INMO 1999 Problem 6

For which positive integer values of $n$ can the set $\{ 1, 2, 3, \ldots, 4n \}$ be split into $n$ disjoint $4$ -element subsets $\{ a,b,c,d \}$ such that in each of these sets $a = \dfrac{b +c +d} {3}$ .