The worlds in the Worlds’ Sphere are numbered 1,2,3,… and connected so that for any integer n≥1, 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?
Problem
Source: Baltic Way 1997
Tags: geometry, 3D geometry, sphere, number theory proposed, number theory