3x3x3 Intermediate Guide:

by: Caleb Lau

Introduction:
First things first: keep in mind that this is, in fact, an intermediate guide, meaning that I expect that you already know how to solve a 3x3x3 cube. This is the next step to take if you have succeeded in solving with my beginner's guide. Also, before you begin, I want to inform/warn you that this method of solving is indeed more advanced than that of the beginner's guide and will require you memorizing 13 (plus inverses/mirrors for a total of 21) algorithms. Let's begin.

Method Overview:
This method is also a layer-by-layer method and it is very similar to the beginner's method except for the last layer and parts of the first two layers.

1. Form a Cross on the Bottom
2. Insert 3 Corner Pieces
3. Insert 3 Edge Pieces using the empty slot
4. Insert Last Corner and Edge Pieces (1 algorithm plus mirror)
5. Orient the Last Layer Edges (1 algorithm plus inverse)
6. Orient the Last Layer Corners (1 algorithm plus mirror)
7. Permute the Last Layer Corners and Edges Simultaneously (13 algorithms plus mirrors/inverses for a total of 21)

If you do not understand the notation, please see my beginner's guide for help.

Step One/Two: Form a Cross on the Bottom Layer and Insert 3 Corners:
This is exactly the same as the first step in the beginner's method. Once again, if you need help, see that tutorial. If you can solve with the beginner method, this should be no problem. Just do as you would the beginner solution, but only put in three corners. See the applet for the desired result.



Step Three: Insert 3 Edge Pieces Using the Empty Slot:
This may sound confusing and you may not get it the first time, but with practice, it should significantly drop your F2L solve times. Because you only have three corners positioned in the bottom layer, you have one emply slot. You can use this slot to reduce the number of moves required to insert an edge. The hardest part will be positioning the "emply slot." This is because there is only one slot, and 3 edge pieces must be placed. This method of the F2L is called "using a working-corner." Use the applets below as guides on how to position the bottom layer and apply the move sequence. The last applet shows an example of how to use the empty slot to insert two corners. Remember, you only need to insert 3 corners.





Step Four: Insert Last Corner and Edge Pieces:
This step is performed the same way you would solve the first two layers in the beginner's solution. See the beginner solution for more information.

Step Five/Six: Orient the Last Layer Edges and Corners:
At this point, the first two layers should be completed. Now the orientation takes place. Do these steps the same way you would do steps four and five of the beginner's method. It should result in the following:



Step Seven: Permute the Last Layer Corners and Edges Simultaneously
This will probably be the hardest step to learn in the Intermediate method. It involves learning 13 (plus inverses/mirrors for a total of 21) algorithms to permute the last layer, as a whole. This is commonly referred to as PLL, or Permutation of the Last Layer.

When you start learning the algorithms, you might be confused as to which ones to use. To clear things up, I will introduce a "block method." If any two (or more) pieces on the top layer are solved (in relation to each other), move them to the right spot using U, U', and U2 turns. Then draw imaginary arrows that show where the other pieces have to go. Find the diagram that matches the case you have, and execute the specified algorithm.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagrams courtesy of Dan Harris.



Diagram courtesy of Dan Harris.


If you have no idea where to start memorizing, my only hint is to do just that: START MEMORIZING. That's the way to do it. I'm pretty sure that there was a study somewhere that stated if you do something repetitively and accurately 37 times, it will be put into your muscle [long term] memory. That is exactly what you want. If you don't start, you won't finish. Take a bold step and memorize. Good Luck. A printable sheet of these algorithms can be found at Dan Harris' Cubestation.

Conclusion:
Thank you for reading this guide on solving at an intermediate level. I hope that this has helped you. Practice and you should be able to average in the 30s (maybe even 20s) with this. If you have any questions, please don't hesitate to contact me.

Happy Cubing!

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