NDLI: The Diameter of the Rubik's Cube Group Is Twenty

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kociemba, Herbert Dethridge, John Rokicki, Tomas Davidson, Morley
Copyright Year	2013
Abstract	We give an expository account of our computational proof that every position of Rubik's Cube can be solved in 20 moves or less, where a move is defined as any twist of any face. The roughly $4.3 \times 10^{19}$ positions are partitioned into about two billion cosets of a specially chosen subgroup, and the count of cosets required to be treated is reduced by considering symmetry. The reduced space is searched with a program capable of solving one billion positions per second, using about one billion seconds of CPU time donated by Google. As a byproduct of determining that the diameter is 20, we also find the exact count of cube positions at distance 15.
Starting Page	1082
Ending Page	1105
Page Count	24
File Format	PDF
ISSN	08954801
DOI	10.1137/120867366
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	27
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-06-19
Access Restriction	Subscribed
Subject Keyword	group theory Explicit machine computation and programs Computational methods Rubik's Cube algorithm performance Distance in graphs
Content Type	Text
Resource Type	Article
Subject	Mathematics

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The Diameter of the Rubik's Cube Group Is Twenty