A group of airplanes is based on a small island. The tank of each plane holds just enough fuel to take it halfway around the world. Any desired amount of fuel can be transferred from the tank of one plane to the tank of another while the planes are in flight. The only source of fuel is on the island. Assume no time is lost while refueling either in the air or on the ground, and that the planes have the same constant ground speed and rate of fuel consumption. At any time, a plane can reverse course and head back to the island base. What is the smallest number of planes that will ensure the flight of one plane around the world and that all planes return safely to the island base?