Solve 2x2x2 with two algorithms

[Slowsolving]

I wanted to learn 2x2x2 in a hurry, so I found a system that only needs two algs. With some practice I got this memorized in a day and have solved 2x2 dozens of times. Could not find reference of it on speedsolving, so thought I'd share.

Here are the videos I found:

part one

part two

You can skip fifteen minutes of video and read the algs right here. I'm assuming white for bottom/first layer, yellow for second layer/top.

Step 1:
Solve first layer (intuitive). If you don't know how, watch the first video for tips.

Step 2:
Orient last layer. R U R' U R U2 R'
Cases for yellow pieces on top face:
one= do U until it is in F/L face
two adjacent = do U until they are in B face
two diagonal = do U until they are in F/L and B/R faces
four = Done! go to step three.
You might need to do the alg several times. Evaluate the case and adjust each time.

Step 3:
Permute last layer. R' F R' B2 R F' R' B2 R2
Case= any two matching pieces on top R/L/F/B layers should be rotated by U into B face. If no pieces match, do the alg, you should have two matching, now you can align and repeat.

The vid mentions another alg to PLL. I don't use this one, but here it is.
L' U' R' U L' U2 R U' R' U2 R L2
Case= any two matching pieces on top R/L/F/B layers should be rotated by U into L face. If no pieces match, do the alg, you should have two matching, now you can align and repeat. I don't recall doing this alg more then twice to reach a solve.

Hope that helps you solve your 2x2x2 quickly :}
Thanks to (youtube) Mindstormscreator for sharing.
Thanks to Ubercuber, Cubenovice and Cride5 for many corrections to my first big alg writeup!

Let me know what you think of the method and/or my writeup.

 

[uberCuber]

Cases for yellow pieces on top face:
three = is that possible? If so, probably same as two

No, it's not possible. That would require twisting a single corner, which cannot be done no matter how many moves you use.



As for the method, you can save yourself from using too many repeititons of Sune (RUR'URU2R' is called Sune) by learning to recognize all 7 cases. (i.e., there are two cases where one corner is oriented, there are two cases where two adjacent corners are oriented, and there are two cases where no corners are oriented)

From there, you can make it so you only require a maximum of two repetitions by learning the mirror of that alg. Instead of doing R U R' U R U2 R', you can do R' U' R U' R' U2 R for a certain case that would otherwise require two repeitions of Sune.

 

[Cride5]

There is a way to solve the 2x2 with just one alg: R U R' U'
http://www.speedsolving.com/forum/showthread.php?23176-Solving-the-2x2-with-8355-The-35-Method

If you understand how to permute 3-corners using commutators, then its possible to solve completely intuitively. If you want to learn how, this is a pretty good resource:
http://www.ryanheise.com/cube/corner_3_cycles.html

 

[Slowsolving]

Wow, thanks for the tips, you guys are rock stars.
I will try to get into the methods you mention some day, I'm still pretty new to cubing.

 

[Cubenovice]

Hope that helps you solve your 2x2x2 quickly :} Let me know what you think of the method and/or my writeup.

Hi Slowsolving,
this approch for the 2nd layer on the 2x2x2 is based on a common beginners method for 3x3x3.
But as you do not have edges on a 2x2x2 you only need half of the 3x3x3 steps.

As already mentioned the next step would be learning the Anti-sune case and then all 7 possible cases.
Have a look at Badmephisto's website and youtube channel: beginner method.
You will recognise the steps and could learn all 7 cases from there.
Then if you like you could move onto this LL system for the 3x3x3. (All this is till prep for even more advanced LL stuff).

A small correction on your notation:
Your
Step 2:
Place last layer. R U R' U R U2 R'
is actually orienting of the coners, not placing.
This step is called OLL = Orient Last Layer
In this step you twist the corners to the correct orientation.
The Sune alg rotates three corners clockwise and their relative position is not changed.

Your
Step 3:
Orient last layer.
R' F R' B2 R F' R' B2 R2is actually placing or permuting the corners in the correct relative positions.
This step is called PLL = Permutation of Last Layer.
The alg you are using is the so-called A-perm which is a well-known commutator that cycles three corners within a face. When two corners are in the right relative position the A-perm will result in 4 correct corners (when applied witht he adjecent corners on the B face).

This alg does exaclty the same on the 3x3x3: just a corners cycle.
The "other" OLL alg will also move edges when applied on a 3x3x3.
Note that in speedsolving the A-perm is executed slightly different: a cube rotation is included so the F and B2 moves become U and D2 moves which are easier to execute.

Another note on step 2:
Step 2:
Place last layer. R U R' U R U2 R'
Cases for yellow pieces on top face:
four = just do the alg
With 4 yellow corners on top you don't aply the alg

Finally: once you have mastered the 7 OLL cases you should definately look up the Ortega method for 2x2x2!

 

[Slowsolving]

Thanks again for all the help guys, and noticing my infinite loop during orient :} It's the first time I wrote something like this.