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Bounds on Rubik's cube and mirror cube configurations Hsu, Grace; Liu, Sissi

Abstract

Given a 3x3x3 mirror cube, we find the number of valid and distinct projections up to and including three 90° turns. Next, we calculate the number of valid permutations of the traditional 3x3x3 Rubik's cube such that it has at least one, two, three, four, five or six faces with the same colour. We then return to the mirror cube and find improved upper bounds for the number of distinct projections.

Item Metadata

Title
Bounds on Rubik's cube and mirror cube configurations
Creator
Hsu, Grace; Liu, Sissi
Date Issued
2012-06-30
Description
Given a 3x3x3 mirror cube, we find the number of valid and distinct projections up to and including three 90° turns. Next, we calculate the number of valid permutations of the traditional 3x3x3 Rubik's cube such that it has at least one, two, three, four, five or six faces with the same colour. We then return to the mirror cube and find improved upper bounds for the number of distinct projections.
Genre
Report
Type
Text
Language
eng
Series
University of British Columbia. Science One Research Projects
Date Available
2012-07-10
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0107234
URI
http://hdl.handle.net/2429/42650
Affiliation
Science, Faculty of
Campus
UBCV
Peer Review Status
Unreviewed
Scholarly Level
Undergraduate
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository
DSpace

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Attribution-NonCommercial-NoDerivatives 4.0 International