Re: 3x3 twisty puzzle talk

On 17/10/2024 09:30, Daniel wrote:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
 

On 15/10/2024 02:27, Daniel wrote:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>

On 07/10/2024 03:32, Daniel wrote:

Hey folks -
Just subbed this NG hoping to get advice on 3x3 twisty cube
technique.
Currently, I'm learning Roux technique and strugling on the four
final
edges - the online wiki's seem to be written for a different sort of
reader because I simply don't understand. The online puzzle solvers
don't utilize predefined techniques.
Is this a good NG for this? Any cubers in here?
I tried a big cubing forum, but the people on there aren't friendly.
Thanks,
Daniel
>

>
I have a Rubik's cube (3x3) and I worked out my own way of solving it
back in 1980.  My method is "logical" [to me] rather than
speed-orientated - I'm not interested in all the speed
record/competition stuff!  The advantage (for me) of my method is that
it only has two phases [edges first, then corners], and doesn't
require memorising a big list of seemingly random looking transforms.
(Also my method uses the basic structure of the cube and similar
puzzles, and so with minor adjustments applies to all the cube
variants on the market.)

Well good for you. I never had the mental fortitude to do it on my
own. Took youtube. You did what all the method creators did, you created
your own algorithms and stuck with it. Part of me wishes I stuck with
it, but oh well it's only a puzzle.
The cube came out in nineteen-eighty. I was six years old and didn't
know pf it until the ads started appearing during after-school tv
shows about two years later, when I was eight. I wanted one instantly
and my mom got it for me about a month later. Never got far with it. Set
it down for many years.
>

I've never heard of Roux technique, but I'll give it a go and try to
help if you have any specific questions, hopefully together with a web
link to the method!

Since my original post, I've done much more reading and found out
that I
was misreading the moves. The Roux method is something I'm exploring to
speed my solves because I intend to do some 2025 competitions in my
local area and get on the boards. I'd like to achieve something less
than forty seconds when I get on the board so my scores aren't at the
bottom of the range. The community in my area isn't too heavy on the
children - there are some college students and older who compete, so I
won't feel too out-of-place.
Roux is unique and gaining in popularity due to the decreased
required
moves to solve the puzzle - hence reducing solve times. It entails
solving a 2x3 area on both sides so that the middle slice and the top
layer are unsolved. Solve the top corners. Once this is accompished, you
only have the middle slice and the top edges to solve.
You can't solve with only slice moves until the corners are solved -
and
there are dozens of algorithms developed for each case. But, I only use
one algorithm for the corners - so it isn't necessary.
For me, Roux's magic is the final four on top. It's elementary to
solve
the bottom layer because there's only two remaining squares. I've
standardized my solves with white layer on the bottom.
Right now I'm simply studying them by learning the relationships of
the
moves and how it makes sense. There is logic behind it, erasing the
notion of randomness. If I could learn chemistry in college, I can learn
these algorithms. I'll include a rough ascii drawing of Roux's
distinction below. I apologize for my horrible ascii art in advance:
               +-----+-----+-----+
              /|     |     |     |
             / |     |     |     |  x and y's denote the solved
            /  |     |     |     |  area. They can be any color.
           +   +-----+-----+-----+
          /|  /|     |     |     |   As you can see, the middle
         / | / |  x  |     |  y  |   slice and top layer are
        /  |/  |     |     |     |   the remains of the solution.
       +   + x +-----+-----+-----+   I didn't draw out the other side
      /|  /|  /|     |     |     |   for brevity's sake.
     / | / | / |  x  |     |  y  |
    /  |/  |/  |     |     |     |
   +   + x + x +-----+-----+-----+
   |  /|  /|  /     /     /     /
   | / | / | /  x  /     /  y  /
   |/  |/  |/     /     /     /
   + x + x +-----+-----+-----+
   |  /|  /     /     /     /
   | / | /  x  /     /  y  /
   |/  |/     /     /     /
   + x +-----+-----+-----+
   |  /     /     /     /
   | /  x  /     /  y  /
   |/     /     /     /
   +-----+-----+-----+
>

>
That's great ascii drawing.  I even understand what it's saying
related to your desctiption of the method.  With my solving technique,

 Hey thanks. I thought it was janky. Almost went into the ascii newsgroup
for draawing suggestions.
 

the last 4 corners I would have to solve as two 3-corner transforms,
which means 16 moves minimum but probably more due to pre/post "setup"
moves.  (Coming from a maths background, I would call those
"conjugation" moves.)  So not efficient.  OTOH with 5 corners to solve

 I studied applied mathematics in college but it's been twenty years. In
the cubing world, the terms permutation and orientation are used. Much
of it seems to derive from mathematicians in teh 1980s who utilized
group theory to study the puzzle after it came out. I found old messages
from the early 1980s on a gopher search.

I was introduced to the cube in my (maths) student days by Prof. John Conway, seeing him playing with one during a college evening meal with us to which he had been invited.  Well now you know my "link to fame"! lol.  (..and I hear you asking "John who?" which is ok, but he was known by many outside mathematician circles, due e.g. to his work on "Game of Life" and "Surreal numbers".  So it's possibly you've heard of him.)  Conway of course loved the cube puzzle which was right up his street, what with the group theory angle and all.  It wouldn't surprise me at all to learn he had published something on the maths of the cube.

 

it would still be two 3-corner transforms unless I'm unlucky...  40
seconds for me would be /really/ fast, but I'm a bit rubbish at the
whole physical twisting of the faces.  The first cube I had was the
complete opposite of "slick" - it had a grating feel when twisting,
and over time the internal workings wore away due to friction and it
became looser and looser until you could almost shake it into separate
pieces! :)

 I utilize a very simple algorithm for the top corner pieces that rotates
the right piece closest to you. It takes two uses of the algorithm to
flip it once, two more to flip it the second time, and two more to
restore the original direction. Alot of speed cubers utilize this
algorithm to warm up before a solve.
 R' D' R D x2
 R = Right slice rotated clockwise
R'= Right slice rotated counter-clock
D = (bottom) down slice rotated clockwise
D'= down slice rotated counter-clock
 I posted a demo of the algorithm repeated on the same corner via rumble:
 https://rumble.com/v5j008h-top-layer-solve-demo.html
 So for the last layer, the beginner routine specifies orienting the edge
pieces first. Let's pretend that you have the cross on top already and
need to finish the corner pieces. The beautiful logic is, the algorithm
I provided on top is all you need to finish. And, the algorithm will be
used to solve the puzzle that is divisible by six. There will always be
a minimum of two corners needing solved.
 ... two corners
 https://rumble.com/v5j01dp-two-corners.html
 ... three corners
 https://rumble.com/v5j01jp-three-corners.html
 ... four corners
 https://rumble.com/v5j01p9-four-corners.html
 So I solve the four corners that way, then solve the edge pieces - and
those are the algorithms I'm learning now.

OK, I see what's going on there.  All those examples are where corner pieces are twisted, but in the right location.  I don't have anything special to handle that, and my 8-move corner transforms displace (just) 3 corners.  E.g. :
    RTR' B' RT'R' B
So if two corners were twisted, I would apply the above, leaving 3 corners displaced, then another routine variation of the above to solve.  2x8 moves to solve + 2x(0,1 or 2 conjugation moves). Let's say 18 moves, which same as your video, assuming you realise that doing your transform 4 times is equivalent to doing its inverse twice (8 moves instead of 16).  I.e.
         (R'D'RD)^4              // 16 moves
       = (R'D'RD)'^2             // (inverse of (R'D'RD) transform done twice)
       = (D'R'DR)^2              // only 8 moves
That holds because (R'D'RD)^6 = 1 [1 = identity transform: all faces left unchanged].  (In group theory world we say (D'R'DR) has "order" 6).
Similarly, your 3 corner twist video uses 3x8 moves + conjugates, I would have to apply my 3-corner transform twice: 16 moves + conjugates!   For your 4-corner twist video you use 2 (R'D'RD)^2 transforms and 2 (R'D'RD)^4 transforms : 2x8 + 2x16 moves + conjugates.  As above, you could use less moves by replacing (R'D'RD)^4 with (D'R'DR)^2, which would lead to  4x8 = 32 moves + conjugates.  With my transform I would need 3 8-moves transforms so 24 moves + conjugates!
So on the face of it your approach isn't efficient regarding number of moves, but of course your moves are very quick to apply.  Maybe my moves are slower in practice as they involve 3 faces (R, T, B) rather than just 2 (R, D).  You are very quick twisting in your video!!  My newest cube (probably 20 years old) cannot be twisted in the way you do!  It is WAAAY to stiff, and there's no way I can perform a twist with just one finger - if I push /really hard/ with one finger I can get a twist started, but it will stop some way before completed, and then I'll have to readjust everything losing finger-position to get the cube components adequately lined up.  Alternatively, what I actually have to do in practice is have firm 3-sided pressure with both left and right hands to make every twist - slow slow slow :)
There is also the question of how you do a 3-corner-cycle permutation? (I.e. one like my transform above.)  You must need one of those, and it won't be more efficient than 8 moves, even if you're ignoring the edges, so in theory you might use that to handle corner twists like I do.  One good feature of your approach is that it takes very little thinking - just being aware of which way each corners need to twist and off you go.  My approach does need thought regarding how to conjugate the transforms correctly, which is something I do when I get there (pausing to consider) rather than knowing it in advance.
Mike.