Crossing the desert

The fifth puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on TwitterFacebook, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

You are responsible for driving an important person across the desert, but the cars that you have been given can only hold enough petrol to cover half of the distance. Being a desert, there are of course no petrol stations along the way. However, you have access to as many cars as you need and can transfer petrol between them.

What is the minimum number of cars that you will need and how can you complete the journey?

WARNING: answer below so scroll slowly to avoid revealing it accidentally.

 

ANSWER

The minimum number of cars required is 4. The journey can be split up as follows.

  • All four cars travel 1/4 of the distance across the desert, each using up one half of a tank.
  • Two of the cars are then emptied leaving two cars remaining, each with a full tank.
  • The two cars travel a further 1/4 of the distance, reaching half-way across the desert, each with one half of a tank remaining.
  • One car is then emptied, leaving one car remaining with a full tank.
  • The final car drives the remaining half of the distance across the desert using the full tank.

Screen Shot 2018-09-19 at 13.43.54

BONUS

How many cars do you need if a full tank of petrol allows each car to travel 1/3 of the distance across the desert? What about if a full tank only reaches 1/4 of the way across? Finally, what is the general rule for the number of cars needed to cross the desert when a full tank of petrol takes you 1/n of the total distance?

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