# Constraint Solving



## qqwref (Sep 16, 2010)

It's pretty fun to solve under constraints. What I mean is that you only allow some kinds of moves, or some ways of solving.

Here's one I tried today: Solve with no D face moves (and no rotations of course). Every move must be a 90-degree turn. You must alternate between moves of the U face and moves of some other face.
Solution:


Spoiler



Cross is trivial. F2L can be solved normally with some tricks; do a VH type thing for EO. Use Sune to permute edges, Niklas to permute corners, Sune to orient corners. (Sune variant: R U R' U R U' R' U' (R U R' U')5.)



Got any other interesting ideas?


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## Joker (Sep 16, 2010)

Only 90 degree turns
No F turns/rotations
F2L slots must be solved in this order: Back Left, Front Right, Back Right, Front Left.
G'luck guys


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## Erzz (Sep 16, 2010)

Are slices and double layer turns allowed?


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## Joker (Sep 16, 2010)

Erzz said:


> Are slices and double layer turns allowed?



Lol that would be kind of cheap since it says no rotations


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## iSpinz (Sep 16, 2010)

Erzz said:


> Are slices and double layer turns allowed?



Typically D being restricted would also restrict u/u'/u2 and e/e'/e2.


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## Forte (Sep 16, 2010)

R U scramble/solve, F2L on B is like, impossible >_>


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## Weston (Sep 16, 2010)

Solve without using one of your hands!


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## Anthony (Sep 16, 2010)

Forte said:


> R U scramble/solve, F2L on B is like, impossible >_>





Weston said:


> Solve without using one of your hands!



I have a feeling that Weston's proposal is significantly harder, Forte.
I mean, have you ever even thought of trying to turn the cube one-handed?


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## qqwref (Sep 16, 2010)

Well, you can try solving it without letting it touch your thumbs. Try doing it with one hand if you're extra hardcore.

I'm more interested in puzzle-theoretic limitations though, not physical ones 

Here's an interesting one: do a solve with only 4-move commutators (X Y X' Y' where X and Y are single moves), plus at most one other quarter turn (in case of parity).


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## oprah62 (Sep 16, 2010)

Without thumbs:
http://www.speedsolving.com/forum/showthread.php?t=22793&highlight=without+thumbs


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## mrCage (Sep 16, 2010)

(Scramble) and solve using solely Y commutators.

R F' R' F is a Y commutator. R F R' F' is a Z commutator.

Obviously i mean for the 3x3x3 cube.

Are all even positions reachable by a series of X commutators?? 

PS! I don't allow conjugates of such commutators.

Per


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## qqwref (Sep 16, 2010)

I'm not sure what you mean by X, Y, Z commutators. Does it have something to do with the "shape" of the 3 edges?


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## AvGalen (Sep 16, 2010)

I love (and hate) really constrainted cubes. Especially a 3x3x3 that is inside a 2x2x2 packaging so you cannot see where it is bandaged


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## flan (Sep 16, 2010)

I like to scramble with only U and R then solve OH while only using R and U' because they are the two easiest OH moves. It's only really the OLL and PLL which is hard


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## cuBerBruce (Sep 16, 2010)

mrCage said:


> (Scramble) and solve using solely Y commutators.
> 
> R F' R' F is a Y commutator. R F R' F' is a Z commutator.
> 
> ...





qqwref said:


> I'm not sure what you mean by X, Y, Z commutators. Does it have something to do with the "shape" of the 3 edges?



Y and Z commutators are standard terms that have appeared in various Rubik's cube literature. David Singmaster attributed them (well, the Y commutator, at least) to Roger Penrose in the cube-lovers email archives. Of course, the "Y" and "Z" derive from the shape formed by the non-fixed pieces.

It's my guess that by "X commutator," mrCage meant either a Y or Z commutator.


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## qqwref (Sep 16, 2010)

Ah. I haven't read much (if any) non-online cube literature. And almost all cube books are impossible to find online.

Here's what I think about solving with Y-comms:


Spoiler



Note that each one does a 3-cycle of edges and two 2-cycles of corners. So only positions with an even edge AND corner permutation are possible.

Let's solve edges first, since it's way easier to do a pure effect on corners. Permutation is obvious and you can flip 2 edges by R'FRF' RU'R'U; thus all even edge positions seem possible.

OK, now corners. You can twist 2 adjacent corners by (R'FRF')3 (LU'L'U)3 (R'FRF')3 (B'UBU')3, so all corner twists are possible and we just have to worry about permutation. I can't prove it, but I think that only even numbers of cycles are possible - that is, you can't do a plain 3-cycle of corners. I did manage to get a 4-cycle and a 2-cycle but they were set up so I couldn't eliminate the 2 without changing the 4 into a 2-2.


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## kdawg123 (Sep 16, 2010)

Try to do it Blindfolded, with one foot, in midair, upside down, without memorization! That's a task.
Also in a more serious note try to solve it after putting all the cubies in random positions, and see how far you can get without having to rearrange them.


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## Weston (Sep 16, 2010)

Oh, its kind of fun to solve it using only PLLs with no setups.

or OLLs... hmmm


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## Toad (Sep 16, 2010)

Solve it using only J perm.

No setup moves, no nothing.



Spoiler



(J perm y)*3


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## Kynit (Sep 17, 2010)

randomtoad said:


> Solve it using only J perm.
> 
> No setup moves, no nothing.


Tried it; stuck with 2 corners twisted or an edge 3-cycle, but it was very fun


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## Toad (Sep 17, 2010)

Kynit said:


> randomtoad said:
> 
> 
> > Solve it using only J perm.
> ...



Use the spoiler...


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## Joker (Sep 17, 2010)

Forte said:


> R U scramble/solve, F2L on B is like, impossible >_>



That's easy...
I used that to train OH


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## hawkmp4 (Sep 17, 2010)

One of my favorites is T and U perms with no setups. Makes you really think about it. It goes back to being a puzzle.
Yes, you can do a U turn with T and U perms, but that takes the fun out of it.
Also, try doing a 2 edge flip with only U perms. Again, makes it a puzzle.


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## Stefan (Sep 17, 2010)

Solve it just with the 6 moves Y-perm, b-i-t-c-h-e-s!


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## Weston (Sep 17, 2010)

Joker said:


> Forte said:
> 
> 
> > R U scramble/solve, F2L on B is like, impossible >_>
> ...



You practiced OH with F2L on B?


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## Joker (Sep 17, 2010)

StefanPochmann said:


> Solve it just with the 6 moves Y-perm, b-i-t-c-h-e-s!



I didn't even know there was a 6 move Y Perm...


Weston said:


> Joker said:
> 
> 
> > Forte said:
> ...



Lol, now I know I read it wrong...I thought he meant the BR F2L slot with F2L on D. :fp .


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## oprah62 (Sep 17, 2010)

Joker said:


> StefanPochmann said:
> 
> 
> > Solve it just with the 6 moves Y-perm, b-i-t-c-h-e-s!
> ...



Fail reference...


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## JonnyWhoopes (Sep 17, 2010)

StefanPochmann said:


> Solve it just with the 6 moves Y-perm, b-i-t-c-h-e-s!



Too soon? Naw... I loled.

OT: 180deg turns. Pretty easy, but I get stuck with an edge three-cycle a lot.


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## qqwref (Sep 17, 2010)

Half turns only is pretty fun. Give it a try on 4x4 or 5x5 too.

A slightly more difficult variant (for 3x3) allows any 180-degree turns and any slice turns.

Also, it's always fun to try slice turns only on 4x4 and above  Basically you can turn any slice except the outermost layers.


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## JonnyWhoopes (Sep 17, 2010)

qqwref said:


> Also, it's always fun to try slice turns only on 4x4 and above  Basically you can turn any slice except the outermost layers.



I've tried that one before, quite difficult IIRC. I'll have to dig my ES out again and give it another shot...


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## Edward (Sep 17, 2010)

http://www.youtube.com/watch?v=SKm5dT1SqEM


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## Stefan (Sep 17, 2010)

qqwref said:


> Also, it's always fun to try slice turns only on 4x4 and above  Basically you can turn any slice except the outermost layers.



I just did that with a 5x5. I got edges very quickly, then centers took me maybe 30 minutes. This is indeed fun.


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## TMOY (Sep 18, 2010)

Lol, got 1:25 on 5^3  Edges are trivial, centers are not hard either.


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## qqwref (Sep 18, 2010)

Too easy, eh? Then try it on the Crazy Cube-I. I actually have no clue how to solve this.


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## Cyrus C. (Sep 18, 2010)

Only quarter turn solving?


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