A whole number of litres of water is distributed among three vessels. A legal move consists of choosing two vessels and pouring from one into the other exactly as many litres as the receiving vessel already contains. For example, if your vessels contain \((4,6,2)\) liters, then a legal move may be turning this into \((8,2,2)\). The vessels are large enough so that overflow never occurs.
Prove that after finitely many legal moves, one of the vessels can be made empty.