Given any five points on a flat surface that are in general position, i.e. no two of them coinciding and no three of them on a straight line, prove that four of these points will always form a convex quadrilateral.
This is the latest proof of mine:
1. Let us start with the observation that a line can intersect three edges of a triangle at most (see below). Regardless of the number of intersected edges (zero, two or three) the maximum number of intersection points is two (point of entry and point of exit).