MathNet 2013 Question 45

Determine all $n\in\mathbb N$ for which $\{1,2,\ldots,3n\}$ can be partitioned into $n$ disjoint three-element subsets $\{a,b,c\}$ in which $b-a$ and $c-b$ are distinct numbers from $\{n-1,n,n+1\}$.