Let $ n\geq 2$ be a positive integer. Find the maximum number of segments with lenghts greater than $ 1,$ determined by $ n$ points which lie on a closed disc with radius $ 1.$
Source: Danube Math Competition 2008
Tags: combinatorics proposed, combinatorics
Let $ n\geq 2$ be a positive integer. Find the maximum number of segments with lenghts greater than $ 1,$ determined by $ n$ points which lie on a closed disc with radius $ 1.$