NL-NWO 1981 Problem 3

We want to split the set of natural numbers from $1$ to $3n$ , where $n$ is a natural number, into $n$ mutually disjoint sets $\{x,y,z\}$ of three elements such that always holds: $x + y = 3z$ . Is this possible for : a) $n = 5$ ? b) $n=10$ ? In both cases, provide either such a split or proof that such a split is not possible.