Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.
First Layer
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).
Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.
Last Layer
PLLs
Look at all the unsolved corners, look if 2 corners need to be switched.
- If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use
- If the two corners that need switched are diagonal from each other, then use
OLLs
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| Note That all algorithms are with the Down face as the Last Layer
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