Around the World by Relay

An airport sits on a great circle around a small planet. Every plane has a tank that holds exactly enough fuel to fly half the way around, flies at the same constant speed, may fly in either direction and turn round at any point, and burns fuel at a constant rate whenever it is airborne. Fuel can be passed between two planes instantly when they are at the same point, any amount up to tank capacity. The only place to land or take on fuel from the ground is the airport, where planes may wait and may refuel instantly, as often as they like. A tank may become empty only at the very instant a plane lands or receives fuel; no plane may ever fly on an empty tank. Every plane must be back at the airport at the end. You want one plane to fly once all the way around the planet, and you may schedule the flights of the others freely. What is the smallest number of planes (including the one that circles the world) that makes this possible?

• geometry

Source: Classic around-the-world airplane puzzle in wide circulation; no traceable original source. Statement written for AxiomIQ.