Euclidean space
Source: Bundeswettbewerb Mathematik 1976, second round, problem 4
November 8, 2003
geometry3D geometryspheregeometric transformationvectorcombinatorics solvedcombinatorics
Problem Statement
Each vertex of the 3-dimensional Euclidean space either is coloured red or blue. Prove that within those squares being possible in this space with edge length 1 there is at least one square either with three red vertices or four blue vertices !