Decanting problem. You are given three vessels A, B, and C of capacities 8, 5, and 3 gallons, respectively. A is filled, while B and C are empty. Divide the liquid in A into two equal quantities. [Hint: Let a, b, and c be the amounts of liquid in A, B, and C, respectively. We have a + b + c = 8 at all times. Since at least one of the vessels is always empty or full, at least one of the following equations must always be satisfied: a = 0, a = 8; b = 0, b = 5; c = 0, c = 3. You will find that with these constraints there are 16 possible states (situations) in this process. Represent this problem by means of a 16-vertex graph. Each vertex stands for a state and each edge for a permissible change of states between its two end vertices. Now when you look at this graph it will be clear to you how to go from state (8, 0, 0) to state (4, 4, 0).] This is the classical decanting problem.