English

Rubik's Cube Scrambling Requires at Least 26 Random Moves

Probability 2024-10-29 v1

Abstract

Scrambling the standard 3x3x3 Rubik's Cube corresponds to a random walk on a group containing approximately 43 quintillion elements. Viewing the random walk as a Markov chain, its mixing time determines the number of random moves required to sufficiently scramble a solved cube. With the aid of a supercomputer, we show that the mixing time is at least 26, providing the first non-trivial bound.

Keywords

Cite

@article{arxiv.2410.20630,
  title  = {Rubik's Cube Scrambling Requires at Least 26 Random Moves},
  author = {Yanlin Qu and Tomas Rokicki and Hillary Yang},
  journal= {arXiv preprint arXiv:2410.20630},
  year   = {2024}
}