2.28 Let $\sigma(S)$ denote the sum of all elements in a non-empty set of integers $S$. Let $A=\left\{a_{1}, a_{2}, \cdots, a_{11}\right\}$ be a set of positive integers such that $a_{1}<a_{2}<\cdots<a_{11}$, and suppose that for each positive integer $n \leqslant 1500$, there exists a subset $S$ of $A$ such that $\sigma(S)=n$. Find the minimum possible value of $a_{10}$.
[Solution] Let $A_{0}=\{1,2,4,8,16,32,64,128,247,248,750\}$, then $A_{0}$ satisfies the requirements of the problem and $a_{10}=248$, so we know that the minimum possible value of $a_{10}$ does not exceed 248.

On the other hand, to ensure that $A$ meets the requirements of the problem, the sum of the first 10 numbers in $A$ must be no less than 750. Since the sum of the first 8 numbers in $A$ is at most 255, the minimum possible value of $a_{9}+a_{10}$ is 495, thus $a_{10}$ must be at least 248. Therefore, the minimum possible value of $a_{10}$ is 248.