Given n positive integers, we want to partition them into two sets A and B so that the sums SA and SB of their elements are as evenly balanced as possible, i.e., there is no other split (A0 , B0 ) such that |SA0 SB0 | < |SA SB|. We use the following greedy algorithm: sort the values in decreasing order, start with empty A and B and always put the next value into the set with the lowest sum (choose any set if their sums are equal). Does this algorithm always produce the most balanced split? Prove it, or find a counterexample.