Question 129
Let $n$ be an integer greater than or equal to $3$, and let $\mathcal{P}_n$ be the collection of all planar (simple) $n$-gons no two distinct sides of which are parallel or lie along some line. For each member $P$ of $\mathcal{P}_n$, let $f_n(P)$ be the least cardinal a cover of $P$ by triangles formed by lines of support of sides of $P$ may have. Determine the largest value $f_n(P)$ may achieve, as $P$ runs through $\mathcal{P}_n$.