Really tough challenge for 3x3x3

[Robert-Y]

If you did U on a solved cube, would it be possible to solve it using only r, u, and f moves?

 

[byu]

I just tried something much easier, I did a solve with r u R and U. Very easy, I build up a 2x2x3 block intuitively, then solve it like petrus, except I use

r' R U r' R U r' R U2 r R' U r R' U r R' U2

and

r' R U r R' U2 r' R U r R'

to flip edges instead of the normal petrus way.

 

[cheiney]

I have the cross done with one slot finished, but I'm kind of afraid to do anything else without messing up everything I just did. How did you end up solving it in the end? It seems like LL would be near impossible to solve with normal OLL and PLL.

 

[AvGalen]

I have the cross done with one slot finished, but I'm kind of afraid to do anything else without messing up everything I just did. How did you end up solving it in the end? It seems like LL would be near impossible to solve with normal OLL and PLL.

Both Ville and I used Corners, Centers, Edges
The second time I did Corners+Center, Edges
Layer by Layer was never an option for me, but should be possible as well

 

[Johannes91]

If you did U on a solved cube, would it be possible to solve it using only r, u, and f moves?

No.

 

[Robert-Y]

Thanks for that Johannes, could you easily prove why it's not possible please?

 

[ThePizzaGuy92]

i couldn't do it on my first try, I will get it soon

 

[Lucas Garron]

Thanks for that Johannes, could you easily prove why it's not possible please?

Center/corner parity.

 

[AvGalen]

Thanks for that Johannes, could you easily prove why it's not possible please?

Stefan posted a link to that prove, Lucas nicely summarized it. It seems like Stefan, Johannes and I all seemed to think every position was possible, then realised only half are

 

[Robert-Y]

Ok thanks Lucas and Arnaud I'm not good with proving stuff on puzzles, but my interest in it is growing and growing. Maybe it's because I'm hopefully going to do maths at university.

Btw, I think I've found an 8 edge orienter: (r u) * 60

 

[byu]

Nice, Robert!

I was too lazy to do this on my cube, so I used alg.garron.us.
Here is the link I used.

 

[Robert-Y]

Also, here's a 10 edge orienter: (r' u r' u') * 45

Ok I think I might be able to do it, I just need to find out algs to permute edges

 

[Robert-Y]

this does nothing lol: (r u' r' u) * 18

 

[qqwref]

One of my old cube programs does this kind of stuff for me. So I decided to make some random algs.

-(r' u r u')9 does two corner 2-cycles. (Same effect as (R' U R U')3.)
-(r2 u r u r' u' r' u' r' u r')5 does two 3-cycles of centers (U-R-F, D-L-B). (USEFUL!!! Solve centers last!)
-(r u r' u' r' f r f')5 does a corner 3-cycle on U. (Same effect as F R' F' L F R F' L'.)
-(((r2 u2)6 f2)2 r2)2 has the same effect as R2 E2 R2 E2.
-(f2 u' r u' r' u f2 u r u r')3 does a 2-corner swap and a 4-center-cycle. (what?)
-(f2 u' r u' r' u f2 u r u r')3 u (r u' r' u' f2 u' r u r' u f2)3 u' does an H-perm on the corners of U.
-r u r' u' r' f r2 u' r' u' r u r' f' u does a corner-edge pair 3-cycle as I said before.
-(r' f r f' u r u' r')9 does a 10-flip (all but DL, DB), which is quite useful.

So I guess you could go about doing the EDGES first with intuition and the R2E2R2E2 alg and the T-perm alg, and then finish the corners using the 2-2-cycle and frfl cycle, and finally do the centers. I dunno.


EDIT: YEAAAAAAAAAAAAAAAH! I solved it! Woohoo! (My post was 23 minutes ago so I guess that's about how long it took, didn't time it, and I messed up a couple times on the edges stage and had to restart)
I did like I said just above. First I solved edges - I got three cross pieces intuitively and then solved everything else with the T-perm alg; at the end I had two edges flipped so I used the 10-flip twice with appropriate setups. Then I did the corners, using (r' u r u')9 for the D corners and the frfl cycle for the U ones; at the end I had some twisted corners so it took me a LOT of applications of frfl with various setups to untangle that. And finally the centers, I had the 2-2-cycle case but I just applied the centers alg I had a few times to fix that. YEAH! I GOT IT! It's really satisfying to finally see a solved cube after all the long algs and setups, I recommend that anyone who thinks they can solve this thing to give it a go.

 

[Lucas Garron]

Here is the link I used.

http://alg.garron.us/?alg=(r_u)60

Anyhow, qqwref, are we going to see an avg12?

 

[byu]

Ah, thanks Lucas. I was trying to get that to work, but I was trying (r u)*60

 

[AvGalen]

Congrats Michael! Very nicely done. I will try to make up an even harder challenge

 

[Lucas Garron]

Congrats Michael! Very nicely done. I will try to make up an even harder challenge

<l r2 R, U u2 d> on 4x4x4? (lowercase = single slice)

 

[Johannes91]

<l' r R, U u d'> on 4x4x4? (lowercase = single slice)

Isn't that isomorphic to <Rw, Uw> on 3x3x3?

Maybe <l' r R, U u> on 4x4x4 or <l' m' r R, U u e'> on 5x5x5? Scary...

 

[qqwref]

Or try Ol' Ridiculous: <Uw, M> on 5x5. You think (u r) on 3x3 takes a long time to repeat? (Uw M) takes 3080 repetitions.

To be honest, I still have trouble solving <r,U> on 4x4 >_> Guess I just suck huh?

Oh, and can you guys use SiGN please? l' m' r R is ridiculously unweildy, whereas 4r looks nice and pretty.