olymmath

KöMaL 2012 K331

    The task is to cross a desert with a car. The width of the desert is 600 km. The capacity of the petrol tank of the car is only enough for 400 km, and the car cannot carry fuel in any other way. The car can travel with an average speed of 50--60 km/h. It needs to start out at 8 a.m. and it is to arrive on the other side by 8 p.m. What is the minimum number of such cars needed, for one of them to be able to cross the desert, while the others return back? It is possible to transfer fuel from one car to another.

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