## Tuesday, January 2, 2018

### Delivering Letter Across The Desert

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