# Talk:1986 AIME Problems/Problem 12

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The solution written here in the AOPS Wiki for this problem seems to incorrect. It is proven that indeed there must be subsets with the same sum when $S$ has more than 5 elements. However, it is not proven that these subsets are disjoint, which is required because the problem condition states that "no two $\textbf{disjoint}$ subsets of $S$ have the same sum," not "no two subsets of $S$ have the same sum."