The Investigation of 15-puzzle, Varikon Boxes, and Similar Variants

The Varikon box, a 3-dimensional variant of the 15-puzzle, is the focus of this investigation. The goal is to investigate three questions: Whether swapping positions of two of its blocks affect its solvability, the number of distinct configurations of the puzzle, and the least number of steps needed for solving the 15-puzzle. First, we introduced our investigation with the same questions, yet for 15-puzzle, specifically using permutation parity to testify one’s solvability, then finding the pattern vice versa that is possible 15-puzzle configurations, and then all of it is mirrored onto the study of Varikon Boxes and other permutational puzzles.