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. But with more things to turn, there needs to be some more notation. The new notation is quite simple. When both layers need to be turned like the image to the left, the format CAPITALlowercase is used, so if an algorithm requires turning both the outer-most layer and the middle one accompanying it (the right face for example), it would say "Rr". If only the inner layer needs to be turned, the algorithm notation will be just the lower-case letter. The denotation of the layer highlighted in the image to the right is "r". Some might say that there are no centers on this cube. This is untrue, though. By definition, a center piece is just a cubelet with one color. There are four centers of each color on this cube, but only when these four are combined together is the "center" formed. Likewise for edges, there aren't any unique edges like there were on the 3x3 cube. Instead there are two of each type of edge on the 4x4 cube. When paired together, it forms a double edge or dedge. Dedges will be explained in greater detail in section III.
Remember how I said there were 4 centers for each color? Well, the first step in solving the 4x4 cube is to pair these up on all sides. At first, I sugges you try messing around with the cube first and try to accomplish this step on your own as it is very intuitive. I won't completely abandon you on this step though since it is fairly challenging to finish without help. Since there is no fixed center piece, 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 by 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. 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 already know this, solve the 3x3 more.]) To create centers, you must first create 2 pairs of 2 center pieces. You can simply join these two pairs up to form the 2x2 center if it won't conflict with the other centers. If it will, line up the pairs as shown in the image to the right and do the algorithm Rr U2 Rr'. A variation on the previous strategy is when you have an L shape and a dot. Simply align the dot so that it will replace one of the lines on the L and do the same algorithm as above.Use these strategies to solve all six centers on the cube.
Note: All the outer faces of the cube may be turned freely during this step without disrupting any 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 outer faces any way you choose to get them both on the same face and make that face the front. To the left, you will see both of the possible cases you can get when you get both edges on the same face. The left-most case is the correct case and what you need to proceed. If you run into the second case, do the algorithm R' D' L F' L' and you should get the first case. The 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 (this is important). If there are no unsolved dedges on the top face, remember that you may freely turn any outer face on the cube to find one.Once you have the scenario depicted, do the algorithm Uu L' U' L Uu'. Since this is an intuitive algorithm, I'll explain what each move does:
Do this for as many edges as possible. More often than not, you will get down to one last pair of dedges (two unsolved on the same face). The procedure for solving these is different than before. Instead of lining up the edge pairs on different layers like before, arrange it with the R' D' L F' L' to get them on the same layer like in the image shown to the left. Once you have done this, use the algorithm Dd R F' U R' F Dd'The edges should now be fixed.
Look familiar? You are now holding in your hands a glorified 3x3 cube and may solve the first two layers accordingly. Don't know how? Use my 3x3 cube tutorial.
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 is our first parity case. 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 the image to the left. It's almost a cross on top, but your last dedge is flipped upside down! How do we fix it? With none other than a twenty-five move algorithm!!! Put the flipped dedge on the front and do the algorithm *deep breath*: Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2 Rr F2 Ll' B2 Rr2 Oh, and this is a bad one to screw up, so don't. Your top cross shoul now be fixed. Continue solving the cube to completion. It is possible to encounter one more parity case and it will occur when you're trying to get your corners in the correct spots before doing your final (R' D' R D)s. If this is the case, just do the (R' D' R D)s anyway and get the top face to be the same color.
Just two algorithms for this one, not much for a description. Here are your algorithms: Leftmost: case 1 Other: case 2 Case 1 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. Case 2 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. Congratulations! Your cube is now solved.