I haven’t spent much time at all on 2x2s. I actually think they’re fun puzzles, but just never really got that into them. I basically got a VCube 2×2 a month after getting into cubing, landed a 27second onvideo solve on my first try, got a 16second solve a few days later, and then shelved it.
When Crazybadcuber posted his excellent 2×2 tutorial (embedded below) the other day, I decided to order a better 2×2 (a WitTwo Type C v1) and try again. The last time I played with a 2×2, I treated it as a 3×3 with no edges. Which, of course, is right. But applying 3×3 algorithms is not very efficient. For example, I used to treat this 2×2 case like this 3×3 case . Of course, the 3×3 algorithm will work. But it takes 12 QTM moves with a couple D layer moves (which I find hard on a 2×2). By contrast, the 2×2specific an alternate 3×3 algorithm takes only 6 QTM moves — and is crazy easy: an F turn to setup, a Sexy Move, and a F’ to finish. EDIT: The key is that these three are equivalent: . Once you ignore edges, there are multiple 3×3 OLL cases to choose from for each 2×2 OLL case. The video tutorial below is fantastic. It is clear, wellproduced, and contains TOC/jump links to navigate to whichever portion you want. Watching it made me realize that 2x2s are all about OLL. (By contrast, 3x3s are all about F2L.) Fortunately, there are far fewer 2×2 OLLs (only 7) than 3×3 OLLs (57) — and many are familiar 3×3 algorithms (such as Sune and AntiSune). A chart with all seven is below. If you can learn these, 2×2 will be a snap — leaving only an intuitive first layer and 2 PLLs (T Perm and Y Perm).
SETUP  ALGORITHM  3×3 ANALOGUES  
better  worse  
R2 U2 R U2 R2  2×2 variant of OLL 21  
F (R U R’ U’) (R U R’ U’) F’  OLL 48 
OLL 22 

(R U R’ U’) (R U2 R’)  OLL 27 (Sune) 

(R U2 R’ U’) (R U’ R’)  OLL 26 (AntiSune) 

F (R U R’ U’) F’  OLL 45 
OLL 23 

(R U R’ U’) (R’ F R F’)  OLL 33  OLL 24 

F (R U’) (R’ U’ R U) (R’ F’)  OLL 37 
OLL 25 
And here is the video tutorial: http://youtu.be/_HAwD4gyTA