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… 

References

SHOWING 1-10 OF 15 REFERENCES
A Mathematical Analysis of The Generalized Oval Track Puzzle
The oval track puzzle (also known as Top Spin) is a game consisting of 20 numbered tiles in an oval shaped track. Also, there is a fixed window (the swapping window) of 4 tiles that reverses the
Proof of Solvability for the Generalized Oval Track Puzzle (revised 04/18/2010)
The oval track puzzle (also known as Top Spin) is a game consisting of 20 numbered tiles in an oval shaped track. Also, there is a fixed window (the swapping window) of 4 tiles that reverses the
Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them
1. An overview of oval tracks 2. The transpose puzzle: an introductory tour 3. The slide puzzle: an introductory tour 4. The Hungarian puzzle: an introductory tour 5. Permutation groups: just enough
A Modern Treatment of the 15 Puzzle
TLDR
The object of the puzzle is to use a sequence of legal moves to switch the positions of blocks 14 and 15 while returning all other blocks to their original positions.
A FRIENDLY INTRODUCTION TO GROUP THEORY
You do, prefrosh. If you’re a math major, then you probably want to pass Math 5. If you’re a chemistry major, then you probably want to take that one chem class I heard involves representation
Advanced Modern Algebra
This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different
A Modern Treatment of the 15
Abstract Algebra: A First Undergraduate Course
  • Waveland Press, Illinois,
  • 1999
Kavoutzis, Proof of Solvability for the Generalized Oval Track Puzzle, Rose-Hulman
  • Undergraduate Math Journal 10 No
  • 2009
  • 2016
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