A Graph-Theoretic Model for a Generic Three-Jug Puzzle

TL;DR

This paper introduces a graph-theoretic model to analyze a generalized three-jug puzzle, providing a method to determine the existence of solutions and sketching an algorithm for solving it.

Contribution

It presents a novel graph-theoretic framework for the three-jug puzzle and offers an algorithmic approach to find solutions in the generalized setting.

Findings

The model can determine whether the puzzle has a solution.

The approach can identify solutions if they exist.

A sketch of an algorithm for solving the puzzle is provided.

Abstract

A classic three-jug puzzle asks, given three jugs $A$, $B$, and $C$ with fixed maximum capacities, with jug $A$ filled with wine to its maximum capacity, whether is it possible to divide the wine into two 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 all. 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.