MathDB
A lot of distances!

Source: Brazilian Math Olympiad 2007, Problem 3

November 2, 2007
floor functioninequalitiestriangle inequalitygeometryangle bisectorgeometry unsolved

Problem Statement

Consider n n points in a plane which are vertices of a convex polygon. Prove that the set of the lengths of the sides and the diagonals of the polygon has at least n/2 \lfloor n/2\rfloor elements.