Event Title

Computational Difficulty and Invariants of the Snake Cube Puzzle

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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

Department

Mathematics

Description

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.

Acknowledgments

Advisor: Anthony Bossman

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Mar 26th, 2:20 PM Mar 26th, 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