# Combinations on superimposed latin squares

Let's have two latin squares. When we superimpose them we obtain a 6x6 superimposed square as shown in the diagram.

By visual inspection we see this contains 15 combinations and their repetitions which are the following.

combinations             number of repetitions
1,2                      2
1,3                      1
1,4                      2
1,5                      3
1,6                      4
2,3                      3
2,4                      3
2,5                      2
2,6                      2
3,4                      4
3,5                      2
3,6                      2
4,5                      2
4,6                      1
5,6                      3


Can someone find two latin squares which, when superimposed give 13 combinations with 2 repetitions and 2 combinations with 5 repetitions?