2011 IMO Problems/Problem 1

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Given any set $A = \{a_1, a_2, a_3, a_4\}$ of four distinct positive integers, we denote the sum $a_1+a_2+a_3+a_4$ by $s_A$. Let $n_A$ denote the number of pairs $(i,j)$ with $1 \leq i < j \leq 4$ for which $a_i+a_j$ divides $s_A$. Find all sets $A$ of four distinct positive integers which achieve the largest possible value of $n_A$.

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