These problems are really brute force, there is no real clever way. I only just listed all possible combinations
HOWEVER, notice in CPhill's answer.
5 19
5 2 8
5 3 7
5 4 6
Since ALL the sets contain a 5, we just subtract 5 from 15.
So we need TWO terms in a set and they add up to 10, and also are unique.
This is quite easy.
1 9
2 8
3 7
4 6
5 5 (doesnt work because cannot repeat digit)
+2863 
