Rubik's Cube Scrambling Requires at Least 26 Random Moves
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917819228094464 |
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| author | Qu, Yanlin Rokicki, Tomas Yang, Hillary |
| author_facet | Qu, Yanlin Rokicki, Tomas Yang, Hillary |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20630 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rubik's Cube Scrambling Requires at Least 26 Random Moves Qu, Yanlin Rokicki, Tomas Yang, Hillary Probability 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. |
| title | Rubik's Cube Scrambling Requires at Least 26 Random Moves |
| topic | Probability |
| url | https://arxiv.org/abs/2410.20630 |