N coloured points on the plane...
Source: 2009 Greek TST,Pr.4
May 24, 2016
combinatoricsColoringminimizationpoint setSegment
Problem Statement
Given are points on the plane such that no three of them are collinear,which are coloured red,green and black.We consider all the segments between these points and give to each segment a "value" according to the following conditions:
i.If at least one of the endpoints of a segment is black then the segment's "value" is .
ii.If the endpoints of the segment have the same colour,re or green,then the segment's "value" is .
iii.If the endpoints of the segment have different colours but none of them is black,then the segment's "value" is .Determine the minimum possible sum of the "values" of the segments.