How to solve last five corners efficiently?

[renyhp]

Let's just say I have a generic scramble that scrambles only five corners. They can be permuted and / or oriented badly.

I know that the "sexy method" uses a "buffer" and repetition of the sexy move to solve them, but that uses a lot of moves. Probably you could just write some computer code to generate all the possible cases and all the possible solves, but there would be too many cases and too many algorithms to learn.

Is there any way other than that?
Thanks in advance

 

[Sajwo]

Solve one corner and do CLL or place one corner and do TCLL

 

[Underwatercuber]

Corner commutators would be pretty efficient probably

 

[Oatch]

5 corners should be able to be solved by 2 corner commutators on average. To maximise efficiency, make sure you set up your comms so that you don't end up with a pure corner twists, in particular 3-twists are the worst (since they require 2 commutators to solve). CLL's sound risky because they may not be edge-safe, unless of course you know the corresponding ZBLL that solves just the corners, but as mentioned before, comms are the way to go because you don't have to know any algs and they're all intuitive.

 

[renyhp]

Well sure they are intuitive, but is there any guide or tutorial, or even list? Probably a lot of cases will be dealt with in similar ways, with commutators. If you limit it to only 5 corners, and by the way I'd say 4 of them belong to the same layer, couldn't you make a decently small list of cases or even some steps to deal with in two or three different ways (depending on the situation)?

 

[Oatch]

Well, all you need to know is how to solve a pure commutator and how a corner twist works, and then (depending on how efficient you want to be) just use some form of conjugation to setup other cases to pure commutators. There are tutorials you can find online if you don't already know how to do them - argubly some of the best come from blindsolving 3-style tutorials.

From there, the following cases you might encounter (but not limited to) include:

Spoiler: 5 corner cases

5-cycle: solve with two 3-cycles.
Disjoint 3-cycle and 2 twisted corners: solve separately with 2 commutators.
5 twisted corners: with the 2-twist commutator, pick a 'buffer' piece and solve all the other corners by twisting them pairwise with the buffer, which will take 4 commutators to solve, or if you know it, use a 3 corner-twist (a ZBLL alg) + a 2 corner twist for the remaining corners.
2 Disjoint Corner Swaps + a twisted corner: use two 3-cycles + a corner twist (note that you will need to break into a new cycle to achieve this)

Spoiler: 4 corner cases

General strategy: most cases can be solved with either two 3-cycles, or a 3-cycle and a 2-corner twist
4 twisted corners: perform 2 corner twists
2 Disjoint Corner Swaps: Use two 3-cycles (again, you will have to break into a new cycle)

Spoiler: < 3 corner cases

3-cycle: Easy - a single comm will do the trick
3 twisted corners: the worst 3-corner case. Use either two 3-cycles (one to change permutation of all pieces, the second to permute them with correct orientation) or a 3 corner-twist alg if you know it.
2 twisted corners: Self explanatory: use the two-twist commutator

I thought it'd be a good idea to group cases by type than by a single alg (because there would be heaps of cases!). This should hopefully give you a general strategy of how to go about solving L5C. I feel that the beauty of commutators is that you can come up with your own solutions, which I feel is a much more elegant method than, say, learning a big list of algs. I highly encourage you to explore the cube and see what you can come up with, for that is how you truly expand your understanding of the puzzle! That being said, if there are any particular cases you are having trouble with (e.g. a tricky 3-cycle), I'd be happy to help with that. Good luck!

 

[renyhp]

Thank you very much! I eventually came across these videos which were VERY useful to fully understand all of these concepts I will practise this technique which seems a lot amusing Thanks again!

 

[xyzzy]

5 twisted corners: with the 2-twist commutator, pick a 'buffer' piece and solve all the other corners by twisting them pairwise with the buffer, which will take 4 commutators to solve, or if you know it, use a 3 corner-twist (a ZBLL alg) + a 2 corner twist for the remaining corners.

There are actually only four cases for 5-twist, and the 2-gen algs are really nice and easy to remember:
(R U2 R' U2 R U R' U')2
(U R U' R' U2 R U2 R')2
(R U R' U' R U2 R' U2)2
(U2 R U2 R' U R U' R')2