Planes Around the World Puzzle - Solution
The Puzzle:
You intend to fly non-stop around the world.
But a full tank only takes you halfway around the world.
However you can arrange many planes exactly like yours to assist with refueling.
You can only use the starting airport, and refueling can be done midair.
Ignoring refueling and turn-around times, what is the minimum number of planes you will need?
Our Solution:
The minimum is three.
Start three planes from the airport (yours and two others). After going 1/8 around, one plane refuels both yours and the other 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 other plane transfers 1/4 tank of fuel to yours, leaving it with 1/2 tank, to take it precisely home again.
Your plane 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 your plane at its 3/4 position, where your plane 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.
The remaining plane 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.
What a trip!