1 Let $X=\{1,2,3, \cdots, 1993\}, A$ be a subset of $X$, and satisfy: (1) For any two numbers $x \neq y$ in $A$, 93 does not divide $x \pm y$. (2) $S(A)=1993$. Find the maximum value of $|A|$.
1. Divide $X$ into 47 subsets: $A_{i}=\{x \mid x \equiv i$, or $x \equiv 93-i(\bmod 93)\}$, $i=0,1,2, \cdots, 46$. For any $x, y \in A_{i}$, we have $x-y \equiv 0(\bmod 93)$, or $x+y \equiv$ $0(\bmod 93)$, so $A$ can contain at most one number from $A_{i}$. Therefore, $|A| \leqslant 47$. Let $A=\{10$, $11, \cdots, 46\} \cup\{93,94, \cdots, 101\} \cup\{84\}$, then $A$ meets the requirement. Hence, the maximum value of $|A|$ is 47.