Constraint Solving

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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:
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?
 
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
 
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).
 
(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 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
 
(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.
 
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:
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.
 
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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