Why can't the sum of the subsets be an odd number? Makes no difference, it's just a sum.imo
When I think of "an exhaustive search algorithm", for a problem, I think it needs to generate ALL the subsets, until it either finds the answer I'm seeking, or all the subsets have been examined, and there is no answer matching my request. If you're looking for something like the bin-packing problem, it can minimize the number of subsets, but has been proven to be no more than 70% effective at finding the correct answer. adak