KöMaL 2009 A476

Let $n \ge$3 be an odd integer, and let $A$={0,1,...,$n$-1} denote the set of residual classes modulo $n$. Call a non-empty subset $B \subset A$ a Dutch set, if for every $a \in A$ and for every $b \in B$ at least one of $b$+$a$ and $b$-$a$ lies in $B$. Determine the smallest possible cardinality of a Dutch set in terms of $n$.