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It's pretty easy to learn intuitively.
On Lars Petrus' website there are algorithms for all cases, I don't know of any other list.
There exists a Thread called
How to get faster using the Petrus Method
maybe have a look there if you find something useful.

So, I’m doing my f2l and after solving two pairs in the front right slot and back left slot, I have a situation which I can only solve really inefficiently.

The other two corner pieces are both solved but the front left edge piece is in the back right slot and vice versa.

All I need to do is swap the front left edge piece and back right edge piece. Is there a beautifully efficient way to do this?

edit: I’ve just realised that there are still many situations that may arise depending on the orientation of the edge pieces...

If at least on if those edges is oriented correctly, then you can do a D2 to pair up one or two pairs. Then take it out and insert it properly. Then deal with the other one.

4 cases: none flipped, right flipped, left flipped, both flipped
2 cases per case: with or without any other slots solved

If neither edges are flipped:
Front left and back right slots are unsolved: D' R L U2 R' L' D
Front left or back right slot solved: (R U R') (L U' L') (R U' R') U (L U L')

E: worked out other cases

Back left is flipped
LF/RB slots solved: R L U' R' (F R' F R) L' U' (L U2 L') U' (L U L')

Front right is flipped
LF/RB slots solved: (F R' F R) U' L U (R U2 R') U' L' U (R U' R' )

Both are flipped
LF/RB slots solved: (L R U' L' R') (F Lw' U' Lw2) U L U' M'

I didn't feel like figuring out cases using empty slots.
Also note that I use ZZ, never really deal with flipped edges, and don't know if there are any fancy CFOP tricks that others might know.

Is it worth my time to try and learn zz-ct if I'm sub 15 already? I'd like to be at least sub 15 with another method than CFOP, and I don't particularly like Roux. ZZ seems interesting, and I'd like to learn a subset that few people have become fast with.

Is it worth my time to try and learn zz-ct if I'm sub 15 already? I'd like to be at least sub 15 with another method than CFOP, and I don't particularly like Roux. ZZ seems interesting, and I'd like to learn a subset that few people have become fast with.

Do it. Changing methods doesn't have a speed cap it's about the enjoyment. Seriously learning a new method does give you improvement in your main method. Try ZZ for 200 solves and aks yourself if you had more fun than you currently have with CFOP.
Might reconsider which Variation to learn

Do FB in instpection and trace one center so you just add one r/r' at the end if you need it. On execution try to only recognise edges already in the R Layer so lookahead in not hindered

Hi, it’s me again, 18 second solver, refining my awful olls...

So, olls 53 and 54... seems so little agreement regarding the best algs for these two cases and also whether or not (generally speaking) you should learn them together as mirrors of one another or learn two right handed algs...

Anyone have anything useful, interesting or unusual to contribute (based on their own self-teaching) before I just go with “jperm’s YouTube mirrors”?

Hi, it’s me again, 18 second solver, refining my awful olls...

So, olls 53 and 54... seems so little agreement regarding the best algs for these two cases and also whether or not (generally speaking) you should learn them together as mirrors of one another or learn two right handed algs...

Anyone have anything useful, interesting or unusual to contribute (based on their own self-teaching) before I just go with “jperm’s YouTube mirrors”?

Random tip: for RrMU algs, you can do a front-back reflection and it'll still be RrMU. Even if you want to learn the alg as a mirror, it doesn't mean you have to learn a lefty version. (This also works for RUD and RUL algs, but it doesn't work for RUF algs: RUF algs become RUB if you mirror them front to back.)

I mainly use r U2 R' U' R U R' U' R U' r' and r' U2 R U R' U' R U R' U r for these cases. If you want, you could also learn all the versions of this alg (lefty/righty, inverses, front-back mirrors) to eliminate pre-AUF completely.

Random tip: for RrMU algs, you can do a front-back reflection and it'll still be RrMU. Even if you want to learn the alg as a mirror, it doesn't mean you have to learn a lefty version. (This also works for RUD and RUL algs, but it doesn't work for RUF algs: RUF algs become RUB if you mirror them front to back.)

I mainly use r U2 R' U' R U R' U' R U' r' and r' U2 R U R' U' R U R' U r for these cases. If you want, you could also learn all the versions of this alg (lefty/righty, inverses, front-back mirrors) to eliminate pre-AUF completely.

Thanks a lot, these are the two I was leaning towards. Do you do the U2 with your left hand on both of them?

I am in the process of learning at least two angles for most of the other olls, I was just faffing around with three different algs for these and I thought I better master one angle first of all!

edit: thanks for the front-back reflection tip. Now I notice you and jperm are doing the same oll 54 but for oll 53 he does lefty reflection (probably because he is left handed) whilst you do back reflection.

Although that now sets me wondering why he doesn’t do back reflection of his lefty alg, so that they are both lefty algs!

I made a mistake when following instructions on how to solve the cube. So I entered all the colours into two separate online solvers, and they both told me that it is IMPOSSIBLE to solve. One of the solvers said a 'corner needs to be twisted'. The problem is that I don't know which corner it is. And I don't know how the cube ended up like this cos I haven't twisted any corners - I have only made regular moves.

I definitely entered the colours correctly on the solvers, so that's not the problem.

Can anyone help?
I've attached some photos. Hopefully someone can help me with this!

The most likely scenario is that a corner accidentally twisted mid-turn by catching on something, and you didn't notice. This should be fairly rare on modern cubes, but it's definitely a thing that still happens.

Twist any one of the corners clockwise. That should make it solvable.

So I'm trying to design a new method for 3x3. Which is similar to freefop and roux, and I want to see if there is an M U alg for every pll.. I already know the obvious ones like Z perm, H perm, U perm, but I need the rest too, like T perm and even the G perms. Anyone know any U algs for the other PLLs?

I need some help getting sub 15. I've been practicing look ahead and it has improved but nothing really happened. I'm pretty sure it is because of full OLL which i learnt just last week.
I average 16sec:
cross - 1.5
f2l - 6.5
LL - 7

Should I work on improving my last layer or continue with f2l? And how'd I go about improving my last layer?