Office Applications and Entertainment, Latin Squares
Vorige Pagina Attachment 7.10.1 About the Author

Construction of order 39 Self Orthogonal Composed Latin Diagonal Squares

Construct an order 35 Self Orthogonal Composed Latin Diagonal Square.

The required order 7 Self orthogonal Latin Diagonal Sub Squares can be constructed based on the sub series:

     {0, 1 ... 6}, {7, 8 ... 13}, {14, 15 ... 20}, {25, 26 ... 31} and {32, 33 ... 38}

with respectively the magic constants s7 = 21, 70, 119, 196 and 245.

Sqrs7
38 20 6 31 13
6 31 13 38 20
13 38 20 6 31
20 6 31 13 38
31 13 38 20 6
Aux4
21 23 24 22
24 22 21 23
22 24 23 21
23 21 22 24

The order 5 Self orthogonal Latin Diagonal Square left above (Sqrs7) is based on the first elements of the Sub Squares, and has been used as a guideline for the construction Step 1.

The order 4 Self orthogonal Latin Diagonal Square right above (Aux4) is based on the sub series 21, 22, 23, 24} and has been used for the construction Step 2.

Step 1
38 37 35 33 32 36 34
35 33 32 36 34 38 37
32 36 34 38 37 35 33
34 38 37 35 33 32 36
37 35 33 32 36 34 38
33 32 36 34 38 37 35
36 34 38 37 35 33 32
20 19 17 15 14 18 16
17 15 14 18 16 20 19
14 18 16 20 19 17 15
16 20 19 17 15 14 18
19 17 15 14 18 16 20
15 14 18 16 20 19 17
18 16 20 19 17 15 14
6 5 3 1 0 4 2
3 1 0 4 2 6 5
0 4 2 6 5 3 1
2 6 5 3 1 0 4
5 3 1 0 4 2 6
1 0 4 2 6 5 3
4 2 6 5 3 1 0
31 30 28 26 25 29 27
28 26 25 29 27 31 30
25 29 27 31 30 28 26
27 31 30 28 26 25 29
30 28 26 25 29 27 31
26 25 29 27 31 30 28
29 27 31 30 28 26 25
13 12 10 8 7 11 9
10 8 7 11 9 13 12
7 11 9 13 12 10 8
9 13 12 10 8 7 11
12 10 8 7 11 9 13
8 7 11 9 13 12 10
11 9 13 12 10 8 7
6 5 3 1 0 4 2
3 1 0 4 2 6 5
0 4 2 6 5 3 1
2 6 5 3 1 0 4
5 3 1 0 4 2 6
1 0 4 2 6 5 3
4 2 6 5 3 1 0
31 30 28 26 25 29 27
28 26 25 29 27 31 30
25 29 27 31 30 28 26
27 31 30 28 26 25 29
30 28 26 25 29 27 31
26 25 29 27 31 30 28
29 27 31 30 28 26 25
13 12 10 8 7 11 9
10 8 7 11 9 13 12
7 11 9 13 12 10 8
9 13 12 10 8 7 11
12 10 8 7 11 9 13
8 7 11 9 13 12 10
11 9 13 12 10 8 7
38 37 35 33 32 36 34
35 33 32 36 34 38 37
32 36 34 38 37 35 33
34 38 37 35 33 32 36
37 35 33 32 36 34 38
33 32 36 34 38 37 35
36 34 38 37 35 33 32
20 19 17 15 14 18 16
17 15 14 18 16 20 19
14 18 16 20 19 17 15
16 20 19 17 15 14 18
19 17 15 14 18 16 20
15 14 18 16 20 19 17
18 16 20 19 17 15 14
13 12 10 8 7 11 9
10 8 7 11 9 13 12
7 11 9 13 12 10 8
9 13 12 10 8 7 11
12 10 8 7 11 9 13
8 7 11 9 13 12 10
11 9 13 12 10 8 7
38 37 35 33 32 36 34
35 33 32 36 34 38 37
32 36 34 38 37 35 33
34 38 37 35 33 32 36
37 35 33 32 36 34 38
33 32 36 34 38 37 35
36 34 38 37 35 33 32
20 19 17 15 14 18 16
17 15 14 18 16 20 19
14 18 16 20 19 17 15
16 20 19 17 15 14 18
19 17 15 14 18 16 20
15 14 18 16 20 19 17
18 16 20 19 17 15 14
6 5 3 1 0 4 2
3 1 0 4 2 6 5
0 4 2 6 5 3 1
2 6 5 3 1 0 4
5 3 1 0 4 2 6
1 0 4 2 6 5 3
4 2 6 5 3 1 0
31 30 28 26 25 29 27
28 26 25 29 27 31 30
25 29 27 31 30 28 26
27 31 30 28 26 25 29
30 28 26 25 29 27 31
26 25 29 27 31 30 28
29 27 31 30 28 26 25
20 19 17 15 14 18 16
17 15 14 18 16 20 19
14 18 16 20 19 17 15
16 20 19 17 15 14 18
19 17 15 14 18 16 20
15 14 18 16 20 19 17
18 16 20 19 17 15 14
6 5 3 1 0 4 2
3 1 0 4 2 6 5
0 4 2 6 5 3 1
2 6 5 3 1 0 4
5 3 1 0 4 2 6
1 0 4 2 6 5 3
4 2 6 5 3 1 0
31 30 28 26 25 29 27
28 26 25 29 27 31 30
25 29 27 31 30 28 26
27 31 30 28 26 25 29
30 28 26 25 29 27 31
26 25 29 27 31 30 28
29 27 31 30 28 26 25
13 12 10 8 7 11 9
10 8 7 11 9 13 12
7 11 9 13 12 10 8
9 13 12 10 8 7 11
12 10 8 7 11 9 13
8 7 11 9 13 12 10
11 9 13 12 10 8 7
38 37 35 33 32 36 34
35 33 32 36 34 38 37
32 36 34 38 37 35 33
34 38 37 35 33 32 36
37 35 33 32 36 34 38
33 32 36 34 38 37 35
36 34 38 37 35 33 32
31 30 28 26 25 29 27
28 26 25 29 27 31 30
25 29 27 31 30 28 26
27 31 30 28 26 25 29
30 28 26 25 29 27 31
26 25 29 27 31 30 28
29 27 31 30 28 26 25
13 12 10 8 7 11 9
10 8 7 11 9 13 12
7 11 9 13 12 10 8
9 13 12 10 8 7 11
12 10 8 7 11 9 13
8 7 11 9 13 12 10
11 9 13 12 10 8 7
38 37 35 33 32 36 34
35 33 32 36 34 38 37
32 36 34 38 37 35 33
34 38 37 35 33 32 36
37 35 33 32 36 34 38
33 32 36 34 38 37 35
36 34 38 37 35 33 32
20 19 17 15 14 18 16
17 15 14 18 16 20 19
14 18 16 20 19 17 15
16 20 19 17 15 14 18
19 17 15 14 18 16 20
15 14 18 16 20 19 17
18 16 20 19 17 15 14
6 5 3 1 0 4 2
3 1 0 4 2 6 5
0 4 2 6 5 3 1
2 6 5 3 1 0 4
5 3 1 0 4 2 6
1 0 4 2 6 5 3
4 2 6 5 3 1 0

Construct an intermediate order 39 square by adding the Auxilliary Square Aux4 and the related rows and columns, to the order 35 Self Orthogonal Composed Latin Diagonal Square as shown below:

Step 2
38 37 35 33 32 36 34 20 19 17 15 14 18 16 0 0 6 5 3 1 0 4 2 0 0 31 30 28 26 25 29 27 13 12 10 8 7 11 9
35 33 32 36 34 38 37 17 15 14 18 16 20 19 0 0 3 1 0 4 2 6 5 0 0 28 26 25 29 27 31 30 10 8 7 11 9 13 12
32 36 34 38 37 35 33 14 18 16 20 19 17 15 0 0 0 4 2 6 5 3 1 0 0 25 29 27 31 30 28 26 7 11 9 13 12 10 8
34 38 37 35 33 32 36 16 20 19 17 15 14 18 0 0 2 6 5 3 1 0 4 0 0 27 31 30 28 26 25 29 9 13 12 10 8 7 11
37 35 33 32 36 34 38 19 17 15 14 18 16 20 0 0 5 3 1 0 4 2 6 0 0 30 28 26 25 29 27 31 12 10 8 7 11 9 13
33 32 36 34 38 37 35 15 14 18 16 20 19 17 0 0 1 0 4 2 6 5 3 0 0 26 25 29 27 31 30 28 8 7 11 9 13 12 10
36 34 38 37 35 33 32 18 16 20 19 17 15 14 0 0 4 2 6 5 3 1 0 0 0 29 27 31 30 28 26 25 11 9 13 12 10 8 7
6 5 3 1 0 4 2 31 30 28 26 25 29 27 0 0 13 12 10 8 7 11 9 0 0 38 37 35 33 32 36 34 20 19 17 15 14 18 16
3 1 0 4 2 6 5 28 26 25 29 27 31 30 0 0 10 8 7 11 9 13 12 0 0 35 33 32 36 34 38 37 17 15 14 18 16 20 19
0 4 2 6 5 3 1 25 29 27 31 30 28 26 0 0 7 11 9 13 12 10 8 0 0 32 36 34 38 37 35 33 14 18 16 20 19 17 15
2 6 5 3 1 0 4 27 31 30 28 26 25 29 0 0 9 13 12 10 8 7 11 0 0 34 38 37 35 33 32 36 16 20 19 17 15 14 18
5 3 1 0 4 2 6 30 28 26 25 29 27 31 0 0 12 10 8 7 11 9 13 0 0 37 35 33 32 36 34 38 19 17 15 14 18 16 20
1 0 4 2 6 5 3 26 25 29 27 31 30 28 0 0 8 7 11 9 13 12 10 0 0 33 32 36 34 38 37 35 15 14 18 16 20 19 17
4 2 6 5 3 1 0 29 27 31 30 28 26 25 0 0 11 9 13 12 10 8 7 0 0 36 34 38 37 35 33 32 18 16 20 19 17 15 14
0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 23 0 0 0 0 0 0 0 24 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 22 0 0 0 0 0 0 0 21 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 12 10 8 7 11 9 38 37 35 33 32 36 34 0 0 20 19 17 15 14 18 16 0 0 6 5 3 1 0 4 2 31 30 28 26 25 29 27
10 8 7 11 9 13 12 35 33 32 36 34 38 37 0 0 17 15 14 18 16 20 19 0 0 3 1 0 4 2 6 5 28 26 25 29 27 31 30
7 11 9 13 12 10 8 32 36 34 38 37 35 33 0 0 14 18 16 20 19 17 15 0 0 0 4 2 6 5 3 1 25 29 27 31 30 28 26
9 13 12 10 8 7 11 34 38 37 35 33 32 36 0 0 16 20 19 17 15 14 18 0 0 2 6 5 3 1 0 4 27 31 30 28 26 25 29
12 10 8 7 11 9 13 37 35 33 32 36 34 38 0 0 19 17 15 14 18 16 20 0 0 5 3 1 0 4 2 6 30 28 26 25 29 27 31
8 7 11 9 13 12 10 33 32 36 34 38 37 35 0 0 15 14 18 16 20 19 17 0 0 1 0 4 2 6 5 3 26 25 29 27 31 30 28
11 9 13 12 10 8 7 36 34 38 37 35 33 32 0 0 18 16 20 19 17 15 14 0 0 4 2 6 5 3 1 0 29 27 31 30 28 26 25
0 0 0 0 0 0 0 0 0 0 0 0 0 0 22 24 0 0 0 0 0 0 0 23 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 21 0 0 0 0 0 0 0 22 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 19 17 15 14 18 16 6 5 3 1 0 4 2 0 0 31 30 28 26 25 29 27 0 0 13 12 10 8 7 11 9 38 37 35 33 32 36 34
17 15 14 18 16 20 19 3 1 0 4 2 6 5 0 0 28 26 25 29 27 31 30 0 0 10 8 7 11 9 13 12 35 33 32 36 34 38 37
14 18 16 20 19 17 15 0 4 2 6 5 3 1 0 0 25 29 27 31 30 28 26 0 0 7 11 9 13 12 10 8 32 36 34 38 37 35 33
16 20 19 17 15 14 18 2 6 5 3 1 0 4 0 0 27 31 30 28 26 25 29 0 0 9 13 12 10 8 7 11 34 38 37 35 33 32 36
19 17 15 14 18 16 20 5 3 1 0 4 2 6 0 0 30 28 26 25 29 27 31 0 0 12 10 8 7 11 9 13 37 35 33 32 36 34 38
15 14 18 16 20 19 17 1 0 4 2 6 5 3 0 0 26 25 29 27 31 30 28 0 0 8 7 11 9 13 12 10 33 32 36 34 38 37 35
18 16 20 19 17 15 14 4 2 6 5 3 1 0 0 0 29 27 31 30 28 26 25 0 0 11 9 13 12 10 8 7 36 34 38 37 35 33 32
31 30 28 26 25 29 27 13 12 10 8 7 11 9 0 0 38 37 35 33 32 36 34 0 0 20 19 17 15 14 18 16 6 5 3 1 0 4 2
28 26 25 29 27 31 30 10 8 7 11 9 13 12 0 0 35 33 32 36 34 38 37 0 0 17 15 14 18 16 20 19 3 1 0 4 2 6 5
25 29 27 31 30 28 26 7 11 9 13 12 10 8 0 0 32 36 34 38 37 35 33 0 0 14 18 16 20 19 17 15 0 4 2 6 5 3 1
27 31 30 28 26 25 29 9 13 12 10 8 7 11 0 0 34 38 37 35 33 32 36 0 0 16 20 19 17 15 14 18 2 6 5 3 1 0 4
30 28 26 25 29 27 31 12 10 8 7 11 9 13 0 0 37 35 33 32 36 34 38 0 0 19 17 15 14 18 16 20 5 3 1 0 4 2 6
26 25 29 27 31 30 28 8 7 11 9 13 12 10 0 0 33 32 36 34 38 37 35 0 0 15 14 18 16 20 19 17 1 0 4 2 6 5 3
29 27 31 30 28 26 25 11 9 13 12 10 8 7 0 0 36 34 38 37 35 33 32 0 0 18 16 20 19 17 15 14 4 2 6 5 3 1 0

The Intermediate Square has to be completed and transformed to a Self Orthogonal Latin Diagonal Square, which can be achieved by means of a set of twenty order 8 Auxiliary Latin Diagonal Squares:

21
32 34 37 38 21 36 35 33
35 33 21 36 37 38 32 34
33 37 34 21 38 35 36 32
36 32 38 35 34 21 33 37
34 38 32 37 36 33 21 35
21 35 36 33 32 37 34 38
37 21 33 34 35 32 38 36
38 36 35 32 33 34 37 21
22
14 16 19 20 22 18 17 15
17 15 22 18 19 20 14 16
15 19 16 22 20 17 18 14
18 14 20 17 16 22 15 19
16 20 14 19 18 15 22 17
22 17 18 15 14 19 16 20
19 22 15 16 17 14 20 18
20 18 17 14 15 16 19 22
23
0 2 5 6 23 4 3 1
3 1 23 4 5 6 0 2
1 5 2 23 6 3 4 0
4 0 6 3 2 23 1 5
2 6 0 5 4 1 23 3
23 3 4 1 0 5 2 6
5 23 1 2 3 0 6 4
6 4 3 0 1 2 5 23
24
30 26 29 24 31 28 27 25
27 25 31 28 29 24 30 26
25 29 26 31 24 27 28 30
28 30 24 27 26 31 25 29
26 24 30 29 28 25 31 27
31 27 28 25 30 29 26 24
29 31 25 26 27 30 24 28
24 28 27 30 25 26 29 31
21
0 2 5 6 22 4 3 1
3 1 22 4 5 6 0 2
1 5 2 22 6 3 4 0
4 0 6 3 2 22 1 5
2 6 0 5 4 1 22 3
22 3 4 1 0 5 2 6
5 22 1 2 3 0 6 4
6 4 3 0 1 2 5 22
23
25 27 30 31 23 29 28 26
28 26 23 29 30 31 25 27
26 30 27 23 31 28 29 25
29 25 31 28 27 23 26 30
27 31 25 30 29 26 23 28
23 28 29 26 25 30 27 31
30 23 26 27 28 25 31 29
31 29 28 25 26 27 30 23
24
7 9 12 13 24 11 10 8
10 8 24 11 12 13 7 9
8 12 9 24 13 10 11 7
11 7 13 10 9 24 8 12
9 13 7 12 11 8 24 10
24 10 11 8 7 12 9 13
12 24 8 9 10 7 13 11
13 11 10 7 8 9 12 24
21
19 15 18 21 20 17 16 14
16 14 20 17 18 21 19 15
14 18 15 20 21 16 17 19
17 19 21 16 15 20 14 18
15 21 19 18 17 14 20 16
20 16 17 14 19 18 15 21
18 20 14 15 16 19 21 17
21 17 16 19 14 15 18 20
21
7 9 12 13 23 11 10 8
10 8 23 11 12 13 7 9
8 12 9 23 13 10 11 7
11 7 13 10 9 23 8 12
9 13 7 12 11 8 23 10
23 10 11 8 7 12 9 13
12 23 8 9 10 7 13 11
13 11 10 7 8 9 12 23
24
32 34 37 38 24 36 35 33
35 33 24 36 37 38 32 34
33 37 34 24 38 35 36 32
36 32 38 35 34 24 33 37
34 38 32 37 36 33 24 35
24 35 36 33 32 37 34 38
37 24 33 34 35 32 38 36
38 36 35 32 33 34 37 24
21
21 1 4 5 6 3 2 0
2 0 6 3 4 5 21 1
0 4 1 6 5 2 3 21
3 21 5 2 1 6 0 4
1 5 21 4 3 0 6 2
6 2 3 0 21 4 1 5
4 6 0 1 2 21 5 3
5 3 2 21 0 1 4 6
22
22 26 29 30 31 28 27 25
27 25 31 28 29 30 22 26
25 29 26 31 30 27 28 22
28 22 30 27 26 31 25 29
26 30 22 29 28 25 31 27
31 27 28 25 22 29 26 30
29 31 25 26 27 22 30 28
30 28 27 22 25 26 29 31
24
14 16 19 20 15 18 17 24
17 24 15 18 19 20 14 16
24 19 16 15 20 17 18 14
18 14 20 17 16 15 24 19
16 20 14 19 18 24 15 17
15 17 18 24 14 19 16 20
19 15 24 16 17 14 20 18
20 18 17 14 24 16 19 15
21
21 26 29 30 31 28 27 25
27 25 31 28 29 30 21 26
25 29 26 31 30 27 28 21
28 21 30 27 26 31 25 29
26 30 21 29 28 25 31 27
31 27 28 25 21 29 26 30
29 31 25 26 27 21 30 28
30 28 27 21 25 26 29 31
22
22 8 11 12 13 10 9 7
9 7 13 10 11 12 22 8
7 11 8 13 12 9 10 22
10 22 12 9 8 13 7 11
8 12 22 11 10 7 13 9
13 9 10 7 22 11 8 12
11 13 7 8 9 22 12 10
12 10 9 22 7 8 11 13
23
23 33 36 37 38 35 34 32
34 32 38 35 36 37 23 33
32 36 33 38 37 34 35 23
35 23 37 34 33 38 32 36
33 37 23 36 35 32 38 34
38 34 35 32 23 36 33 37
36 38 32 33 34 23 37 35
37 35 34 23 32 33 36 38
21
7 9 12 13 8 11 10 21
10 21 8 11 12 13 7 9
21 12 9 8 13 10 11 7
11 7 13 10 9 8 21 12
9 13 7 12 11 21 8 10
8 10 11 21 7 12 9 13
12 8 21 9 10 7 13 11
13 11 10 7 21 9 12 8
22
22 33 36 37 38 35 34 32
34 32 38 35 36 37 22 33
32 36 33 38 37 34 35 22
35 22 37 34 33 38 32 36
33 37 22 36 35 32 38 34
38 34 35 32 22 36 33 37
36 38 32 33 34 22 37 35
37 35 34 22 32 33 36 38
23
23 15 18 19 20 17 16 14
16 14 20 17 18 19 23 15
14 18 15 20 19 16 17 23
17 23 19 16 15 20 14 18
15 19 23 18 17 14 20 16
20 16 17 14 23 18 15 19
18 20 14 15 16 23 19 17
19 17 16 23 14 15 18 20
24
24 1 4 5 6 3 2 0
2 0 6 3 4 5 24 1
0 4 1 6 5 2 3 24
3 24 5 2 1 6 0 4
1 5 24 4 3 0 6 2
6 2 3 0 24 4 1 5
4 6 0 1 2 24 5 3
5 3 2 24 0 1 4 6

The twenty Auxiliary Squares are based on the five sub series defined above and the series {21, 22, 23, 24}.

Replace the applicable Sub Squares (of the Intermediate Square) together with the corresponding sections of the 'Crosses' by the contents of these Auxiliary Squares as shown below:

Step 3
32 34 37 38 21 36 35 14 16 19 20 22 18 17 33 15 0 2 5 6 23 4 3 1 30 26 29 24 31 28 27 25 13 12 10 8 7 11 9
35 33 21 36 37 38 32 17 15 22 18 19 20 14 34 16 3 1 23 4 5 6 0 2 27 25 31 28 29 24 30 26 10 8 7 11 9 13 12
33 37 34 21 38 35 36 15 19 16 22 20 17 18 32 14 1 5 2 23 6 3 4 0 25 29 26 31 24 27 28 30 7 11 9 13 12 10 8
36 32 38 35 34 21 33 18 14 20 17 16 22 15 37 19 4 0 6 3 2 23 1 5 28 30 24 27 26 31 25 29 9 13 12 10 8 7 11
34 38 32 37 36 33 21 16 20 14 19 18 15 22 35 17 2 6 0 5 4 1 23 3 26 24 30 29 28 25 31 27 12 10 8 7 11 9 13
21 35 36 33 32 37 34 22 17 18 15 14 19 16 38 20 23 3 4 1 0 5 2 6 31 27 28 25 30 29 26 24 8 7 11 9 13 12 10
37 21 33 34 35 32 38 19 22 15 16 17 14 20 36 18 5 23 1 2 3 0 6 4 29 31 25 26 27 30 24 28 11 9 13 12 10 8 7
0 2 5 6 22 4 3 25 27 30 31 23 29 28 19 1 7 9 12 13 24 11 10 26 8 38 37 35 33 32 36 34 15 18 21 20 17 16 14
3 1 22 4 5 6 0 28 26 23 29 30 31 25 16 2 10 8 24 11 12 13 7 27 9 35 33 32 36 34 38 37 14 20 17 18 21 19 15
1 5 2 22 6 3 4 26 30 27 23 31 28 29 14 0 8 12 9 24 13 10 11 25 7 32 36 34 38 37 35 33 18 15 20 21 16 17 19
4 0 6 3 2 22 1 29 25 31 28 27 23 26 17 5 11 7 13 10 9 24 8 30 12 34 38 37 35 33 32 36 19 21 16 15 20 14 18
2 6 0 5 4 1 22 27 31 25 30 29 26 23 15 3 9 13 7 12 11 8 24 28 10 37 35 33 32 36 34 38 21 19 18 17 14 20 16
22 3 4 1 0 5 2 23 28 29 26 25 30 27 20 6 24 10 11 8 7 12 9 31 13 33 32 36 34 38 37 35 16 17 14 19 18 15 21
5 22 1 2 3 0 6 30 23 26 27 28 25 31 18 4 12 24 8 9 10 7 13 29 11 36 34 38 37 35 33 32 20 14 15 16 19 21 17
38 36 35 32 33 34 37 7 9 12 13 8 11 10 21 23 26 29 30 31 28 27 25 24 22 1 4 5 6 3 2 0 17 16 19 14 15 18 20
6 4 3 0 1 2 5 20 18 17 14 15 16 19 24 22 33 36 37 38 35 34 32 21 23 8 11 12 13 10 9 7 26 29 30 31 28 27 25
7 9 12 13 23 11 10 32 34 37 38 24 36 35 2 27 20 19 17 15 14 18 16 8 33 0 6 3 4 5 21 1 25 31 28 29 30 22 26
10 8 23 11 12 13 7 35 33 24 36 37 38 32 0 25 17 15 14 18 16 20 19 9 34 4 1 6 5 2 3 21 29 26 31 30 27 28 22
8 12 9 23 13 10 11 33 37 34 24 38 35 36 3 28 14 18 16 20 19 17 15 7 32 21 5 2 1 6 0 4 22 30 27 26 31 25 29
11 7 13 10 9 23 8 36 32 38 35 34 24 33 1 26 16 20 19 17 15 14 18 12 37 5 21 4 3 0 6 2 30 22 29 28 25 31 27
9 13 7 12 11 8 23 34 38 32 37 36 33 24 6 31 19 17 15 14 18 16 20 10 35 2 3 0 21 4 1 5 27 28 25 22 29 26 30
23 10 11 8 7 12 9 24 35 36 33 32 37 34 4 29 15 14 18 16 20 19 17 13 38 6 0 1 2 21 5 3 31 25 26 27 22 30 28
12 23 8 9 10 7 13 37 24 33 34 35 32 38 5 30 18 16 20 19 17 15 14 11 36 3 2 21 0 1 4 6 28 27 22 25 26 29 31
13 11 10 7 8 9 12 31 29 28 25 26 27 30 22 24 6 4 3 0 1 2 5 23 21 15 18 19 20 17 16 14 33 36 37 38 35 34 32
14 16 19 20 15 18 17 38 36 35 32 33 34 37 23 21 13 11 10 7 8 9 12 22 24 28 27 30 25 26 29 31 1 4 5 6 3 2 0
17 24 15 18 19 20 14 6 5 3 1 0 4 2 27 9 25 31 28 29 30 21 26 34 16 7 13 10 11 12 22 8 32 38 35 36 37 23 33
24 19 16 15 20 17 18 3 1 0 4 2 6 5 25 7 29 26 31 30 27 28 21 32 14 11 8 13 12 9 10 22 36 33 38 37 34 35 23
18 14 20 17 16 15 24 0 4 2 6 5 3 1 28 10 21 30 27 26 31 25 29 35 19 22 12 9 8 13 7 11 23 37 34 33 38 32 36
16 20 14 19 18 24 15 2 6 5 3 1 0 4 26 8 30 21 29 28 25 31 27 33 17 12 22 11 10 7 13 9 37 23 36 35 32 38 34
15 17 18 24 14 19 16 5 3 1 0 4 2 6 31 13 27 28 25 21 29 26 30 38 20 9 10 7 22 11 8 12 34 35 32 23 36 33 37
19 15 24 16 17 14 20 1 0 4 2 6 5 3 29 11 31 25 26 27 21 30 28 36 18 13 7 8 9 22 12 10 38 32 33 34 23 37 35
20 18 17 14 24 16 19 4 2 6 5 3 1 0 30 12 28 27 21 25 26 29 31 37 15 10 9 22 7 8 11 13 35 34 23 32 33 36 38
31 30 28 26 25 29 27 10 21 8 11 12 13 7 9 34 32 38 35 36 37 22 33 16 2 14 20 17 18 19 23 15 0 6 3 4 5 24 1
28 26 25 29 27 31 30 21 12 9 8 13 10 11 7 32 36 33 38 37 34 35 22 14 0 18 15 20 19 16 17 23 4 1 6 5 2 3 24
25 29 27 31 30 28 26 11 7 13 10 9 8 21 12 35 22 37 34 33 38 32 36 17 3 23 19 16 15 20 14 18 24 5 2 1 6 0 4
27 31 30 28 26 25 29 9 13 7 12 11 21 8 10 33 37 22 36 35 32 38 34 15 1 19 23 18 17 14 20 16 5 24 4 3 0 6 2
30 28 26 25 29 27 31 8 10 11 21 7 12 9 13 38 34 35 32 22 36 33 37 20 6 16 17 14 23 18 15 19 2 3 0 24 4 1 5
26 25 29 27 31 30 28 12 8 21 9 10 7 13 11 36 38 32 33 34 22 37 35 18 4 20 14 15 16 23 19 17 6 0 1 2 24 5 3
29 27 31 30 28 26 25 13 11 10 7 21 9 12 8 37 35 34 22 32 33 36 38 19 5 17 16 23 14 15 18 20 3 2 24 0 1 4 6

The order 39 Self Orthogonal Composed Latin Diagonal Square shown above is ready to be used for the construction of an order 39 Composed Simple Magic Square.

Vorige Pagina About the Author