Gourds: a sliding-block puzzle with turning

11/02/2020 ∙ by Joep Hamersma, et al. ∙ 0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 7

page 15

page 18

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.