Subset-sum problem is NP-complete. I presume so is the problem of determining, given a positive integer $p$, whether in a set of positive integers $\{x_1,x_2,...,x_n\}$ there is a subset which sums to one of the numbers $\{p-1,p,p+1\}$. Am I correct?I've been struggling to reduce standard Subset-sum to this variation, but for no good so far. Can you see any other reduction? Or could give me a hint on this  one? Perhaps I'm fixed for that Subset-sum and don't some other obvious possibility.
Subset-sum variation, multiple sums
complexity theory;reductions;np hard
Hint: Given an instance $\{x_1,\ldots,x_n\},T$ of SUBSET-SUM, construct the instance $\{2x_1,\ldots,2x_n\},2T$ of your problem.