MathDB

C4

Part of JOM 2015 Shortlist

Problems(1)

Coloring on a plane

Source: Junior Olympiad of Malaysia Shortlist 2015 C4

7/17/2015
Nikees has a set SS of nn points on a plane and decides to colour them. All (n2)\dbinom{n}{2} 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 PP, the two endpoints of the longest line segment connecting PP must be of the same colour.
(b) For each point PP, the two endpoints of the shortest line segment connecting PP must be of the same colour.
combinatorics