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While solving with CFOP, I have the following situation. The bottom side is solved. On the front face, I have the left-center and right-center pieces swapped. How can I swap these pieces? I know that this will affect the top face.

I realize by swapping them, they can face either direction, since an edge piece can be oriented 2 ways. Therefore, I could use 3 separate algorithms. (One for same front face switch position, one for left front to become the right front while the right front gets flipped to the left, and one where the right front becomes the left front while the left front gets flipped when moved to the right).

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    $\begingroup$ How about posting some pictures of your cube? $\endgroup$
    – Anonymous
    Jan 4, 2021 at 14:51
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    $\begingroup$ I'm not sure if I understand your description correctly. But one way, to swap the two edge pieces that are sitting right and left next to the front-facing center would be: F2 U2 F2 U2 F2. $\endgroup$
    – npkllr
    Jan 4, 2021 at 15:26
  • $\begingroup$ That's it! Thanks! I should have know this, since I do this on a solved cube. What if one, or both, of those edges were reversed? $\endgroup$
    – user6603680
    Jan 4, 2021 at 22:54

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The standard F2L pair algorithms cover all cases, but if you want intuitive rather than fast solution then actually you should not solve layer by layer. As someone commented, F2 U2 F2 U2 F2 works if the edges in question are oriented suitably. However, it is clearly troublesome otherwise. Since it seems that you are not looking for just memory work (otherwise you should just memorize all the F2L pair algorithms), I recommend you instead solve F2L as follows:

  1. Solve the cross on the bottom layer.
  2. Solve only 3 corners on the bottom layer.
  3. Use the unsolved bottom corner to facilitate solving 3 of the middle layer edges. You see, you can rotate the bottom layer to align that unsolved corner with any middle layer edge position and then easily chuck the edge piece in (because you do not care about messing up the unsolved corner).
  4. Solve the last corner-edge pair in any way you want.

If you want to further understand the cube and not rely on any memorized algorithms at all, you should take a look at this post on solving general permutation puzzles, which includes a section on the 3×3×3 cube. In particular, instead of solving F2L completely, one can solve F2L minus one pair and then fix the parity before solving the last 5 edges and then the last 5 corners as described in the linked post.

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  • $\begingroup$ As an aside, this is one of the main techniques used in (beginner) Fewest Moves Challenge, which is almost entirely intuitive. $\endgroup$
    – magnesium
    Jun 5, 2022 at 6:33
  • $\begingroup$ @magnesium: Hang on, which technique? The linked post? I'm of course aware that commutators are one of the main techniques, but I would not believe that the entire method in the linked post is, since it was developed almost entirely by myself and would certainly be idiosyncratic. =) $\endgroup$
    – user21820
    Jun 5, 2022 at 10:27
  • $\begingroup$ Sorry, specifically it was the part about F2L-1 (f2l minus 1 pair). Normally you get to that stage just by building blocks, not by solving the cross, but the idea is the same. Then use a combination of intuition and commutators to solve the last 5 edges and 5 corners. $\endgroup$
    – magnesium
    Jun 5, 2022 at 12:34
  • $\begingroup$ @magnesium: Ah yes I suspected you meant that, and yes indeed (long time ago) when I want to get a few-moves solution I do that kind of block building! And then try to find commutators that cancel some moves. =) $\endgroup$
    – user21820
    Jun 5, 2022 at 12:35
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Whenever I have a middle layer edge piece reversed in place OR in the wrong position altogether, I lift it up to top layer with R Ui Ri Ui Fi U F. It has to be on the right side of the front face at the start.

To get it back in the correct position, start by aligning it with the correct side by rotating the top (U). Turn the cube so that that side with the aligned piece is the Front. Then see whether you need to go to the right or left. If you need to go right, first do a U, then same that you just did: R Ui Ri Ui Fi U F.

If you need to go left, first do a Ui, and then do the mirror: Li U L U F Ui Fi

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