BALTIC-WAY 2015 Problem 1

For $n \geq 2$, an equilateral triangle is divided into $n^{2}$ congruent smaller equilateral triangles. Determine all ways in which real numbers can be assigned to the $\frac{(n+1)(n+2)}{2}$ vertices so that three such numbers sum to zero whenever the three vertices form a triangle with edges parallel to the sides of the big triangle.