Question 66
Given positive integer $n$, let $S = \{1, 2, \dots, n\}$. Find the minimum of $|A\Delta S| + |B\Delta S| + |C\Delta S|$ for nonempty finite sets $A$ and $B$ of real numbers, where $C = \{a + b \mid a \in A, b \in B\}$, $X\Delta Y = \{x \mid x$ belongs to exactly one of $X$ and $Y\}$, $|X|$ denotes the number of elements of a finite set $X$.