We have had some lovely solutions for this problem. Some of you made long lists like Marion from Tattingstone:

A B
2 1 1 1 possibility
3 1
2		 2
1		 2 possibilities
4 1
2
3		 3
2
1		 3 possibilities
5 1
2
3
4		 4
3
2
1		 4 possibilities
6 1
2
3
4
5		 5
4
3
2
1		 5 possibilities
7 1
2
3
4
5
6		 6
5
4
3
2
1		 6 possibilities
8 2
3
4
5
6		 6
5
4
3
2		 5 possibilities
9 3
4
5
6		 6
5
4
3		 4 possibilities
10 4
5
6		 6
5
4		 3 possibilities
11 5
6		 6
5		 2 possibilities
12 6 6 1 possibility
Marion's solution.

Fiona from Tattingstone drew a table:

1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

Therefore;

Fiona's solution.

Here is another solution with some pictures from Martha at Tattingstone:

Martha's solution.

Does this give us more proof of the result? How does it prove it?