Algebraic Structure of the Varikon Box
Abstract
The 15-Puzzle is a well studied permutation puzzle. This paper explores the group structure of a three-dimensional variant of the 15-Puzzle known as the Varikon Box, with the goal of providing a heuristic that would help a human solve it while minimizing the number of moves. First, we show by a parity argument which configurations of the puzzle are reachable. We define a generating set based on the three dimensions of movement, which generates a group that acts on the puzzle configurations, and we explore the structure of this group. Finally, we show a heuristic for solving the puzzle by writing an element of the symmetry group as a word in terms of a generating set, and we compute the shortest possible word for each puzzle configuration.
Cite
@article{arxiv.2006.01296,
title = {Algebraic Structure of the Varikon Box},
author = {Jason d'Eon and Chrystopher L. Nehaniv},
journal= {arXiv preprint arXiv:2006.01296},
year = {2020}
}
Comments
9 pages, 10 figures