Is this variant of the subset sum problem easier to solve?

Question

I have a problem related to the subset sum problem and am wondering if the differences make it easier, i.e. solvable in a reasonable amount of time.

Given a value V,

Answer 1

Well, for one thing since you're specifying size=L then even if you can't think of anything clever and just use brute force you'll have (N choose L) separate sums in the worst case, so it's a bit better than n^^L (well, L+1, as you'd then sum each subset).

Answer 2

I'm not prepared to present a proof, but that sounds like it might be amenable to a dynamic programming scheme: tabulate the list of subsets of size 2use them to computer subsets of size 3, etc, so that hyou only need to examine a small collection of prospects.