each side and diagonal of a regular n-gon is colored red or blue
Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1997 p2
February 20, 2020
Coloringregular polygoncombinatorics
Problem Statement
Each side and diagonal of a regular -gon () for odd is colored red or blue. One may choose a vertex and change the color of all segments emanating from that vertex. Prove that, no matter how the edges were colored initially, one can achieve that the number of blue segments at each vertex is even. Prove also that the resulting coloring depends only on the initial coloring.