Alfred,

I am going to assume that the addends have to be positive integers. The easiest solution is to just count them. If the addends have to be positive integers then the least possible addend is 1. If one on them is 1 then the possibilities are

1,1,8
1,2,7
1,3,6
1,4,5

If none of the addends is a 1 then the smallest possible addend is a 2 and the possibilities are

2,2,6
2,3,5
2,4,4

If neither a 1 or 2 are addends then the smallest possible is 3 and the only possibility is

3,3,4

Harley