Two diagonals have the same colouring before and after
Source:
April 19, 2013
Problem Statement
The vertices of a convex -gon are enumerated with integers from to . Each side and diagonal of the -gon is colored either red or blue. Prove that, for an arbitrary renumeration of vertices, one can find integers and such that the segment connecting the vertices numbered and before the renumeration has the same color as the segment connecting the vertices numbered and after the renumeration.