# 1 Day to 2016 Final Call

Find the largest positive integer $$k$$ that satisﬁes the property: The set of positive integers can be partitioned into $$k$$ subsets $$A_{1}, A_{2}, \ldots , A_{k}$$ such that for all integers $$n \ge 15$$ and all $$i \in \{\ 1,2, \ldots, k \}\$$, there exist two distinct elements of $$A_{i}$$ whose sum is $$n$$.

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