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.
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}
}