Ravi has a tap, a drain and just two containers, one holding exactly 4 litres and the other exactly 6 litres. He may fill a container to the brim, empty one out completely, or pour from one into the other until the first is empty or the second is full. Which of these amounts can he never measure out exactly?

Every allowed move sets a container to 0, to 4 or to 6, or shifts water between the two, and every one of those amounts is even, so each container always holds an even number of litres and so does the pair together. 5 is odd, so it can never appear. The others are all reachable: 6 litres is one container filled; 10 litres is both filled; and 2 litres comes from filling the 6-litre container and pouring it into the 4-litre one, which leaves 6 − 4 = 2 behind. The trap is that 5 lies comfortably between 4 and 6 and so feels easy, but 'between the two sizes' is not the test — divisibility by 2 is.