How To Solve 72 Standard Rubik Variants With Just 9 Simple Formulas

By Phong Nguyễn Như

Rubik's Cube, invented by Ernö Rubik in 1974, is a intelligent, fun game, that was the world's best-selling game of the twentieth century, and is still in vogue today.
The original Rubik's Cube, or 3*3*3 Rubik, is a six-sided, six-color cube, cut by six slices, distributed on three axes of Oxyz coordinate system, yielding 27 (3*3*3) Rubik's pieces.
There are many ways to solve the standard Rubik's Cube, this book uses the pRubik procedure to solve it. The pRubik procedure consists of 3 steps, using 9 formulas, each consisting of a number of simple rotation steps. Of these 9 formulas, there are 2 pairs with 4 dual formulas, and 2 similar formulas, so actually only 6 independent formulas, therefore it's easy to remember the procedure.
The Standard Rubik has many standard variants which are variations on the pattern of Rubik's faces, on the Rubik's body shape, on distribution and direction of the cutting planes, on the shape of cutting surfaces, on the size of variants, and on the number of axes of variants. All of these standard variants can be solved using the pRubik procedure.
This book sequentially shows how to solve 72 standard variants, including 36 simple variants and 36 complex variants. Simple variants, solved in [3], include: Void 1, Potato Chips, Convex Concave, Sandwich 1, Coloured Corner, Red Cap, House of Science, Cylinder, Octagonal Prism, Void 2, Ball, Ball in Cube, C-Virus, Anis Star, Twisted Cube, House 1, Mirror Cube, Colour Cube, Fisher, Windmill, Mirror Fisher, Mirror Windmill, Fluffy, Pandora, Sandwich 2, Rainbow 1, Rainbow 2, Cube 2*2*2, Mirror Cube 2*2*2, Window 2*2*2, Megaminx 2*2*2, House 2*2*2, Mouse 2*2*2, Buffalo 2*2*2, Elephant 2*2*2, Cat 2*2*2.
Complex variants, solved in [4], include: Maze 1, Maze 2, Arrow, Shepherd, Dice, Blackpink, Chemistry, Math 1, Math 2, Number, Sudoku, Case, House 2, Penrose, Star, Egg, Heart, Orange, Peach, Lemon, Pear, Apple, Hexagonal Dipyramid, Hexagonal Diamond, Hexagonal UFO, 4-Corner, Mastermorphix, Axis, Mirror Axis, Crazy Fisher, Crazy Windmill, Ghost, Phoenix, Kilominx, Megaminx, Phoenix Megaminx.

• Language: English
• Publisher: Phong Nguyễn Như
• Release date: Jan 30, 2022
• ISBN: 9781005591588

Phong Nguyễn Như

Nguyen Nhu Phong is a Senior Lecturer at the Industrial Systems Engineering Department, HCM City University of Technology (HCMUT), Vietnam. He is also an IEEE member, and a SAP ERP specialist.He received his Master of Engineering at Asian Institute of Technology (1997), and his Bachelor of Engineering at HCMUT, Vietnam (1987).He was a member of the Project of building ISE program (1999) and the leader of the Project of improving the program (2007-2012). He was the deputy dean of the Faculty of Mechanical Engineering in period of 2002-2007, and the former head of the ISE department in period of 2007-2012.He is the authors of 24 books in Statistics, Operations Research, Scientific Research Methodology, Design of Experiment, Engineering Economy, Production Management, Inventory Management, Quality Management, Lean Production, Lean Six Sigma, MRPII, ERP, Fuzzy Theories & Applications.He is also the authors of 49 papers including 38 conference papers, 7 international conference papers, 4 journal papers, and 120 web papers. His research topics include Soft Computing; Lean Six Sigma; Resource Planning MRPII - ERP.

Book preview

HOW TO SOLVE 72 STANDARD RUBIK VARIANTS

WITH JUST 9 SIMPLE FORMULAS

Phong Nguyen Nhu

2022

LIST OF 72 STANDARD RUBIK VARIANTS

RUBIK SERIES

Other ebooks by the same author in this series include:

1- How to solve 36 variants of the standard Rubik with just 9 simple formulas.

2- How to solve 36 complex variants of the standard Rubik with just 9 simple formulas.

3- How to solve 72 variants of the standard Rubik with just 9 simple formulas. (ebook 1 & 2).

4- How to solve 27 Non-Standard Rubik Variants with simple formulas.

5- How to solve 64 Rubiks with simple formulas. (ebook 1 & 4).

6- How to solve 100 Rubiks with simple formulas. (ebook 3 & 4).

For more information on the above ebooks, please visit:

https://www.smashwords.com/profile/view/nnphong.

CONTENTS

Preface

Chapter 1: The History of Rubiks

1.1 The father of Rubik's Cube

1.2 Some historical milestones

Chapter 2: The Standard Rubik

2.1 The Rubik's Colors

2.2 The Rubik's Pieces

2.3 The Rubik's Structure

Chapter 3: Solving the Standard Rubik

3.1 Basic Rubik's Rotations

3.2 The pRubik procedure

Chapter 4: Standard Variants

4.1 Pattern Variants

4.2 Shape Variants

4.3 Cuts-Distributed Variants

4.4 Cuts-Oriented Variants

4.5 Cuts-Shaped Variants

4.6 Size Variants

4.7 Spindle Variants

4.8 Combination Variants

Chapter 5: Solving Standard Variants

5.1 Solving Pattern Variants

5.2 Solving Shape Variants

5.3 Solving Cuts-Distributed Variants

5.4 Solving Cuts-Oriented Variants

5.5 Solving Cuts-Shaped Variants

5.6 Solving Cuts-and-Pattern Variants

5.7 Solving 2*2*2 Size Variants

5.8 Solving Spindle Variants

References

PREFACE

Rubik's Cube, invented by Ernö Rubik in 1974, is an intelligent, fun game, that was the world's best-selling game of the twentieth century, and is still in vogue today.

The original Rubik's Cube, or 3*3*3 Rubik, is a six-sided, six-color cube, cut by six slices, distributed on three axes of Oxyz coordinate system, yielding 27 (3*3*3) Rubik's pieces.

There are many ways to solve the standard Rubik's Cube, this book uses the pRubik procedure to solve it. The pRubik procedure consists of 3 steps, using 9 formulas, each consisting of a number of simple rotation steps. Of these 9 formulas, there are 2 pairs with 4 dual formulas, and 2 similar formulas, so actually only 6 independent formulas, therefore it's easy to remember the procedure.

The Standard Rubik has many standard variants which are variations on the pattern of Rubik's faces, on the Rubik's body shape, on distribution and direction of the cutting planes, on the shape of cutting surfaces, on the size of variants, and on the number of axes of variants. All of these standard variants can be solved using the pRubik procedure.

This book sequentially shows how to solve 72 standard variants, including 36 simple variants and 36 complex variants. Simple variants, solved in [3], include: Void 1, Potato Chips, Convex Concave, Sandwich 1, Colored Corner, Red Cap, House of Science, Cylinder, Octagonal Prism, Void 2, Ball, Ball in Cube, C-Virus, Anis Star, Twisted Cube, House, Mirror Cube (Silver & Gold), Color Cube (Pink, Yellow, Green, Blue), Fisher, Windmill, Mirror Fisher (Silver & Gold), Mirror Windmill (Silver & Gold), Fluffy, Pandora, Sandwich 2, Rainbow 1, Rainbow 2, 2*2*2 Cube, 2*2*2 Mirror, Window, 2*2*2 Megaminx, 2*2*2 House, Mouse, Buffalo, Elephant, Cat.

Complex variants, solved in [4], include: Maze 1, Maze 2, Arrow, Shepherd, Dice, Blackpink, Chemistry, Math 1, Math 2, Number, Sudoku, Case, House 2, Penrose, Star, Egg, Heart, Orange, Peach, Lemon, Pear, Apple, Hexagonal Dipyramid, Hexagonal Diamond, Hexagonal UFO, 4-Corner, Mastermorphix, Axis, Mirror Axis, Crazy Fisher, Crazy Windmill, Ghost, Phoenix, Kilominx, Megaminx, Phoenix Megaminx.

The author hopes that readers will have an enjoyable time, reading this book to learn and solve the above 72 Rubiks.

Although the author has spent a lot of time and effort, but the book will probably have many mistakes, the author is looking forward to receiving comments from readers to make the book better and better. Would you please send comments to:

Phong Nguyen Nhu .

Tel: [phone].

Email: nguyenphong.bku@gmail.

Web: www.isem.edu.vn

Sincerely grateful.

CHAPTER 1

THE HISTORY OF RUBIKS

1.1 The father of the Rubik's Cube

Ernö Rubik is the father of the Rubik's Cube, one of the world's best-selling toys of the twentieth century and it is still in vogue today, with many variants.

Ernö Rubik

According to Wikipedia, Ernõ Rubik was born in Budapest in a family whose father was an aircraft engineer at the Esztergom factory and his mother was a poet. He graduated from University of Budapest (Műszaki Egyetem) in 1967 as an architectural engineer, starting to study sculpture and interior architecture.

1.2 Some milestones of Rubik's history

According to Wikipedia, some notable milestones in Rubik's history are as follows:

From 1971 to 1975, Erño Rubik worked as an architect, then became a professor at Budapest College of Applied Arts (Iparművészeti Főiskola). A teaching tool, called Magic Cube, built to help students understand 3D objects, with the aim of solving the structural problem of moving parts independently without breaking the whole object.

In 1975, Rubik applied for a patent in Hungary for the Magic Cube.

In 1977, the first test batches of the Magic Cube were produced and released in toy stores in Budapest.

In 1979, Tibor Laczi brought a Magic Cube to the Nuremberg Toy Fair in Germany, with permission from Ernő Rubik. The Magic Cube was noticed by Tom Kremer, and they signed an agreement with Ideal Toys to release the Magic Cube worldwide.

In 1980, the Magic Cube was renamed after its inventor, the Rubik's cube, or Rubik for short. Rubik debuted at international toy fairs in London, Paris, Nuremberg and New York, and won the special toy of the year award in Germany, the UK, France and the US.

In 1981, the Rubik's Cube became a craze, and it is estimated that around 200 million Rubik's Cubes were sold worldwide in period from 1980 to 1983.

In 1983, Ernô Rubik founded Studio Rubik, where he designed furniture and games.

In 1990, Ernõ Rubik became president of the Hungarian Technical Academy (Magyar Mérnöki Akadémia). At the academy, he founded the World Cube Association.

CHAPTER 2

THE STANDARD RUBIK

2.1 The Rubik's Colors

The standard Rubik is a cube with 6 faces, one color on each face. The color system of the standard Rubik's cube includes 6 colors:

White, Yellow, Red, Orange, Green, and Blue.

The color distribution for the six faces of the standard Rubik is as follows. The colors on opposite faces include:

White - Yellow, Red - Orange, Green - Blue.

If the white face is placed at the bottom of the cube, the yellow face will be at the top of the Cube. The remaining faces, if viewed from the top, will be distributed clockwise as follows:

Green - Red - Blue - Orange.

The standard Rubik

2.2 The Rubik’s pieces

Consider a Cartesian Coordinate System in 3-dimensional space, Oxyz, with 3 axes Ox, Oy, Oz as shown below.

Cartesian coordinate system in 3-dimensional space, Oxyz

Place the Rubik's cube in the coordinate system so that 1 vertex of the Rubik is at the origin, the edges of the Rubik coincide with the Ox, Oy, Oz axes as shown below.

Rubik's cube in Oxyz coordinate system.

Then cut the Rubik's cube by 6 cutting planes C1, C2, C3, C4, C5, C6.

C1, C2, perpendicular to the Ox axis, create 3 equal layers along the Ox axis.

C3, C4, perpendicular to the Oy axis, create 3 equal layers along the Oy axis.

C5, C6, perpendicular to the Oz axis, create 3 equal layers along the Oz axis.

6 cutting planes in the coordinate system Oxyz.

The above six cutting planes will divide the Rubik's cube into many pieces, with the shape of a small cube. The total number of pieces is calculated as follows:

N = 333 = 27

Therefore, the standard Rubik's Cube is considered to be of size 333. However, the piece in the center of the cube is invisible, the number of pieces, visible on the outside, is:

N - 1 = 27 – 1 = 26

2.3 The Rubik's Structure

If the invisible piece of the standard Rubik is placed at the origin of the Oxyz coordinate system, so that the axes are parallel to the sides of the Rubik, then the standard Rubik has 3 rotation axes:

Ox axis rotates horizontally from back to front.

Oy axis rotates horizontally from left to right.

Oz axis rotates vertically from bottom to top.

Standard Rubik's pieces include 3 types:

Centers.

Sides.

Corners.

Centers, Sides, and Corners

Centers are pieces in center, lying on the axis of rotation of the Rubik's Cube. With 3 axes of rotation, the centers of the Rubik include:

2 centers on the Ox axis, at the back and the front of the Rubik.

2 centers on the Oy axis, on the left and the right of the Rubik.

2 centers on the Oz axis, on the top and the bottom of the Rubik.

Sides are pieces that lie on the edges of the Rubik's cube and connect two adjacent centers. The Rubik's Cube has 12 edges, and there are 12 sides in the middle of the Rubik's edges.

Corners are pieces located at the corners of the Rubik's cube. Corners are surrounded by edges. A Rubik's cube has 8 corners, and has 8 pieces of corner.

So the standard Rubik's Cube has a total of 26 pieces, in which:

6 centers on the axes of rotation.

12 sides connecting centers.

8 cornerssurrounded by edges.

On the other hand, the Rubik's cube can be viewed as consisting of 3 layers:

Layer 1, L1, at the bottom, has 9 pieces, including 1 center, 4 sides and 4 corners.

Layer 2, L2, in the middle, has 8 pieces, including 4 centers, 4 sides.

Layer 3, L3, at the top, has 9 pieces, including 1 center, 4 sides and 4 corners, same as layer 1.

Rubik’s layers

CHAPTER 3

SOLVING THE STANDARD RUBIK

There are many ways to solve standard Rubik, here choose the simplest way, in the sense of few formulas, each formula has the fewest rotations, so it's easiest to remember. Before solving, however, let's define the basic Rubik's rotations.

3.1 The Basic Rubik's Rotations

Place the Rubik's cube vertically, according to the Oxyz axis system, the 6 Rubik's faces include:

The top (Up) and bottom (Down) faces follow the Oz axis.

The left (Left) and right (Right) faces follow the Oy axis.

The front (Front) and back (Back) sides follow the Ox axis.

Basic Rubik's rotations along the Oz axis on the top (Up) and bottom (Down) faces include:

U: rotate the top face clockwise.

U': rotate the top face counterclockwise.

D: rotate the bottom face clockwise.

D': rotate the bottom face counterclockwise.