A set of n positive numbers has 2^n subsets. We'll call a set "nice" if none of those subsets have the same sum. {2, 4, 5, 8} is one such nice set. Since none of the subsets has the same sum, we can sort the subsets by sum: [{}, {2}, {4}, {5}, {2, 4}, {2, 5}, {8}, {4, 5}, {2, 8}, {2, 4, 5}, {4, ...