elrog
Member
I have come up with a 2x2 method that is probably more of a begginer method. It would take 20 algorithms. This method would take 3 steps with the first being the most complex.
Step 1: partially orient corners and seperate top and bottom corners
Step2: orient corners
Step 3BL
In the first step, you will make sure that none of your top and bottom colored stickers are on the left and right sides. I'll call corners with the top/bottom color on the left and right sides bad, while corners that don't have the top/bottom color on the left/right sides will be good.
To keep a corner in a good position, you may do L, R, U2, F2, D2, and B2 moves, thus, if you do a 90 degree turn of the U, D, F, or B face, you will change the good corners
in that layer to bad and vice-versa. Doing this is much like solving edge permutation on the 3x3. You do have to keep in mind that any corner with the top/bottom colors on the top/bottom will not change to bad if you do a U or D turn, and like-wise with F and B while having the top/bottom color on the front/back sides.
You should also remember that you should always make the right and left sides be the sides with fewer top/bottom colors on them. You will always be able to get no more than 2 top/bottom stickers on the left/right sides. Seperating the top and bottom colors out afterwards is very simple and should be fairly easy to begginers. On average, I'd say step 1 takes about 4-6 moves after some practice getting used to it.
Due to the restrictions already placed on corner orientation, orienting all 8 corners takes only 15 algorithms. I have not created algorithms for these, but they shouldn't be to hard to come up with. If this method seems interesting to anyone I may put the work into generating them. After you do this, you apply a PBL algorithm of which there are 5 of.
For a more advanced version of this method, PBL and orientation could be combined into one step, but this would take a large number of algorithms because it would restrict your ability to AUF creating more PBL cases. Another similar mathod that is more advanced would be to seperate out the top/bottom corners while making sure that they have an "even" permutation in the top and bottom layers. You could then orient all of the corners with 36 algorithms, and finish with PBL. I would be very surprised if this hasn't been thought of before.
If a 3x3 varient of this method were to be made, it would most likely include solving edge orientation before restricting the corner orientation, and solving something else at the same time as PBL.
Step 1: partially orient corners and seperate top and bottom corners
Step2: orient corners
Step 3BL
In the first step, you will make sure that none of your top and bottom colored stickers are on the left and right sides. I'll call corners with the top/bottom color on the left and right sides bad, while corners that don't have the top/bottom color on the left/right sides will be good.
To keep a corner in a good position, you may do L, R, U2, F2, D2, and B2 moves, thus, if you do a 90 degree turn of the U, D, F, or B face, you will change the good corners
in that layer to bad and vice-versa. Doing this is much like solving edge permutation on the 3x3. You do have to keep in mind that any corner with the top/bottom colors on the top/bottom will not change to bad if you do a U or D turn, and like-wise with F and B while having the top/bottom color on the front/back sides.
You should also remember that you should always make the right and left sides be the sides with fewer top/bottom colors on them. You will always be able to get no more than 2 top/bottom stickers on the left/right sides. Seperating the top and bottom colors out afterwards is very simple and should be fairly easy to begginers. On average, I'd say step 1 takes about 4-6 moves after some practice getting used to it.
Due to the restrictions already placed on corner orientation, orienting all 8 corners takes only 15 algorithms. I have not created algorithms for these, but they shouldn't be to hard to come up with. If this method seems interesting to anyone I may put the work into generating them. After you do this, you apply a PBL algorithm of which there are 5 of.
For a more advanced version of this method, PBL and orientation could be combined into one step, but this would take a large number of algorithms because it would restrict your ability to AUF creating more PBL cases. Another similar mathod that is more advanced would be to seperate out the top/bottom corners while making sure that they have an "even" permutation in the top and bottom layers. You could then orient all of the corners with 36 algorithms, and finish with PBL. I would be very surprised if this hasn't been thought of before.
If a 3x3 varient of this method were to be made, it would most likely include solving edge orientation before restricting the corner orientation, and solving something else at the same time as PBL.
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