# How Do You Fix an Oval Track Puzzle?

@article{Nash2018HowDY, title={How Do You Fix an Oval Track Puzzle?}, author={David A. Nash and Sara L. Randall}, journal={Mathematics Magazine}, year={2018}, volume={91}, pages={348 - 358} }

The oval track group, $OT_{n,k}$, is the subgroup of the symmetric group, $S_n$, generated by the basic moves available in a generalized oval track puzzle with $n$ tiles and a turntable of size $k$. In this paper we completely describe the oval track group for all possible $n$ and $k$ and use this information to answer the following question: If the tiles are removed from an oval track puzzle, how must they be returned in order to ensure that the puzzle is still solvable? As part of this…

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