Modeling the 15 Tile Puzzle Through the Lens of Group Theory
History and Overview
2022-01-04 v1 Group Theory
Abstract
In this piece, we examine one variant of the infamous 15 Tile Puzzle and develop a mathematical backing behind why it is unsolvable. Using concepts of permutations, bijectivity, and cycle transpositions, we not only prove how to model this puzzle as a group but also how to determine if a certain configuration of the puzzle is reachable.
Cite
@article{arxiv.2112.11634,
title = {Modeling the 15 Tile Puzzle Through the Lens of Group Theory},
author = {Viren Khandal},
journal= {arXiv preprint arXiv:2112.11634},
year = {2022}
}
Comments
2 pages, 3 figures, 2 proofs