How to solve a 4x4 Rubik's Cube

[rushyrulz]

This is an original work that I am using for CIST 1300 at the University of Nebraska at Omaha during the fall 2012 semester.

Welcome to my 4x4 Rubik's Cube tutorial thread. WARNING: this is not a
thread for beginning cubers, if you can't solve the 3x3 cube, you won't stand a
chance with the 4x4. You can find my 3x3 tutorial
here.

This tutorial was designed to not function unless you have either read my 3x3
tutorial or already know how to solve the cube. If you haven't mastered the 3x3
(able to solve in <2:30), you're in the wrong thread.

Disclaimers/warnings aside, let's get this thing rollin' shall we??

Table of Contents
I. .....Some new notation
II. ....Creating the centers
III. ...Making the dedges
IV. ...Solving the first two layers
V. ....Top cross parity
VI. ...Basic Method permutation parity
VII. ..2-look OLL/PLL permutation parity
-----------------------------------------------------

I. Some new notation

The basic notation on the cube is pretty much the same as the 3x3 with a few
exceptions. The standard cube notation for Right, Up, Down, Left, Front, (and
rarely) Back will remain the same (R, U, D, L, F, B), but
additionally, on the 4x4 cube, you will notice that there are more than just 3 layers
to be dealt with. With one more layer comes one more form of possible movement.

The notation used to denote turning two of the layers at the same time (half the
cube) is expressed in the form "Aa, of course A isn't a
legitimate layer on the cube, but I just used it for an example. One algorithm you
will be using later for a special parity case is this: Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2
Rr F2 Ll' B2 Rr2. Notice that this algorithm contains several instances of the new
notation.

Another new type of notation is just the single lowercase letter a. This is used to
represent a turn of the inside layer on a given face. To put it simply, it's turning
both the outside layers, except for the outermost. (see picture below). It's not a hard
to grasp, but it's crucial that you understand the difference between A, a, and Aa.

Rr:


r:


Finally, you might have noticed already that there are no centers on this cube, but
when you think about the definition of a center piece, it's just a cubelet with only 1
sticker on it. There are center pieces on this cube, there are just 4 for each color!
This will be explained in greater detail in the next section.

In addition to the surplus of center pieces, there are also double the edge pieces.
For each edge piece of any given 2 colors, there is a twin with the exact same 2
colors on it. When these two 'twins' have been matched up, they are called a
dedge (double edge). These dedges will be explained in
greater detail in section III.

Now that notation is out of the way, it's time to move on to the next step!

II. Creating the centers

Remember how I said there were 4 cubelets for each color? Well, the first step in
solving the 4x4 is to pair these up on all sides. At first, I suggest you try messing
around with the cube first and try to do this step on your own, for it is fairly intuitive.
I'm not going to leave you all alone though, here are some tips to help you out:

1. There is no fixed center piece on any of the sides, so you have to actually learn
how the centers are supposed to be so you don't end up having an unsolvable
cube. The way I ALWAYS start with the 4x4 is first solving the red center, then the
white center to the left of the red center, and finally the blue center above the
white/red corner:

example:


Once these centers are done, you can use the opposites of these colors to solve
the remaining centers (opposites are blue/green, white/yellow, red/orange [if you
didn't know this already, solve the 3x3 some more])

2. Here is the method used to match up 2 pairs of center pieces without disturbing
the rest of the centers: Put what you're aligning in the same column as what you're
putting it with and do the algorithm: Rr U2 Rr'. This is an
intuitive algorithm and can also be used on the left side, experimentation works
best.

image form:


Orient your cube like this (bottom set of vertical reds to the front) and do the
algorithm above.

3. This is a variation on the above case where you have an L-like shape on the top
face and a single dot on the front face. Arrange it so that the dot, when flipped up to
the top layer will be in the same position as the corner of the L (this can be
achieved by rotating the front face). When it's properly oriented, there isn't really a
specific algorithm that goes with this, but with the instance in the image below, it's
Rr U Rr'. Basically what you're doing is flipping the single center up, pairing it with
one from the L, turning the top face to get what you just solved out of the way of the
Rr' which will undo the Rr from the beginning of the algorithm. At the same time, it
puts the center pair that you just moved back in place and completed the center.

image:


Like I said, there isn't really an algorithm that goes with this, but you should be able
to figure it out with intuition.

Now that the centers are solved (and in the CORRECT position) lets move on to
the scavenger hunt:

III. Making the dedges

Note: All the normal faces (U,D,R,L,F,B) can be turned freely during this stage
without risk of messing up previous progress.

The purpose of this step is to pair edge pieces with their twins to create "dedges".
The first step in doing so is to find these edge pairs. Once you find 2 that are alike,
twist the normal faces any way you choose to get them both on the same face and
make that face the front. Here is where you can get one of two cases:

First:
(assume the other red edge is a red/green edge as well.)

Second:
(assume the other green edge is a green/red edge as well.)

The first case is correct and what you want to proceed. If you run into the second
case, do the algorithm R' D' L F' L' and you should get the first
case.

Note: It won't always look exactly like the image, but the concept is to
have the two edges on the same face, but with different colors facing you (like in
first image).

This next step involves an intuitive algorithm. I'll just use one specific case and
leave you to figure out the other permutations of the same algorithm on your own.

Once you get the first case, turn the top layer until an unmatched pair is on the left
side (in this case [yes this is important]). Do the algorithm: Uu L' U' L
Uu'. Basically what this is doing is:
1. pairing up your dedge (Uu)
2. putting it in the top layer (L')
3. moving it out of the way (U')
4. replacing it with an unpaired dedge (L) [this is why the unmatched pair is
important]
5. Fixing your centers (Uu')

Instead of memorizing that algorithm, think of it as those 5 steps. Always put the
unmatched pair to the right if you're going to be turning the Uu layers to the right
(Uu') and put the unmatched pair to the left if you're going to be turning the Uu
layers to the left (Uu). The rest should follow the pattern.

example image:


-The unmatched pair is on the left since the edge being paired needs to be rotated
left
-The newly formed dedge will be moved up to the top and moved out of the way to
be replaced by the unmatched dedge.
-Fix the centers with Uu'
Once you do this a few times you might possibly run into your first parity case. This
one isn't too bad, but it occurs when you're down to your final 2 unsolved dedges.

Thankfully, there is a fixed algorithm for this case, but first you need to arrange the
front face so it looks like the image below using the (R' D' L F' L') algorithm from
before if necessary:

example image:
(assuming the edges you can't fully see are red/green and yellow/orange)

Once you get to this stage, do the algorithm Dd R F' U R' F Dd'.
The edges should now be fixed.

Look familiar? The end is near.

IV. Solving the first two layers

Your cube is now a 3x3. Solve the first two layers accordingly.

That was easy

V. Top cross parity

That last step was easy, this one won't be. If you have a dot, L, line, or cross
already, congratulations, you just skipped an extremely annoying step. If you have
3/4 of a line or 3/4 of a cross, uncongratulations, here we go..

This, my friends, is your first true encounter of parity at its finest. If you have 3/4 of
a line, pretend it's an L and try to solve for the cross and you should get something
similar to this:



It's almost a cross on top, but you're last dedge is flipped upside down. How do we
fix it? With none other than a 25 move algorithm!!! WOOOOOOOOT.. no? Well,
just face the cube so the screwed up dedge is facing you and do (takes a deep
breath):
Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2 Rr F2 Ll' B2 Rr2

This is a bad one to screw up, so don't. Your top cross should now be fixed.

Continue solving the cube to completion. Don't worry if you encounter another
parity case in the end. This will happen when you're putting the corners in the
right spots. If they won't all match up no matter how many (U' L' U R U' L U R')s you
do, just do the final (R' D' R D)s and get the correct color to the top and continue
and finish solving. I will cover the parity cases in the next section.

VI. Basic Method permutation parity

-Thanks to cry4eternity to helping me out with this section. It's greatly appreciated.-

Ready for some more 25+ move algorithms? Good, because there's 2 special
parity cases in the basic method.

One:


Two:


If you get case one, do the algorithm:
2Uu 2Ll 2U 2l 2U 2Ll 2Uu F' U' F U F R' 2F U F U F' U' F R
With the two unsolved corners on the top face, facing the front.

If you get case two, do the algorithm:
2Uu 2Ll 2U 2l 2U 2Ll 2Uu R U' L 2U R' U R L' U' L 2U R' U L' U

With one of the corners on the top face on the bottom right, the other on the top face
on the upper left. Alternatively, you can do U R U' L' U R' U' L
to turn it into the adjacent case, so you only have to memorize one insanely long
algorithm.

Your cube should be solved.

Alternate method: (pending 2-look OLL/PLL tutorial next week)

VII. 2-look OLL/PLL permutation parity

The one and only permutation case for this method is short and sweet:



2 edges are swapped, the other 2 are solved. If the two edges are opposite, make
sure one of them is facing you, if they are adjacent, do this from any side (as long
as the top is still the same)

Algorithm: Uu2 Rr2 U2 r2 U2 Rr2 Uu2

If you had the adjacent case, you will need to do an edge rotation algorithm, then..

Your cube should be solved.

Congratulations! You have just solved the 4x4 cube! Have a brownie.



Algorithm quick reference:

Align middle without screwing up the rest:
put what you're aligning in the same column as what you're putting it with and do:

Rr U2 Rr'

Edge pairing:

Uu L' U' L Uu'

Edge in the wrong position:

R' D' L F' L'

Last 2 edges:
Line up so the pairs are in the same row and:

Dd R F' U R' F Dd'

Top Cross parity:

Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2 Rr F2 Ll' B2 Rr2

2-look OLL/PLL parity:

Uu2 Rr2 U2 r2 U2 Rr2 Uu2

Basic parity (diag):
U R U' L' U R' U' L

Basic parity (solve from diag):
2Uu 2Ll 2U 2l 2U 2Ll 2Uu R U' L 2U R' U R L' U' L 2U R' U L' U

Basic Parity (adj):
2Uu 2Ll 2U 2l 2U 2Ll 2Uu F' U' F U F R' 2F U F U F' U' F R