Question 131
Suppose that $S_{1}, S_{2}, S_{3}, \ldots$ are sets of integers such that no integer is contained in more than one $S_{n}$; every $S_{n}$ has exactly two elements; and the sum of the elements of $S_{n}$ is $n$. Prove that there exist infinitely many values of $n$ with the following property: one of the elements of $S_{n}$ is greater than $13 n / 7$.