Modeling the 15 Tile Puzzle Through the Lens of 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.
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