I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 6
Source:
April 10, 2012
Problem Statement
Let each of the vertices of a regular -gon (polygon of 9 equal sides and equal angles) be coloured black or white .
Show that there are two adjacent verices of same colour.
Show there are three vertices of the same colour forming an isosceles triangle.