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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 Emo 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 3x3x3 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.

The project's aim is to write a software program to simulate the traditional 3x3x3 Rubik's

Cube. The virtual cube is used for simulating the cube and keeping track of the moves.

Instead of using the physical cube to design and test any algorithms. It is better to do it

with a virtual cube. Besides the basic operations which can be applied on the normal

Rubik's Cube, the program also implemented the features which can help to scramble

and solve the cube with built-in algorithms. The virtual cube was created using

OpenGL/SDL which are C++ graphic libraries for rendering and defining 2D, 3D


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his 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

refer to the entire cube.


Six faces of the Cube will be differentiated by 6 different solid colors: white, yellow,

blue, green, red and orange. The model we use to give the demonstrations in this thesis

is: white is opposite yellow, blue is opposite green and red is opposite orange; and this

is currently the most popular sold model also (Dempsey 1988.). The face is currently

facing you when you hold the Cube is the front face, then the face opposite the front is

the back face, the face above or on the top of the front is the up face, the face opposite

the up is the down face, the face directly to the left of the front is left face; and the face

directly to the right of the front is the right face. The demonstration of faces can be seen

in Graph

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 xnxnxnxn Cube Algorithms 2022 PDF download

How to solve xnxnxnxn Cube 2022

The Cube consists of smaller cubes which are called cubies. In the actual physical

cube, just 26 cubies are visible, the 27th cubie in the center does not exist. There are 3

different types of cubies: center cubies, edge cubies and corner cubies. These cubies

can be seen in graph 2. In total, there are 6 center cubies, 12 edge cubies and 8 corner

cubies. After any sequence of moves or rotations, center cubies will be replaced by

other center positions, edge cubies will be replaced by other edge cubies, and corner

cubies will be replaced by other corner cubies.

blue: center cubie

yellow: edge cubie

red: corner cubie

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GRAPH 2. Cuibes of a Rubik's Cube

On each face, there are 9 squares which are called facets. They are usually covered

by colored stickers. And there are total 6 x 9 = 54 facets on a cube. There are also 3

types of facets: center facets, edge facets and corner facets based on their positions.


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