Office Applications and Entertainment, Latin Squares
Vorige Pagina Attachment 8.10.1 About the Author

Construction of order 41 Self Orthogonal Composed Latin Diagonal Squares

Construct an order 40 Self Orthogonal Composed Latin Diagonal Square.

The required order 8 Self orthogonal Latin Diagonal Sub Squares can be constructed based on the sub series:

    {0, 1 ... 7}, {8, 9 ... 15}, {16, 17 ... 23}, {24}, {25, 26 ... 32} and {33, 34 ... 40}

with respectively the magic constants s8 = 28, 92, 156, 228 and 292

Sqrs8
33 25 0 16 8
16 8 25 0 33
8 0 16 33 25
0 33 8 25 16
25 16 33 8 0

The order 5 Self orthogonal Latin Diagonal Square shown above is based on the first elements of the Sub Squares, and has been used as a guideline for the construction of the square shown below.

Step 1
33 40 39 38 34 35 36 37
39 34 33 36 40 37 38 35
37 36 35 34 38 39 40 33
34 39 40 37 33 36 35 38
35 38 37 40 36 33 34 39
40 33 34 35 39 38 37 36
38 35 36 33 37 40 39 34
36 37 38 39 35 34 33 40
25 32 31 30 26 27 28 29
31 26 25 28 32 29 30 27
29 28 27 26 30 31 32 25
26 31 32 29 25 28 27 30
27 30 29 32 28 25 26 31
32 25 26 27 31 30 29 28
30 27 28 25 29 32 31 26
28 29 30 31 27 26 25 32
0 7 6 5 1 2 3 4
6 1 0 3 7 4 5 2
4 3 2 1 5 6 7 0
1 6 7 4 0 3 2 5
2 5 4 7 3 0 1 6
7 0 1 2 6 5 4 3
5 2 3 0 4 7 6 1
3 4 5 6 2 1 0 7
16 23 22 21 17 18 19 20
22 17 16 19 23 20 21 18
20 19 18 17 21 22 23 16
17 22 23 20 16 19 18 21
18 21 20 23 19 16 17 22
23 16 17 18 22 21 20 19
21 18 19 16 20 23 22 17
19 20 21 22 18 17 16 23
8 15 14 13 9 10 11 12
14 9 8 11 15 12 13 10
12 11 10 9 13 14 15 8
9 14 15 12 8 11 10 13
10 13 12 15 11 8 9 14
15 8 9 10 14 13 12 11
13 10 11 8 12 15 14 9
11 12 13 14 10 9 8 15
16 23 22 21 17 18 19 20
22 17 16 19 23 20 21 18
20 19 18 17 21 22 23 16
17 22 23 20 16 19 18 21
18 21 20 23 19 16 17 22
23 16 17 18 22 21 20 19
21 18 19 16 20 23 22 17
19 20 21 22 18 17 16 23
8 15 14 13 9 10 11 12
14 9 8 11 15 12 13 10
12 11 10 9 13 14 15 8
9 14 15 12 8 11 10 13
10 13 12 15 11 8 9 14
15 8 9 10 14 13 12 11
13 10 11 8 12 15 14 9
11 12 13 14 10 9 8 15
25 32 31 30 26 27 28 29
31 26 25 28 32 29 30 27
29 28 27 26 30 31 32 25
26 31 32 29 25 28 27 30
27 30 29 32 28 25 26 31
32 25 26 27 31 30 29 28
30 27 28 25 29 32 31 26
28 29 30 31 27 26 25 32
0 7 6 5 1 2 3 4
6 1 0 3 7 4 5 2
4 3 2 1 5 6 7 0
1 6 7 4 0 3 2 5
2 5 4 7 3 0 1 6
7 0 1 2 6 5 4 3
5 2 3 0 4 7 6 1
3 4 5 6 2 1 0 7
33 40 39 38 34 35 36 37
39 34 33 36 40 37 38 35
37 36 35 34 38 39 40 33
34 39 40 37 33 36 35 38
35 38 37 40 36 33 34 39
40 33 34 35 39 38 37 36
38 35 36 33 37 40 39 34
36 37 38 39 35 34 33 40
8 15 14 13 9 10 11 12
14 9 8 11 15 12 13 10
12 11 10 9 13 14 15 8
9 14 15 12 8 11 10 13
10 13 12 15 11 8 9 14
15 8 9 10 14 13 12 11
13 10 11 8 12 15 14 9
11 12 13 14 10 9 8 15
0 7 6 5 1 2 3 4
6 1 0 3 7 4 5 2
4 3 2 1 5 6 7 0
1 6 7 4 0 3 2 5
2 5 4 7 3 0 1 6
7 0 1 2 6 5 4 3
5 2 3 0 4 7 6 1
3 4 5 6 2 1 0 7
16 23 22 21 17 18 19 20
22 17 16 19 23 20 21 18
20 19 18 17 21 22 23 16
17 22 23 20 16 19 18 21
18 21 20 23 19 16 17 22
23 16 17 18 22 21 20 19
21 18 19 16 20 23 22 17
19 20 21 22 18 17 16 23
33 40 39 38 34 35 36 37
39 34 33 36 40 37 38 35
37 36 35 34 38 39 40 33
34 39 40 37 33 36 35 38
35 38 37 40 36 33 34 39
40 33 34 35 39 38 37 36
38 35 36 33 37 40 39 34
36 37 38 39 35 34 33 40
25 32 31 30 26 27 28 29
31 26 25 28 32 29 30 27
29 28 27 26 30 31 32 25
26 31 32 29 25 28 27 30
27 30 29 32 28 25 26 31
32 25 26 27 31 30 29 28
30 27 28 25 29 32 31 26
28 29 30 31 27 26 25 32
0 7 6 5 1 2 3 4
6 1 0 3 7 4 5 2
4 3 2 1 5 6 7 0
1 6 7 4 0 3 2 5
2 5 4 7 3 0 1 6
7 0 1 2 6 5 4 3
5 2 3 0 4 7 6 1
3 4 5 6 2 1 0 7
33 40 39 38 34 35 36 37
39 34 33 36 40 37 38 35
37 36 35 34 38 39 40 33
34 39 40 37 33 36 35 38
35 38 37 40 36 33 34 39
40 33 34 35 39 38 37 36
38 35 36 33 37 40 39 34
36 37 38 39 35 34 33 40
8 15 14 13 9 10 11 12
14 9 8 11 15 12 13 10
12 11 10 9 13 14 15 8
9 14 15 12 8 11 10 13
10 13 12 15 11 8 9 14
15 8 9 10 14 13 12 11
13 10 11 8 12 15 14 9
11 12 13 14 10 9 8 15
25 32 31 30 26 27 28 29
31 26 25 28 32 29 30 27
29 28 27 26 30 31 32 25
26 31 32 29 25 28 27 30
27 30 29 32 28 25 26 31
32 25 26 27 31 30 29 28
30 27 28 25 29 32 31 26
28 29 30 31 27 26 25 32
16 23 22 21 17 18 19 20
22 17 16 19 23 20 21 18
20 19 18 17 21 22 23 16
17 22 23 20 16 19 18 21
18 21 20 23 19 16 17 22
23 16 17 18 22 21 20 19
21 18 19 16 20 23 22 17
19 20 21 22 18 17 16 23
25 32 31 30 26 27 28 29
31 26 25 28 32 29 30 27
29 28 27 26 30 31 32 25
26 31 32 29 25 28 27 30
27 30 29 32 28 25 26 31
32 25 26 27 31 30 29 28
30 27 28 25 29 32 31 26
28 29 30 31 27 26 25 32
16 23 22 21 17 18 19 20
22 17 16 19 23 20 21 18
20 19 18 17 21 22 23 16
17 22 23 20 16 19 18 21
18 21 20 23 19 16 17 22
23 16 17 18 22 21 20 19
21 18 19 16 20 23 22 17
19 20 21 22 18 17 16 23
33 40 39 38 34 35 36 37
39 34 33 36 40 37 38 35
37 36 35 34 38 39 40 33
34 39 40 37 33 36 35 38
35 38 37 40 36 33 34 39
40 33 34 35 39 38 37 36
38 35 36 33 37 40 39 34
36 37 38 39 35 34 33 40
8 15 14 13 9 10 11 12
14 9 8 11 15 12 13 10
12 11 10 9 13 14 15 8
9 14 15 12 8 11 10 13
10 13 12 15 11 8 9 14
15 8 9 10 14 13 12 11
13 10 11 8 12 15 14 9
11 12 13 14 10 9 8 15
0 7 6 5 1 2 3 4
6 1 0 3 7 4 5 2
4 3 2 1 5 6 7 0
1 6 7 4 0 3 2 5
2 5 4 7 3 0 1 6
7 0 1 2 6 5 4 3
5 2 3 0 4 7 6 1
3 4 5 6 2 1 0 7

Construct an intermediate order 41 square by adding a row (25) and a column (25), to the order 40 Self Orthogonal Composed Latin Diagonal Square as shown below:

Step 2
33 40 39 38 34 35 36 37 25 32 31 30 26 27 28 29 0 7 6 5 1 2 3 4 0 16 23 22 21 17 18 19 20 8 15 14 13 9 10 11 12
39 34 33 36 40 37 38 35 31 26 25 28 32 29 30 27 6 1 0 3 7 4 5 2 0 22 17 16 19 23 20 21 18 14 9 8 11 15 12 13 10
37 36 35 34 38 39 40 33 29 28 27 26 30 31 32 25 4 3 2 1 5 6 7 0 0 20 19 18 17 21 22 23 16 12 11 10 9 13 14 15 8
34 39 40 37 33 36 35 38 26 31 32 29 25 28 27 30 1 6 7 4 0 3 2 5 0 17 22 23 20 16 19 18 21 9 14 15 12 8 11 10 13
35 38 37 40 36 33 34 39 27 30 29 32 28 25 26 31 2 5 4 7 3 0 1 6 0 18 21 20 23 19 16 17 22 10 13 12 15 11 8 9 14
40 33 34 35 39 38 37 36 32 25 26 27 31 30 29 28 7 0 1 2 6 5 4 3 0 23 16 17 18 22 21 20 19 15 8 9 10 14 13 12 11
38 35 36 33 37 40 39 34 30 27 28 25 29 32 31 26 5 2 3 0 4 7 6 1 0 21 18 19 16 20 23 22 17 13 10 11 8 12 15 14 9
36 37 38 39 35 34 33 40 28 29 30 31 27 26 25 32 3 4 5 6 2 1 0 7 0 19 20 21 22 18 17 16 23 11 12 13 14 10 9 8 15
16 23 22 21 17 18 19 20 8 15 14 13 9 10 11 12 25 32 31 30 26 27 28 29 0 0 7 6 5 1 2 3 4 33 40 39 38 34 35 36 37
22 17 16 19 23 20 21 18 14 9 8 11 15 12 13 10 31 26 25 28 32 29 30 27 0 6 1 0 3 7 4 5 2 39 34 33 36 40 37 38 35
20 19 18 17 21 22 23 16 12 11 10 9 13 14 15 8 29 28 27 26 30 31 32 25 0 4 3 2 1 5 6 7 0 37 36 35 34 38 39 40 33
17 22 23 20 16 19 18 21 9 14 15 12 8 11 10 13 26 31 32 29 25 28 27 30 0 1 6 7 4 0 3 2 5 34 39 40 37 33 36 35 38
18 21 20 23 19 16 17 22 10 13 12 15 11 8 9 14 27 30 29 32 28 25 26 31 0 2 5 4 7 3 0 1 6 35 38 37 40 36 33 34 39
23 16 17 18 22 21 20 19 15 8 9 10 14 13 12 11 32 25 26 27 31 30 29 28 0 7 0 1 2 6 5 4 3 40 33 34 35 39 38 37 36
21 18 19 16 20 23 22 17 13 10 11 8 12 15 14 9 30 27 28 25 29 32 31 26 0 5 2 3 0 4 7 6 1 38 35 36 33 37 40 39 34
19 20 21 22 18 17 16 23 11 12 13 14 10 9 8 15 28 29 30 31 27 26 25 32 0 3 4 5 6 2 1 0 7 36 37 38 39 35 34 33 40
8 15 14 13 9 10 11 12 0 7 6 5 1 2 3 4 16 23 22 21 17 18 19 20 0 33 40 39 38 34 35 36 37 25 32 31 30 26 27 28 29
14 9 8 11 15 12 13 10 6 1 0 3 7 4 5 2 22 17 16 19 23 20 21 18 0 39 34 33 36 40 37 38 35 31 26 25 28 32 29 30 27
12 11 10 9 13 14 15 8 4 3 2 1 5 6 7 0 20 19 18 17 21 22 23 16 0 37 36 35 34 38 39 40 33 29 28 27 26 30 31 32 25
9 14 15 12 8 11 10 13 1 6 7 4 0 3 2 5 17 22 23 20 16 19 18 21 0 34 39 40 37 33 36 35 38 26 31 32 29 25 28 27 30
10 13 12 15 11 8 9 14 2 5 4 7 3 0 1 6 18 21 20 23 19 16 17 22 0 35 38 37 40 36 33 34 39 27 30 29 32 28 25 26 31
15 8 9 10 14 13 12 11 7 0 1 2 6 5 4 3 23 16 17 18 22 21 20 19 0 40 33 34 35 39 38 37 36 32 25 26 27 31 30 29 28
13 10 11 8 12 15 14 9 5 2 3 0 4 7 6 1 21 18 19 16 20 23 22 17 0 38 35 36 33 37 40 39 34 30 27 28 25 29 32 31 26
11 12 13 14 10 9 8 15 3 4 5 6 2 1 0 7 19 20 21 22 18 17 16 23 0 36 37 38 39 35 34 33 40 28 29 30 31 27 26 25 32
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 0 0 0 0 0 0 0 0 0 0 0 0 0
0 7 6 5 1 2 3 4 33 40 39 38 34 35 36 37 8 15 14 13 9 10 11 12 0 25 32 31 30 26 27 28 29 16 23 22 21 17 18 19 20
6 1 0 3 7 4 5 2 39 34 33 36 40 37 38 35 14 9 8 11 15 12 13 10 0 31 26 25 28 32 29 30 27 22 17 16 19 23 20 21 18
4 3 2 1 5 6 7 0 37 36 35 34 38 39 40 33 12 11 10 9 13 14 15 8 0 29 28 27 26 30 31 32 25 20 19 18 17 21 22 23 16
1 6 7 4 0 3 2 5 34 39 40 37 33 36 35 38 9 14 15 12 8 11 10 13 0 26 31 32 29 25 28 27 30 17 22 23 20 16 19 18 21
2 5 4 7 3 0 1 6 35 38 37 40 36 33 34 39 10 13 12 15 11 8 9 14 0 27 30 29 32 28 25 26 31 18 21 20 23 19 16 17 22
7 0 1 2 6 5 4 3 40 33 34 35 39 38 37 36 15 8 9 10 14 13 12 11 0 32 25 26 27 31 30 29 28 23 16 17 18 22 21 20 19
5 2 3 0 4 7 6 1 38 35 36 33 37 40 39 34 13 10 11 8 12 15 14 9 0 30 27 28 25 29 32 31 26 21 18 19 16 20 23 22 17
3 4 5 6 2 1 0 7 36 37 38 39 35 34 33 40 11 12 13 14 10 9 8 15 0 28 29 30 31 27 26 25 32 19 20 21 22 18 17 16 23
25 32 31 30 26 27 28 29 16 23 22 21 17 18 19 20 33 40 39 38 34 35 36 37 0 8 15 14 13 9 10 11 12 0 7 6 5 1 2 3 4
31 26 25 28 32 29 30 27 22 17 16 19 23 20 21 18 39 34 33 36 40 37 38 35 0 14 9 8 11 15 12 13 10 6 1 0 3 7 4 5 2
29 28 27 26 30 31 32 25 20 19 18 17 21 22 23 16 37 36 35 34 38 39 40 33 0 12 11 10 9 13 14 15 8 4 3 2 1 5 6 7 0
26 31 32 29 25 28 27 30 17 22 23 20 16 19 18 21 34 39 40 37 33 36 35 38 0 9 14 15 12 8 11 10 13 1 6 7 4 0 3 2 5
27 30 29 32 28 25 26 31 18 21 20 23 19 16 17 22 35 38 37 40 36 33 34 39 0 10 13 12 15 11 8 9 14 2 5 4 7 3 0 1 6
32 25 26 27 31 30 29 28 23 16 17 18 22 21 20 19 40 33 34 35 39 38 37 36 0 15 8 9 10 14 13 12 11 7 0 1 2 6 5 4 3
30 27 28 25 29 32 31 26 21 18 19 16 20 23 22 17 38 35 36 33 37 40 39 34 0 13 10 11 8 12 15 14 9 5 2 3 0 4 7 6 1
28 29 30 31 27 26 25 32 19 20 21 22 18 17 16 23 36 37 38 39 35 34 33 40 0 11 12 13 14 10 9 8 15 3 4 5 6 2 1 0 7

The Intermediate Square has to be transformed to a Self Orthogonal Latin Diagonal Square, which can be achieved by means of a set of five order 9 Auxiliary Latin Diagonal Squares:

A91
33 35 37 24 39 40 38 36 34
36 34 40 37 38 39 24 33 35
34 39 35 40 33 24 36 38 37
38 33 24 36 34 35 40 37 39
24 40 39 38 37 36 35 34 33
35 37 34 39 40 38 33 24 36
37 36 38 33 24 34 39 35 40
39 24 33 35 36 37 34 40 38
40 38 36 34 35 33 37 39 24
A92
8 10 12 24 14 15 13 11 9
11 9 15 12 13 14 24 8 10
9 14 10 15 8 24 11 13 12
13 8 24 11 9 10 15 12 14
24 15 14 13 12 11 10 9 8
10 12 9 14 15 13 8 24 11
12 11 13 8 24 9 14 10 15
14 24 8 10 11 12 9 15 13
15 13 11 9 10 8 12 14 24
A93
16 18 20 24 22 23 21 19 17
19 17 23 20 21 22 24 16 18
17 22 18 23 16 24 19 21 20
21 16 24 19 17 18 23 20 22
24 23 22 21 20 19 18 17 16
18 20 17 22 23 21 16 24 19
20 19 21 16 24 17 22 18 23
22 24 16 18 19 20 17 23 21
23 21 19 17 18 16 20 22 24
A94
24 26 28 32 30 31 29 27 25
27 25 31 28 29 30 32 24 26
25 30 26 31 24 32 27 29 28
29 24 32 27 25 26 31 28 30
32 31 30 29 28 27 26 25 24
26 28 25 30 31 29 24 32 27
28 27 29 24 32 25 30 26 31
30 32 24 26 27 28 25 31 29
31 29 27 25 26 24 28 30 32
A95
24 1 3 7 5 6 4 2 0
2 0 6 3 4 5 7 24 1
0 5 1 6 24 7 2 4 3
4 24 7 2 0 1 6 3 5
7 6 5 4 3 2 1 0 24
1 3 0 5 6 4 24 7 2
3 2 4 24 7 0 5 1 6
5 7 24 1 2 3 0 6 4
6 4 2 0 1 24 3 5 7

The five Auxiliary Squares are based on the five sub series defined above and the number 24 .

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

Step 3
33 35 37 24 39 40 38 36 25 32 31 30 26 27 28 29 0 7 6 5 1 2 3 4 34 16 23 22 21 17 18 19 20 8 15 14 13 9 10 11 12
36 34 40 37 38 39 24 33 31 26 25 28 32 29 30 27 6 1 0 3 7 4 5 2 35 22 17 16 19 23 20 21 18 14 9 8 11 15 12 13 10
34 39 35 40 33 24 36 38 29 28 27 26 30 31 32 25 4 3 2 1 5 6 7 0 37 20 19 18 17 21 22 23 16 12 11 10 9 13 14 15 8
38 33 24 36 34 35 40 37 26 31 32 29 25 28 27 30 1 6 7 4 0 3 2 5 39 17 22 23 20 16 19 18 21 9 14 15 12 8 11 10 13
24 40 39 38 37 36 35 34 27 30 29 32 28 25 26 31 2 5 4 7 3 0 1 6 33 18 21 20 23 19 16 17 22 10 13 12 15 11 8 9 14
35 37 34 39 40 38 33 24 32 25 26 27 31 30 29 28 7 0 1 2 6 5 4 3 36 23 16 17 18 22 21 20 19 15 8 9 10 14 13 12 11
37 36 38 33 24 34 39 35 30 27 28 25 29 32 31 26 5 2 3 0 4 7 6 1 40 21 18 19 16 20 23 22 17 13 10 11 8 12 15 14 9
39 24 33 35 36 37 34 40 28 29 30 31 27 26 25 32 3 4 5 6 2 1 0 7 38 19 20 21 22 18 17 16 23 11 12 13 14 10 9 8 15
16 23 22 21 17 18 19 20 8 10 12 24 14 15 13 11 25 32 31 30 26 27 28 29 9 0 7 6 5 1 2 3 4 33 40 39 38 34 35 36 37
22 17 16 19 23 20 21 18 11 9 15 12 13 14 24 8 31 26 25 28 32 29 30 27 10 6 1 0 3 7 4 5 2 39 34 33 36 40 37 38 35
20 19 18 17 21 22 23 16 9 14 10 15 8 24 11 13 29 28 27 26 30 31 32 25 12 4 3 2 1 5 6 7 0 37 36 35 34 38 39 40 33
17 22 23 20 16 19 18 21 13 8 24 11 9 10 15 12 26 31 32 29 25 28 27 30 14 1 6 7 4 0 3 2 5 34 39 40 37 33 36 35 38
18 21 20 23 19 16 17 22 24 15 14 13 12 11 10 9 27 30 29 32 28 25 26 31 8 2 5 4 7 3 0 1 6 35 38 37 40 36 33 34 39
23 16 17 18 22 21 20 19 10 12 9 14 15 13 8 24 32 25 26 27 31 30 29 28 11 7 0 1 2 6 5 4 3 40 33 34 35 39 38 37 36
21 18 19 16 20 23 22 17 12 11 13 8 24 9 14 10 30 27 28 25 29 32 31 26 15 5 2 3 0 4 7 6 1 38 35 36 33 37 40 39 34
19 20 21 22 18 17 16 23 14 24 8 10 11 12 9 15 28 29 30 31 27 26 25 32 13 3 4 5 6 2 1 0 7 36 37 38 39 35 34 33 40
8 15 14 13 9 10 11 12 0 7 6 5 1 2 3 4 16 18 20 24 22 23 21 19 17 33 40 39 38 34 35 36 37 25 32 31 30 26 27 28 29
14 9 8 11 15 12 13 10 6 1 0 3 7 4 5 2 19 17 23 20 21 22 24 16 18 39 34 33 36 40 37 38 35 31 26 25 28 32 29 30 27
12 11 10 9 13 14 15 8 4 3 2 1 5 6 7 0 17 22 18 23 16 24 19 21 20 37 36 35 34 38 39 40 33 29 28 27 26 30 31 32 25
9 14 15 12 8 11 10 13 1 6 7 4 0 3 2 5 21 16 24 19 17 18 23 20 22 34 39 40 37 33 36 35 38 26 31 32 29 25 28 27 30
10 13 12 15 11 8 9 14 2 5 4 7 3 0 1 6 24 23 22 21 20 19 18 17 16 35 38 37 40 36 33 34 39 27 30 29 32 28 25 26 31
15 8 9 10 14 13 12 11 7 0 1 2 6 5 4 3 18 20 17 22 23 21 16 24 19 40 33 34 35 39 38 37 36 32 25 26 27 31 30 29 28
13 10 11 8 12 15 14 9 5 2 3 0 4 7 6 1 20 19 21 16 24 17 22 18 23 38 35 36 33 37 40 39 34 30 27 28 25 29 32 31 26
11 12 13 14 10 9 8 15 3 4 5 6 2 1 0 7 22 24 16 18 19 20 17 23 21 36 37 38 39 35 34 33 40 28 29 30 31 27 26 25 32
40 38 36 34 35 33 37 39 15 13 11 9 10 8 12 14 23 21 19 17 18 16 20 22 24 26 28 32 30 31 29 27 25 1 3 7 5 6 4 2 0
0 7 6 5 1 2 3 4 33 40 39 38 34 35 36 37 8 15 14 13 9 10 11 12 27 25 31 28 29 30 32 24 26 16 23 22 21 17 18 19 20
6 1 0 3 7 4 5 2 39 34 33 36 40 37 38 35 14 9 8 11 15 12 13 10 25 30 26 31 24 32 27 29 28 22 17 16 19 23 20 21 18
4 3 2 1 5 6 7 0 37 36 35 34 38 39 40 33 12 11 10 9 13 14 15 8 29 24 32 27 25 26 31 28 30 20 19 18 17 21 22 23 16
1 6 7 4 0 3 2 5 34 39 40 37 33 36 35 38 9 14 15 12 8 11 10 13 32 31 30 29 28 27 26 25 24 17 22 23 20 16 19 18 21
2 5 4 7 3 0 1 6 35 38 37 40 36 33 34 39 10 13 12 15 11 8 9 14 26 28 25 30 31 29 24 32 27 18 21 20 23 19 16 17 22
7 0 1 2 6 5 4 3 40 33 34 35 39 38 37 36 15 8 9 10 14 13 12 11 28 27 29 24 32 25 30 26 31 23 16 17 18 22 21 20 19
5 2 3 0 4 7 6 1 38 35 36 33 37 40 39 34 13 10 11 8 12 15 14 9 30 32 24 26 27 28 25 31 29 21 18 19 16 20 23 22 17
3 4 5 6 2 1 0 7 36 37 38 39 35 34 33 40 11 12 13 14 10 9 8 15 31 29 27 25 26 24 28 30 32 19 20 21 22 18 17 16 23
25 32 31 30 26 27 28 29 16 23 22 21 17 18 19 20 33 40 39 38 34 35 36 37 2 8 15 14 13 9 10 11 12 0 6 3 4 5 7 24 1
31 26 25 28 32 29 30 27 22 17 16 19 23 20 21 18 39 34 33 36 40 37 38 35 0 14 9 8 11 15 12 13 10 5 1 6 24 7 2 4 3
29 28 27 26 30 31 32 25 20 19 18 17 21 22 23 16 37 36 35 34 38 39 40 33 4 12 11 10 9 13 14 15 8 24 7 2 0 1 6 3 5
26 31 32 29 25 28 27 30 17 22 23 20 16 19 18 21 34 39 40 37 33 36 35 38 7 9 14 15 12 8 11 10 13 6 5 4 3 2 1 0 24
27 30 29 32 28 25 26 31 18 21 20 23 19 16 17 22 35 38 37 40 36 33 34 39 1 10 13 12 15 11 8 9 14 3 0 5 6 4 24 7 2
32 25 26 27 31 30 29 28 23 16 17 18 22 21 20 19 40 33 34 35 39 38 37 36 3 15 8 9 10 14 13 12 11 2 4 24 7 0 5 1 6
30 27 28 25 29 32 31 26 21 18 19 16 20 23 22 17 38 35 36 33 37 40 39 34 5 13 10 11 8 12 15 14 9 7 24 1 2 3 0 6 4
28 29 30 31 27 26 25 32 19 20 21 22 18 17 16 23 36 37 38 39 35 34 33 40 6 11 12 13 14 10 9 8 15 4 2 0 1 24 3 5 7

The order 41 Self Orthogonal Composed Latin Diagonal Square shown above is ready to be used for the construction of an order 41 Composed Simple Magic Square.

Vorige Pagina About the Author