Manhattan life

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Common patterns.

[Quote]:http://lar5.com/cube/blox.html

Finally, some examples can be found below.

[Quote]:http://lar5.com/cube/examples.html

Only 12 possible positions remain. 1 of them is the solved case. Here is how to solve the 11 others:

Beginner
8 of the 12 have this position with three permutated edges (or it's mirror image). You have to learn the solution on the left (and its mirror image). For historical reasons, it is called Allan™.

If you get one of the other positions, you can just do Allan™, and you will be in a "single Allan™" position.

(An Allan™ can actually be done using only 2 Sune™, as seen to the right, if you really don't want
to learn many move sequences).

Intermediate
There are only 2 other possible cases. Bert™ to the left happens 2/12 of the time, Arne™ to the right, 1/12.

Learn them by heart. And learn to do them fast. You will always need them!

Advanced
Here are some alternative solutions, that may fit your style better.

World Champion Dan Knights favors this solution to Bert™. It's a little less straightforward, but can be done in just 4 movements. He explains how with a video here.

I think of the first alternative Arne solution as a 'brute force' one. The second is more of a 'finesse' solution. And the third (Thanks to Doug Li) can be done without shifting your grip. All can probably be done faster by many, despite using more turns, depending on your twisting style.

The other thing you can do is to plan ahead and learn many special top layer cases in the earlier steps, so you can avoid this step much more often than 1 time out of 12.

The advanced cubist will instinctively mix up the cube when this step has been completed, thereby forcing himself to start again at step 1.

[Quote]:http://lar5.com/cube/fas7.html

Beginner
So far we have the edges twisted right, and the corners placed right. The next step is twisting the corners right. This can all be done by one simple move sequence seen to the right. I call it Sune™. It twists three corners, leaving one untwisted. It also moves edges, but we don't care about that yet.

Step 6 can always be done with 2 Sunes or less. You do need to learn it to use this method.

To talk about how to use Sune™ we need to define the concept the Sune™'s target. The target of a Sune™ in the example is the yellow sticker. In words, the target is the sticker on the corner opposite the side of the first Sune™ turn that is left untwisted. Or in other words, the first turn of a Sune™ targets the sticker that (a) is on the opposite side from the side of the first turn, and (b) of the two corner stickers there, it targets the one on the side that is turned up.

Once you've understood the target concept, you only have these three rules to keep in mind. If the final layer is red...

* ...with no correct corners, target a red sticker. This leaves one correct corner.
* ...with one correct corner, target like the animation on the top of page.
* ...with two correct corners, target a non red sticker of an incorrectly twisted corner. This leaves one correct corner.

Three corners is an impossible position, and four correct corners is of course the solved position.

Here are examples of zero, one and two correct corners. The target is yellow, or orange when it's both red and a target.

Intermediate
Doing Sune™ backwards and mirror imaged should also be on your repertoire. Which sticker is the target of a backwards Sune™ is left as an excercise for the reader.

Here are the two most useful other move sequences. The first is a double Sune, and the second is a Bruno.

Advanced
You need to learn a lot of move sequences, and you need to learn to recignize them quickly. Most of the time there is a move sequence that solves this step directly, without going to step 7.

There are only 49 possible position here.

[Quote]:http://lar5.com/cube/fas6.html

Now we're at the final layer. Here we do not think as much. We recognise patterns and apply rules.

Common mistake: If the edges are not twisted right here, you have either not done step 3 correctly, or screwed up the edges by breaking the 2x2x3 in step 4.

When starting this step, you should have only one layer remain unsolved, and the edges in it already correctly twisted ("forming a cross"). In this step we will place the top corners correctly, nothing else. That means the red/blue/white corner should be between the red, blue and white centers, but it's red sticker does not have to be facing the red center. The corners normally look pretty unsolved after completing step 5, you have to inspect them to know they're right.

To do this we need a tool that moves the top corners without twisting the top edges. This tool is Niklas™, and you can see it to the right.

In the example, don't worry about how the corners get twisted, just note that the two white cornes swap position. (Turn 8 is just to align the corners to the centers to show clearly how the corners move. Niklas is a 7 turn sequence.)

Beginner
These are the odds:
1/6 of the time, the corners will already be correct. You can go to step 6.
1/6 of the time, two corners diagonally opposed will have switched positions.
4/6 of the time, two adjacent corners will have switched positions.

First we need to find which two corners (if any) that have switched positions. That's easy. Just turn the top layer until two corners are in correct positions. The two others are either correct or need swapping. There are only four positions to check.

Niklas™ will swap the two corners opposite the layer where you make its first move. For the diagonal case, two Niklas™es are needed. You can start with any Niklas™, and that will give you the adjacent case.

You can do this by just looking at the top layer corners, but I find it much easier to turn it so the colors match up with the rest of the cube. You waste a move but gain time.

Intermediate
The fast way to check corners that I use is to find two adjacent corners with the same (non top) color, and move them to the side of that color. If the corners are correct, all 4 will be in place. If adjacent corners are switched, two will be correct, and you can see which ones. If diagonal corners are switched, all four corners will be placed wrong.

Example: Start with the red/blue/white one. Red is the top color, so only blue and white are interesting. Start with blue. Check if any of the adjacent corners have a blue sticker. If so move those corners to the blue side. If not, do the same for white.

Here is a useful move sequence that directly switches two corners diagonally. It is a different (and as good) way of doing Eve.

Note that Niklas™ twists the corners in the same way as Sune™ does, so the same "target" rules apply. A Niklas™ that hits a target starts with the same turn as a Sune™ that hits the same target. About half the time you can avoid one Sune™ this way.

Advanced
For the advanced cuber, the steps 5-7 meld together to one single step of dozens or even hundreds of special cases. To achieve real speed, you need to be able to remember them in a fraction of a second.

[Quote]:http://lar5.com/cube/fas5.html