Constraint Solving

[qqwref]

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?

 

[Joker]

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

 

[Erzz]

Are slices and double layer turns allowed?

 

[Joker]

Are slices and double layer turns allowed?

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

 

[iSpinz]

Are slices and double layer turns allowed?

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

 

[Forte]

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

 

[Weston]

Solve without using one of your hands!

 

[Anthony]

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

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? o_O

 

[qqwref]

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).

 

[oprah62]

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

 

[mrCage]

(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

 

[qqwref]

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?

 

[AvGalen]

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

 

[flan]

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

 

[cuBerBruce]

(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

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.

 

[qqwref]

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.

 

[kdawg123]

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.

 

[Weston]

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

or OLLs... hmmm

 

[Toad]

Solve it using only J perm.

No setup moves, no nothing.

Spoiler

(J perm y)*3

 

[Kynit]

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