The Most Spectacular, Stupendous, Sweeping, Slick, Straightforward Rubik’s Cube Tutorial the Web Has Ever Known (and Likely Ever Will Know) – Part 4 (Completing the Cube)

NOTE THAT THE OTHER PARTS OF THE TUTORIAL ARE IN PROGRESS AND WILL BE PUBLISHED SHORTLY

STEP 4: PERMUTING THE LAST LAYER (PLL)

The good student you are, you’ve now studied the Cross, First Two Layers, and OLL Beginner’s Method tutorials.  If you followed them closely, your cube should like this.  The bottom face should be all white, the top face should be all yellow, and the first two layers should be solved.  The last layer, indicated in gray, is likely to be a bit jumbled.  (There is a 1/16 chance that the previous OLL step actually solved the cube completely.)

The goal in this last step is to orient (“permute,” in cube-speak) the last layer pieces into the correct positions without disturbing the top face, bottom face, or first two layers.

We approach this in two stages: first, orienting the cornerssecond, orienting the edges.

STEP 4a: Permuting the Top Layer Corners (Headlights)

The goal here is to orient the yellow corners into the correct relative position to one another. This can be achieved with a single algorithm applied either once or twice.  As with other algorithms, the only complicated part is knowing how to orient the cube.

For this step, cube orientation is governed by “headlights” in the top layer. Headlights occur when you have matching colors in the top layer corners of one face.  We ignore the top layer edges when determining whether there are headlights; a “solved” top layer with three matching colors is considered headlights.  In simplest terms, you want to orient the cube so that the headlights are in the back face (pointing away from you), as in the above diagrams.  (In these diagrams, the first two layers are illustrative only.  So long as the bottom two layers are solved, it does not matter which bottom layers color is facing back or the relative position of the top layer to the bottom two layers.)

algorithm: R’   F   R’   B2   R   F’   R’   B2   R2

positioning: yellow face up and…
– if no face has headlights, any face can be the back
– if only one face has headlights, back face is the face with headlights
– if all four faces have headlights, skip this step

Rob’s video: here

Again, the key is positioning. Below are a handful of examples of the proper orientation of the different configurations you may encounter.

ONE FACE WITH HEADLIGHTS (SOLVED OR UNSOLVED)
orient headlights toward the back
NO FACE WITH HEADLIGHTS
orientation does not matter
(will need to perform algorithm twice)
FOUR FACES WITH HEADLIGHTS (ONE OR NONE SOLVED)
skip to next step

As with the other steps, you may need to apply the algorithm twice — only once if you start with headlights on one (but not all) faces, and twice if you start with no headlights. If you need to perform the algorithm twice be sure to re-orient the cube with the headlights toward the back before applying the algorithm again.

STEP 4b: Permuting the Top Layer Corners (Voila!)

Now just one step remains between you and a solved cube!  At this point, your cube should have an all white bottom face, all yellow top face, bottom and middle layers solved, and all four corners properly oriented relative to one another. That means that the top layer will have headlights on all four sides; one or none of the faces may be solved (with a matching edge between the headlights).

Don’t get confused if those top layer corners are not properly oriented vis-à-vis the bottom two layers.  In fact, there’s only a 1 in 4 chance that they will be be lined up with the bottom two layers after the previous step.  The below cubes are just one or two U or U’ turns away from having the top layer corners lined up with the bottom layers.  Do that now, before proceeding.

Unlike with the other stages, I’m not going to point you to Rob’s video tutorial. Instead, here is the easier algorithm I use:

algorithm: F2   U(’)   R’   L   F2   R   L’   U(’)  F2

positioning: yellow face up and…
– if no solved face, any face toward back (algorithm in either direction)
– if one solved face, solved face toward back
(algorithm direction based on unsolved edges)

The two U turns are flagged (with the optional inverse indicator) because you apply them both as U or both as U’, depending on which of two cases you encounter.  As the diagrams below show, if a face is entirely solved, with headlights on the others, the three unsolved edges will each need to move in either a clockwise or counter-clockwise manner.  To do this, orient the solved face toward the back (facing away from you), and then apply the algorithm with either U (clockwise) or U’ (counter-clockwise) top face turns.

apply algorithm clockwise

F2  U  R’  L  F2  R  L’  U  F2

apply algorithm counter-clockwise

F2  U’  R’  L  F2  R  L’  U’  F2

If you have headlights on all four cases, with no face solved, orient any face toward the back and perform the algorithm in either direction.  After performing it once, you’ll have a solved face.  Proceed as described above, orienting the solved face toward the back and applying the algorithm clockwise or counter-clockwise depending on the edges.

Guess what?  If you followed the above perperly, you’re done! Congratulations!

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3 thoughts on “The Most Spectacular, Stupendous, Sweeping, Slick, Straightforward Rubik’s Cube Tutorial the Web Has Ever Known (and Likely Ever Will Know) – Part 4 (Completing the Cube)

  1. Pingback: learning the H and Z perms « adventures in cubing

  2. Pingback: The Most Spectacular, Stupendous, Sweeping, Slick, Straightforward Rubik’s Cube Tutorial the Web Has Ever Known (and Likely Ever Will Know) – Part 2 (F2L) | adventures in cubing

  3. Pingback: The Most Spectacular, Stupendous, Sweeping, Slick, Straightforward Rubik’s Cube Tutorial the Web Has Ever Known (and Likely Ever Will Know) – Introduction | adventures in cubing

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