step 5 can be done as 2 gen- use the algs for square one.
Steps 4&5, while they can be combined, cannot always be done using CLL (although CLL is a subset of the set required) as it requires the orientation and permutation of 6 corners rather than the 4 that CLL deals with.
If you only have an adgecent swap on top or a diagonal swap, it needs to be 3 gen.
 
So recently I've been playing around with columns first methods and came up with this method. Its similar to PCMS; the other columns first method I came across but different in how the columns are formed.
~snip~

Using this method I managed to get a 34 second ao12 with no specific practise using the method (I am 29sec ao50 using roux- my main method. It is also faster than what I can do with any other method- including CFOP, petrus, ZZ and heise.) I would say that the method could easily be even better as I used no specialised algs- only square one corner permutation and COLL were used.
 
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step 5 can be done as 2 gen- use the algs for square one (barring two cases which are still only three gwn so are still quite fast)
The probability of them being solved with 2-gen is 1/6. Saying it's "only two cases" is true to an extent, but those two cases are far more likely than the 2-gen case.
Steps 4&5, while they can be combined, cannot always be done using CLL (although CLL is a subset of the set required) as it requires the orientation and permutation of 6 corners rather than the 4 that CLL deals with.
Looks like I misunderstood steps 4 and 5 to only mean LL corners. However I think solving pairs for step 3 could make this method faster since it would allow you to quickly solve steps 4 and 5 in one alg.
 
Looks like I misunderstood steps 4 and 5 to only mean LL corners. However I think solving pairs for step 3 could make this method faster since it would allow you to quickly solve steps 4 and 5 in one alg.
Good suggestion. It does seem to be more efficient. I guess I just used the R edges because I'm not an F2L user really.

But then, this essentially turns petrus into roux with L5E as opposed to LSE...
 
I've recently started thinking about making a last slot method, and here are my ideas so far.

1) SITS (Skipping in the Snow - play on words for Winter Variation and LL skip): Skip the LL entirely if there is a 1x2x2 LL block, all edges are oriented, and the last F2L pair can be inserted using R U' R'.
2) RU'R'LS: Skips LL entirely if the R U' R' WV case occurs.
3) COPLS (Corner Orientation Permutation Last Slot): Basically CxLL, but performed from the last slot when the last F2L pair can be inserted using R U' R'. Can be used to replace COLL, CLL, or CMLL.
4) SuperEJF2L: Forces an EPLL case from after EJF2L case is set up.

I'm thinking that either COPLS or Super EJF2L is the most practical and usable, but I'd like to hear what you guys think.
 
I've recently started thinking about making a last slot method, and here are my ideas so far.

1) SITS (Skipping in the Snow - play on words for Winter Variation and LL skip): Skip the LL entirely if there is a 1x2x2 LL block, all edges are oriented, and the last F2L pair can be inserted using R U' R'.
2) RU'R'LS: Skips LL entirely if the R U' R' WV case occurs.
3) COPLS (Corner Orientation Permutation Last Slot): Basically CxLL, but performed from the last slot when the last F2L pair can be inserted using R U' R'. Can be used to replace COLL, CLL, or CMLL.
4) SuperEJF2L: Forces an EPLL case from after EJF2L case is set up.

I'm thinking that either COPLS or Super EJF2L is the most practical and usable, but I'd like to hear what you guys think.

the first idea sounds an awful lot like the tripod method but I would be interested to explore the other ideas! :-)
 
the first idea sounds an awful lot like the tripod method but I would be interested to explore the other ideas! :-)

Yeah, I was thinking of calling it something Tripod-related like "Snow-Covered Camera" or something like that but SITS was a better acronym. The main reason I included the 1x2x2 block was to decrease the amount of cases needed to learn and to improve recognition.
 
Step 1) solve the e-slice
Step 2) correct and corner parity (1 in 2 chance)
Step 3) orient all corners- I usually do this by orienting four corners first then bringing them to the bottom and then using roux algs for the top layer. This step can probably be made more efficient by using an alg that does a sune on the top and a sune on the bottom and then repeating
Step 4) bring corners to the correct layers- intuitive
Step 5) permute all corners (can be done using the algs on square one)

This sounds similar to solving a cuboid, but I'm not sure.
 
It just occurred to me that L5E would be a great way to finish off Petrus. The steps are as follows:
1) Build a 2x2x2 block
2) Extend to 2x2x3 block
3) Place fr and br edges (this is the orientation I use for Petrus)
4) Orient corners
5) Permute corners
6) y (because I don't want to use s moves in a speedsolve)
7) L5E

All steps from 3-5 are 2-gen.
Step 7 can be treated as 2-gen as well using only U and M moves.

This method can also be used in conjunction with Yau and and the fourth cross edge can essentially not be a required step for Yau and can be done along with the other edges.

Or, you could do EO, and skip a step for the L5E.
 
I've recently started thinking about making a last slot method, and here are my ideas so far.

1) SITS (Skipping in the Snow - play on words for Winter Variation and LL skip): Skip the LL entirely if there is a 1x2x2 LL block, all edges are oriented, and the last F2L pair can be inserted using R U' R'.
2) RU'R'LS: Skips LL entirely if the R U' R' WV case occurs.
3) COPLS (Corner Orientation Permutation Last Slot): Basically CxLL, but performed from the last slot when the last F2L pair can be inserted using R U' R'. Can be used to replace COLL, CLL, or CMLL.
4) SuperEJF2L: Forces an EPLL case from after EJF2L case is set up.

I'm thinking that either COPLS or Super EJF2L is the most practical and usable, but I'd like to hear what you guys think.

Rob Yau proposed COPLS a while back, I think the conclusion was that recognition was too nasty, though I suppose with sufficiently good lookahead, it could be done.

Super EJF2L, on the other hand, sounds pretty interesting. How many algs would it have?
 
Rob Yau proposed COPLS a while back, I think the conclusion was that recognition was too nasty, though I suppose with sufficiently good lookahead, it could be done.

Super EJF2L, on the other hand, sounds pretty interesting. How many algs would it have?

Yeah, I thought that someone would have proposed COPLS before me.

I think Super EJF2L would be 96 algorithms (16 EJF2L cases, 6 possible corner permutations). But that's a bit much...
 
So, I came up with a method for 2x2, and is very similar to the tripod method for 3x3.

Step one: Layer-1

Step 2: Corner in BLU

Step 3. Choose from one of 42 algs to solve the cube. These would all be 3 gen [R,U,F], and would be fairly efficient.
 
I have a question. I've "created" (not sure if the idea has been thought of before) a "new" (not sure if you could call it that) method (extension) for 2x2 called Twisty Ortega, or TO. It basically enhances the first step of Ortega to make it extremely quick and easy at the small expense of a few extra algorithms for the second step. Also, it suggests learning more PBL algorithms to reduce cube rotations and AUFs. Here's the basic idea:

Solve a side with one corner permitted to be disoriented. This step rarely takes more than 3 moves, making lookahead to the second step very quick and easy.
In one of 23 algorithms, orient all corners on the cube (7 OLLs + 14 algs for OLLs with a twisted first side corner). This step is called TOLL, or Twisty OLL. All of these are <R,U> 2-gen
In one of 14 algorithms, solve the rest of the puzzle. This step is called PBL/P2L, or I sometimes call it EPBL for "Enhanced Permutation of Both Layers."

I have learned all of the algorithms and have this method in complete, active use. I use this method for all solves and even used it at the Peach State 2015 competition and got a sub-5 Round 1 average (https://www.youtube.com/watch?v=L-yluXWOL30) and ended up in the top 10 (I think) for that first round. I globally average around 4.6-4.7 with this method. I also like this method because it provides a much wider array of options on how to solve the first side. I'll often work out multiple ways to solve a side to try to find a nice, fingertrickeable (that's a new word, I guess) 1st step with an easy 2nd step. I was wondering, since this method is fully developed and in use, if I should create a separate thread for this. Here are some example solves on alg.cubing.net

Example solve #1
Example solve #2

If you want more example solves, please tell me.
 
Stupid 2X2 idea that might not be possible, but oh well.

Make a 1x1x2 block on the left

Make the cube so that you can solve the rest using only U, U', U2, and R2

Wouldn't that be Sortega?

I have a question. I've "created" (not sure if the idea has been thought of before) a "new" (not sure if you could call it that) method (extension) for 2x2 called Twisty Ortega, or TO. It basically enhances the first step of Ortega to make it extremely quick and easy at the small expense of a few extra algorithms for the second step. Also, it suggests learning more PBL algorithms to reduce cube rotations and AUFs. Here's the basic idea:

Solve a side with one corner permitted to be disoriented. This step rarely takes more than 3 moves, making lookahead to the second step very quick and easy.
In one of 23 algorithms, orient all corners on the cube (7 OLLs + 14 algs for OLLs with a twisted first side corner). This step is called TOLL, or Twisty OLL. All of these are <R,U> 2-gen
In one of 14 algorithms, solve the rest of the puzzle. This step is called PBL/P2L, or I sometimes call it EPBL for "Enhanced Permutation of Both Layers."

I have learned all of the algorithms and have this method in complete, active use. I use this method for all solves and even used it at the Peach State 2015 competition and got a sub-5 Round 1 average (https://www.youtube.com/watch?v=L-yluXWOL30) and ended up in the top 10 (I think) for that first round. I globally average around 4.6-4.7 with this method. I also like this method because it provides a much wider array of options on how to solve the first side. I'll often work out multiple ways to solve a side to try to find a nice, fingertrickeable (that's a new word, I guess) 1st step with an easy 2nd step. I was wondering, since this method is fully developed and in use, if I should create a separate thread for this. Here are some example solves on alg.cubing.net

Example solve #1
Example solve #2

If you want more example solves, please tell me.

Do you have algs for TOLL/EPBL? I'd be interested in learning this method, either for fun or as a main method. This seems extremely interesting and easy to use, so I'm willing to learn it.
 
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Do you have algs for TOLL/EPBL? I'd be interested in learning this method, either for fun or as a main method. This seems extremely interesting and easy to use, so I'm willing to learn it.

I actually learned a different set of TOLL algs that include <R, U, F> 3-gen algorithms, and those are what's posted on my Google Sites page. I'll finish generating the <R, U> algorithms and link later today (Monday). It's quite a fun method to use. Plus, a lot of algorithms are super-easy to learn (one is a double sexy, another is a double sledgehammer, etc.)

Also, I've been thinking about a way to do the 2x2 method you were talking about. Could it be like ZZ for 2x2, but with CPBar instead of EOLine? I would definitely learn this. CPBar would be a butt to master, though. EDIT: Would this be an example solve?
 
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