THE ROLE OF ALGORITHMS IN SOLVING RUBIK’S CUBE

Abstract

The Rubik’s Cube, a widely recognized combinational puzzle which provides a rich mathematical structure that has become an important object of study in discrete mathematics. Algorithms developed for solving it reveals how systematic sequences of moves can efficiently guide an immense state space of over possible configurations. Within the mathematical field, these algorithms describe core concepts such as permutation, symmetry, computation, optimization, and the study of algorithmic complexity. Thus, the Rubik’s Cube serves as a unique and comprehensible model for exploring how mathematical reasoning can be applied to solve high-dimensional, contrived problems. Regardless of significant progress in deriving optimal solutions such as God’s Number, heuristic algorithms, and group-theoretic approaches gaps remain in connecting theoretical optimality with practical algorithmic performance. Existing research basically focuses either on pure mathematical analysis of the cube’s structure or on speed-solving techniques, leaving limited work that combines these perspectives. Furthermore, there remains a need for deeper exploration of how algorithms help with variations of the cube, including higher-order cubes and non-standard configurations. The aim of this research is to analyze and evaluate the mathematical foundations that support algorithms for solving the Rubik’s Cube, and to investigate improved algorithmic strategies that justify theoretical optimality with practical usability. This study will adopt a mixed approach of mathematical and computational methods, involving group-theoretic modelling, analysis of permutation structures, algorithmic model, and comparative assessment of existing solving methods. Through this, the research seeks to contribute to a deeper understanding of the mathematical principles commanding Rubik’s Cube algorithms.