Let S be a subset of {1,2,…,9}, such that the sums formed by adding each unordered pair of distinct numbers from S are all different. For example, the subset {1,2,3,5} has this property, but {1,2,3,4,5} does not, since the pairs {1,4} and {2,3} have the same sum, namely 5.
What is the maximum number of elements that S can contain? combinatorics unsolvedcombinatorics