Ultimate challenge

[cmhardw]

I will try this challenge, but I must first also do my own surprise challenge (which I haven't had time to finish yet)! Nice idea Per, it sounds difficult, but I am excited to try it!

And yes I will follow the spirit of your challenge, just as I understand the spirit of my challenge as well.

Try looking at the list of stipulations I made for the final variation in my surprise challenge thread, I am curious if these are sufficient to precisely describe what exactly we mean by the "spirit" of this kind of forced turns challenge.

Chris

 

[qqwref]

I tried a harder version of the challenge where you cannot put a U or D face turn between consecutive U's. I could only get halfway though.

Spoiler

x [to make the F turns be U turns ]
L2 U B2 U R' U F2 U R U R U B' U B2 U [block]
F' U L U F U B U B' U L' U F U R2 U R U R2 U F' U [opposite block, finish cross]

Hope this works. Can anyone continue from here?


EDIT: I have a proof that we can ALWAYS create a solution, without any U or D turns except for the U turn that happens every other turn.
Consider a sequence such as "R U". This sequence has some order x; so (R U)^(x-1) will be equivalent to the sequence U' R'. (I'll call this sequence (R U)'.) Thus, the sequence (for instance) F U (R U)' has the effect F R'. We can actually construct any 2-qtm sequence (not counting the D face) using the following sequences and their obvious variants:
- We can create F2 by (F U)(F' U)' and U2 by (F2 U)'(F2)(F2 U)'(F2), so we can reverse any turn.
- F R' = (F U)(R U)', F B' = (F U)(B U)', F U is obvious, U' F' = (F U)'.
If the solution is not of even qtm, just add (F2 U)'(F2) for a U move or (F U)(F2 U)'(F2) for an F move.
So just think of any solution, then write each 2-qtm part (and the extra 1-qtm part if there is one) as above.

 

[Stefan]

You probably mean substring, not subsequence.

Is it ok if i call it a subsequence of turns?

That doesn't change anything, as that sounds just like what we meant already (don't know what else we could mean). I suspect you misunderstand the two terms and their difference. To make it clear: If you forbid identity subsequences, then you forbid RUR' because it contains RR'.

- We can create F2 by (F U)(F' U)'

I think you're just hiding your identity parts, not avoiding them, so this seems invalid.

 

[mrCage]

You probably mean substring, not subsequence.

Is it ok if i call it a subsequence of turns?

That doesn't change anything, as that sounds just like what we meant already (don't know what else we could mean). I suspect you misunderstand the two terms and their difference. To make it clear: If you forbid identity subsequences, then you forbid RUR' because it contains RR'.

- We can create F2 by (F U)(F' U)'

I think you're just hiding your identity parts, not avoiding them, so this seems invalid.

So then it's forbidden by two reasons, so what??!!

Per

 

[qqwref]

- We can create F2 by (F U)(F' U)'

I think you're just hiding your identity parts, not avoiding them, so this seems invalid.

If there's an identity, couldn't we just remove it? I can't think of any way this procedure would create an identity that isn't of the form <move> U <move> U ... <move> U.

 

[Stefan]

If there's an identity, couldn't we just remove it? I can't think of any way this procedure would create an identity that isn't of the form <move> U <move> U ... <move> U.

You said: F R' = (F U)(R U)'
Remove the U U' identity and you get F R'.

 

[TMOY]

Which U U' identity ? (R U)' is here R U repeated 104 times, not U' R'.