Aircraft Puzzle

Minimum Number of Aircrafts needed

On Bagshot Island, there is an airport.

The airport is the home base 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?

Assume that  –

All of the aircraft must return safely to the airport.

All the planes have to make it back safely so you can’t give all your fuel away to another plane.
Refueling is an extremely fast process.

Solution : 

 The fewest number of aircraft is 3!
Imagine there are 3 aircraft A, B, and C.

A is going to fly around the world. All three aircraft start at the same time in the same direction. After 1/6 of the circumference, B passes 1/3 of its fuel to C and returns home, where it is refueled and starts immediately again to follow A and C.

C continues to fly alongside A until they are 1/4 of the distance around the world. At this point, C completely fills the tank of A which is now able to fly to a point 3/4 of the way around the world. C has now only 1/3 of its full fuel capacity left which is not enough to get back.

Now in the same manner as before both B and C fully refueled and fly towards A. Again B refuels C and returns home to be refueled. C reaches A at the point where it has flown 3/4 around the world. All 3 aircraft can safely return to the home base if the refueling process is applied analogously as for the first phase of the flight.