Question 10
Let $\mathcal{P}$ be a regular $17$-gon; we draw in the $\binom{17}{2}$ diagonals and sides of $\mathcal{P}$ and paint each side or diagonal one of eight different colors. Suppose that there is no triangle (with vertices among vertices of $\mathcal{P}$) whose three edges all have the same color. What is the maximum possible number of triangles, all of whose edges have different colors?