Given an instance (s, k) of the subset-sum problem, where s is a set of integers and k is another integer, we transform it into an instance s’ = s ∪ { x, y } of the partition problem, where x = sum(s) + k, y = 2sum(s) – k, and sum(s) = σx∈s x. prove that s’ can be constructed from s in polynomial time and there exists a subset x ⊆ s’ such that sum(x) = k iff s’ can be partitioned into x and y such that sum(x) = sum(y), where s’ = x∪y and x∩y = ∅