triangle with colorued vertices on 101-gon
Source: 2014 China TST 3 Day 1 Q2
April 5, 2014
combinatorics proposedcombinatorics
Problem Statement
Let be a regular -gon, and colour every vertex red or blue. Let be the number of obtuse triangles satisfying the following: The three vertices of the triangle must be vertices of the -gon, both the vertices with acute angles have the same colour, and the vertex with obtuse angle have different colour.
Find the largest possible value of .
Find the number of ways to colour the vertices such that maximum is acheived. (Two colourings a different if for some the colours are different on the two colouring schemes).