This problem originated by Martin Gardner, and posed to me by
Gary Jackoway (4/2008).

You have an air force base on an island.  You want to fly a plane all
the way around the world without landing.  For simplicity imagine that
the island is on the equator and you want to fly right around the
equator, essentially a circle.  All planes fly at the same speed and
carry the same amount of fuel, which is just enough for a trip HALF
way around the world.  All planes may transfer fuel to each other
instantaneously in flight.  What is the minimum number of planes
required so that one plane can circumnavigate the globe with all
planes returning to the island safely.  No ditching planes along the
way.