Method idea

[nlCuber22]

Steps -
1) Make a cross on any color regardless of the permutation of the edges.
2) Build 3 corner-edge pairs and insert them into their correct slots, similar to what you would do if you were using MGLS.
3) Solve the last slot and use partial edge control if needed. 1 algorithm needed for this step, R' F R F'.
4) Orient the rest of the last layer edges if needed. 2 algorithms needed for this step.
5) Use COLL to permute and orient all last layer corners. 42 algorithms to learn for this step. I recommend Jason Baum's website at jmbaum.110mb.com
6) Permute the remaining edges on the U and D layer with 1 algorithm. 21 algorithms for this step including rotations and mirrors. Working on getting and optimizing algs.

66 algorithms to learn total, a few which are exceptionally easy and you probably already know them.

Example solve -
Scramble - L' R2 F2 R D' U' B L' B D B2 D U' L' F' R' L2 D' L' D' U F' R2 D F2

Spoiler

x2 y'
F' R' F2
U' R' U R U L' U' L
y U2 R U' R' L' U L
R U2 R' y U L' U' L
U' R U' R'
U' R2 D' R U2 R' D R U2 R
U2 R2 U' F2 B2 D B2 R2 U' F2 R2 F2 U'

Discuss.

 

[miniGOINGS]

Umm... why?

 

[nlCuber22]

Umm... why?

Is that all you can come up with?
I want to hear other people's opinions on the method, and just in general things I can do to make it better. (if it is even original)

 

[4Chan]

Interesting and original! (To my knowledge)

How many cases for last 8 edges on U and D are there?


Inb4 "cfop is beter lol"

 

[nlCuber22]

Interesting and original! (To my knowledge)

How many cases for last 8 edges on U and D are there?


Inb4 "cfop is beter lol"

Thank you.

The number of the cases for the last step is something I was hoping someone here could help me find - to be honest I have no idea how to calculate that.

 

[4Chan]

As many cases as Sq-1 edge perms? (I think)

Since sq-1 has those U and D perms for edges.

 

[Cyrus C.]

I like it. I'm pretty sure it's original. To do step 3 you'd have to know ZBF2L to do it algorithmically though. What's the average move count? The last step would use a lot of D moves though, wouldn't it.

@4Chan: Over 50.

 

[miniGOINGS]

Well, you can have parity or not.

If not parity, on U you can have either Ua, Ub, H, Z, or solved. On D you can have Ua, Ub, H, Z, or solved. That is 24 cases (+ solved).
If there is parity, you can have Adj, Opp, Oa, Ob, or K on U and D. That is 25 cases.

Total of 49 without mirrors, inverses, and rotations. So unless I am mistaken, Cola is wrong.

EDIT: Oh and nlCuber, about my original post, I was wondering if you had thougt about it's advantages/disadvantages yet.

 

[Cyrus C.]

Okay, I was including mirrors. Either way, I still like the method, I just think it would be a bit Algorithm heavy, unless you were to do some parts (like a 3 edge cycle incorporating both the U & D faces, & you used set-up moves,) intuitively.

 

[miniGOINGS]

Okay, I was including mirrors. Either way, I still like the method, I just think it would be a bit Algorithm heavy, unless you were to do some parts (like a 3 edge cycle incorporating both the U & D faces, & you used set-up moves,) intuitively.

With mirrors it would be significantly less, I might calculate that now.

 

[Cyrus C.]

Okay, I was including mirrors. Either way, I still like the method, I just think it would be a bit Algorithm heavy, unless you were to do some parts (like a 3 edge cycle incorporating both the U & D faces, & you used set-up moves,) intuitively.

With mirrors it would be significantly less, I might calculate that now.

What? Wouldn't mirrors almost double it?

 

[miniGOINGS]

What? Wouldn't mirrors almost double it?

Nonono, my 49 count is without using mirrors. Meaning that the Ua Perm and Ub Perm are completely different cases. With mirrors they would be the same (well actually, mirrors).

 

[nlCuber22]

Well, you can have parity or not.

If not parity, on U you can have either Ua, Ub, H, Z, or solved. On D you can have Ua, Ub, H, Z, or solved. That is 24 cases (+ solved).
If there is parity, you can have Adj, Opp, Oa, Ob, or K on U and D. That is 25 cases.

Total of 49 without mirrors, inverses, and rotations. So unless I am mistaken, Cola is wrong.

EDIT: Oh and nlCuber, about my original post, I was wondering if you had thougt about it's advantages/disadvantages yet.

Yep, that's what I was thinking (that you couldn't have an irregular case and a regular case on U & D, unlike Square-1)

 

[miniGOINGS]

So far, for the non-parity case, I have 10 non mirror/rotation/solved cases.

 

[miniGOINGS]

Wow.

24 non-parity non-mirror/rotation --> 10 non-parity mirror/rotation
25 parity non-mirror/rotation --> 11 parity mirror/rotation
----------------------------------------------------------------
49 non-mirror/rotation --> 21 mirror/rotation

How's that?

 

[nlCuber22]

Wow.

24 non-parity non-mirror/rotation --> 10 non-parity mirror/rotation
25 parity non-mirror/rotation --> 11 parity mirror/rotation
----------------------------------------------------------------
49 non-mirror/rotation --> 21 mirror/rotation

How's that?

You should feel accomplished.

And I feel like I just did something useful.

So, 40 COLL + 21 PEBL (Permute Edges Both Layers)
= 61 algorithms total+algs for orienting last layer edges which would make 63, 64 if you count R' F R F' for partial edge control.

The 3rd step is probably unnecessary.

 

[miniGOINGS]

Yea, you could probably try and throw ZZ or Petrus into it to give you the EO'd LL, not sure how well that would work though...

Don't forget 2 additional algs for COLL when the corners are already oriented. And some of the 21 algs are extremely easy and well known, such as the U Perm and U2 M2 U2 M2.

Anything else you want? How about my list of COLL's?

 

[Cyrus C.]

Nlcuber, are you actually going to use this, or are you just theorizing?

 

[nlCuber22]

Yea, you could probably try and throw ZZ or Petrus into it to give you the EO'd LL, not sure how well that would work though...

Don't forget 2 additional algs for COLL when the corners are already oriented. And some of the 21 algs are extremely easy and well known, such as the U Perm and U2 M2 U2 M2.

Anything else you want? How about my list of COLL's?

Not sure about that either, maybe someone who uses ZZ or Petrus could help with that.

Okay, so that would make 66 algs, minus things like U2 M2 U2 M2 and R' F R F'.
Also, sure, you can give me your COLL's if you want, however, I'm using Jason Baum's site for the time being.

@Cyrus - Depends. I want to find all of the pros and cons before I make a decision to use it as my main method. I already know several of the algorithms for it from previous knowledge. Even if I don't use it all the time, I will for some cases, such as a 1 move cross (which would only be useful with this method, as in it would be a normal cross for a CFOP solve because the pieces aren't permuted correctly). Plus, knowing COLL is helpful anyway. And what if I made a mistake with my cross while doing a CFOP solve? I could just continue solving because I know this method.

 

[Cyrus C.]

maybe someone who uses ZZ or Petrus could help with that.

How could they help? I use Petrus.