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 Post subject: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Jul 28, 2012 4:08 am 
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Official Okamoto & Haseda Quarter Cube from Japan (Latch cube II)

Puzzle size and weight
Size : 57x57x57 mm
Weight : 110 g
Packaging : small clear box

Designed by Katsuhiko Okamoto and Takafumi Haseda
Produced by Chronos Co.Ltd., Tokyo Japan
(c)2011 Katsuhiko Okamoto and Takafumi Haseda

Enjoy!!


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Quarter Cube from Japan.png
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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Jul 28, 2012 4:19 am 
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what is? any video???

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Jul 28, 2012 6:50 am 
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By the looks of it, it's a latch cube where the latching is based off the centres rather than the edges. I'm guessing that the line has to be kept inside the stickers on the centre. So the U face can only be moved U, it can't be moved U2 or U' (or any further... thus only a quarter move in one direction is allowed)... at which point the only move available to it would be U'.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Jul 28, 2012 8:01 am 
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Yes this is 1/4 turn Cube
similar to Tomz Constrained Cube - all face 90 degree

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Jul 29, 2012 4:23 pm 
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Just when I thought the Latch Cube couldnt get any harder... -_-

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Jul 29, 2012 5:38 pm 
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KozehCubes wrote:
Just when I thought the Latch Cube couldnt get any harder... -_-

So compared to the Latch cube, how would this one rank in difficulty?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Jul 29, 2012 9:21 pm 
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So basically only 6 possible quarter face turns are available from any position rather than 6 x 3 = 18 possible face turns. I wonder what God's number would be for this puzzle? Presumably 3 times more than the standard cube - 60 moves or thereabouts...

And I wonder if any configurations would become inaccessible?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Mon Jul 30, 2012 3:00 pm 
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I wish I had the time to make a GAP-file for this one.


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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Mon Jul 30, 2012 3:22 pm 
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I wonder if a hybrid of the two Latch Cubes could be made... maybe have it so that two opposite faces have restricted turning like Latch II, and have four latching edges, two latching in either direction. I don't think so, but could the puzzle lock up so that some faces would become permanently blocked? If all the edges latched to the same direction, I think all edges could be latching.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Thu Aug 02, 2012 3:23 pm 
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A quick and short reivew as below,
Official Okamoto & Haseda Quarter Cube from Japan @ HK Now Store
http://www.youtube.com/watch?v=Ih3UqD0d ... e=youtu.be

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Thu Aug 02, 2012 4:38 pm 
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KelvinS wrote:
So basically only 6 possible quarter face turns are available from any position rather than 6 x 3 = 18 possible face turns. I wonder what God's number would be for this puzzle? Presumably 3 times more than the standard cube - 60 moves or thereabouts...

And I wonder if any configurations would become inaccessible?


I just tested an it's easy to make a 3-cycle of edges under these restrictions ([R', F, R, F']) and easy to make a pure corner 3-cycle ([R', F, R, F', D', F, R', F', R, D]). Combined with the ability to do a quarter turn (4-cycle of edges and corners) all states are reachable.

Of course, this puzzle has some level of center-orientation visibility which increases the number of states a bit but if you ignore that then it's the same number of states as a Rubik's Cube.

As for god's number, I'm sure it is much less than 60. In face-turn-metric we know god's number is 20. There is a state known to require 26 moves in quarter-turn metric. One would assume that additional restrictions further increase the number of required moves for some states but triple is very unlikely. I'd guess something like 30 to 35 moves.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 03, 2012 9:27 pm 
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Quarter Cube looks much easier than Latch Cube, because you can do F2 by just doing [F [R U' R' U]x6 F].

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 03, 2012 10:02 pm 
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leonid wrote:
Quarter Cube looks much easier than Latch Cube, because you can do F2 by just doing [F [R U' R' U]x6 F].
I don't see how this works. [R U' R' U]x6 is a NOP. F can't be followed by another F even if you sandwich in [R U' R' U]x6.

EDIT: and since when have you been in Mt. View? You're probably 10 min away from me.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 03, 2012 11:50 pm 
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I got to thinking about this more...

It isn't enough to show that you can make 3-cycles of pieces or generate a half-turn without violating constraints. For example, here is a sequence that performs a half-turn under the constraints imposed by this puzzle:
[B', U', R', U, R, B, L', U', B', U, B, L, B', D', R', F, R, F', U, F', U', F, D, B, L, B, U', F, U, F', U', F, U, F', U', F, U, F', B', L', F', L, F, L', F', L, F, L', F', L, F, L', B, R', L', F, L, F', L', F, L, F', L', F, L, F', R, B']

However you can't just substitute this sequence in whenever you need a half-turn because it assumes each face is in the center of its twistability (it can turn a quarter turn either CW or CCW). If you need to use a quarter-turn setup you may get into a situation where you can't apply this sequence anymore.

Now I'm not sure this puzzle can actually reach all the Rubik's Cube states.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 12:06 am 
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bmenrigh wrote:
I got to thinking about this more...
Now I'm not sure this puzzle can actually reach all the Rubik's Cube states.


So bmenrigh, any further insight into my question above: "So compared to the Latch cube, how would this one rank in difficulty?"

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 12:41 am 
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EDIT: This post assumes that each face has three positions it can be in so if it is in the middle position it can either be turned CW or CCW. That may not actually be correct! At the time of writing it isn't clear how the puzzle functions.

rline wrote:
So bmenrigh, any further insight into my question above: "So compared to the Latch cube, how would this one rank in difficulty?"

Probably MUCH easier.

First I'll define some useful sequences:

Flip two edges in bottom layer:
EF: [L', U', F', R, F, R', D, R', D', R, U, L]

Edge 2-2 swap across bottom layer (preserves orientation):
EN: [B', D', L', D, L, B, R', D', B', D, B, R, B', U', L', F, L, F', D, F', D', F, U, B]

Edge 2-2 swap across bottom layer (flips 2):
EO: [F', D', R', D, R, F, L', D', F', D, F, L]

Edge 3-cycle in bottom layer:
ET: [F', D', R', D, R, F]

Corner 2-2 swap (in X) across bottom layer:
CX: [F, R, D', L, D, L', D', L, D, L', D', L, D, L', R', F']

Corner 2-2 swap (in ||) across bottom layer:
CE: [B, U, F, D', F', D, F, D', F', D, F, D', F', D, U', B']

Corner 3-cycle in bottom layer:
CT: [B', L, B, L', R', L, B', L', B, R]

Corner pair twist in bottom layer:
CO: [R', B, R, B', R', B, R, B', R', B, R, B', L, F', B', R, B, R', B', R, B, R', B', R, B, R', F, L']

Corner tripple-twist in bottom layer (like Sune):
CS: [F', D', R', D, R, F, L', D', F', D, F, L, B', D', L', D, L, B, R', D', B', D, B, R]


Solving recipe:
  • 1: Put all faces at their midpoint
  • 2: Solve top layer using intuition or commutators while preserving each face at their midpoint (should be very easy)
  • 3: Solve middle layer using a combination of [D, F, D', F', D', R', D, R] to put edges into the middle layer and when necessary EF, EN, EO and ET to setup the sequence
  • 4: Fully solve edges using EF, EN, EO, and ET
  • 5: Cycle corners with CX, CT, and CE
  • 6: Orient corners with CO and CS

Obviously these routines aren't really optimized and I'm sure there are much shorter strategies but this is pretty much guaranteed to work in all cases. All of the sequences provided assume each face is in the midpoint position and they all preserve each face in the midpoint position when the sequence is done. Instead of using quarter-turn setups you have to use the sequences as setups.

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Last edited by Brandon Enright on Sat Aug 04, 2012 5:23 pm, edited 1 time in total.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 12:46 am 
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bmenrigh wrote:
[B', U', R', U, R, B, L', U', B', U, B, L, B', D', R', F, R, F', U, F', U', F, D, B, L, B, U', F, U, F', U', F, U, F', U', F, U, F', B', L', F', L, F, L', F', L, F, L', F', L, F, L', B, R', L', F, L, F', L', F, L, F', L', F, L, F', R, B']

If this cube can only do quarter turns, I'm not sure how F', U, F' or B, L, B could work.

bmenrigh wrote:
...each face is in the center of its twistability (it can turn a quarter turn either CW or CCW).

Maybe I'm wrong about how this cube works, but as I understand, at no point can a face turn both CW or CCW.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 12:59 am 
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oBNoo wrote:
bmenrigh wrote:
[B', U', R', U, R, B, L', U', B', U, B, L, B', D', R', F, R, F', U, F', U', F, D, B, L, B, U', F, U, F', U', F, U, F', U', F, U, F', B', L', F', L, F, L', F', L, F, L', F', L, F, L', B, R', L', F, L, F', L', F, L, F', L', F, L, F', R, B']

If this cube can only do quarter turns, I'm not sure how F', U, F' or B, L, B could work.

bmenrigh wrote:
...each face is in the center of its twistability (it can turn a quarter turn either CW or CCW).

Maybe I'm wrong about how this cube works, but as I understand, at no point can a face turn both CW or CCW.

Preceding F', U, F' is an F which cancels out the first F'.

I'm operating under the assumption that each face can either turn CW, or CCW, but not a full half-turn. That is, there are 3 positions each face can be in. Is this not correct?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 1:14 am 
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I assumed the outer portion of the centers with the two semicircular stickers are constrained by the lines in the very center which do not rotate (I hope that makes sense). That's what it seemed like from the video but I may be wrong.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 3:54 am 
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Calvin, can you please clarify which assumptions about the functionality of this Cube are correct?
Anyway, I got curious enough and ordered one from you :)

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 4:18 am 
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When you make a quarter turn on this puzzle, the only available move is that moves opposite.
Therefore there can never be a situation where you do F followed by an F without an F' in the middle.
Is there going to be a whole latch cube series?


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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 5:43 pm 
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rline wrote:
bmenrigh wrote:
I got to thinking about this more...
Now I'm not sure this puzzle can actually reach all the Rubik's Cube states.


So bmenrigh, any further insight into my question above: "So compared to the Latch cube, how would this one rank in difficulty?"

Okay assuming each face only has two states that can be toggled back and forth (this is different than my previous assumption) then I still think it'll be much easier.

Unfortunately if each face has only two states it is much harder for me to create a step-by-step solving recipe because even basic commutators like F R' F' R may or may not be able to be done without first performing and F and R setup moves to get them toggled the right way.

Solving-wise I don't think this creates a huge hurdle though. The approach I'd take is to use intuitive setups combined with [1,1] commutators to solve all of the edges. This will take some thinking because you'll have to figure out which options are available to you in each state the puzzle happens to be in but it shouldn't be hard.

I would then permute all the corners into their correct position. This can be done with 2-2 swaps and 3-cycles rather easily. Use [1,1]x3 for 2-2 swaps and [[1:1],1] routines for 3-cycles. Again you'll have to first setup the faces you want to use into the right toggled position but that won't be too limiting to really stop you from permuting corners easily.

I'm stuck right now on how to twist corners and I have a nagging suspicion that you might not be able two twist corners once all edges are solved and you've permuted all corners into their correct spots. I have to keep thinking about it.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 6:15 pm 
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bmenrigh wrote:
As for god's number, I'm sure it is much less than 60... I'd guess something like 30 to 35 moves.

Are you sure about this having thought about it more?

I still think the number is much greater, about 60 or so, and am still not convinced that all states are accessible.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 7:12 pm 
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KelvinS wrote:
bmenrigh wrote:
As for god's number, I'm sure it is much less than 60... I'd guess something like 30 to 35 moves.

Are you sure about this having thought about it more?

I still think the number is much greater, about 60 or so, and am still not convinced that all states are accessible.
Well my estimate was on the assumption that each face had three states. If each one only has two I don't have a lot of gut feeling to go on.

There might be fewer states since it seems like there might be a restriction on the twists available to corners based on the parity of the edges. I'm really not sure.

So lets take a look at the calculation for a Rubik's cube:
? log(((8! * 12! / 2) * (2^11 * 3^7)) / (6*3)) / log(5*3) + 1
% = 16.62

So assuming every turn gets you to a new state the lower-bound on God's number is 17 moves.


Taking an extreme extension of this, lets say that on this Latch cube II, not only can it reach all Rubik's Cube states but that each center has two orientations available to it:

? log(((8! * 12! / 2) * (2^11 * 3^7 * 2^6)) / 6) / log(5) + 1
% = 30.56

So we're looking at a lower bound on god's number of 31.

And we might as well scale up our lower bound by how wrong it is for the Rubik's cube:

? (20 / 17) * 31
% = 36.47

So 37 seems like a reasonable ballpark estimate. It could be lower than this if the center orientations don't matter (I don't know if they do) or if fewer states are available compared to the Rubik's cube.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 7:27 pm 
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Still doesn't make much sense. Even if ALL moves were possible, but each half turn would have to be made as 2 separate quarter turns, then this would increase the minimum number of moves from 20 to about 30, assuming that half of the 20 moves are half turns.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 7:35 pm 
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KelvinS wrote:
Still doesn't make much sense. Even if ALL moves were possible, but each half turn would have to be made as 2 separate quarter turns, then this would increase the minimum number of moves from 20 to about 30, assuming that half of the 20 moves are half turns.
For the same solution, yes. The cool thing is that there are multiple sequences that can arrive at particular state so in the case of the Rubik's cube, the longest known quarter-turn-metric position is 26 moves away.

So if you have a half-turn-heavy solution it's better not to spend two quarter turns on each move and instead solve that position a completely different (and quarter-turn-friendly) way.

Even if we impose the same sort of quarter-turn penalty:

? (20 / 17) * 31.0 * (26 / 20)
%11 = 47.41

48 moves is still much less than 60 and we're starting to get very generous with the estimations.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 7:39 pm 
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You have a point, though as we're both relying heavily on intuition, let's agree to split the difference: 54 moves - until one of us, or somebody else can prove some more meaningful upper and lower bounds.

PS. It would be hilarious if 54 turned out to be the exact answer, given how randomly we arrived at the number. :lol:

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 7:46 pm 
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KelvinS wrote:
You have a point, though as we're both relying heavily on intuition, let's agree to split the difference: 54 moves - until one of us, or somebody else can prove some more meaningful upper/lower bounds. :lol:

Heck that's practically a proof.

God's Number for the Latch Cube II is 54 moves.

Proof:
See above

QED

:lol:

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 7:58 pm 
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As with the original cube, it would be interesting to consider the superflip in particular...

Assuming the superflip is even accessible, how many moves would be required to flip just one pair of edges? Then multiply that number by 6 to get an upper bound...

So I'm guessing at least 10 moves to flip each pair of edges.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 8:11 pm 
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KelvinS wrote:
As with the original cube, it would be interesting to consider the superflip in particular...

Assuming the superflip is even accessible, how many moves would be required to flip just one pair of edges? Then multiply that number by 6 to get an upper bound...

So I'm guessing at least 10 moves to flip each pair of edges.
Yeah the superflip would be a good situation to look at.

The trouble with looking at flipping just two edges is that on a Rubik's Cube that takes a minimum of 14 moves. 14 * 6 = 84 which is obviously a gross overestimate. The same would happen if we only looked at a pair on this restricted / bandaged puzzle.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 8:13 pm 
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bmenrigh wrote:
Yeah the superflip would be a good situation to look at.

The trouble with looking at flipping just two edges is that on a Rubik's Cube that takes a minimum of 14 moves. 14 * 6 = 84 which is obviously a gross overestimate. The same would happen if we only looked at a pair on this restricted / bandaged puzzle.
Good point. Then how about using a ratio of 17/14 * min. moves per flipped pair to get a lower bound?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sat Aug 04, 2012 9:23 pm 
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KelvinS wrote:
bmenrigh wrote:
Yeah the superflip would be a good situation to look at.

The trouble with looking at flipping just two edges is that on a Rubik's Cube that takes a minimum of 14 moves. 14 * 6 = 84 which is obviously a gross overestimate. The same would happen if we only looked at a pair on this restricted / bandaged puzzle.
Good point. Then how about using a ratio of 17/14 * min. moves per flipped pair to get a lower bound?
I think it would require modifying an existing cube solving program to get an estimate for the number of moves required to flip two edges.

I've looked at the solutions Cube Explorer finds and they all violate the restrictions of this puzzle pretty badly.

If we programmed it with the restrictions we'd be able to measure all sorts of properties besides just flipping edges and get a much better estimate of god's number for it.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 2:00 am 
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Bmenrigh, thanks for your thoughts on this one.
Quote:
I'm stuck right now on how to twist corners and I have a nagging suspicion that you might not be able two twist corners once all edges are solved

Wouldn't we be able to do something like setups + (F'RFR')x2 U (RF'R'F)x2 U' ? Or are there restrictions I'm not understanding?
Quote:
Calvin, can you please clarify which assumptions about the functionality of this Cube are correct?
Anyway, I got curious enough and ordered one from you

Looking at that video again, I tend to think there are only 2 states. I hope calvin might confirm what's correct. Like Konrad, I ordered one because I'm intrigued, and I find that's a good ingredient for an enjoyable puzzle.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 2:22 am 
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rline wrote:
Quote:
I'm stuck right now on how to twist corners and I have a nagging suspicion that you might not be able two twist corners once all edges are solved

Wouldn't we be able to do something like setups + (F'RFR')x2 U (RF'R'F)x2 U' ? Or are there restrictions I'm not understanding?

Hey that works!
[F', R, F, R', F', R, F, R', U', F', R, F, R', F', R, F, R', U, F', R, F, R', F', R, F, R']

Nice approach. I was trying to twist corners via the standard layering of 2 symmetrical permutations on top of each other. Every way I tried it, I ended up violating a constraint.

I guess I never noticed that (F'RFR')x2 twists a corner in place, making this a trivial standard commutator within the constraints of the puzzle.

This sequence will be usable on any constrained cube where three turnable faces meet at a corner. Good find!

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 2:41 am 
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bmenrigh wrote:
rline wrote:
Quote:
I'm stuck right now on how to twist corners and I have a nagging suspicion that you might not be able two twist corners once all edges are solved

Wouldn't we be able to do something like setups + (F'RFR')x2 U (RF'R'F)x2 U' ? Or are there restrictions I'm not understanding?

Hey that works!
[F', R, F, R', F', R, F, R', U', F', R, F, R', F', R, F, R', U, F', R, F, R', F', R, F, R']

Nice approach. I was trying to twist corners via the standard layering of 2 symmetrical permutations on top of each other. Every way I tried it, I ended up violating a constraint.

I guess I never noticed that (F'RFR')x2 twists a corner in place, making this a trivial standard commutator within the constraints of the puzzle.

This sequence will be usable on any constrained cube where three turnable faces meet at a corner. Good find!

Thanks.

What's this bit for?
Quote:
F', R, F, R', F', R, F, R'
It's not part of the main twist is it? By the way, how are you coming up with all these sequences? Do you have a simulator of it, or are you simulating it on a real cube?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 4:08 am 
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rline wrote:
...Hey that works!
[F', R, F, R', F', R, F, R', U', F', R, F, R', F', R, F, R', U, F', R, F, R', F', R, F, R']

Nice approach. ...

rline wrote:
What's this bit for?
Quote:
F', R, F, R', F', R, F, R'
It's not part of the main twist is it? ...
Hi rline, Brandon uses the same sequence [F', R, F, R']X2 three times, while you inverse it after the U turn. It is usually used orientating three corners. Interestingly, I came up with the same idea as you. :) We'll see how it works in reality.
And I have the same question to Brandon, how did you find all these sequences? Have you checked how many are still usable, if the later assumption about the constraints is correct (two states per face only)?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 12:07 pm 
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Konrad wrote:
rline wrote:
What's this bit for?
Quote:
F', R, F, R', F', R, F, R'
It's not part of the main twist is it? ...
Hi rline, Brandon uses the same sequence [F', R, F, R']X2 three times, while you inverse it after the U turn. It is usually used orientating three corners. Interestingly, I came up with the same idea as you. :) We'll see how it works in reality.

Yeah doing it 3 times is just me being stupid. If you invert the X part you get a shorter routine that also works:
[F', R, F, R', F', R, F, R', U', R, F', R', F, R, F', R', F, U]

The reason I didn't invert the routine is that I didn't try. Under the assumption that faces only have two states, not all routines can be mirrored or rotated. For example, suppose you were using [R',F']x3 and you wanted to mirror it about the plane containing the FR and BL edges. You'd get [F,R]x3 and that requires the state of F and R to be toggled before it can be done. That is, it contradicts the previous assumption that R and F must first be turned CCW before they can be turned CW.

So under somewhat limiting restrictions about what you can do with a sequence I just decided throw the baby out with the bathwater and ignore inverting and mirroring and rotating of sequences. This is a useful mental abstraction but produced dumb & inefficient routines. I traded less thought for more moves.

Konrad wrote:
And I have the same question to Brandon, how did you find all these sequences? Have you checked how many are still usable, if the later assumption about the constraints is correct (two states per face only)?

Most of my "useful sequences" several posts up assumed that each face has 3 states rather than 2. Most of the sequences don't work with only 2. I have edited my post at the top to warn folks about what assumption I was using.

For finding these sequences I'm just sitting down with Gelatinbrain's 3.1.2 and clicking away. When assuming each face has 3 states, I assumed face started out in the middle position so it can start out by turning either CW or CCW but after that I keep track so make sure I don't turn it the same direction again.

When assuming each face has 2 states I just assume that whichever direction I need the face to go the first time I use the face in a sequence, it's already able to go that direction. After that I just keep track of the toggle "parity" of the face to make sure I don't go the same direction again. Of course, assuming that the face can always go whatever direction you need at the start will mean physically you'll first have to turn faces to the right position to do a sequence. This is going to make physically solving a bit more tricky and require more thinking.

Please don't assume any routine I've posted here is actually efficient. I was just finding them by hand and not trying to be efficient at all.

I've watched Calvin's video again and it seems like each face having only two states is probably the right assumption for this puzzle. To summarize how I think it can be solved:

Suggested Solving Recipe under the 2-states-per-face assumption:
1) Solve all edges with intuition and [1,1] commutators. You'll have to be resourceful due to the restrictions but this step doesn't seem terribly hard.

2) Permute all corners with a combination of 2-2 swaps (use [R', F, R, F', R', F, R, F', R', F, R, F'] or [R', F', R, F, R', F', R, F, R', F', R, F]) and 3-cycles (use [R', F, R, B', R', F', R, B] and other variations).

3) Orient all corners with [F', R, F, R', F', R, F, R', U', R, F', R', F, R, F', R', F, U] or [R', F', R, F, R', F', R, F, L, F', R', F, R, F', R', F, R, L'].

The "tricky" part of actually solving this puzzle is that not every face is going to start out in the state you need it to and sometimes the setup moves you will need to use to get each face into the right toggled state will move the pieces you want to cycle.

Suppose you need R to be toggled before you start a sequence but you don't want to move the UFB corner. You'll probably find yourself doing setups like [B, R', B'] to get R into the right state without moving the corner. In general I assume there will be a lot of [1:1] setups for every sequence to get the faces toggled.

Note that most of the routines are built on a [R,F]xN base sequence. The relationship between F and R will change. Sometimes you'll be doing it where R and F start out turning the same direction (R F R' F') and sometimes opposite directions (R F' R' F) depending on what turns are available to you based on the toggle state of R and F. You can build most of these routines off of either construction so it'll be good to memorize the effects of using both same or both different.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 12:45 pm 
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bmenrigh wrote:
...[F', R, F, R', F', R, F, R', U', R, F', R', F, R, F', R', F, U]

The reason I didn't invert the routine is that I didn't try. Under the assumption that faces only have two states, not all routines can be mirrored or rotated. For example, suppose you were using [R',F']x3 ....
Hi Brandon, I guess you should mention that the [R',F']x3 is in commutator notation equivalent to [R',F',R,F,R',F',R,F,R',F',R,F] not to [R',F',R',F',R',F'] (which is not possible on the Quarter Cube). Some could interpret it incorrectly. In my view, [R',F']x3 without further clarification can be interpreted both ways.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 1:10 pm 
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Konrad wrote:
bmenrigh wrote:
...[F', R, F, R', F', R, F, R', U', R, F', R', F, R, F', R', F, U]

The reason I didn't invert the routine is that I didn't try. Under the assumption that faces only have two states, not all routines can be mirrored or rotated. For example, suppose you were using [R',F']x3 ....
Hi Brandon, I guess you should mention that the [R',F']x3 is in commutator notation equivalent to [R',F',R,F,R',F',R,F,R',F',R,F] not to [R',F',R',F',R',F'] (which is not possible on the Quarter Cube). Some could interpret it incorrectly. In my view, [R',F']x3 without further clarification can be interpreted both ways.

Yeah you're right. Sometimes we're a bit loose with our notation. Indeed I mean to expand the [X, Y] commutator and then apply it several times.

Sometimes I feel sorry for the poor Internet denizens that don't have a forum account and don't understand all of the history behind our posts when they need to decipher what the heck we mean.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 4:20 pm 
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Quote:
The "tricky" part of actually solving this puzzle is that not every face is going to start out in the state you need it to and sometimes the setup moves you will need to use to get each face into the right toggled state will move the pieces you want to cycle.

Yeah this is what I've been thinking after reading these posts and thinking about it. I feel much better about my purchase now, as I think it might have an added frustration factor that will make it worthwhile.

So does gelatinbrain (or anything else) have some kind of blocking function inbuilt, where you can specify that certain faces can only be in certain states (similar to how you can specify that some faces are bandaged on the circlepuzzles sim.)?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 05, 2012 4:33 pm 
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Maybe before actually solving, you could set the centers to their "solved" states. You'd have to memorize how they're all supposed to go, but then you could work around that making sure that after a sequence, the centers are back where they're supposed to be.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Mon Aug 06, 2012 3:09 pm 
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bmenrigh wrote:
leonid wrote:
Quarter Cube looks much easier than Latch Cube, because you can do F2 by just doing [F [R U' R' U]x6 F].
I don't see how this works. [R U' R' U]x6 is a NOP. F can't be followed by another F even if you sandwich in [R U' R' U]x6.

EDIT: and since when have you been in Mt. View? You're probably 10 min away from me.


Oops, I think now I know how this puzzle functions. The "bar" in each center is fixed and you can only turn the faces in a way that the "bar" must be in between the two "arcs", so each face can turn in only one way.

And I've been in MTV for about 6 months now.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Sun Aug 12, 2012 11:03 am 
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Okamoto & Haseda Quarter Cube
at WitEden
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http://www.witeden.com/goods.php?id=453


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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 17, 2012 2:14 am 
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My quarter cube arrived today.

Quote:
Oops, I think now I know how this puzzle functions. The "bar" in each center is fixed and you can only turn the faces in a way that the "bar" must be in between the two "arcs", so each face can turn in only one way.

I can confirm that this assumption of two states is correct. I made a short video at

http://youtu.be/iaPLg7nsaik

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 17, 2012 4:47 am 
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My Latch Cube II arrived yesterday. It's a really fun puzzle. Mine was in a solved state where every face could turn only clockwise. The edges and corners are always both in an even permutation when the puzzle is in this state, which seems obvious when you think about it, because the puzzle can only return to that state after an even number of quarter turns.

I find it a lot easier to solve than the Latch Cube (I) and I'd rate it as about as challenging as a mid-level Crazy/Planet 3x3x3. I scrambled the puzzle by mistake while fiddling around with sequences and I had solved it around 2 hours later.

Like the original Latch Cube, a natural way to solve the quarter cube is edges first, then permute the corners, and finally orient the corners. I solve all the edges with white stickers intuitively, then place a couple of edges around the next layer, then finish the edges using a combination of 4-move and 6-move sequences. The corners are quite easy to solve because simple algos can be applied to any orientation of the cube: a [3,1] commutator to permute 3 corners around a face, then an [8,1] commutator to twist a pair of adjacent corners.


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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 17, 2012 9:34 am 
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Julian wrote:
[...]I solve all the edges with white stickers intuitively, then place a couple of edges around the next layer, then finish the edges using a combination of 4-move and 6-move sequences. The corners are quite easy to solve because simple algos can be applied to any orientation of the cube: a [3,1] commutator to permute 3 corners around a face, then an [8,1] commutator to twist a pair of adjacent corners.
I'm having trouble figuring out what 6-move sequences you could be using here. Any hints?
EDIT: It just occurred to me that you could be doing [1:[1,1]] but I wouldn't call that a special sequence. I'd say you're just using a setup with a 4-move [1,1] commutator. Perhaps you're doing something different?

The rest of your solve sounds exactly like my strategy outlined above.

Since the 2-states-per-face puzzle is so easily solved, that should mean any combination of 2, 3, and 4 states-per-face variants should also be just as easily solved. The extra states on some faces just give you more setup move freedom and you can continue to pretend the faces have the 2-states-per-face restriction for executing sequences.

Can you comment on how much harder you think having some faces locked in place (1-state-per-face) would make the puzzle? It seems to me just having one face locked in place wouldn't really increase the difficulty much but I could see how having more than one locked might make things a bit challenging.

That is, do you think making this Latch cube II solution just a bit more generic can handle this whole class of restricted cubes (Constrained Cubes)?

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Fri Aug 17, 2012 6:33 pm 
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bmenrigh wrote:
Julian wrote:
[...]I solve all the edges with white stickers intuitively, then place a couple of edges around the next layer, then finish the edges using a combination of 4-move and 6-move sequences.
I'm having trouble figuring out what 6-move sequences you could be using here. Any hints?
EDIT: It just occurred to me that you could be doing [1:[1,1]] but I wouldn't call that a special sequence. I'd say you're just using a setup with a 4-move [1,1] commutator.
Yes, my 6-move sequences are just FRUR'U'F' and FURU'R'F', but I'm so used to thinking of them in full that I don't naturally see them as [1:[1,1]], even though they are! I use them by themselves and also in combination with each other with rotations in the y axis to cycle three edges around the U face without flipping any of them in 18 moves, either to set up an edge for solving into the middle layer with a simple [1,1], or to finish solving all the edges.
bmenrigh wrote:
Since the 2-states-per-face puzzle is so easily solved, that should mean any combination of 2, 3, and 4 states-per-face variants should also be just as easily solved. The extra states on some faces just give you more setup move freedom and you can continue to pretend the faces have the 2-states-per-face restriction for executing sequences.
I think that if one of the faces of the quarter cube could only turn counterclockwise from the solved position, with all the others turning clockwise, that would break the symmetry and make the solve quite a bit harder, even without including 3- or 4-state faces. A puzzle having one face with 3 states and the rest with 2 states would be interesting and possibly difficult.
bmenrigh wrote:
Can you comment on how much harder you think having some faces locked in place (1-state-per-face) would make the puzzle? It seems to me just having one face locked in place wouldn't really increase the difficulty much but I could see how having more than one locked might make things a bit challenging.
Some of the Crazy/Planet 3x3x3 puzzles end up with solves using 3-5 faces once the reduction phase is complete, which can be quite tricky even with the moving faces able to turn freely. I guess the question is whether the combination of one or more fixed faces with restricted faces could lead to a very difficult puzzle, and I think it could.
bmenrigh wrote:
That is, do you think making this Latch cube II solution just a bit more generic can handle this whole class of restricted cubes (Constrained Cubes)?
I don't think so.


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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Mon Aug 20, 2012 4:34 pm 
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I had a great time playing with this cube over the weekend. In my opinion, it's a fantastic puzzle. It's not really easy to figure out, but there was a definite joy in discovering how to solve it logically and piece-by-piece every time. By far the edges (particularly those after the 1st four) caused me the greatest amount of solving-stress. I really recommend if anyone is undecided about this that they should get it. It's a good puzzle and it's refreshing to receive such a well-made and problem-free puzzle.

For anyone interested or curious, I did make some solving videos. You can find them here.

Quote:
Can you comment on how much harder you think having some faces locked in place (1-state-per-face) would make the puzzle? It seems to me just having one face locked in place wouldn't really increase the difficulty much but I could see how having more than one locked might make things a bit challenging.

I agree with Julian that having some faces locked would make it much harder. I think even having one face locked in place would increase the difficulty.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Mon Aug 20, 2012 4:54 pm 
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Julian wrote:
bmenrigh wrote:
Since the 2-states-per-face puzzle is so easily solved, that should mean any combination of 2, 3, and 4 states-per-face variants should also be just as easily solved. The extra states on some faces just give you more setup move freedom and you can continue to pretend the faces have the 2-states-per-face restriction for executing sequences.
I think that if one of the faces of the quarter cube could only turn counterclockwise from the solved position, with all the others turning clockwise, that would break the symmetry and make the solve quite a bit harder, even without including 3- or 4-state faces. A puzzle having one face with 3 states and the rest with 2 states would be interesting and possibly difficult.

Sorry for the delayed response, I didn't see yours. Correct me if I'm wrong but I thought the 2-state faces toggle back and forth. If you had a puzzle that was 5 faces start clockwise and 1 starts counter-clockwise, couldn't you just turn the counter-clockwise face to start? After doing this you now have an all-clockwise puzzle with a "different color scheme". Solve to this other color scheme and then undo the original turn.

Also, can you tell if this puzzle can reach all the states a Rubik's cube can reach? If so can't you just treat a 3-state or fully unrestricted face as though it is a 2-state face and still be able to solve it exactly like this puzzle?

I agree though that totally blocked faces could be hard.

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 Post subject: Re: Okamoto & Haseda Quarter Cube from Japan (Latch cube II)
PostPosted: Mon Aug 20, 2012 6:11 pm 
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bmenrigh wrote:
Sorry for the delayed response, I didn't see yours. Correct me if I'm wrong but I thought the 2-state faces toggle back and forth. If you had a puzzle that was 5 faces start clockwise and 1 starts counter-clockwise, couldn't you just turn the counter-clockwise face to start? After doing this you now have an all-clockwise puzzle with a "different color scheme". Solve to this other color scheme and then undo the original turn.
Yes, you're right, you could. It seems obvious now that you point it out!

Thinking about it more now, the same idea could be used if there were 3 clockwise-starting and 3 counter-clockwise starting faces, which should be an equivalent puzzle to 1 CCW and 5 CW, as is 5 CCW and 1 CW. In each case we could set all the faces to turn clockwise, knowing that we're a quarter turn away from an even permutation of corners and edges, then we could choose a face to solve into a displaced color scheme, solve normally otherwise, and turn that face at the end. (I haven't tried solving the Latch Cube II so that an even number of faces can only turn counter-clockwise at the end, but it wouldn't be too confusing to do with 2 such faces opposite each other.)

bmenrigh wrote:
Also, can you tell if this puzzle can reach all the states a Rubik's cube can reach? If so can't you just treat a 3-state or fully unrestricted face as though it is a 2-state face and still be able to solve it exactly like this puzzle?
Yes, the puzzle can reach all states. I had been thinking that a single 3-state face could cause complications but now I see that it wouldn't matter.

bmenrigh wrote:
I agree though that totally blocked faces could be hard.
I shall try a scramble and solve without moving the gray face at all, and see how it goes. Then with two adjacent and non-adjacent stationary faces.


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