Question : On island, there is an airport. The airport is the homebase of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle. The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel. What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport i.e.

• Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.
• Each airplane must have enough fuel to return to airport.
• The time and fuel consumption of refueling can be ignored.

The minimum is three.

Start three planes A,B,C together from the airport. After going 1/8 around, plane C refuels both A and B plane with 1/4 of a tank each, leaving it with 1/4 of a tank which is precisely enough to take it home.

Two planes continue with a full tank again. Reaching 1/4 around the plane B transfers 1/4 tank of fuel to A, leaving it with 1/2 tank, to take it precisely home again.

Plane A is now full at 1/4 and can go to 3/4 with that fuel.

The first returning plane refuels and start off the other way meeting plane A at its 3/4 position, where plane A is empty and the meeting one is half empty. Sharing their fuel they have both 1/4 tank left which can take them to the 7/8 position.

Plane C has arrived there in the meanwhile with 3/4 tank giving 1/4 to the other now empty planes.

All three planes have now 1/4 and can return home.