Office Applications and Entertainment, Latin Squares
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Maximum Achievable Symmetry (Latin Patterns)
Row Symmetry

11
3 5 4 5 1 3
4 3 1 2 6 5
3 2 6 3 1 6
4 2 2 2 6 5
4 4 2 4 6 1
3 5 6 5 1 1
36
3 6 5 3 3 1
2 4 2 1 6 6
1 3 5 5 2 5
5 1 1 4 4 6
6 4 3 2 4 2
4 3 5 6 2 1
60
5 2 5 4 1 4
3 5 1 2 4 6
6 2 2 4 1 6
3 5 2 2 6 3
1 4 5 4 6 1
3 3 6 5 3 1
49
3 5 5 4 1 3
3 6 2 1 3 6
6 1 5 4 2 3
5 2 2 2 6 4
1 6 2 4 4 4
3 1 5 6 5 1
52
4 2 5 1 3 6
5 6 2 3 4 1
3 1 4 6 2 5
3 5 2 1 4 6
4 1 3 6 5 2
2 6 5 4 3 1
24
5 5 2 3 1 5
3 1 3 6 3 5
1 6 6 4 2 2
2 2 4 4 6 3
6 1 2 3 4 5
4 6 4 1 5 1

Column Symmetry

420
4 4 2 5 3 3
5 2 2 5 5 2
1 6 5 2 1 6
1 4 3 4 6 3
4 2 3 1 5 6
6 3 6 4 1 1

Mixed Symmetry

41
3 5 6 1 1 5
2 4 2 6 3 4
2 4 3 4 2 6
3 2 2 4 6 4
5 1 3 5 6 1
6 5 5 1 3 1
14
4 5 3 4 1 4
4 3 5 1 5 3
1 2 6 2 5 5
1 2 2 4 6 6
6 3 3 4 3 2
5 6 2 6 1 1
22
1 5 5 3 1 6
3 4 1 5 3 5
2 3 4 2 4 6
4 2 1 6 6 2
5 3 4 3 5 1
6 4 6 2 2 1
74
4 6 4 2 2 3
1 3 1 5 5 6
2 4 3 4 2 6
5 1 4 3 5 3
5 1 3 5 6 1
4 6 6 2 1 2
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