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The aim of the thesis was to write a software program to simulate the traditional 3x3x3
Rubik’s Cube and also introduce and explain the algorithm for solving the cube by means
of group theory. The virtual cube was created using OpenGL/SDL which are C++ graphic
libraries for rendering and defining 2D, 3D images.
Rubik’s Cube is not only well-known as a best-selling toy all over the world but it can also
be used as a tool to employ a rich underlying mathematical structure. And in this thesis
work, we show that Rubik’s Cube can be explained using group theory which is a brand of
modern abstract algebra.
The thesis first introduces the structure and notations of the Cube and the mathematical
background including permutation and group theory. The next part provides the architecture
and the essential features of the software. After that, the strategy for solving the cube and
the explanation of the application of the virtual cube for applying the algorithms will be
described. The final part shows some of the lacking features that need to be improved in
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xnxnxnxn cube algorithms pdf

xnxn cube algorithms pdf

xnxnxnxn cube algorithms pdf xnxn cube algorithms pdf Rubik’s Cube, permutation, group theory, algorithm, OpenGL, simulator xnxnxnxn cube algorithms pdf

CONTENTS
GRAPHS ……………………………………………………………………………………………………… v
TABLES ……………………………………………………………………………………………………… vi
FOREWORD ………………………………………………………………………………………………. vii
ABBREVIATIONS ………………………………………………………………………………………. viii
1. INTRODUCTION …………………………………………………………………………………….. 1
1 RUBIK’S CUBE………………………………………………………………………………………. 2
1.1 Structure …………………………………………………………………………………………………….. 2
1.2 Notations ……………………………………………………………………………………………………. 4
1.3 Bounds on Rubik’s Cube ………………………………………………………………………….. 6
3 IMPLEMENTATION AND DESIGN……………………………………………………………. 8
3.1 Overview …………………………………………………………………………………………………….. 8
3.2 GUI………………………………………………………………………………………………………………. 9
3.2.1 Console windows………………………………………………………………………………. 10
3.2.2 SDL windows……………………………………………………………………………………… 10
3.3 Architecture ……………………………………………………………………………………………… 11
3.3.1 Diagrams…………………………………………………………………………………………. 11
3.3.2 Rubik’s Cube class ………………………………………………………………………… 13
3.3.3 Implementation of Rubik’s Cube moves ………………………………………. 16
3.4 Development platform……………………………………………………………………………… 20
3.5 Software requirements…………………………………………………………………….. 20
3.5.1 Code Blocks as an IDE………………………………………………………………….. 20
3.5.2 OpenGL with SDL…………………………………………………………………………. 21
3.6 SDL features used in this program…………………………………………………. 22
3.6.1 Video……………………………………………………………………………………………… 23
3.6.2 Timers……………………………………………………………………………………………. 23
3.6.2 Input events ……………………………………………………………………………………. 24
4 ALGORITHM………………………………………………………………………………………… 26
4.1 Permutation………………………………………………………………………………………………. 26
4.2 Group Theory………………………………………………………………………………………. 28
4.2.1 Definitions and properties …………………………………………………………….. 28
4.2.2 Special classes of group……………………………………………………………….. 30
4.3 Cycle structure of cube moves ………………………………………………………… 31

xnxnxnxn cube algorithms pdf

 

nxnx cube algorithms pdf

xnxnxnxn cube algorithms pdf nxnx cube algorithms pdf Rubik’s Cube is probably one of the most illustrious puzzles up to date. And the reason
made it so prominent is still not certain. Since its invention in 1974 by Hungarian
sculptor and professor of architecture Erno Rubik, it has captured the imagination of
millions of all age and is widely considered to be the world’s best-selling toy. There are
competitions held every year for cube lover to compete the records and organized by
WCA (World Cube Association). The current world record for a single time on
the 3×3×3 Rubik’s Cube in competition is 5.25 seconds, set by Collin Burns in April
2015. There is a variation of cubes which are sold commercially from 2x2x2 to 7x7x7.
This paper will discuss about the traditional 3x3x3 Rubik’s Cube, one that is simple
enough to study and understand but complex enough to exploit and investigate from
many points of view.

xnxnxnxn cube algorithms pdf

xnxnxnxn cube algorithms pdf

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nxnx cube solution This chapter provides us with the basic understanding of the structure of Rubik’s Cube,
the notations of the Cube’s rotations and some calculations on the bounds of the Cube.
In this paper, we use the word “the Cube” or sometimes “Rubik’s Cube” in this paper to
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