Puzzles Involving Polycubes, Triangulations and Polyhexes

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Three related types of puzzles are featured in this book. All involve labeling the

vertices or edges of graphs. The first type of graph is a polycube. The vertices are

labeled with a specific set of numbers and the puzzle involves obtaining a labeling in

which the four vertices belonging to each face of a constituent cube have the same

sum. The second type of graph is a plane triangulation. The puzzle involves labeling

the edges of each constituent triangle so that the sum is the same for each triangle.

The third type of graph is a polyhex. For this type of graph the vertices are labeled

with integers so that the sum of the six points bounding each hexagon is the same.

Problems and research questions are included at the end of each Section, and all

puzzle solutions are provided.