Graph theory, order divisible by 3

Question

Let G be a graph such that every vertex is in exactly ten triangles (10 distinct subgraphs with are isomorphic to K$_3$). Prove that the order of the graph is divisible by 3.

I think this might involve Euler's formula, but not sure how to apply it?

Answer 1

HINT

Make a bipartite graph with bipartition $X,Y$, where $X$ contains all $n$ vertices, $Y$ contains all triangles. Draw an edge between $X$ and $Y$ when the vertex is on the triangle. Now count edges from both sides.