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Labeling a self intersecting polygon

Source: Saudi Arabia BMO TST Day II Problem 4

August 3, 2014
inequalitiestriangle inequalitygeometry unsolvedgeometry

Problem Statement

Let nn be an integer greater than 22. Consider a set of nn different points, with no three collinear, in the plane. Prove that we can label the points P1, P2,…,PnP_1,~ P_2, \dots , P_n such that P1P2…PnP_1P_2 \dots P_n is not a self-intersecting polygon. (A polygon is self-intersecting if one of its side intersects the interior of another side. The polygon is not necessarily convex )
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