Computational Difficulty and Invariants of the Snake Cube Puzzle
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Department
Mathematics
Abstract
The snake cube is a popular puzzle that has been analyzed for its computational difficulty and shown to be NP-complete. Conceiving of the puzzle as a Hamiltonian path in an n×n×n graph, we offer a novel mathematical analysis by considering invariants of the puzzle. This allows us to determine necessary conditions for a particular snake cube to be solvable and eliminate a large class of possible puzzles as unsolvable. In particular, we establish upper and lower bounds on the possible number of straight components in solvable snake cube puzzles which exactly determines the number of maximal straight components in the classical 3×3×3 puzzle.
Thesis Record URL
https://digitalcommons.andrews.edu/honors/255/
Session
Department of Mathematics
Event Website
https://www.andrews.edu/services/research/research_events/conferences/urs_honors_poster_symposium/index.html
Start Date
3-26-2021 2:20 PM
End Date
3-26-2021 2:40 PM
Computational Difficulty and Invariants of the Snake Cube Puzzle
The snake cube is a popular puzzle that has been analyzed for its computational difficulty and shown to be NP-complete. Conceiving of the puzzle as a Hamiltonian path in an n×n×n graph, we offer a novel mathematical analysis by considering invariants of the puzzle. This allows us to determine necessary conditions for a particular snake cube to be solvable and eliminate a large class of possible puzzles as unsolvable. In particular, we establish upper and lower bounds on the possible number of straight components in solvable snake cube puzzles which exactly determines the number of maximal straight components in the classical 3×3×3 puzzle.
https://digitalcommons.andrews.edu/honors-undergraduate-poster-symposium/2021/symposium/25
Acknowledgments
Advisor: Anthony Bossman