Question 5
You have a large number of congruent equilateral triangular tiles on a table and you want to fit $n$ of them together to make a convex equiangular hexagon (i.e., one whose interior angles are $120^\circ$). Obviously, $n$ cannot be any positive integer. The first three feasible $n$ are $6$, $10$ and $13$. Show that $12$ is not feasible but $14$ is.