Let $n$ be an integer greater than $2$. Consider a set of $n$ different points, with no three collinear, in the plane. Prove that we can label the points $P_1,~ P_2, \dots , P_n$ such that $P_1P_2 \dots P_n$ 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 )
Problem
Source: Saudi Arabia BMO TST Day II Problem 4
Tags: inequalities, triangle inequality, geometry unsolved, geometry