RS-SMO 2013 Problem 4

Determine all natural numbers $n$ for which there is a partition of $\{1,2,...,3n\}$ in $n$ pairwise disjoint subsets of the form $\{a,b,c\}$ , such that numbers $b-a$ and $c-b$ are different numbers from the set $\{n-1, n, n+1\}$ .