3x3 PBL Theoretical Method (3BL) (CFOP Variant)

[Duncan Kimmett]

Nvmnd. It has something that cube explorer offers that it doesn't. I'm working with 4x4 parity algs, and since cube explorer has a painting feature, it is very easy to implement them. This does not do that.

 

[Imsoosm]

ur signature says 3x3 Qiyi MS

didn't u have a gan 12?

I did, but I liked the Qiyi MS over the gan 12 lol

 

[CornerTwisted]

Well at least it's fewer cases than 5-style

I can't get over this.

 

[Jorian Meeuse]

Also there are 109 non-Parity cases ( including PLL ) and 110 Parity cases. 219 in total.

How did you get those numbers?

Btw good point, you did include the pll skip on top which I didn't, but I feel like you also included H and O cases
Including the pll skip on top but not H and O cases it would give
6 x 22 = 132 cases excluding normal PLL
That is actually a big con of this method, you never get a PLL skip lol

 

[Duncan Kimmett]

Just finished the Adj. cross edges cases, all 22.

 

[Duncan Kimmett]

How did you get those numbers?

Btw good point, you did include the pll skip on top which I didn't, but I feel like you also included H and O cases
Including the pll skip on top but not H and O cases it would give
6 x 22 = 132 cases excluding normal PLL
That is actually a big con of this method, you never get a PLL skip lol

Oh that is a massive con. I think it could be worth it since almost all algs where you would have had PLL skip are extremely easy

 

[Duncan Kimmett]

How did you get those numbers?

Btw good point, you did include the pll skip on top which I didn't, but I feel like you also included H and O cases
Including the pll skip on top but not H and O cases it would give
6 x 22 = 132 cases excluding normal PLL
That is actually a big con of this method, you never get a PLL skip lol

Also PLL skip is just f2 then your U perm and f2 (f2 (Ub/Ua perm) f2), and then Z perm is just double rotate.

 

[Duncan Kimmett]

Just finished the Opp. Cross edges cases!

 

[Duncan Kimmett]

How did you get those numbers?

Btw good point, you did include the pll skip on top which I didn't, but I feel like you also included H and O cases
Including the pll skip on top but not H and O cases it would give
6 x 22 = 132 cases excluding normal PLL
That is actually a big con of this method, you never get a PLL skip lol

Are you considering that there is no such thing as PLL skip on Adj., Opp., W,

 

[Jorian Meeuse]

Are you considering that there is no such thing as PLL skip on Adj., Opp., W,

Wdym? Of course there isn't

 

[Duncan Kimmett]

Wdym? Of course there isn't

Sorry, I got confuzzled, I guess it was because I wrote this at 10 pm. I do not understand what I was thinking.

 

[Silky]

How did you get those numbers?

Btw good point, you did include the pll skip on top which I didn't, but I feel like you also included H and O cases
Including the pll skip on top but not H and O cases it would give
6 x 22 = 132 cases excluding normal PLL
That is actually a big con of this method, you never get a PLL skip lol

Just plugged it into Batch, lol. But your breakdown is correct:

21 PLLs x 4 EPLLs = 84
PLL = 21
EPLL on D = 4
22 Parity PLLs x 5 Parity EPLLs = 110
Total : 219

So 219 - 22 -22 -21 -21 = 133 excluding PLL, H, Oa, Ob.
Edit: -1 for H + PLL Skip. 132 Total.

 

[Duncan Kimmett]

So It is 133 Algs instead of 129 Algs?

 

[Silky]

So It is 133 Algs instead of 129 Algs?

I gave the entire breakdown above. You tell me, idk what you are or are not generating.

 

[Jorian Meeuse]

Just plugged it into Batch, lol. But your breakdown is correct:

21 PLLs x 4 EPLLs = 84
PLL = 21
EPLL on D = 4
22 Parity PLLs x 5 Parity EPLLs = 110
Total : 219

So 219 - 22 -22 -21 -21 = 133 excluding PLL, H, Oa, Ob.
Edit: -1 for H + PLL Skip. 132 Total.

2 mistakes here: for the O cases, you should also subtract 22. This makes for a final 131. But then, at the start, you said PLL = 21, and you proceed to subtract 22 for PLL at the end, making the total of 131 1 short. The actual number is 132. Just 6 x 22.

 

[hyn]

U can reduce the EPLL on D cases to just Solved, Z and one of the Uperms using just D moves
Adj and W can D or D' to either Uperm, Opp is a D or D' away from a Z perm, and the Os have been accounted for
So it'll just be 63+2 = 65
D or D' just does 3 edge swaps so parity on bottom is easily avoidable

 

[Silky]

2 mistakes here: for the O cases, you should also subtract 22. This makes for a final 131. But then, at the start, you said PLL = 21, and you proceed to subtract 22 for PLL at the end, making the total of 131 1 short. The actual number is 132. Just 6 x 22.

I didn't list the cases in order. All the numbers are correct tho.

U can reduce the EPLL on D cases to just Solved, Z and one of the Uperms using just D moves
Adj and W can D or D' to either Uperm, Opp is a D or D' away from a Z perm, and the Os have been accounted for
So it'll just be 63+2 = 65
D or D' just does 3 edge swaps so parity on bottom is easily avoidable

Can you show an example of this? This doesn't sound right to me.

 

[hyn]

Just swap DF and DR, then do a D

 

[Duncan Kimmett]

I gave the entire breakdown above. You tell me, idk what you are or are not generating.

I am not gonna generate the algs for u perm cross or z perm cross because I think you could probably just rotate twice for z perm and for U perm: f2 (Ub perm) f2, or f2 (UA perm) f2.

 

[Duncan Kimmett]

U can reduce the EPLL on D cases to just Solved, Z and one of the Uperms using just D moves
Adj and W can D or D' to either Uperm, Opp is a D or D' away from a Z perm, and the Os have been accounted for
So it'll just be 63+2 = 65
D or D' just does 3 edge swaps so parity on bottom is easily avoidable

I thought of that, but one of the best pros is the x-cross ability, and having to align a piece makes x-crosses harder. Idk, I think that I should include that as a thing to mention in the doc to let people know if they ever want to learn algs, only 65 are really NEEDED. Your opinion?