Problem

Source: Turkey TST 1999 - P6

Tags: conics, parabola, combinatorics proposed, combinatorics



Prove that the plane is not a union of the inner regions of finitely many parabolas. (The outer region of a parabola is the union of the lines not intersecting the parabola. The inner region of a parabola is the set of points of the plane that do not belong to the outer region of the parabola)