Gourds: a sliding-block puzzle with turning
Abstract
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.
Keywords
Cite
@article{arxiv.2011.00968,
title = {Gourds: a sliding-block puzzle with turning},
author = {Joep Hamersma and Marc van Kreveld and Yushi Uno and Tom C. van der Zanden},
journal= {arXiv preprint arXiv:2011.00968},
year = {2020}
}
Comments
15 pages + 3 pages appendix, including 18 figures