A Graph-Theoretic Model for a Generic Three Jug Puzzle

Abstract: In a classic three jug puzzle we have three jugs $A$, $B$, and $C$ with some fixed capacities. The jug $A$ is fully filled with wine to its capacity. The goal of the puzzle is to divide the wine into two equal halves by pouring it from one jug to another without using any other measuring devices. However, we consider a generic version of the three jug puzzle and present an independent graph theoretic model to determine whether the puzzle has a solution at first place. If it has a solution, then the same can be determined using this model. We also present the sketch of an algorithm to determine the solution of the puzzle.