We have two containers: one has a capacity of three gallons of water, the other five gallons. Both are initially empty, although we have access to a large water fountain. We can take a non-full container and fill it completely up with the water, or we can completely empty a container (with water in it) into the fountain, or we can pour the contents of one container into the other until either the first is empty or the second is full. Our goal is to find a sequence of actions we can take to end up with exactly four gallons of water in one container (and none in the other container).