Rubik's Cube/Introduction
This revision Ray Calvin Baker 04:30, 10 November 2011 (UTC) was begun after discovering "Speed Cubing" pages in the Wikiversity: I am DELIGHTED to discover that several other people share an interest in "The Cube"! As a (once upon a time) professional Mathematician and Computer Scientist, I would have been embarrassed NOT to find a solution! But how can I prove that I succeeded? Simple! My method is so clumsy that no one else will ever want to dispute that it's mine! But it is a COMPLETE method, so it may be of interest to beginners in Cubology. There are, of course, many other methods of solving The Cube; so I think it reasonable to invite you to find your own personal method. Be careful -- you cannot just pick parts of several methods and always expect them to work together seamlessly. You need ONE COMPLETE METHOD that works for you!
My notation does not agree (yet) with that of the rest of the speed cubing community. I used L and R for Left and Right, T and B for Top and Bottom (This creates a conflict with "back"), and F and K for Front and bacK.
The existing community seems to use L and R for Left and Right, U and D for Up and Down, and F and B for Front and Back. This looks good to me (no conflicts!), so I will begin to change my text to agree with the nore common usage.
Progress for conversion from LRTBFK to LRUDFB: | Progress for installation:
[ ] Chapter Zero | [OK] Installed
[ ] Chapter One | [OK] Installed
[ ] Chapter Two | [OK] Installed
[ ] Chapter Three | [OK] Installed
[ ] Chapter Four | [OK] Installed
[ ] Chapter Five | [OK] Installed
[ ] Chapter Six | [OK] Installed
[ ] Chapter Seven | [OK] Installed
[ ] Chapter Eight | [OK] Installed
[ ] Chapter Nine | [OK] Installed
[ ] Chapter Ten | [OK] Installed
[ ] Chapter Eleven | [OK] Installed
| Initial installation complete.
Empty boxes, "[ ]", indicate "work to be done"; "[OK]" indicates "this conversion complete".
I tried to add links for chapters 0 through 3. Several attempts actually worked!
+---------------------------------------------------------------------------------------------+ | I have discovered (by experiment) that HTML tags make my formatted text look better. | | | | HOW TO FIND YOUR VERY OWN PERSONAL WAYS TO SOLVE RUBIK'S CUBE | | (Preliminary April 20, 2007 version) | | by Mr. Ray Calvin Baker | | Free Public Domain Educational Material | | | | Several people have written books describing ways to solve Rubik's Cube. Most of my books | | are in storage now, but I thought it might be interesting to write out a solution of my | | own, especially for "middle school" students. The title of this book is NOT "How to Solve | | Rubik's Cube" -- instead of just showing you how to solve the Cube, I want to help you find | | your very own personal ways to do that! (I will show you A way, but I am sure that you will | | want to find better ways!) | | | | This is a journal of my attempts to rediscover A WAY to solve the Cube. There are better, | | faster ways to solve the Cube than this -- I want you to discover some of them for | | yourself. You may find other methods in books, articles by other writers, and on the | | internet. Many of these showcase someone's most sophisticated methods. This journal of mine | | showcases some of my most clumsy methods, because I want you to experience the excitement | | of solving a very large problem for yourself. If you read my account carefully, and learn | | to read the diagrams, and understand your Cube, YOU WILL be able to solve the Cube. You may | | also be able to better understand what other writers have written about the Cube. | | | | Although I may mention a few fancy mathematical techniques, for the most part I will try to | | SHOW you pictures and diagrams. The greater the number of ways you can find to look care- | | fully at the Cube and visualize it in your mind, the more likely you are to FIND YOUR VERY | | OWN PERSONAL WAYS TO SOLVE RUBIK'S CUBE. | | | | Since this is a journal, it can contain a lot of the "internal chatter" that goes on in my | | mind as I work on parts of the puzzle. I hope this does not seem stupid to you; I hope it | | helps you to learn to think in some of the ways professional problem solvers use. Even | | though I have tried to express my thoughts in words, to share with you, I believe that most | | of my personal thinking is done in pictures and diagrams. Since diagrams and pictures are | | multi-dimensional, you may guess that I am not a linear thinker. (You would be correct.) | | Please bear with me if you think my writing style is tangled and repetitious! (It is!) You | | probably have your own personal, best ways of thinking, too. Please learn to use and enjoy | | them! | | | | This account is dedicated to the students of Christian Center School, in the hope that they | | will be encouraged to explore further some of the "mathematics without arithmetic". Please | | let me know if you think I can rewrite parts of this article more simply or more clearly! | | This is for YOU! | | | | Special thanks are due to the teachers and students who helped me by carefully checking | | every word and diagram, and every step of the solution, as they unscrambled boxes full of | | Cubes! | | | | Teachers: Students: | | Mrs. Baker (Music teacher) Romeo | | | | Get your name in here, too! Find a mistake, or tell me about your ideas to write a chapter | | more clearly. | | | | An apology is due to teachers of the English language. After decades of programming | | computers in applications where it is vitally important to quote literal strings exactly, I | | still try to make quotations exact, punctuation marks and all. In other words, "This is an | | example of non-standard usage of quotation marks.". What shall I do if I wish to refer to, | | or quote, passages which contain quotation marks, """", and apostrophes, "''"? I hope you | | can at least understand the extent of some of my technical problems! | | | # Some of you may like arithmetic, so I will include a few ways to count and calculate some # # arithmetical stuff about Rubik's Cube. These sections are optional, and are set off by the # # "#" marks. The main use of arithmetic will be simply to show that we have ways to solve ANY # # scrambled Rubik's Cube, and to help us track progress toward a solution of this famous # # (notorious?) puzzle. # | | | | | | | TABLE OF CONTENTS and | | List of Diagrams | | | | Chapter Zero - - - - - - - - - - The Cube |
| | | Chapter One - - - - - - - - - - Problem Solving Strategies |
| | | Chapter Two - - - - - - - - - - Using Pictures, Diagrams, Notation, and Abbreviations |
| DIAGRAM 2-1. An Intact Rubik's Cube, Showing How Some Parts Are Named | | DIAGRAM 2-2. Diagram of a Partially Disassembled Cube | | DIAGRAM 2-3. Another Perspective of a Partially Disassembled Cube | | DIAGRAM 2-4. The Physicist's Method -- How to Disassemble the Cube | | DIAGRAM 2-5. Another View -- How to Disassemble the Cube | | DIAGRAM 2-6. FRONT Clockwise Move and FRONT Counterclockwise Move | | DIAGRAM 2-7. The FRONT Twice Move | | DIAGRAM 2-8. BOTTOM Clockwise and BOTTOM Counterclockwise Moves | | DIAGRAM 2-9. BOTTOM Counterclockwise Move | | DIAGRAM 2-10. BOTTOM Clockwise and BOTTOM Counterclockwise Are Invers Operations | | DIAGRAM 2-11. Peeking at the BOTTOM Side to See Bv and B^ More Clearly | | DIAGRAM 2-12. BACK Clockwise Move and BACK Countertclockwise Move | | DIAGRAM 2-13. LEFT Clockwise Move and LEFT Counterclockwise Move | | DIAGRAM 2-14. RIGHT Clockwise Move and RIGHT Counterclockwise Move | | DIAGRAM 2-15. TOP Clockwise Move and TOP Counterclockwise Move | | DIAGRAM 2-16. Three Types of Layers | | DIAGRAM 2-17. Each Face of the Cube Takes a Moment on TOP | | DIAGRAM 2-18. We Return the Cube to its Original Orientation | | DIAGRAM 2-19. Six More Ways to Rotate the Entire Cube | | DIAGRAM 2-20. Four More Ways to Rotate the Entire Cube | | DIAGRAM 2-21. An Explanation of an Isometric Drawing With A Cube | | | | Chapter Three - - - - - - - - - Some Simple Moves -- Positioning Four Corner Cubies |
| DIAGRAM 3-1. The Goal of Chapter Three. | | DIAGRAM 3-2. Correct Position with Correct and Incorrect Orientations | | | | Chapter Four - - - - - - - - - - Ignoring Details -- Moving Corner Cubies |
| DIAGRAM 4-1. Blank Diagrams for Planning Moves | | DIAGRAM 4-2. I Found a Three-Way Swap | | DIAGRAM 4-3. An Experiment Which Seemed Useless | | DIAGRAM 4-4. Three More Moves Provide a Useful Two-Cubie Interchange | | DIAGRAM 4-5. Summary of FRONT RIGHT TOP and BOTTOM FRONT RIGHT SWAP | | DIAGRAM 4-6. How Do You Swap Diagonally Opposite Cubies? | | DIAGRAM 4-7. Plan for SWAPping Diagonally Opposite Cubies the Hard Way | | DIAGRAM 4-8. Ten Stages in SWAP Diagonally Opposite Cubies the Hard Way | | DIAGRAM 4-9. Preparing to Locate the Final Four Corner Cubies | | DIAGRAM 4-10. Introducing More Abbreviated Diagrams | | DIAGRAM 4-11. The First Set of Six Possibilities | | DIAGRAM 4-12. The Second Set of Siz Possibilities | | DIAGRAM 4-13. The Third Set of Six Possibilities | | DIAGRAM 4-14. The Final Set of Six Possibilities | | | | Chapter Five - - - - - - - - - - Keeping Track of Lots of Details -- Rotating Corner Cubies |
| DIAGRAM 5-1. Diagram for Orienting Corner Cubies -- Position Zero | | DIAGRAM 5-2. What FRONT Clockwise Did | | DIAGRAM 5-3. What RIGHT Counterclockwise Did -- Position Two | | DIAGRAM 5-4. Comparing Position Zero With Position Two | | DIAGRAM 5-5. After Six Turns | | DIAGRAM 5-6. Unwrapping the Cube | | DIAGRAM 5-7. Unwrapped Cube After Six Moves | | DIAGRAM 5-8. Developing a New Type of Diagram | | DIAGRAM 5-9. The Peculiar Arithmetic of Rotate by 120 Degrees | | | | Chapter Six - - - - - - - - - - Customize Your Moves -- Commutation |
| DIAGRAM 6-1. Example Step One | | DIAGRAM 6-2. Example Step Two | | DIAGRAM 6-3. Example Step Three | | DIAGRAM 6-4. Summary: How to Undo One Move | | | | Chapter Seven - - - - - - - - - Finishing the Orientation of Corner Cubies |
| DIAGRAM 7-1. Typical Coded Rotation Problems | | DIAGRAM 7-2. A Sequence of Moves Which Changes Orientations od Corner Cubies | | DIAGRAM 7-3. Repeating the Sequence of Moves | | DIAGRAM 7-4. A Sucessful Experiment | | DIAGRAM 7-5. Solving a Typical Problem | | DIAGRAM 7-6. Solving Three Corners Rotated in Same Direction | | DIAGRAM 7-7. Find a Solution For a Rotation Problem | | DIAGRAM 7-8. Find Second Corner Cubie to Rotate, Then Apply These Moves | | DIAGRAM 7-9. Is the FRONT LEFT TOP Corner Cubie Properly Oriented? | | DIAGRAM 7-10. X Marks Our Progress | | | | Chapter Eight - - - - - - - - - Moving Edge Cubies |
| DIAGRAM 8-1. The Down-Slice Move | | DIAGRAM 8-2. Turn the TOP Layer Twice | | DIAGRAM 8-3. The Up-Slice Move | | DIAGRAM 8-4. Exchanging Three Edge Cubies | | DIAGRAM 8-5. Recommended Way to Position Edge Cubies | | DIAGRAM 8-6. A New Type of Diagram Emphasizes the Edge Cubies | | DIAGRAM 8-7. Positioning Cubie #2 Without Disturbing #1 | | DIAGRAM 8-8. Positioning Cubie #3 Without Disturbing #2 Or #1 | | | | Chapter Nine - - - - - - - - - - Rubik's Maneuver -- How to Flip Two Edge Cubies |
| DIAGRAM 9-1. A Cube in Need of Rubik's Maneuver | | DIAGRAM 9-2. Instructions for Rubik's Maneuver | | DIAGRAM 9-3. Special Case Not Handled by Instuctions in Chapter Eight | | DIAGRAM 9-4. The Unscrambled Cube | | | | Chapter Ten - - - - - - - - - - Reference Summary of Useful Operations |
| INTERCHANGE THREE CORNER CUBIES | | INTERCHANGE TWO CORNER CUBIES | | CHANGE ORIENTATION OF TWO CORNER CUBIES | | INTERCHANGE THREE EDGE CUBIES | | CHANGE ORIENTATION OF TWO EDGE CUBIES | | | | Chapter Eleven - - - - - - - - - I GET A TASTE OF MY OWN PRESCRIPTIONS |
| There is a "hidden" sub-group -- I need to find a way to solve it, too. | | | | Chapter Twelve - - - - - - - - - MY (YOUR) VERY OWN PERSONAL WAY TO SOLVE RUBIK'S CUBE |
| (You need to write this chapter yourself!) | | | *---------------------------------------------------------------------------------------------*
Ray Calvin Baker 15:09, 29 October 2011 (UTC)