Minimum planes to go around the world | Puzzles for Interview - Interview Preparation PDF Download

Introduction

On an island, there is an airport with an unlimited number of identical airplanes. Each airplane can fly exactly 1/2 way around the world, along a great circle, and can refuel in flight without losing speed or spilling fuel. However, the island is the only source of fuel. The puzzle is to find the minimum number of airplanes required to get one airplane all the way around the world, assuming that all airplanes must return safely to the airport.

Solution

To solve this puzzle, we need to divide the journey into different parts and use a few planes to refuel others. Let's assume that the total circumference of the world is 300 units, so every plane can run 150 units. We need three airplanes: X, Y, and Z.

Part 1

Airplane X will go around the world. After flying 50 units, airplane Y passes 1/3rd of its fuel to airplane Z and returns as it has enough fuel to go back to the airport. Now, airplane Z has enough fuel for 150 units (completely filled).

Part 2

At 1/4th of the distance around the world, airplane Z has fuel for 125 units, and airplane X has fuel for 75 units. Airplane Z completely fills the tank of airplane X, which can now fly to a point 3/4 of the way around the world. Now, airplane Z has fuel for 50 units, which is not enough to get back to the airport.

Part 3

But, airplane Y reaches airplane Z in time to refuel it, and both airplanes Y and Z can return safely to the airport. Both airplanes Y and Z get refueled and fly towards airplane X. Again, airplane Y refuels airplane Z and returns to the airport to be refueled.

Part 4

Airplane Z reaches airplane X at the point where it has flown 3/4 around the world. This time, airplanes Y and Z come from the other direction so that the distance left is 1/4. All 3 aircraft can safely return to the home base.

Conclusion

Therefore, we need three airplanes to get one airplane all the way around the world and return safely to the airport. By using this method, we can make sure that all the planes return safely without wasting any fuel.