9 |
G2 |
E5 |
C8 |
B1 |
I4 |
D7 |
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|
77 |
63 |
64 |
21 |
4 |
17 |
52 |
29 |
42 |
20049 |
|
I5 |
G9 |
H1 |
C3 |
A4 |
B8 |
F7 |
D2 |
E6 |
|
|
|
|
|
35 |
40 |
11 |
70 |
78 |
46 |
27 |
5 |
57 |
20049 |
|
D8 |
E4 |
B2 |
H7 |
I6 |
F1 |
C9 |
A5 |
G3 |
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11 |
24 |
7 |
45 |
46 |
32 |
67 |
80 |
57 |
20049 |
|
B2 |
C6 |
A7 |
E9 |
F1 |
D5 |
H4 |
I8 |
G3 |
|
|
|
|
|
45 |
65 |
8 |
75 |
52 |
33 |
58 |
19 |
14 |
369 |
|
E9 |
H2 |
A8 |
I3 |
F7 |
D6 |
G4 |
C1 |
B5 |
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40 |
53 |
30 |
65 |
78 |
61 |
18 |
19 |
5 |
20049 |
|
E4 |
F8 |
D3 |
H2 |
I6 |
G7 |
B9 |
C1 |
A5 |
|
|
|
|
|
13 |
28 |
79 |
23 |
62 |
38 |
51 |
66 |
9 |
20049 |
|
B4 |
D1 |
I7 |
C5 |
G8 |
E2 |
F6 |
H3 |
A9 |
|
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|
72 |
73 |
59 |
13 |
26 |
3 |
38 |
51 |
34 |
20049 |
|
H9 |
I1 |
G5 |
B4 |
C8 |
A3 |
E2 |
F6 |
D7 |
|
|
|
|
|
60 |
21 |
50 |
1 |
18 |
67 |
43 |
29 |
80 |
369 |
|
G6 |
C3 |
F5 |
A1 |
B9 |
H4 |
E7 |
D2 |
I8 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
A6 |
E3 |
I9 |
F5 |
G2 |
B8 |
H4 |
C1 |
D7 |
|
|
|
|
|
369 |
20049 |
369 |
20049 |
20049 |
20049 |
369 |
20049 |
369 |
20049 |
|
A2 |
B7 |
C6 |
D9 |
E5 |
F1 |
G4 |
H3 |
I8 |
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H9 |
F8 |
A7 |
C3 |
G2 |
E1 |
D6 |
B5 |
I4 |
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|
G6 |
D1 |
A8 |
H7 |
E5 |
B3 |
I2 |
F9 |
C4 |
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Prime Magic Square n9:1a |
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Prime Matrix n9:1b |
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Rotation Square n9:3a |
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Euler Matrix n9:3b |
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|
257 |
199 |
53 |
347 |
367 |
421 |
271 |
73 |
223 |
2211 |
|
257 |
199 |
53 |
347 |
367 |
421 |
271 |
73 |
223 |
|
|
|
|
|
48 |
25 |
77 |
31 |
2 |
63 |
44 |
15 |
64 |
20049 |
|
F3 |
C7 |
I5 |
D4 |
A2 |
G9 |
E8 |
B6 |
H1 |
|
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|
|
263 |
379 |
61 |
373 |
163 |
193 |
281 |
139 |
359 |
2211 |
|
263 |
379 |
61 |
373 |
163 |
193 |
281 |
139 |
359 |
|
|
|
|
|
35 |
6 |
55 |
39 |
16 |
68 |
49 |
20 |
81 |
20049 |
|
D8 |
A6 |
G1 |
E3 |
B7 |
H5 |
F4 |
C2 |
I9 |
|
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|
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|
|
401 |
71 |
173 |
349 |
59 |
277 |
311 |
457 |
113 |
2211 |
|
401 |
71 |
173 |
349 |
59 |
277 |
311 |
457 |
113 |
|
|
|
|
|
40 |
11 |
72 |
53 |
24 |
73 |
30 |
7 |
59 |
20049 |
|
E4 |
B2 |
H9 |
F8 |
C6 |
I1 |
D3 |
A7 |
G5 |
|
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|
|
137 |
337 |
149 |
83 |
197 |
79 |
419 |
479 |
331 |
2211 |
|
137 |
337 |
149 |
83 |
197 |
79 |
419 |
479 |
331 |
|
|
|
|
|
79 |
50 |
21 |
56 |
36 |
4 |
69 |
37 |
17 |
20049 |
|
I7 |
F5 |
C3 |
G2 |
D9 |
A4 |
H6 |
E1 |
B8 |
|
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|
97 |
251 |
241 |
43 |
283 |
439 |
449 |
101 |
307 |
2211 |
|
97 |
251 |
241 |
43 |
283 |
439 |
449 |
101 |
307 |
|
|
|
|
|
60 |
28 |
8 |
70 |
41 |
12 |
74 |
54 |
22 |
20049 |
|
G6 |
D1 |
A8 |
H7 |
E5 |
B3 |
I2 |
F9 |
C4 |
|
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|
|
|
|
211 |
103 |
461 |
239 |
131 |
409 |
127 |
463 |
67 |
2211 |
|
211 |
103 |
461 |
239 |
131 |
409 |
127 |
463 |
67 |
|
|
|
|
|
65 |
45 |
13 |
78 |
46 |
26 |
61 |
32 |
3 |
20049 |
|
H2 |
E9 |
B4 |
I6 |
F1 |
C8 |
G7 |
D5 |
A3 |
|
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|
467 |
293 |
313 |
41 |
431 |
167 |
157 |
233 |
109 |
2211 |
|
467 |
293 |
313 |
41 |
431 |
167 |
157 |
233 |
109 |
|
|
|
|
|
23 |
75 |
52 |
9 |
58 |
29 |
10 |
71 |
42 |
20049 |
|
C5 |
I3 |
F7 |
A9 |
G4 |
D2 |
B1 |
H8 |
E6 |
|
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|
|
|
151 |
397 |
317 |
383 |
389 |
179 |
89 |
37 |
269 |
2211 |
|
151 |
397 |
317 |
383 |
389 |
179 |
89 |
37 |
269 |
|
|
|
|
|
1 |
62 |
33 |
14 |
66 |
43 |
27 |
76 |
47 |
20049 |
|
A1 |
G8 |
D6 |
B5 |
H3 |
E7 |
C9 |
I4 |
F2 |
|
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|
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|
|
|
|
227 |
181 |
443 |
353 |
191 |
47 |
107 |
229 |
433 |
2211 |
|
227 |
181 |
443 |
353 |
191 |
47 |
107 |
229 |
433 |
|
|
|
|
|
18 |
67 |
38 |
19 |
80 |
51 |
5 |
57 |
34 |
20049 |
|
B9 |
H4 |
E2 |
C1 |
I8 |
F6 |
A5 |
G3 |
D7 |
|
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|
2211 |
2211 |
2211 |
2211 |
2211 |
2211 |
2211 |
2211 |
2211 |
2211 |
|
|
|
|
|
|
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|
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|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
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|
2211 |
|
257[27] |
379 |
173 |
83 |
283 |
409 |
157 |
37 |
433 |
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
F3 |
A6 |
H9 |
G2 |
E5 |
C8 |
B1 |
I4 |
D7 |
|
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|
|
|
227 |
397 |
313 |
239 |
283 |
79 |
311 |
139 |
223 |
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
B9 |
G8 |
F7 |
I6 |
E5 |
A4 |
D3 |
C2 |
H1 |
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|
Prime Magic Square n9:2a |
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|
Prime Matrix n9:2b |
|
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|
Rotation Square n9:4a |
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|
Euler Matrix n9:4b |
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|
|
157 |
373 |
401 |
191 |
379 |
83 |
197 |
331 |
149 |
2261 |
|
157 |
373 |
401 |
191 |
379 |
83 |
197 |
331 |
149 |
|
|
|
|
|
60 |
13 |
45 |
35 |
48 |
25 |
68 |
73 |
2 |
369 |
|
G6 |
B4 |
E9 |
D8 |
F3 |
C7 |
H5 |
I1 |
A2 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
89 |
367 |
307 |
397 |
211 |
409 |
97 |
151 |
233 |
2261 |
|
89 |
367 |
307 |
397 |
211 |
409 |
97 |
151 |
233 |
|
|
|
|
|
21 |
28 |
65 |
40 |
6 |
77 |
63 |
16 |
53 |
20049 |
|
C3 |
D1 |
H2 |
E4 |
A6 |
I5 |
G9 |
B7 |
F8 |
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
59 |
227 |
439 |
107 |
479 |
313 |
347 |
163 |
127 |
2261 |
|
59 |
227 |
439 |
107 |
479 |
313 |
347 |
163 |
127 |
|
|
|
|
|
50 |
79 |
8 |
11 |
72 |
55 |
24 |
31 |
39 |
369 |
|
F5 |
I7 |
A8 |
B2 |
H9 |
G1 |
C6 |
D4 |
E3 |
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
317 |
179 |
139 |
47 |
103 |
383 |
193 |
457 |
443 |
2261 |
|
317 |
179 |
139 |
47 |
103 |
383 |
193 |
457 |
443 |
|
|
|
|
|
1 |
23 |
75 |
70 |
56 |
36 |
49 |
44 |
15 |
20049 |
|
A1 |
C5 |
I3 |
H7 |
G2 |
D9 |
F4 |
E8 |
B6 |
|
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|
|
|
|
|
|
421 |
337 |
251 |
173 |
241 |
223 |
431 |
53 |
131 |
2261 |
|
421 |
337 |
251 |
173 |
241 |
223 |
431 |
53 |
131 |
|
|
|
|
|
18 |
62 |
52 |
78 |
41 |
4 |
30 |
20 |
64 |
20049 |
|
B9 |
G8 |
F7 |
I6 |
E5 |
A4 |
D3 |
C2 |
H1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
433 |
293 |
257 |
449 |
181 |
41 |
61 |
263 |
283 |
2261 |
|
433 |
293 |
257 |
449 |
181 |
41 |
61 |
263 |
283 |
|
|
|
|
|
67 |
38 |
33 |
46 |
26 |
12 |
7 |
59 |
81 |
20049 |
|
H4 |
E2 |
D6 |
F1 |
C8 |
B3 |
A7 |
G5 |
I9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
353 |
79 |
199 |
277 |
71 |
461 |
467 |
311 |
43 |
2261 |
|
353 |
79 |
199 |
277 |
71 |
461 |
467 |
311 |
43 |
|
|
|
|
|
43 |
51 |
58 |
27 |
10 |
71 |
74 |
3 |
32 |
369 |
|
E7 |
F6 |
G4 |
C9 |
B1 |
H8 |
I2 |
A3 |
D5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
359 |
269 |
167 |
271 |
109 |
281 |
229 |
113 |
463 |
2261 |
|
359 |
269 |
167 |
271 |
109 |
281 |
229 |
113 |
463 |
|
|
|
|
|
29 |
66 |
19 |
5 |
76 |
42 |
17 |
54 |
61 |
20049 |
|
D2 |
H3 |
C1 |
A5 |
I4 |
E6 |
B8 |
F9 |
G7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
73 |
137 |
101 |
349 |
487 |
67 |
239 |
419 |
389 |
2261 |
|
73 |
137 |
101 |
349 |
487 |
67 |
239 |
419 |
389 |
|
|
|
|
|
80 |
9 |
14 |
57 |
34 |
47 |
37 |
69 |
22 |
369 |
|
I8 |
A9 |
B5 |
G3 |
D7 |
F2 |
E1 |
H6 |
C4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2261 |
2261 |
2261 |
2261 |
2261 |
2261 |
2261 |
2261 |
2261 |
2261 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
20049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2261 |
|
157[28] |
367 |
439 |
47 |
241 |
41 |
467 |
113 |
389 |
|
|
|
|
|
369 |
20049 |
369 |
20049 |
20049 |
20049 |
369 |
20049 |
369 |
20049 |
|
G6 |
D1 |
A8 |
H7 |
E5 |
B3 |
I2 |
F9 |
C4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
73 |
269 |
199 |
449 |
241 |
383 |
347 |
151 |
149 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
I8 |
H3 |
G4 |
F1 |
E5 |
D9 |
C6 |
B7 |
A2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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