Rubik

Next, the 1 x 1 x 1 cube.  This cube consists of one six sided cubie with no sliding pieces.  To solve this cube, pick it up and inspect the center color of each side.  If each side is a single color already, which is almost always the case, the cube is already solved, so no algorithm is needed.  If the fewer than six sides are not in the solved position already, someone has tampered with the cube to make it unsolvable.  In that case, the cube must be disassembled and then reassembled with the proper configuarion in order to be solveable.

23

The 2 x 2 x 2 cube provides much more challenge than the 1 x 1 x 1, but is still easier to solve than standard issue and larger cubes.  Because the cube has an even number of tiles on each face, there is no center tile to track which side is which, as there is on odd-sized (1, 3, 5, 7, etc.) cubes. 

    There are many methods to solve the cube, but the trick I use to solve is to break the cube down step by step.  The first step is to solve the bottom layer, then the last step is to solve the top layer.  Solving the bottom layer can be done intuitively, but the last layer will require some memorization of algorithms.

Step 1: Solve the bottom layer

    To solve the bottom layer, first choose a color to make the bottom layer.  It doesn't matter which color you choose, but it is usually easier in the long run if you consistently choose the same color.  I usually choose white, becuase it usually has the logo sticker, and I rather prefer not to have to keep looking at the logo, for some reason.

    After you choose a color to make the bottom layer, align a piece with that color so that the bottom color is on the bottom of the cube.  Inspect that piece for the two other colors that are not the bottom color.  Find one of the other two pieces that also has the bottom color and one of the other two colors of your first piece.  Align that piece so that it is adjacent to the first piece with the bottom colors and the other matching colors facing the same direction as one another.

    Repeat this bottom layer matching process for the other two cubies that contain the bottom color, making certian that if you break up the bottom layer, that you can reconnect everything when you are done with each piece.

    Now you should have a complete bottom layer.  Take a second or two to make certain that the entire bottom face matches all four pieces, and that each side on the bottom layer has two matching colors.  If any of the colors on the bottom layer do not match, you will have to do some rearranging before continuing with this method.

Step 2: The top layer

    The second layer is much more difficult to solve.  Algorithms will be used exclusively in this method, so that the bottom layer can be restored each time it is broken.

    First, find two adjacent cubies that have any color that is not the top color (all of the pieces that remain scrambled will have a side that is the top color now) and align those two with the side that has the bottom layer of the same shared color.  The colors will probably not match facing the correct side, but they should belong to the cubie that goes in that position.

    Inspect those two pieces' other colors compared to the colors on the other two sides, to the left and to the right of the side with matching color.  These two cubies will either match or be switched.  If the two pieces are switched, it means that the color on the left matches the third color of the cubie on the right.  To switch the two pieces, use the following algorithm:

Lu Tr Ld Cw Tl Cc Lu Tl Ld

    Next, check the two cubies on the opposite side and do the same algorithm with that side facing you if and only if the two cubies are in swapped position.

    You are almost done, but the last step is the trickiest one.  You will now have to orient all of the cubies into the correct direction.  The trouble is that it is only possible to orient three at a time, so unless you have all four already oriented or have exactly one cubie oriented, you will have to perform this algorithm more than once.

    Rotate the entire cube so that you have the piece that you do NOT wish to reorient in the upper left corner.  Then perform the following algorithm to rotate the other three corner cubies clockwise:

Ru Tl Rd Tl Ru T2 Rd

    After a few of that algorithm it should be solved.

33

The 3 x 3 x 3 Rubik's Cube is considered the Standard sliding cube puzzle.  The puzzle is much more challenging than the 2 x 2 x 2, and although it can be solved much more quickly than the 4 x 4 x 4 cube, it is not that much easier.

To jump quickly to the beginner solution method, click here.

To jump quickly to the intermediate solution method, click here.

To see a table comparing different methods, including some advanced ones, click here.

The strategy that I use to solve the 3 x 3 x 3 cube is very similar to that of solving the 2 x 2 x 2.

    First, I make a plus sign on the bottom layer (white), by aligning the bottom edges with the bottom color facing down, and the colors matching sides facing out.  This should be easy to do.  If it is too hard, then I suggest taking some time to play around with the cube and pay attention to how the cubies rearrange themselves when you perform variuos twists.

    The second step is to complete the corners of the bottom layer and the edges of the middle layer together.  There is a method to solve these seperately, but it requires memorization of an algorithm that really isn't necessary.  So the basic idea is this: 

    A. Find an edge piece with two colors that are NOT the color of the top layer.

    B. Find the corner piece that has both of those two colors, plus the color of the bottom layer.

    C. Place those two pieces adjacent to one another on the top layer in such a way that the orientation of the colors match.

    D. Place the two pieces together into the correct corner and edge like you would with a 2 x 2 x 2.

    E. Repeat for all of the other edge-corner pairs.

    Now that the bottom and middle layers are done, it's time to tackle the top layer.  There are many different approaches to solving the top layer.  If you hate algorithms, you aren't going to like this part, but you can get by with as few as three algorithms.  If you can think in mirror images, it can cut down on the number of steps tremendously, with certain solutions.  Some advanced speed-solvers use dozens of algorithms to lump different steps together, even to the point of memorizing enough algorithms to solve the top layer in one look.  If you have that much memory, you may wish to devote it to medical science.

    I prefer an intermediate approach.  It won't win me any races, and it won't impress professional cube solvers, but these algorithms will all prove useful with more than one approach to solving.

    Ok, so, the first substep is to align two matching colors with the appropriate face, like you would do with a 2 x 2 x 2.  The next substep is to determine which corners need to swap.  If no corners need to swap, then skip to the next substep, otherwise use these algorithms:

Swap two facing corners:

Lu Tr Ld Cw Tl Cc Lu Tl Ld

Swap all four corners:

Lu Tr Ld Cw T2 Cc Lu Tl Ld

    Why bother to remember both?  Well, it doesn't do any harm, because only one move is different, and it'll save you from repeating the algorithm about a quarter of the time.

    Once the corners are in the correct place, it is time to orient them, just like with the 2 x 2 x 2.  Learning the mirror image algorithm can save you a step about half of the time.

Hold the top left and rotate the other corners counter-clockwise:

Ru Tl Rd Tl Ru T2 Rd

Hole the top right and rotate the other corners clockwise:

Lu Tr Ld Tr Lu T2 Ld

~ There are some modifications to these algorithms that can be handy if you want to cut down on your time.  These are pretty easy to remember, with a little practice, and they can prove handy about 10% of the time, so it's up to you:

Rotate two opposite corners clockwise and the other two counter-clockwise (hold with the top sides facing out):

Ru Tl Rd Tl [Ru Tr Rd Tl] Ru T2 Rd

Rotate the near left corner clockwise and the far right corner counter-clockwise:

Ru Tl Rd Tl [Ru Tr Rd Tl] [Ru Tr Rd Tl] Ru T2 Rd

The other case I know is a different form, so it is harder to remember - use it when you see two top sides adjacent to one another and the others opposite of one another.  Hold the cube to that the adjacent tops both face left, then perform:

Ru T2 R2 Tr R2 Tr R2 T2 Ru

~

    By now, the top edges should be the only thing left unsolved.

    The shortest algorithms for moving the pieces are mirror images (you only need to memorize one, then either use it multiple times, oruse your brain to translate it into a mirror image).  I call these "Simple Left" and "Simple Right," to designate whether the piece that remains in the same orientation goes to the left or to the right.

    If you start here (picture) do (algorithm):

Mu Tl Md T2 Mu Tl Md

or

(Mu Tl Md) T2 (rep)

(mirror)

Mu Tr Md T2 Mu Tr Md

or

(Mu Tr Md) T2 (rep)

    You will also need a minimum of two more algorithms to orient the cubies, but I'll also include a third that is useful about 15% of the time.  I call the first pattern "Arrow," becuase I see an arrow when I look at it,  I call the second shape "I," as it is shaped like the capital letter i, and the third "X."  It is easier to remember the first two by remembering the set of moves: "Ml R2 M2 Rd T2 Ru M2 R2 Mr Ru T2":

Cw Ml R2 M2 Rd T2 Ru M2 R2 Mr Ru T2 Rd Cc (move middle left or right)

or

Cw [common] Rd Cc

Rd Ml R2 M2 Rd T2 Ru M2 R2 Mr Ru T2 (move middle left or right)

or

Rd [common]

Mu T2 Md T2 Mu Tr Md T2 Mu T2 Md Tl

or

((Mu/d,d/u T2)2 Mu/d Tr/l)2

    There are two more types of algorithms that I find useful enough of the time to memorize.  One that permutes without orienting and its mirror image, which is also its inverse, which I call "F left" and "F right," to distinguish the direction of flow of the traversing piece.  The other just seems to pop up more often, but it has seperate mirror image, inverse, and mirrored inverse.  I call these "G-A right," "G-A left," "G-B right," and "G-B left," to distinguish the static side and whether the pattern is normal or inverted.

C2 Tl Mu T2 Md Tl C2

or

(C2 Tl Mu/d T) [backwards]

C2 Tr Mu T2 Md Tr C2

or

(C2 Tr Mu/d T) [backwards]

Md Cc Ld Cw Mu Cc Lu Cw

or

(Md/u Cc Ld/u Cw)2

Md Cw Rd Cc Mu Cw Ru Cc

or

(Md/u Cw Rd/u Cc)2

Cc Ld Cw Md Cc Lu Cw Mu

or

(Cc Ld/u Cw Md/u)2

Cw Rd Cc Md Cw Ru Cc Mu

or

(Cw Rd/u Cc Md/u)2

If none of these algorithms fit the bill, I suggest using Simple Right or Simple Left and then following up with Arrow, I, or X to complete the solution using two steps.

43

    The 4 x 4 x 4 cube is more of a challenge than the 3 x 3 x 3, but the strategy is quite simple, as long as you know how to solve the 3 x 3 x 3 and have some time to reduce the cube by matching face pieces.

    My strategy is to first pair each face piece with another of the same color intuitively, then match the face pairs, carefully remembering the color scheme of the solved cube (if you switch two sides, you'll have troubles later and have to back-track).  Next pair edge pieces with matching colors, which is intuitive at first, but you will need an algorithm for at least the last few pairs, as you will need to not break the pairs you have so far.

    If the two sides are mirror images, use:

br Ru Cc Tl Rd Cw bl

    If not, use:

Lu b2 Ru Cc Tl Rd Cw b2

    Once all of the faces and edges are paired together, solve the cube like a 3 x 3 x 3.  You may end up with two possible issues with the last layer that were not possible on a 3 x 3 x 3.  The first is that instead of three cubies on the edge being swapped, only two are.  The other is called a parity mismatch, and that one is quite a pain to correct.

Swap two edges on the top layer:

r2 T2 r2 T2 t2 r2 t2

Parity issue: