100-gon
Source: Germany Bundeswettbewerb Mathematik 2001, Round 2, Problem 1
January 17, 2004
geometryperimetercombinatorics solvedcombinatorics
Problem Statement
10 vertices of a regular 100-gon are coloured red and ten other (distinct) vertices are coloured blue. Prove that there is at least one connection edge (segment) of two red which is as long as the connection edge of two blue points.
[hide="Hint"]Possible approaches are pigeon hole principle, proof by contradiction, consider turns (bijective congruent mappings) which maps red in blue points.