Problem

Source: Baltic Way 1997

Tags: geometry, 3D geometry, sphere, number theory proposed, number theory



The worlds in the Worlds’ Sphere are numbered 1,2,3, and connected so that for any integer n1, Gandalf the Wizard can move in both directions between any worlds with numbers n,2n and 3n+1. Starting his travel from an arbitrary world, can Gandalf reach every other world?