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This solution refers to the original cube. This version is white on top, red, blue, green and orange on the sides and yellow down under. If your cube looks differently, you may have to exchange all occurences of one color with another.
Everybody who has spend some time with the cube should be able to arrange one side correctly. With a little bit extra effort it should also be possible, to get the first ring of stones to match its neighbours as well.
I will assume that you have started with the white side; of course you could start with any other side as well, but then some of the descriptions below will not match the situation of your cube.
So you have done the white side plus the first ring of stones in such a way that
all stones on the first ring match their neighbour's colour.
The white side faces upwards. Turn the middle ring until the center stones match the colours of the top ring. This whould always work.
The middle ring
Now the edge pieces from the second ring are to be arranged. All pieces missing are either on the bottom ring or they are somewhere on the second ring.
A single edge piece is moved from the bottom ring to its final position on the middle ring as follows:
If an edge piece is already in the right position, but flipped, you will first have to place some other element there and then re-insert it the right way round.
After placing all edge pieces in this manner, the first two rings are done.
2. Placing the yellow edge pieces
Turn the cube upside down, so that yellow is on top. We will continue by positioning the yellow edge pieces by switching positions of adjacent pairs:
3. Flipping edge pieces
Usually, some edge pieces will be flipped and have their yellow face on the side of the cube. Hold the cube so that a flipped edge piece is on the right:
Warning: The cube will look a bit chaotic after this sequence, but don't worry about this now!
After flipping one piece like this, only turn the top ring (not the whole cube) until the next piece to be flipped is on the right.
After all edge pieces are flipped, the cube should look normal again. If not ... start over.
Franco Erpf noted on this one:
Under some constellation this won't work:
If two opposing edge pieces are flipped, but the other two are not, this sequence will lead to all four pieces being flipped (right becomes wrong and vice-versa). This will repeat indefinitely.
Use the sequence from step 1 to remove one of the edge pieces. Turn the cube by 90 degrees so that yellow is on the side. Reinsert the removed edge piece from the other side with the appropriate sequence from step 1. After this, you can continue with step 3.
4. Placing the corners
Now we want to position the corners correctly. This sequence was sent to be by Volker Bartels.
If you have one corner that is correctly positioned, you can use ont the following two sequences to rotate the remaining three corners into the correct position (or use the other sequence twice - same thing).
A: Correct corner front left, rotation counter-clockwise:
B: Correct corner front right, rotation clockwise:
If no corner is at the correct position, just use one these twi sequences. After that, one corner should be correct.
5. Flipping the corners
The final step is to flip the corners to bring the yellow side up. Hold the cube such that a corner to be flipped is in the front right position.
A: Yellow is to move from the front to the top:
B: Yellow is to move from the side to the top:
As with flipping the edges, the cube will look confusing before final results. And again, we will only turn the top ring to flip the corner, not the whole cube.
If you want to learn less moves, you can just stick with 5 A and repeat it twice if yellow is on the side.
One final twist of the top ring and you are done!
Rubik's Cube 2x2x2
Besides that I only have the 3x3x3 solution here, but there are more puzzles. Other solutions can be found via the Rubik's Homepage. Habe fun!