1992 USAMO Problems/Problem 3

For a nonempty set $S$ of integers, let $\sigma(S)$ be the sum of the elements of $S$ . Suppose that $A = \{a_1, a_2, \ldots, a_{11}\}$ is a set of positive integers with $a_1 < a_2 < \cdots < a_{11}$ and that, for each positive integer $n \le 1500$ , there is a subset $S$ of $A$ for which $\sigma(S) = n$ . What is the smallest possible value of $a_{10}$ ?