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Solving Rubik’s Cube with Non-Standard Moves
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Still another thesis on Rubik’s cube? Is there still something new to write on that puzzle? In this document, we approach the cube with a rather unusual question: “how would you solve the cube if, instead of using the 6 classical rotations, you were restricted to a set of arbitrary moves?” To answer that question, we will dive into group theory.

Inspired by some previous work on the factorization of the symmetric group, we have developed an algorithm that answers our initial question. However, being able to solve the cube with any set of moves has a trade-off: while some algorithms solve the cube in 20 moves, ours requires several thousands.

One could go further than this thesis by: improving our algorithm, providing rigourous bounds on its complexity, or generalizing the algorithm to the n × n × n cube.

 

Place, publisher, year, edition, pages
2014.
Series
TRITA-MAT-E, 2014:55
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-151379OAI: oai:DiVA.org:kth-151379DiVA: diva2:748282
External cooperation
Université Catholique de Louvain, Belgien
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2014-09-18 Created: 2014-09-18 Last updated: 2014-09-18Bibliographically approved

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