MathDB
Two diagonals have the same colouring before and after

Source:

April 19, 2013

Problem Statement

The vertices of a convex 19911991-gon are enumerated with integers from 11 to 19911991. Each side and diagonal of the 19911991-gon is colored either red or blue. Prove that, for an arbitrary renumeration of vertices, one can find integers kk and ll such that the segment connecting the vertices numbered kk and ll before the renumeration has the same color as the segment connecting the vertices numbered kk and ll after the renumeration.