CAPS 2021 Problem 3

For any two convex polygons $P_1$ and $P_2$ with mutually distinct vertices, denote by $f(P_1, P_2)$ the total number of their vertices that lie on a side of the other polygon. For each positive integer $n \ge 4$ , determine $$\max \{ f(P_1, P_2) ~ | ~ P_1 ~ \text{and} ~ P_2 ~ \text{are convex} ~ n \text{-gons} \}.$$ (We say that a polygon is convex if all its internal angles are strictly less than $180^\circ$ .)

Josef Tkadlec (Czech Republic)