A race car is set to make a lap around a track. The track has fuel depots spaced around it. If all the fuel from all the depots is put into the tank of the race car, it has exactly enough fuel to drive once around the track before running out of fuel.

The race car is to start at one of the depots, pick up the fuel and continue to the next, pick up that fuel, and so on until the car reaches its starting point or runs out of gas. (The car has no fuel before picking up the fuel at the starting depot.)

Is it always possible to choose a starting depot so the car can make the complete lap?

Let Depot A hold the required fuel to get to Depot B. 
Let Depot B hold the required fuel to get to Depot C, etc.

Starting at any depot, and going in the preplanned route, the car will always have enough fuel to get to the next destination and so make it back to the initial depot.

Posted by brianjn on 2009-11-02 23:29:30