INMO 2020 Problem 5

Infinitely many equidistant parallel lines are drawn in the plane. A positive integer $n \geq 3$ is called frameable if it is possible to draw a regular polygon with $n$ sides all whose vertices lie on these lines and no line contains more than one vertex of the polygon.

(a) Show that $3,4,6$ are frameable.

(b) Show that any integer $n \geq 7$ is not frameable. (c) Determine whether 5 is frameable.