Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle
Combinatorics
2022-11-01 v1
Abstract
Segerman's 15+4 puzzle is a hinged version of the classic 15-puzzle, in which the tiles rotate as they slide around. In 1974, Wilson classified the groups of solutions to sliding block puzzles. We generalize Wilson's result to puzzles like the 15+4 puzzle, where the tiles can rotate, and the sets of solutions are subgroups of the generalized symmetric groups. Aside from two exceptional cases, we see that the group of solutions to such a puzzle is always either the entire generalized symmetric group or one of two special subgroups of index two.
Keywords
Cite
@article{arxiv.2210.16930,
title = {Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle},
author = {Patrick Garcia and Angela Hanson and David Jensen and Noah Owen},
journal= {arXiv preprint arXiv:2210.16930},
year = {2022}
}