Random Cubing Discussion

[guysensei1]

Is it possible to get to all regular 5x5 positions using only 4x4 style scrambles (no Bw, Lw or Dw), similarly can you get to all regular 7x7 states without using 3B, 3L and 3D?

 

[Matt11111]

Today's wtf monent: I was hand-scrambling a 3x3 while not really paying attention to the cube. When I stopped and looked down, the last move I was making brought the cube back to solved. I knew hand scrambles were bad, but ... what?!?

You just pulled a RedKB.

 

[Berkmann18]

Is it possible to get to all regular 5x5 positions using only 4x4 style scrambles (no Bw, Lw or Dw), similarly can you get to all regular 7x7 states without using 3B, 3L and 3D?

No as some of them does require those moves.

 

[Berd]

Lol wow! the closest i've had is a corner skip.

I remember that

 

[not_kevin]

No as some of them does require those moves.

I was thinking about this, actually... I think it's possible. I haven't fleshed out the proof, but here's some intuition:

If we can show that we can move the corners, edges, wings, and centers however we want (independent of the other pieces, that is), then that should be enough. Corners and edges are given, since there isn't any restriction on <F,B,L,R,U,D>. Wings can be shown to be given because it's definitely possible to solve wings relative to their midges without <Bw,Lw,Dw> - just do beginners-style 3-cycles over and over, flipping edges around using rotations and R U R' F R' F' R.

The final thing I want to prove is centers - intuitively, we can use a heavily-modified version of U2 to always push the targets to a place that the U2 alg is in our set (eg, the location Fru, which we can do by f' u f U2 f u' f' - so, moving a piece like Bdl could be done with B2 u2 [Fru alg] u2 B2). Not super sure how to handle niklas-like cases yet, but it shouldn't be hard.

Obviously, it's not gonna be move-efficient, and a random-move 4x4 scrambler won't have a reasonable distribution of 5x5 states, but that's not the question at hand Remember that you can reach all 3x3 states without ever doing a D move! You can just do L R F2 B2 U L R F2 B2 every time you would normally get one

 

[Cale S]

Is it possible to get to all regular 5x5 positions using only 4x4 style scrambles (no Bw, Lw or Dw), similarly can you get to all regular 7x7 states without using 3B, 3L and 3D?

Yes

Spoiler: replace all Lw moves with this

L U2 B2 F2 D2 Rw' R D2 F2 B2 U2 B2 F2 R2 Rw2 D Rw R' U R2 U' R Rw' U R2 U' D' Rw2 R2 D Rw R' U R2 U' R Rw' U R2 U' D' Rw2 R2 D Rw R' U R2 U' R Rw' U R2 U' D' Rw2 R2 B2 F2

and replace Dw and Bw with variations of that

 

[Berkmann18]

I was thinking about this, actually... I think it's possible. I haven't fleshed out the proof, but here's some intuition:

If we can show that we can move the corners, edges, wings, and centers however we want (independent of the other pieces, that is), then that should be enough. Corners and edges are given, since there isn't any restriction on <F,B,L,R,U,D>. Wings can be shown to be given because it's definitely possible to solve wings relative to their midges without <Bw,Lw,Dw> - just do beginners-style 3-cycles over and over, flipping edges around using rotations and R U R' F R' F' R.

The final thing I want to prove is centers - intuitively, we can use a heavily-modified version of U2 to always push the targets to a place that the U2 alg is in our set (eg, the location Fru, which we can do by f' u f U2 f u' f' - so, moving a piece like Bdl could be done with B2 u2 [Fru alg] u2 B2). Not super sure how to handle niklas-like cases yet, but it shouldn't be hard.

Obviously, it's not gonna be move-efficient, and a random-move 4x4 scrambler won't have a reasonable distribution of 5x5 states, but that's not the question at hand Remember that you can reach all 3x3 states without ever doing a D move! You can just do L R F2 B2 U L R F2 B2 every time you would normally get one

Good point.


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[qqwref]

Yes

Spoiler: replace all Lw moves with this

L U2 B2 F2 D2 Rw' R D2 F2 B2 U2 B2 F2 R2 Rw2 D Rw R' U R2 U' R Rw' U R2 U' D' Rw2 R2 D Rw R' U R2 U' R Rw' U R2 U' D' Rw2 R2 D Rw R' U R2 U' R Rw' U R2 U' D' Rw2 R2 B2 F2

and replace Dw and Bw with variations of that

More efficient version (22 htm):
U2 B2 F2 D2 Rw' D2 B2 F2 U D' L2 U' D' Rw U D L2 U' D' Rw' U2 D2

 

[Username]

Today is 10 years since Anssi's first feet WR's (and the start of his long dominance) and his 3x3 Avg WR.

 

[qqwref]

More efficient version (22 htm):
U2 B2 F2 D2 Rw' D2 B2 F2 U D' L2 U' D' Rw U D L2 U' D' Rw' U2 D2

Even shorter (17 htm) and with only one Rw:
U2 B2 F2 U D' L2 U' D' Rw' D U L2 D U' F2 B2 U2

 

[guysensei1]

Defining solved to mean having a piece in the correct location but not necessarily in the right orientation, given a random state scramble, what are the probabilities of having n solved pieces for n=1 to 20?

 

[shadowslice e]

Defining solved to mean having a piece in the correct location but not necessarily in the right orientation, given a random state scramble, what are the probabilities of having n solved pieces for n=1 to 20?

I'm guessing centres are fixed?

Because if not N</=1

But seriously would full dots (all 6) be 20 or 0 in your thinking?

 

[guysensei1]

I'm guessing centres are fixed?

Because if not N</=1

But seriously would full dots (all 6) be 20 or 0 in your thinking?

Solved with respect to centers.
dots is 2 because the 2 corners are twisted but still in the same position.

 

[CornerCutter]

Hi there,

When your scrambling your cube from like cubetimer.com, does it really matter if you scramble it exactly how the alg says how to do it? If I did a U instead of a U' in the scramble it wouldn't really matter, it is still scrambled well.

Just a fun thought.

 

[Torch]

Hi there,

When your scrambling your cube from like cubetimer.com, does it really matter if you scramble it exactly how the alg says how to do it? If I did a U instead of a U' in the scramble it wouldn't really matter, it is still scrambled well.

Just a fun thought.

Yes, it does matter. Scrambles are generated to produce a specific random state of the cube, so changing one move will generate a completely different cube state.

 

[willtri4]

Hi there,

When your scrambling your cube from like cubetimer.com, does it really matter if you scramble it exactly how the alg says how to do it? If I did a U instead of a U' in the scramble it wouldn't really matter, it is still scrambled well.

Just a fun thought.

It's not a big deal if you misscramble. You should try to scramble correctly, but it's not like you'll get a scramble that's much more or less difficult. Also, the scrambles on cubetimer.com are not random state (i.e. they're bad), try cstimer.net

 

[FastCubeMaster]

I was hand scrambling a few solves, and then one solve I did, as I started F2L, I realised it was the EXACT SAME scramble as the one I did right before that solve.
As I finished the solve it was same OLL and same PLL and everything.

I scramble pretty fast and I'm sure it's more moves than a scramble from CStimer, so I was surprised!

 

[Isaac Lai]

I was hand scrambling a few solves, and then one solve I did, as I started F2L, I realised it was the EXACT SAME scramble as the one I did right before that solve.
As I finished the solve it was same OLL and same PLL and everything.

I scramble pretty fast and I'm sure it's more moves than a scramble from CStimer, so I was surprised!

It's pretty commonplace.

 

[Cale S]

I was hand scrambling a few solves, and then one solve I did, as I started F2L, I realised it was the EXACT SAME scramble as the one I did right before that solve.
As I finished the solve it was same OLL and same PLL and everything.

I scramble pretty fast and I'm sure it's more moves than a scramble from CStimer, so I was surprised!

I've had this happen to me like 6 times in a row with some skewb handscrambles

 

[Teoidus]

I was hand scrambling a few solves, and then one solve I did, as I started F2L, I realised it was the EXACT SAME scramble as the one I did right before that solve.
As I finished the solve it was same OLL and same PLL and everything.

I scramble pretty fast and I'm sure it's more moves than a scramble from CStimer, so I was surprised!

I only use generated scrambles for this exact reason--I'm too paranoid of my hands now