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Numberlink is a puzzle game in which players are given a grid with nodesmarked with a natural number, $n$, and asked to create $n$ connections withneighboring nodes. Connections can only be made with top, bottom, left andright neighbors, and one cannot have more than two connections between anyneighboring nodes. In this paper, we give a mathematical formulation of thepuzzles via graphs and give some immediate consequences of this formulation.The main result of this work is an algorithm which provides insight intocharacteristics of these puzzles and their solutions. Finally, we give a fewopen questions and further directions.

A Mathematical Foundation for the Numberlink Game