• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 35,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

Random Cubing Discussion

Joined
Jul 23, 2008
Messages
496
Likes
1
Location
California, USA
WCA
2008YOUN02
YouTube
notkevin888
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 :p 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 :)
 
Joined
Jan 18, 2014
Messages
2,397
Likes
885
Location
Iowa, USA
WCA
2014SCHO02
YouTube
mathtornado7
Joined
Dec 24, 2014
Messages
243
Likes
1
Location
London, United Kingdom
WCA
2014BERK02
YouTube
Maximilian Berkmann
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 :p 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.


Sent from my iPod touch using Tapatalk
 
Joined
Nov 24, 2013
Messages
5,134
Likes
481
Location
singapore
WCA
2014WENW01
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?
 
Joined
Jun 16, 2015
Messages
2,873
Likes
800
Location
Hampshire, England
YouTube
Shadowslice
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 :p

But seriously would full dots (all 6) be 20 or 0 in your thinking?
 
Joined
Aug 6, 2013
Messages
1,441
Likes
580
Location
Austell, GA, USA
WCA
2014GOSL01
YouTube
channel/UC9uTb1qyRStw1KjP832V_Tw
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.:D
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.
 
Joined
Feb 9, 2015
Messages
428
Likes
83
Location
Asheville, NC
WCA
2015BELO03
YouTube
Will Belote
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.:D
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
 
Joined
Jun 30, 2015
Messages
1,324
Likes
558
Location
Brisbane, Australia
WCA
2015PEAR02
YouTube
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!
 
Joined
Dec 21, 2014
Messages
1,331
Likes
65
Location
Singapore
WCA
2015LAII01
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.
 
Joined
Jan 18, 2014
Messages
2,397
Likes
885
Location
Iowa, USA
WCA
2014SCHO02
YouTube
mathtornado7
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
 
Top