MathDB

For

n\geq 2

, an equilateral triangle is divided into

n^2

congruent smaller equilateral triangles. Detemine 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.

Problem Statement