Analysis of the picture cube puzzle

TL;DR

This paper introduces a mathematical model for the picture cube puzzle, analyzes its properties, and explores the number of moves needed to solve it, including computational results and a generalization to finite groups.

Contribution

It provides a novel mathematical framework for analyzing the picture cube puzzle and extends the problem to finite groups.

Findings

Determined the minimum number of moves to solve the puzzle

Developed a mathematical model for the puzzle

Extended the analysis to finite group generalizations

Abstract

In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the description of computational results. We also give a generalization of the problem for finite groups.