COMING SOON! PQDT Open is getting a new home!

ProQuest Open Access Dissertations & Theses will remain freely available as part of a new and enhanced search experience at

Questions? Please refer to this FAQ.

Dissertation/Thesis Abstract

God's Number in the Simultaneously-Possible Turn Metric
by Gould, Andrew James, Ph.D., The University of Wisconsin - Milwaukee, 2017, 63; 10686488
Abstract (Summary)

In 2010 it was found that God’s number is 20 in the face turn metric. That is, if the Rubik’s cube hasn’t been disassembled, it can always be solved in 20 twists or fewer, but sometimes requires 20 twists. However, the face turn metric only allows one face to be turned at a time for a total of 18 generators, or 18 possible twists at any time. This dissertation allows opposing, parallel faces to be twisted independent amounts at the same time and still get counted as 1 twist for a total of 45 generators. A new optimal-solving program was constructed, and the results so far show that God’s number is at least 16 for the simultaneously-possible turn metric.

I note that in 3 dimensions the simultaneously-possible turn metric is the same as the axial turn metric (or robot turn metric), but not in 4 dimensions nor higher (e.g. 2×2×2×2, 3×3×3×3, 4×4×4×4, etc.—not to be confused with the 3-dimensional 4×4×4 cube). This difference is also described.

Supplemental Files

Some files may require a special program or browser plug-in. More Information

Indexing (document details)
Advisor: Volkmer, Hans
Commitee: Lauko, Istvan, Wade, Bruce, Willenbring, Jeb, Xie, Dexuan
School: The University of Wisconsin - Milwaukee
Department: Mathematics
School Location: United States -- Wisconsin
Source: DAI-B 79/04(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: ATM, God, RTM, Rubik, SPTM
Publication Number: 10686488
ISBN: 978-0-355-56471-6
Copyright © 2021 ProQuest LLC. All rights reserved. Terms and Conditions Privacy Policy Cookie Policy