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I've been experimenting with using Y-permutations to solve the 2x2 cube as described here. I ended up with the cube solved but for a single face where the opposite corners were swapped and disoriented. I managed to solve the cube, but I wonder if there is a shorter algorithm to accomplish this task.

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If you're using Y-perms, then simply rotate a face containing one of the corners 90 degrees, to position them opposite each other. This is called a setup move. Doing so puts the two corners opposite each other, and a Y-perm will then swap the correct corners.

You can then undo that setup move after completing the Y-perm by rotating the face back in place.

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Let the corners you want to swap be on the top left and bottom right of the top layer like this

Execute the algorithm: R U' R' U' F2 U' R U R' D R2 where green is F and red is L

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