Analysis of the Snake Cube Puzzle and Adjacency Criteria

The snake cube is a puzzle that consists of straight and turn pieces attached by a string that folds into a n x n x n cube. Finding solutions for large cubes is difficult, so finding necessary conditions for solutions is crucial. Using computational algorithms and mathematical proofs, I find improved bounds for the maximum number of straight pieces in a given puzzle size. In particular, I introduce and apply the adjacency criterion to identify groups of puzzles that are unsolvable. Additionally, I find a connection between the number of puzzles that adhere to the adjacency criterion and generalized Fibonacci sequences.