MathDB

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)

Problem Statement