MathNet 2014 Question 11

Let $\Sigma = \{1,2,3,\ldots,n\}$. We want to make a partition of the set $\Sigma$ into three subsets $A$, $B$ and $\Gamma$ mutually disjoint with $A \cup B \cup \Gamma = \Sigma$ and such that the sums of their elements $S_A$, $S_B$ and $S_\Gamma$, respectively, are equal. Examine if that is possible, in the following cases
(α) $n = 2014$; (β) $n = 2015$; (γ) $n = 2018$. (A. Fellouris)