Combining separation with PBL

[Zarxrax]

I've been thinking recently about combining the separation and PBL steps of the guimond method. But I have to wonder why someone hasn't already done this? I would imagine the number of algs to be fewer than the OFOTA method. And sure, recognition might be a bit difficult, but I think cubers with good lookahead would be able to see the full solution during inspection. Movecount for the solve would probably be around 14 moves total.

Does anyone know how to count the number of algs this would need? I believe that since some PBLs can be done from multiple angles, that would decrease the number of algs needed, right?

 

[deadalnix]

You'll 2 520 cases. Or 1260 if you allow to flip the puzzle upside down.

Probably less using symetries and so on, but it's huge anyway.

 

[Zarxrax]

Holy crap, that many??!
Can you explain how you calculated it? Because I'm always trying to calculate these sorts of things.

 

[Stini]

Basically you have only solved the orientation of each piece. You have left 8! = 40320 permutations. Top and bottom layers can be adjusted though, so the total number of cases would be then 8!/(4*4) = 2520. Then you can reduce this number to half by flipping the cube. Some of the position are the symmetrical though, so this number is just an approximation.

 

[Stini]

Another way of thinking would be that you can always solve at least one of the pieces by rotating the cube (let's say DFL). Then you have 7! = 5040 permutations left, but you can only adjust the top layer, so total number of cases is 7!/4 = 1260, which is the same as stated above.

 

[DavidWoner]

I've learned the obvious ones, like U' R2 U R2 U' R2 etc or just doing U2 y R2 U' R2 instead of R2 U R2. Forcing layer minus one corner isn't that hard, and that would greatly reduce the number of cases. I still don't think using it as a full method is practical btw.

Also I remember Justin mentioning that Bence Barat has done some work developing this method.