i'm wondering if there is a 3x3x3 case in which at least one of EP or CP is not correct and which requires more than 2 moves to pair up a corner and an edge. the only ones i could find are correctely permuted.
i'm wondering if there is a 3x3x3 case in which at least one of EP or CP is not correct and which requires more than 2 moves to pair up a corner and an edge. the only ones i could find are correctely permuted.
Well, technically this position has both corners and edges permuted incorrectly. (But if you look at the cube in a mirror, they will seem to be permuted correctly, ignoring centers and ignoring that the corners will appear to be stickered incorrectly with respect to the cube's actual color scheme.)
B2 U2 L2 U2 F2 R2 U2 R2 D' B2 F2 L' R' D2 L' R' U'
Orientation of the top and bottom edges doesn't matter in the above case.
I would guess that less symmetrical such cases also exist.
If EP is correct, then placing a corner anywhere other than its correct position will make it within 2 moves of being paired up with at least one of the three edges that it could be paired up with. Therefore, if EP is correct, CP must also be correct in order to satisfy the given condition.
(It seems strange to me that someone seems to think Speedcubing Help/Questions is a better fit for this topic than Puzzle Theory. Explanation?)