Coloring on a plane
Source: Junior Olympiad of Malaysia Shortlist 2015 C4
July 17, 2015
combinatorics
Problem Statement
Nikees has a set of points on a plane and decides to colour them. All line segments are drawn and they have distinct lengths. Find the maximum number of colours that are used at least once, given that:(a) For each point , the two endpoints of the longest line segment connecting must be of the same colour. (b) For each point , the two endpoints of the shortest line segment connecting must be of the same colour.