# 2 gen corner permutation



## Lykos (Jul 19, 2016)

Hello,

I heard doing corner permutation with 2-gen algorithms on 2x2 is impossible. When I try it out, it seems intuitively impossible to permute corners of the top layer while preserving the bottom layer using 2-gen algs. But I still don't really see why. The fact that edge orientation with a 2 gen alg is impossible is easy to understand, but for corner permutation, I don't really get it yet. Can anyone explain me? Is there any invariant that is preserved by every turn and that stops the corners from being permuted or something like that?


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## guysensei1 (Jul 19, 2016)

On a 2x2, perform (R U)*7 R

You've permuted 2 corners


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## shadowslice e (Jul 19, 2016)

This page is pretty good
Essentially, there are three groups you can have for 6 corners which are reachable using {R, U} generators within each group but only 1 group contains the solved state. The Briggs method has a method of transforming each to the Solvable group but is not exactly easy to recognise quickly.
The solvable group only has one other CP case in it: Adj/Opp


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