Dissection Puzzles Composed of Multicolor Polyominoes

Abstract

Dissection puzzles leverage geometric dissections, wherein a set of puzzle pieces can be reassembled in various configurations to yield unique geometric figures. Mathematically, a dissection between two 2D polygons can always be established. Consequently, researchers and puzzle enthusiasts strive to design unique dissection puzzles using the fewest pieces feasible. In this study, we introduce novel dissection puzzles crafted with multi-colored polyominoes. Diverging from the traditional aim of establishing geometric dissection between two 2D polygons with the minimal piece count, we seek to identify a common pool of polyomino pieces with colored faces that can be configured into multiple distinct shapes and appearances. Moreover, we offer a method to identify an optimized sequence for rearranging pieces from one form to another, thus minimizing the total relocation distance. This approach can guide users in puzzle assembly and lessen their physical exertion when manually reconfiguring pieces. It could potentially also decrease power consumption when pieces are reorganized using robotic assistance. We showcase the efficacy of our proposed approach through a wide range of shapes and appearances.