# What is the smallest number of airplanes needed to ensure the complete flight of one plane around the world?

+1 vote
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There are a group of airplanes on an island. The tank of each airplane contains just enough fuel to fly halfway around the world. Any amount of fuel can be transferred from one plane to another while in the air. The only fuel source is on the island. It is assumed that all planes burn fuel at the same rate and fly at the same speed.
What is the smallest number of airplanes needed to ensure the complete flight of one plane around the world?
All planes should return safely to the island.

posted Jul 16

3

-Start three planes from the airport.
-After going 1/8 around, one plane refuels the other two 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.

Similar Puzzles

There is an air base on the equator. The maximum amount of fuel that a plane can contain would be only sufficient for it to fly halfway around the world.

For at least one plane to finish a trip around the world, how many planes do you need at least?

A trip around the world!
Logic Level 3

There is an air base on the equator. The maximum amount of fuel that a plane can contain would be only sufficient for it to fly halfway around the world.

For at least one plane to finish a trip around the world, how many planes do you need at least?

Details and assumptions:
Same plane doesn't depart twice or more.
The airplanes can use their fuel until it's empty. Starting the airplane doesn't take any time.
Every plane moves at the same speed, and on the same airway.
Assume the planes and air base are dimensionless, and thus, can turn directions instantly.
The plane can only be fueled via aerial refueling, and the amount of time the process takes is negligible.
Every plane starts at the air base and must return to the air base.

+1 vote

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