Semi Latin Squares (9 x 9)

Office Applications and Entertainment, Magic Squares
	Attachment 9.2.8	About the Author

Composed Magic Squares (9 x 9)
Unique Orthogonal Frames, Non-Lattin

1

45 5 73 6 8 18 55 79 80
77 37 9 76 74 64 27 3 2
1 81 41
10 72
19 63
28 54
36 46
75 7
78 4

A1

8 4 0 5 7 8 0 6 7
4 0 8 3 1 0 8 2 1
0 8 4
0 8
0 8
0 8
8 0
2 6
5 3

B1

4 0 8 0 0 1 6 8 8
8 4 0 8 8 7 2 0 0
0 8 4
1 7
2 6
3 5
3 5
8 0
8 0

2

45 5 73 4 10 19 54 79 80
77 37 9 78 72 63 28 3 2
1 81 41
7 75
8 74
36 46
55 27
64 18
76 6

A2

8 4 0 3 0 0 8 6 7
4 0 8 5 8 8 0 2 1
0 8 4
6 2
7 1
8 0
0 8
0 8
3 5

B2

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
0 8
3 5
6 2
7 1
8 0

3

45 5 73 7 8 18 54 79 80
77 37 9 75 74 64 28 3 2
1 81 41
10 72
19 63
27 55
36 46
76 6
78 4

A3

8 4 0 6 7 8 8 6 7
4 0 8 2 1 0 0 2 1
0 8 4
0 8
0 8
8 0
8 0
3 5
5 3

B3

4 0 8 0 0 1 5 8 8
8 4 0 8 8 7 3 0 0
0 8 4
1 7
2 6
2 6
3 5
8 0
8 0

4

45 5 73 4 10 27 46 79 80
77 37 9 78 72 55 36 3 2
1 81 41
7 75
8 74
28 54
63 19
64 18
76 6

A4

8 4 0 3 0 8 0 6 7
4 0 8 5 8 0 8 2 1
0 8 4
6 2
7 1
0 8
8 0
0 8
3 5

B4

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
0 8
3 5
6 2
7 1
8 0

5

45 5 73 4 18 19 46 79 80
77 37 9 78 64 63 36 3 2
1 81 41
7 75
8 74
28 54
55 27
72 10
76 6

A5

8 4 0 3 8 0 0 6 7
4 0 8 5 0 8 8 2 1
0 8 4
6 2
7 1
0 8
0 8
8 0
3 5

B5

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
0 8
3 5
6 2
7 1
8 0

6

45 5 73 3 6 7 72 78 80
77 37 9 79 76 75 10 4 2
1 81 41
18 64
27 55
28 54
36 46
63 19
74 8

A6

8 4 0 2 5 6 8 5 7
4 0 8 6 3 2 0 3 1
0 8 4
8 0
8 0
0 8
8 0
8 0
1 7

B6

4 0 8 0 0 0 7 8 8
8 4 0 8 8 8 1 0 0
0 8 4
1 7
2 6
3 5
3 5
6 2
8 0

7

45 5 73 6 8 19 55 78 80
77 37 9 76 74 63 27 4 2
1 81 41
10 72
18 64
28 54
36 46
75 7
79 3

A7

8 4 0 5 7 0 0 5 7
4 0 8 3 1 8 8 3 1
0 8 4
0 8
8 0
0 8
8 0
2 6
6 2

B7

4 0 8 0 0 2 6 8 8
8 4 0 8 8 6 2 0 0
0 8 4
1 7
1 7
3 5
3 5
8 0
8 0

8

45 5 73 7 8 19 54 78 80
77 37 9 75 74 63 28 4 2
1 81 41
10 72
18 64
27 55
36 46
76 6
79 3

A8

8 4 0 6 7 0 8 5 7
4 0 8 2 1 8 0 3 1
0 8 4
0 8
8 0
8 0
8 0
3 5
6 2

B8

4 0 8 0 0 2 5 8 8
8 4 0 8 8 6 3 0 0
0 8 4
1 7
1 7
2 6
3 5
8 0
8 0

9

45 5 73 6 18 28 36 78 80
77 37 9 76 64 54 46 4 2
1 81 41
8 74
10 72
19 63
55 27
75 7
79 3

A9

8 4 0 5 8 0 8 5 7
4 0 8 3 0 8 0 3 1
0 8 4
7 1
0 8
0 8
0 8
2 6
6 2

B9

4 0 8 0 1 3 3 8 8
8 4 0 8 7 5 5 0 0
0 8 4
0 8
1 7
2 6
6 2
8 0
8 0

10

45 5 73 7 18 27 36 78 80
77 37 9 75 64 55 46 4 2
1 81 41
8 74
10 72
19 63
54 28
76 6
79 3

A10

8 4 0 6 8 8 8 5 7
4 0 8 2 0 0 0 3 1
0 8 4
7 1
0 8
0 8
8 0
3 5
6 2

B10

4 0 8 0 1 2 3 8 8
8 4 0 8 7 6 5 0 0
0 8 4
0 8
1 7
2 6
5 3
8 0
8 0

11

45 5 73 3 4 8 75 76 80
77 37 9 79 78 74 7 6 2
1 81 41
19 63
27 55
28 54
36 46
64 18
72 10

A11

8 4 0 2 3 7 2 3 7
4 0 8 6 5 1 6 5 1
0 8 4
0 8
8 0
0 8
8 0
0 8
8 0

B11

4 0 8 0 0 0 8 8 8
8 4 0 8 8 8 0 0 0
0 8 4
2 6
2 6
3 5
3 5
7 1
7 1

12

45 5 73 3 4 19 64 76 80
77 37 9 79 78 63 18 6 2
1 81 41
8 74
27 55
28 54
36 46
72 10
75 7

A12

8 4 0 2 3 0 0 3 7
4 0 8 6 5 8 8 5 1
0 8 4
7 1
8 0
0 8
8 0
8 0
2 6

B12

4 0 8 0 0 2 7 8 8
8 4 0 8 8 6 1 0 0
0 8 4
0 8
2 6
3 5
3 5
7 1
8 0

13

45 5 73 7 10 19 54 76 80
77 37 9 75 72 63 28 6 2
1 81 41
8 74
18 64
27 55
36 46
78 4
79 3

A13

8 4 0 6 0 0 8 3 7
4 0 8 2 8 8 0 5 1
0 8 4
7 1
8 0
8 0
8 0
5 3
6 2

B13

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
1 7
2 6
3 5
8 0
8 0

14

45 5 73 7 10 19 54 76 80
77 37 9 75 72 63 28 6 2
1 81 41
4 78
8 74
36 46
55 27
64 18
79 3

A14

8 4 0 6 0 0 8 3 7
4 0 8 2 8 8 0 5 1
0 8 4
3 5
7 1
8 0
0 8
0 8
6 2

B14

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
0 8
3 5
6 2
7 1
8 0

15

45 5 73 8 10 18 54 76 80
77 37 9 74 72 64 28 6 2
1 81 41
7 75
19 63
27 55
36 46
78 4
79 3

A15

8 4 0 7 0 8 8 3 7
4 0 8 1 8 0 0 5 1
0 8 4
6 2
0 8
8 0
8 0
5 3
6 2

B15

4 0 8 0 1 1 5 8 8
8 4 0 8 7 7 3 0 0
0 8 4
0 8
2 6
2 6
3 5
8 0
8 0

16

45 5 73 7 10 27 46 76 80
77 37 9 75 72 55 36 6 2
1 81 41
4 78
8 74
28 54
63 19
64 18
79 3

A16

8 4 0 6 0 8 0 3 7
4 0 8 2 8 0 8 5 1
0 8 4
3 5
7 1
0 8
8 0
0 8
6 2

B16

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
0 8
3 5
6 2
7 1
8 0

17

45 5 73 7 18 19 46 76 80
77 37 9 75 64 63 36 6 2
1 81 41
4 78
8 74
28 54
55 27
72 10
79 3

A17

8 4 0 6 8 0 0 3 7
4 0 8 2 0 8 8 5 1
0 8 4
3 5
7 1
0 8
0 8
8 0
6 2

B17

4 0 8 0 1 2 5 8 8
8 4 0 8 7 6 3 0 0
0 8 4
0 8
0 8
3 5
6 2
7 1
8 0

18

45 5 73 8 19 27 36 76 80
77 37 9 74 63 55 46 6 2
1 81 41
7 75
10 72
18 64
54 28
78 4
79 3

A18

8 4 0 7 0 8 8 3 7
4 0 8 1 8 0 0 5 1
0 8 4
6 2
0 8
8 0
8 0
5 3
6 2

B18

4 0 8 0 2 2 3 8 8
8 4 0 8 6 6 5 0 0
0 8 4
0 8
1 7
1 7
5 3
8 0
8 0

19

45 5 73 8 10 18 55 75 80
77 37 9 74 72 64 27 7 2
1 81 41
6 76
19 63
28 54
36 46
78 4
79 3

A19

8 4 0 7 0 8 0 2 7
4 0 8 1 8 0 8 6 1
0 8 4
5 3
0 8
0 8
8 0
5 3
6 2

B19

4 0 8 0 1 1 6 8 8
8 4 0 8 7 7 2 0 0
0 8 4
0 8
2 6
3 5
3 5
8 0
8 0

20

45 5 73 4 6 27 54 75 80
77 37 9 78 76 55 28 7 2
1 81 41
10 72
18 64
19 63
46 36
74 8
79 3

A20

8 4 0 3 5 8 8 2 7
4 0 8 5 3 0 0 6 1
0 8 4
0 8
8 0
0 8
0 8
1 7
6 2

B20

4 0 8 0 0 2 5 8 8
8 4 0 8 8 6 3 0 0
0 8 4
1 7
1 7
2 6
5 3
8 0
8 0

21

45 5 73 8 19 28 36 75 80
77 37 9 74 63 54 46 7 2
1 81 41
6 76
10 72
18 64
55 27
78 4
79 3

A21

8 4 0 7 0 0 8 2 7
4 0 8 1 8 8 0 6 1
0 8 4
5 3
0 8
8 0
0 8
5 3
6 2

B21

4 0 8 0 2 3 3 8 8
8 4 0 8 6 5 5 0 0
0 8 4
0 8
1 7
1 7
6 2
8 0
8 0

22

45 5 73 3 6 28 55 74 80
77 37 9 79 76 54 27 8 2
1 81 41
10 72
18 64
19 63
46 36
75 7
78 4

A22

8 4 0 2 5 0 0 1 7
4 0 8 6 3 8 8 7 1
0 8 4
0 8
8 0
0 8
0 8
2 6
5 3

B22

4 0 8 0 0 3 6 8 8
8 4 0 8 8 5 2 0 0
0 8 4
1 7
1 7
2 6
5 3
8 0
8 0

23

45 5 73 3 8 19 64 72 80
77 37 9 79 74 63 18 10 2
1 81 41
6 76
7 75
46 36
54 28
55 27
78 4

A23

8 4 0 2 7 0 0 8 7
4 0 8 6 1 8 8 0 1
0 8 4
5 3
6 2
0 8
8 0
0 8
5 3

B23

4 0 8 0 0 2 7 7 8
8 4 0 8 8 6 1 1 0
0 8 4
0 8
0 8
5 3
5 3
6 2
8 0

24

45 5 73 6 7 18 63 72 80
77 37 9 76 75 64 19 10 2
1 81 41
4 78
8 74
46 36
54 28
55 27
79 3

A24

8 4 0 5 6 8 8 8 7
4 0 8 3 2 0 0 0 1
0 8 4
3 5
7 1
0 8
8 0
0 8
6 2

B24

4 0 8 0 0 1 6 7 8
8 4 0 8 8 7 2 1 0
0 8 4
0 8
0 8
5 3
5 3
6 2
8 0

25

45 5 73 4 7 28 55 72 80
77 37 9 78 75 54 27 10 2
1 81 41
8 74
18 64
19 63
46 36
76 6
79 3

A25

8 4 0 3 6 0 0 8 7
4 0 8 5 2 8 8 0 1
0 8 4
7 1
8 0
0 8
0 8
3 5
6 2

B25

4 0 8 0 0 3 6 7 8
8 4 0 8 8 5 2 1 0
0 8 4
0 8
1 7
2 6
5 3
8 0
8 0

26

45 5 73 3 27 28 36 72 80
77 37 9 79 55 54 46 10 2
1 81 41
6 76
7 75
18 64
63 19
74 8
78 4

A26

8 4 0 2 8 0 8 8 7
4 0 8 6 0 8 0 0 1
0 8 4
5 3
6 2
8 0
8 0
1 7
5 3

B26

4 0 8 0 2 3 3 7 8
8 4 0 8 6 5 5 1 0
0 8 4
0 8
0 8
1 7
6 2
8 0
8 0

27

45 5 73 4 7 28 63 64 80
77 37 9 78 75 54 19 18 2
1 81 41
8 74
10 72
27 55
46 36
76 6
79 3

A27

8 4 0 3 6 0 8 0 7
4 0 8 5 2 8 0 8 1
0 8 4
7 1
0 8
8 0
0 8
3 5
6 2

B27

4 0 8 0 0 3 6 7 8
8 4 0 8 8 5 2 1 0
0 8 4
0 8
1 7
2 6
5 3
8 0
8 0

28

45 5 73 4 8 27 63 64 80
77 37 9 78 74 55 19 18 2
1 81 41
7 75
10 72
28 54
46 36
76 6
79 3

A28

8 4 0 3 7 8 8 0 7
4 0 8 5 1 0 0 8 1
0 8 4
6 2
0 8
0 8
0 8
3 5
6 2

B28

4 0 8 0 0 2 6 7 8
8 4 0 8 8 6 2 1 0
0 8 4
0 8
1 7
3 5
5 3
8 0
8 0

29

45 5 73 4 7 36 55 64 80
77 37 9 78 75 46 27 18 2
1 81 41
8 74
10 72
19 63
54 28
76 6
79 3

A29

8 4 0 3 6 8 0 0 7
4 0 8 5 2 0 8 8 1
0 8 4
7 1
0 8
0 8
8 0
3 5
6 2

B29

4 0 8 0 0 3 6 7 8
8 4 0 8 8 5 2 1 0
0 8 4
0 8
1 7
2 6
5 3
8 0
8 0

30

45 5 73 4 8 36 54 64 80
77 37 9 78 74 46 28 18 2
1 81 41
7 75
10 72
19 63
55 27
76 6
79 3

A30

8 4 0 3 7 8 8 0 7
4 0 8 5 1 0 0 8 1
0 8 4
6 2
0 8
0 8
0 8
3 5
6 2

B30

4 0 8 0 0 3 5 7 8
8 4 0 8 8 5 3 1 0
0 8 4
0 8
1 7
2 6
6 2
8 0
8 0

31

45 5 73 3 8 46 54 55 80
77 37 9 79 74 36 28 27 2
1 81 41
6 76
7 75
19 63
64 18
72 10
78 4

A31

8 4 0 2 7 0 8 0 7
4 0 8 6 1 8 0 8 1
0 8 4
5 3
6 2
0 8
0 8
8 0
5 3

B31

4 0 8 0 0 5 5 6 8
8 4 0 8 8 3 3 2 0
0 8 4
0 8
0 8
2 6
7 1
7 1
8 0

32

45 5 73 4 7 46 54 55 80
77 37 9 78 75 36 28 27 2
1 81 41
6 76
8 74
18 64
63 19
72 10
79 3

A32

8 4 0 3 6 0 8 0 7
4 0 8 5 2 8 0 8 1
0 8 4
5 3
7 1
8 0
8 0
8 0
6 2

B32

4 0 8 0 0 5 5 6 8
8 4 0 8 8 3 3 2 0
0 8 4
0 8
0 8
1 7
6 2
7 1
8 0

33

45 5 73 18 19 28 46 55 80
77 37 9 64 63 54 36 27 2
1 81 41
4 78
7 75
8 74
72 10
76 6
79 3

A33

8 4 0 8 0 0 0 0 7
4 0 8 0 8 8 8 8 1
0 8 4
3 5
6 2
7 1
8 0
3 5
6 2

B33

4 0 8 1 2 3 5 6 8
8 4 0 7 6 5 3 2 0
0 8 4
0 8
0 8
0 8
7 1
8 0
8 0

About the Author