Hey, I now have gotten EO down pretty well, but I’m having trouble doing CO intuitively for some reason. Could you help? GJ on the pb btw!

Edit from future: TL;DR Setup to one of the 3 move insert cases or the single move case

Thanks! One super basic yet still optimal way of doing CO is to literally try every possible sequence of moves of increasing length.

Now this way is obviously inefficient time-wise, and only works if you want your solution to be 2-gen RU, so here’s kind of what I do:

Reduce it to one of the 3-move cases, R U R’, R U’ R’, R U2 R’. Just memorize these 3 cases and know how they can look. I can’t really explain it but you kinda just do it....

Here’s an example on 2x2-

Scr: R2 F2 R F R' F U2 F R U

I see red/orange is bad because it’s the L OLL case which takes 5 moves (z’ y F’ L’ U2 L F) so I notice white/yellow, the pattern looks just like the R U2 R’ case, so, I do R U2 R’ and that’s my CO.

A note about CO is that for he final move, it doesn’t matter if you do R or R’, so find which one influences Phase 2 better.

So for that 2x2 example, R U2 R does it as well as R U2 R’.

On 2x2, almost every time I do one of the 3-move cases if I do CO, so I’m pretty used to them.

Because they’re only 3 moves, you can easily find an optimal CO solution doing this, and in fact, basically all CO cases to a 3-move case and maybe cancel an R move or something.

R2 U2 R’ is just R to setup to R U2 R’ then cancel R’s to get R2 U2 R’

A simple sune (do R’ U’ R U’ R’ U2 R to setup this example) is just R2, now it’s a 3-move case, so you do U’ R U’ R’, so your CO solution for Sune is R2 U’ R U’ R’

But for 3x3, 2-gen CO just doesn’t work out, because during Phase 1 you may have EO and E edges solved so everything will break your E-layer edges.

So a trick is to make a “commutator”(not really) by doing stuff like R U’ L’ F2 L U R’ and now you’ve just made an alg that flips 2 corners and preserves EO and E Edges. R U D’ R2 U’ D R’ is another I just made up right now in 10 seconds.

Also, if you only have corners to twist in Phase 1, you can freely do any Half-Turns to change the unsolved corners positions but not affect EO or E Edges.

Hope this helped!

I know Kociemba is the best FMC method because the speedsolving logo is in G1. Lol

Lol yep it is, it’s also in a Half-Turn-Only state too.

One day I should FMC the speedsolving logo xD I’m pretty sure I can tell the entire state, because if it’s in HTO state then I don’t think you can have just 3 adj. sides solved but the other part not solved, so I’m gonna give it a shot sometime lolz