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arXiv · 2112.11634

Modeling the 15 Tile Puzzle Through the Lens of Group Theory

Viren Khandal
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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.

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Viren Khandal. 2021-12-22. Modeling the 15 Tile Puzzle Through the Lens of Group Theory. https://doi.org/10.13140/rg.2.2.32023.29609

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