combinatorics and paths on cubes
Source: RMO District 2005, 8th Grade, Problem 3
March 5, 2005
geometry3D geometrypigeonhole principle
Problem Statement
Prove that no matter how we number the vertices of a cube with integers from 1 to 8, there exists two opposite vertices in the cube (e.g. they are the endpoints of a large diagonal of the cube), united through a broken line formed with 3 edges of the cube, such that the sum of the 4 numbers written in the vertices of this broken lines is at least 21.