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Within 9 numbers

Source: Canada 2002

March 5, 2006
combinatorics unsolvedcombinatorics

Problem Statement

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