Cars Across the Desert

A military car carrying an important letter must cross a desert. 

There is no petrol station on the desert and the car has space only for petrol that lasts to the middle of the desert.

There are also other cars that can transfer their petrol into one another.

How can the letter be delivered?

This is how letter can be delivered!

Source 

Delivering Letter Across The Desert

What was the task?

We need 4 such cars to deliver the letter across the desert successfully.

Let's divide the entire route into 6 parts. That means the distance that car can travel (half the total path in desert) is divided into 3 parts. To travel each part car requires 1/3rd of it's petrol in the tank.

1. At first 1/6th of total path, all cars are 2/3rd full. Now 2/3rd of the petrol from 1 car can be used to fill 1/3rd of tanks in other 2 cars (1/3 + 1/3 = 2/3). This way, we would have 2 cars full while 1 car 2/3rd full. We are leaving behind the empty car, taking 3 cars forward.

Stage 1

2. At next 1/6th of the distance, 2 full cars will use 1/3rd of their petrol hence would be 2/3rd full. And the car that was 2/3rd at previous stage would be not 1/3rd full. At this stage, the petrol from car that is 1/3rd full can be used to fill tank of 1 car completely. So we are leaving behind one another empty car here & taking fully filled car & 2/3rd filled car for next stage.

Stage 2

3. For next 1/6th of the total distance, the car that was fully filled would have 2/3rd petrol. And the car which was 2/3rd at previous stage would be now 1/3rd filled. The petrol of this car can be used to fill the tank of the first car. Now we have 1 car fully filled while other one is empty. So we can leave behind the empty car & use fully filled car for the rest half of the journey. Remember, a car which tank is full can travel half the total path.

Stage 3