Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle

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 t...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Garcia, Patrick, Hanson, Angela, Jensen, David, Owen, Noah
Format: Article
Language:English
Subjects:
Sliding
Subgroups
Tiles
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422