Kamis, 25 Februari 2010

Step 1

The goal in this step is to build a 2x2x2 block. Or more precisely, to place one corner and its three neighboring edges in their correct positions, solving 4 out of the 20 cube pieces.
Beginner
For the beginner it is often easiest to pick a corner that you will always start with. This makes it easy to find the pieces you need. We will use the blue-yellow-orange corner. This means that the three edges are the blue-orange, the orange-yellow, and the blue-yellow.
First find the 4 pieces you need, and then try to build the 2x2x2. It's not really hard, but it can take a while if you're a rookie. It's best to try yourself for a while, to get a feel for it, but if it still doesn't work out, look at the description below.

There are many special cases, but this is the basic way I solve it. Remember, we're trying to join up 1 corner, 3 edges and 3 centers.

1. Pair up the corner with an edge.
2. Pair up another edge with a center.
3. Join the pairs from 1 & 2 to make a 2x2x1 block.
4. Join the remaining edge with the 2 remaining centers.
5. Put it all together in the final move.

This animation shows a concrete example

1. Pair corner with blue-orange edge. [Turn 1]
2. Pair up orange-yellow edge with orange center. [Turn 2]
3. Join. [Turn 3-4]
4. Blue-yellow edge fitted between blue and yellow center.[Turn 5-7]
5. All done! [Turn 8]

Intermediate
After you can easily do one corner, you should start looking at all 8 corners and choosing to start with the one that is fastest to solve. Normally, one or two are real easy (and some are hard). Picking the easy one makes quite a difference. It can be a difficult transition to use different colors all the time, but it is worth it. After a while you'll be completely used to it.

At competitions, there is normally a 15 second period where you get to look at the cube before timing starts. This is what you do during that time (though 2-5 seconds are usually enough).
Advanced:
Try to be aware of where the four pieces are at all times. You should be able to visualise the full step solution in your mind before starting.

Spend a lot of time looking at this step, and you will start seeing 5 moves ahead or more surprisingly often.

Here are my solutions for 4 random cube positions. When you can choose between 8 corners you should get 1-2 less moves on average

Step 2

After step 1, we have a solved part of the cube, and we have three sides that we can move freely, without breaking what we have accomplished. Not bad!

In step 2 we expand what we have to a 2x2x3 block. That is, we add one corner and two edges to the solved block, going from 4 to 7 solved pieces of 20.
Beginner
Choose one of the three possible corners to expand to. We will use the green-yellow-orange corner, and of course the yellow-green and green-orange edges.

This is quite similar to how you work in step 1, join the corner with one of the edges and work from there. When you're familiar with step 1 you should have no problem.

But be sure not to break up the 2x2x2 block! You need to be aware where it is at all times. Otherwise it's back to step 1...
Intermediate
You have three corners to choose from. It's important to pick the easiest, just like in step 1.

The hardest positions are when a piece is in it's right position, but twisted the wrong way. The easiest way to deal with that is to just pick another corner to solve!
Advanced

These simple and very useful moves (to the right) took me months to figure out (actually I didn't, someone I taught showed me...), since it involves breaking the holy 2x2x2 block. As an exercise, try to find how to do the the third example cube above in 7 moves instead of 9 by breaking the 2x2x2. It's not easy, so here is a hint: First move: turn green layer 1/4 clock wise. Second move breaks the 2x2x2 (highlight to show hint)

Sometimes, the first move of step 3 will be the opposite of the last move in this phase. So with some foresight you can skip both. Also, while doing the last turn of step 2, you can often stop half way, and fix a pair of bad edges midway. See the examples page for several examples of this.

For more advanced techniques, check out the block building page.

Step 3

The basic idea of the method is to solve the entire cube from here by just turning the 2 free sides. But if you try to do that, you soon discover that some edges are always twisted the wrong way. We call those the "bad" edges. We need to fix that before we move on. Step 3 is this fix.

Step 3 can seem incomprehensible before you "get" it, but it is really the simplest step in the method.
Beginner
If you don't like the beginner instructions, take a look at the intermediate ones. You may like that approach more.

Basically, we need to do 2 things in step 3.

1. Identify the bad edges.
There are 7 edges not part of the 2x2x3. Pick any one of them, say the red/blue one. Using only the 2 free layers (that is, not breaking up the 2x2x3), place it between the red and blue center pieces. If it's twisted right, it's good. Otherwise it's bad. That's all. Make a (mental or on paper) note of it, and check the next edge. When checking the second and later edges, do not try to keep the previous edges in place. It is not only extremely difficult, but also completely unnecessary. Once you know if an edge is good or bad, you know.

2. Turn bad edges into good edges.
There are always an even number of bad edges. You can make them good in pairs. The simplest way is the 3 move sequence shown to the right. Just place two bad edges in the positions of the colored edges, and do it. Check that your edges actually became good the first times, to be sure you're doing it right.

Continue until you're sure all edges are good.
Intermediate
Since we only want to know if an edge would be correctly twisted if it was placed in its correct location, we don't have to waste moves actually moving it there.

It is easy to see which edges are bad without moving them. Let's call the colors of the two remaining centers A and B (red and white in the illustrations). Ignore everything except the stickers on the (unsolved) edges with color A or B. There are the four simple rules to remember: 1. An edge with an A color sticker next to the A color center is good.
2. An edge with an A color sticker away from the A color center is bad.
3. An edge with a B color sticker next to the A color center is bad.
4. An edge with a B color sticker away from the A color center is good.

Rule 1
red next to red
is good
Rule 2
red away from red
is bad
Rule 3
white next to red
is bad
Rule 4
white away from red
is good

The usual advice applies in step 3 as well: Look ahead, and try to make a good beginnin

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