# 3x3 scrambler experiment



## Filipe Teixeira (May 27, 2021)

after some folks confirmed that you can scramble a 3x3 like a megaminx (https://www.speedsolving.com/thread...ory-question-thread.56699/page-8#post-1442214) I tried to make my own scrambler with react

check it out: https://www.filipeteixeira.com.br/scrambler/



Spoiler: how it was made


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## PapaSmurf (May 27, 2021)

That's pretty cool. I doubt it will be used in any large capacity at all (current scrambling is already pretty good), but it's really fun to scramble with that. I wish it was better than what we have atm.


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## Filipe Teixeira (May 27, 2021)

maybe some maths or trial and error can define a better length of the sentences for an optimal scrambling


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## WarriorCatCuber (May 27, 2021)

This is really cool! Not very useful, but still epic!


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## xyzzy (May 28, 2021)

On a completely objective level, this is pretty useless – it doesn't provide the same guarantees of scramble quality that the existing methods do, and it doesn't seem especially ergonomic either.

But still, it seems cool, and it's not like everything we make have to be maximally useful for everything anyway.


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## rokicki (May 28, 2021)

Forget scrambling. Do a regular scramble, then solve a 1x1x3 row on the UL edge (ignoring centers), then try to solve the rest of the way using just r and d. It's pretty challenging . . .


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## Cubing Forever (May 28, 2021)

rokicki said:


> Forget scrambling. Do a regular scramble, then solve a 1x1x3 row on the UL edge (ignoring centers), then try to solve the rest of the way using just r and d. It's pretty challenging . . .


Corner permutation should be solved for that to be possible right?


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## Filipe Teixeira (May 28, 2021)

Cubing Forever said:


> Corner permutation should be solved for that to be possible right?


I understood that no
if you're able to scramble CP/EP/EO/CO with <rdU> then the opposite is true


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## Filipe Teixeira (May 28, 2021)

rokicki said:


> Forget scrambling. Do a regular scramble, then solve a 1x1x3 row on the UL edge (ignoring centers), then try to solve the rest of the way using just r and d. It's pretty challenging . . .


a new method is born
(but I think you should be allowed to throw some U moves here and there...)


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## Cubing Forever (May 28, 2021)

Filipe Teixeira said:


> I understood that no
> if you're able to scramble CP/EP/EO/CO with <rdU> then the opposite is true


Yes but Tomas was talking about <r, d>not<r, d, U>
It's definitely possible to scramble and solve EO, CO, EP and CP using <r, d, U> but not <r2, d2, U> like megaminx


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## Filipe Teixeira (May 28, 2021)

Cubing Forever said:


> Yes but Tomas was talking about <r, d>not<r, d, U>
> It's definitely possible to scramble and solve EO, CO, EP and CP using <r, d, U> but not <r2, d2, U> like megaminx


my scrambler is not just double turns like megaminx


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## rokicki (May 28, 2021)

Oops, you're right; you can't solve everything with just <r,d>; the centers and corners are mutually restricted.

Okay, scramble with just <r,d> and then solve with <r,d> (no U). I think it's pretty challenging!


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## Christopher Mowla (May 28, 2021)

rokicki said:


> Oops, you're right; you can't solve everything with just <r,d>; the centers and corners are mutually restricted.
> 
> Okay, scramble with just <r,d> and then solve with <r,d> (no U). I think it's pretty challenging!


It looks like it's not possible to do a single 3-cycle of corners. (I should have known that!)

But here are sequences I found for all other basic cases (in less than an hour):

2 corner twist:
[d' (d2 r' d2 r d2 r d2 r')3 d, r]

4 corner twist:
[d' (d2 r' d2 r d2 r d2 r')3 d, r2]

Corner 2 2-cycle
(r' d2 r' d2 r d2 r d2)3

2 Edge flip:
[(r d r' d' r' d)3 , (r d2 r d2)3]

Edge 3-cycle
[[(r d2 r d2)3, d2], r]


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## rokicki (May 28, 2021)

Great job! I have an edge 3-cycle in 16 moves, an edge two-flip in 30 moves, a corner two-twist in 28, and a corner double-2-cycle in 24 moves. None of these are necessarily optimal; all are commutators or repeated algorithms. I cheated; I used a computer to generate the algs. Still, quite challenging.


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## Christopher Mowla (May 28, 2021)

rokicki said:


> Great job! I have an edge 3-cycle in 16 moves, an edge two-flip in 30 moves, a corner two-twist in 28, and a corner double-2-cycle in 24 moves. None of these are necessarily optimal; all are commutators or repeated algorithms. I cheated; I used a computer to generate the algs. Still, quite challenging.


I new you were cooking a recipe! My goal was to post first!

I guess this is the analogue to 2-Gen type 5 for the 4x4x4. (Hence my interest!)

P.S.

You couldn't find a shorter solution than 24 moves for the corner 2 2-cycle? (That's what I got too.)


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## rokicki (May 28, 2021)

Indeed, there are no shorter corner pairs of 2-cycles. Indeed, the coset of corner perms that preserve edges, centers, and corner orientations (for one particular corner orientation convention) looks like this:


```
1 0
   4 23
  18 24
  14 25
  14 27
   9 28
```

so quite deep.

Fixing edge orientations *starts* at 28 moves (and there is indeed a 28-move 2-edge flip):


```
1 0
  76 28
  62 29
254 30
198 31
195 32
185 33
  48 34
   5 35
```

Fixing corner orientations is easier:


```
1 0
  84 24
  16 25
  30 26
  20 28
  86 30
   6 31
```

The deepest position I've found overall (so far) is 36 moves but I suspect there's at least a distance-37 position.


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## Christopher Mowla (May 28, 2021)

rokicki said:


> Fixing edge orientations *starts* at 28 moves (and there is indeed a 28-move 2-edge flip):
> 
> .
> .
> ...


Wow, I thought it would be the other way around! Nice analysis! Where is @xyzzy ?


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## Filipe Teixeira (May 28, 2021)

I'm glad my silly experiment led into an interesting new method  
you guys are awesome


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## xyzzy (May 28, 2021)

Christopher Mowla said:


> Where is @xyzzy ?


Busy, but since I was summoned…

@Ben Whitmore generated a bunch of algs for this before. Also, I feel like I saw some activity on ⟨Rw,Uw⟩ solving methods not too long ago, although now that I'm looking for it again, I can't find it.


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## PapaSmurf (May 28, 2021)

xyzzy said:


> Busy, but since I was summoned…
> 
> @Ben Whitmore generated a bunch of algs for this before. Also, I feel like I saw some activity on ⟨Rw,Uw⟩ solving methods not too long ago, although now that I'm looking for it again, I can't find it.


That's because it was on the FTO discord server. Yeah, <rd> is just a transformed <ru>, so it's the same thing. We could reverse engineer this to make a potentially more ergonomic RS scrambler. Something like reduce to <RrUu> to <RU> could work, although I know next to nothing about this kinda thing.


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## GenTheThief (May 28, 2021)

I found a way to solve the cube in the <Rw,Uw> moveset a little over a year ago. Corners can be solved normally, and centers can be solve with a set up move and a wide uperm to cycle them. My main issue was finding a way to solve edges. Eventually I found a really long 3 cycle:

3 wide u-perms and 3 wide back u-perms, twice. It did the equivalent of [R B R', S]. If you do it three times, it flips DR and DF.

It's pretty rough and not efficient, but I'm pretty proud of it regardless.


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## Christopher Mowla (May 29, 2021)

GenTheThief said:


> It's pretty rough and not efficient, but I'm pretty proud of it regardless.


Maybe you should look into bandaged cubes. If you don't want to buy them, you can play with them virtually by using CubeTwister. For example, I removed pieces from the 4x4x4 when finding this algorithm set for the AI cube v2 for someone on twistypuzzles. (Post 1 | Post 2)


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## WarriorCatCuber (May 31, 2021)

xyzzy said:


> Busy, but since I was summoned…
> 
> @Ben Whitmore generated a bunch of algs for this before. Also, I feel like I saw some activity on ⟨Rw,Uw⟩ solving methods not too long ago, although now that I'm looking for it again, I can't find it.


Yeah, I believe that a challenge was posted on the 2-gen example solve game, but that might have been as long as a year ago.


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