2x2 PLL

[nitrocan]

I am using the ortega method to solve the 2x2, but im having problems seeing the pll. I know all the algoritms, but after i do the first layers orientation, I can't instantly recognize the first layer's situation. Any ideas?

 

[AvGalen]

The first layers's permutation doesn't change when you do the second layers orientation (unless you use very uncommon algs).

That means you can determine the first layers permutation during your inspection. There are only 3 possibilities for the first layers permutation:
0 horizontal bars
1 horizontal bar
4 horizontal bars

 

[nitrocan]

i guess my problem is determining the first layer permutation during inspection ill try that. thanks

 

[tim]

Does anyone know the worst case for the first step for ortega and how many moves are required?

 

[AvGalen]

I guess the worst case for Ortega would be 6 moves (like 8 moves is the worst for the cross on 3x3x3). I don't know for sure. Just like the cross the first step for Ortega is intuitive. I have never seen a list of all possible cases

 

[Swordsman Kirby]

I guess the worst case for Ortega would be 6 moves (like 8 moves is the worst for the cross on 3x3x3). I don't know for sure. Just like the cross the first step for Ortega is intuitive. I have never seen a list of all possible cases

I calculated all the possibilites a month ago or so. If I'm not mistaken, no more than 6 moves is necessary for a single color. What was more surprising is that the average is 3.97 moves.

 

[AvGalen]

Those are not surprising numbers to me. I was expecting 6 and 4 based on my experience. I guess that means my intuitive first layer is pretty optimal.

 

[Kenneth]

Hard to not be optimal when it is 3 turns

But for some of the cases there are 3-4 turn solutions that is not intuitive, situations that takes like 5-7 intuitive turns, those you have to learn an alg for to be optimal.

Example: F U' R' .... do R U F' to scramble
Another one: F R U' R' ... scramle R U R' F'

Arnaud: "The first layers's permutation doesn't change when you do the second layers orientation (unless you use very uncommon algs)."

I always used R U Ra' U' Ra U R' for the pi-case, it changes FDL<->FDR. It's really fast after some practice, try it and you will not change back later

And it is also useful to alter the pemutation of FL when doing OLL, you can solve FL, go from 1 pair to no pairs or if you swap one of the pair-pices to one other you will have 1 pair also after the OLL.

 

[AvGalen]

Those 2 examples weren't a problem. I would solve them optimally IF I would start on that D-face.

I didn't understand the R U Ra' U' Ra U R' alg. For the pi-case I just use FRUR'U'RUR'U'F'. Yours looks faster but I don't know what Ra means. I tried "Right All" meaning a cube rotation like x but that didn't look right.

Influencing the first layer permutation by learning more OLL's seems usefull when you can predict tthe permutation of the second layer and don't like the combination of FL and SL permutations

 

[Swordsman Kirby]

I guess the worst case for Ortega would be 6 moves (like 8 moves is the worst for the cross on 3x3x3). I don't know for sure. Just like the cross the first step for Ortega is intuitive. I have never seen a list of all possible cases

I calculated all the possibilites a month ago or so. If I'm not mistaken, no more than 6 moves is necessary for a single color. What was more surprising is that the average is 3.97 moves.

Turns out I'm wrong! The maximum is 5 moves.

1
6
32
177
491
238

Here's CLL:

1
6
36
205
908
2586
1856
72

 

[AvGalen]

Now that was unexpected. So 4 moves on average, 5 moves maximum and you skip the first step about once every thousand solves.

CLL would mean layer-by-layer approach (leaving only corners last layer to be done?)

 

[Swordsman Kirby]

Now that was unexpected. So 4 moves on average, 5 moves maximum and you skip the first step about once every thousand solves.

CLL would mean layer-by-layer approach (leaving only corners last layer to be done?)

Well, remember this doesn't account for color-neutrality.

Yes, LBL approach with one-look last layer.

Also:

0
1
6
32
187
997
4504
12144
7420
224

Orient+separate.

 

[Kenneth]

Those 2 examples weren't a problem. I would solve them optimally IF I would start on that D-face.

I didn't understand the R U Ra' U' Ra U R' alg. For the pi-case I just use FRUR'U'RUR'U'F'. Yours looks faster but I don't know what Ra means. I tried "Right All" meaning a cube rotation like x but that didn't look right.

Ra = R L is a "antislice" on 3x3x3, 2x2x2 has no slices so Ra U it is the same as R2 F or R2 (x') U but it is faster to do R L U, it's a really simple to do trigger.

Influencing the first layer permutation by learning more OLL's seems usefull when you can predict tthe permutation of the second layer and don't like the combination of FL and SL permutations

Because I know a lot of EG-algs I do that almost every time I do Ortega and got 1 pair in FL, if I can't solve it I go to a perm I lke (1+0 mostly). If FL is solved I go CLL and no pairs I end the FL part by doing Ra U2 Ra' (solves FL permutation) and then CLL.

To play around with manipulations you can always learn this wery short Sune + 1 FL pair:

R D' R2 y L2 D' L

 

[AvGalen]

Those 2 examples weren't a problem. I would solve them optimally IF I would start on that D-face.

I didn't understand the R U Ra' U' Ra U R' alg. For the pi-case I just use FRUR'U'RUR'U'F'. Yours looks faster but I don't know what Ra means. I tried "Right All" meaning a cube rotation like x but that didn't look right.

Ra = R L is a "antislice" on 3x3x3, 2x2x2 has no slices so Ra U it is the same as R2 F or R2 (x') U but it is faster to do R L U, it's a really simple to do trigger.

Influencing the first layer permutation by learning more OLL's seems usefull when you can predict tthe permutation of the second layer and don't like the combination of FL and SL permutations

Because I know a lot of EG-algs I do that almost every time I do Ortega and got 1 pair in FL, if I can't solve it I go to a perm I lke (1+0 mostly). If FL is solved I go CLL and no pairs I end the FL part by doing Ra U2 Ra' (solves FL permutation) and then CLL.

To play around with manipulations you can always learn this wery short Sune + 1 FL pair:

R D' R2 y L2 D' L

So R U Ra' U' Ra U R' is actually R U R' L' U' R L U R'. That is indeed a great alg!

I understand the principle behind manipulations like R D' R2 y L2 D' L, but that is way to advanced for me