Problem 30 (1991 AHSME)

For any set $S$, let $|S|$ denote the number of elements in $S$, and let $n(S)$ be the number of subsets of $S$, including the empty set and the set itself. If $A$, $B$, and $C$ are sets for which $n(A) + n(B) + n(C) = n(A \cup B \cup C)$ and $|A| = |B| = 100$, then what is the minimum possible value of $|A \cap B \cap C|$?