MathDB
Gandalf visiting worlds numbered n, 2n or 3n+1

Source: Baltic Way 1997

January 28, 2011
geometry3D geometryspherenumber theory proposednumber theory

Problem Statement

The worlds in the Worlds’ Sphere are numbered 1,2,3,…1,2,3,\ldots and connected so that for any integer n≥1n\ge 1, Gandalf the Wizard can move in both directions between any worlds with numbers n,2nn,2n and 3n+13n+1. Starting his travel from an arbitrary world, can Gandalf reach every other world?
Back to ProblemsView on AoPS