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 Post subject: Re: Latch cube by okamoto
PostPosted: Wed Aug 18, 2010 5:14 am 
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[Moderator: Posts merged in from the New Puzzles thread here.]


Because the edges control things I'm attempting to solve using an edges first approach. So far I have managed to get all 12 edges correctly positioned and oriented. Now I have to start in on the corners but haven't managed to get far with them yet :)


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 Post subject: Re: Latch cube by okamoto
PostPosted: Wed Aug 18, 2010 11:48 am 
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You've done the hard part! Actually all you have to do first is get the *arrows* correctly positioned, i.e., white arrows in the correct slots on the blue, gray, and red faces, and black arrows in the correct spots on the other faces. This is slightly easier than actually getting each edge in the right place.

From there, you can treat it as a semi-normal twisty puzzle (albeit one with reduced symmetries), and build up a library of transforms made of short sequences that leave the arrows correctly positioned.

At least, that's the approach I took. I ended up needing very few primitive transforms, though the combinations of them to do corner positioning and orienting wound up rather long.


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 Post subject: Re: Latch cube by okamoto
PostPosted: Thu Aug 19, 2010 5:12 am 
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I received mine this morning and after hours of study I finally solved it!

I also solve edges first. with white face as the bottom, first make a cross, then solve the edges with black arrows and then the other two in the second layer, finally solve the top layer in two steps which need some tricks.
corners are quite easy to solve, the general 3-corner circulation (not sure about the name) can do everything.


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 Post subject: Re: Latch cube by okamoto
PostPosted: Thu Aug 19, 2010 12:01 pm 
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You solved it in less than a day??? Where's the bow-down smiley when you need it...


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 Post subject: Re: Latch cube by okamoto
PostPosted: Fri Aug 20, 2010 9:21 am 
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one day is impressive... I'm still having issues getting all the edges sorted out...


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 Post subject: Re: Latch cube by okamoto
PostPosted: Fri Aug 20, 2010 10:21 am 
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I'm not able to design new puzzles and can only make some simple shape shift, so my interest lies in collecting new puzzles and solving them. :lol:
One step to arrange 3 black-arrow edges is without a definite way and I have to spend 3-4 minutes to find good set-ups and reverses. that is the only hard step and I hope there's a better solution which doesnot need so much spatial thinking.


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 Post subject: Re: Latch cube by okamoto
PostPosted: Sun Aug 22, 2010 1:36 pm 
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I, through a fluke, managed to get all the arrows sorted out, and all the edges solved...
time to brush up on my corner commuters :) This one has been quite the trick for me,
as I'm usually a corners first cuber...


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 Post subject: Re: Latch cube by okamoto
PostPosted: Mon Aug 23, 2010 4:32 am 
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Does it have any deadlock permutations, where it is impossible to return it back to the solved state. (That would be evil!) :lol:

Per

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 Post subject: Re: Latch cube by okamoto
PostPosted: Mon Aug 23, 2010 5:33 am 
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chuchudengren wrote:
I took one picture some time ago and since the camera is not at hand I could not offer more. Hope it helps

Thanks. I don't have a pic handy at the moment either, but I think that shows it pretty well. Only thing missing is the edge piece the plunger fits into.

perfredlund wrote:
Does it have any deadlock permutations, where it is impossible to return it back to the solved state. (That would be evil!) :lol:

No... every move is reversible (just keep turning in the same direction), so every sequence of moves is reversible. However, you could assemble it in an impossible state which does not violate any of the usual parity constraints.


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 Post subject: Re: Latch cube by okamoto
PostPosted: Mon Aug 30, 2010 6:54 am 
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I have solved my Latch Cube twice with a similar method as mentioned above: edges first.
I find it pretty hard and I could not describe a real method, how to solve that first phase - the edges.
It's more an "ad hoc" inventing what to do next. When you have solved the edges, the corners are not so hard.
I ordered yesterday a second Latch Cube (the first was delivered from Japan to Germany very fast :) ) and I'll put Cubesmith stickers on that one. I prefer ordinary stickers with just the arrows on them, as others have stated. :)

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 Post subject: Re: Latch cube by okamoto
PostPosted: Mon Aug 30, 2010 12:47 pm 
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I'm still having trouble with the corners last after getting the edges in place...
Any recommendations on good commuters for this?

I like the look of the circular arc stickers... And so far mine have held up ok...

-D


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 Post subject: Re: Latch cube by okamoto
PostPosted: Mon Aug 30, 2010 4:34 pm 
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Derek Bosch wrote:
I'm still having trouble with the corners last after getting the edges in place...
Any recommendations on good commuters for this?...
Here is an example:
Assumption: All edges are in place
Hold the faces with black arrows as F,R,D
In the notation of a normal 3x3x3 use the commutator (please highlight) { R U‘ L‘ U R‘ U‘ L U }
(With the arrows = latches placed as described above this translates to: { (R‘)3 U3 L3 U R‘ U3 L U) }

Here is a net after executing this algorithm on a solved cube:

Image

Two corners can be oriented in place by (normal 3x3x3 notation): { (R F' R' F)*2 U' (F' R F R')*2 U }
this turns UFR clockwise and UFL counterclockwise.

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 Post subject: Re: Latch cube by okamoto
PostPosted: Mon Aug 30, 2010 6:08 pm 
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Location: bay area, california
thanks! I'm feeling quite out of it, as I should have tried those by now :)

D


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 Post subject: Re: Latch cube by okamoto
PostPosted: Tue Aug 31, 2010 4:45 am 
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Derek Bosch wrote:
thanks! I'm feeling quite out of it, as I should have tried those by now :)

D
Here is another example:
Hold the faces with black arrows as U, F, R
This sequence { R‘ F‘ L F R F‘ L‘ F (normal 3x3x3 notation, translates to R' F‘ L (F‘)3 (R‘)3 F‘ L3 (F‘)3 for the described configuration) } does another corner 3-cycle, but leaves the corners differently oriented.

Here is a net how a solved cube looks after executing this algorithm:

Image

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 Post subject: Re: Latch cube by okamoto
PostPosted: Tue Aug 31, 2010 11:26 am 
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thanks, konsassen!
I'm makiing much more progress now... should have it solved soon, unless I screw up again :)


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 Post subject: Re: Latch cube by okamoto
PostPosted: Tue Aug 31, 2010 5:00 pm 
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I use the basic commutators like in a regular 3x3x3. If some faces get stuck in the middle of an algorithm, I would (1) reverse what I have done to the beginning state, (2) use some slice moves as setup moves to remove the edges that cause trouble, (3) apply the algorithm again, (4) reverse the setup moves. I use slice moves to setup because they never change corner pieces.

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 Post subject: Re: Latch cube by okamoto
PostPosted: Tue Aug 31, 2010 8:21 pm 
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Woohoo! Just solved it for the first time! Thanks for all the help everyone!

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 Post subject: Re: Latch cube by okamoto
PostPosted: Wed Sep 01, 2010 7:32 am 
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schuma wrote:
I use the basic commutators like in a regular 3x3x3.....
I assume that you are talking about the second phase, solving the corners, when the edges are solved, right?
What do you call the basic commutators, BTW?
There are so many different methods and strategies around that it is hard for me to judge what is considered "basic" :)

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 Post subject: Re: Latch cube by okamoto
PostPosted: Wed Sep 01, 2010 8:19 am 
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konsassen wrote:
I assume that you are talking about the second phase, solving the corners, when the edges are solved, right?
What do you call the basic commutators, BTW?
There are so many different methods and strategies around that it is hard for me to judge what is considered "basic" :)


Yes, I was talking about the second phase. By "basic commutators", I meant the algorithms that you mentioned earlier in this thread, including the 8-move algorithms to do a 3-cycle, and the 18-move algorithm to rotate two corners. Just all you mentioned, nothing else.

I didn't specify these algorithms, because the principle of using setup moves to avoid locking is not limited to these algorithms. If one has some other favorite algorithms, they can certainly try to use them with setup moves.

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 Post subject: Re: Latch cube by okamoto
PostPosted: Wed Sep 01, 2010 10:11 pm 
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I finally got mine solved... Thanks for the help...
The first phase is still a bit of a mystery - not sure if I have a good strategy or not for getting the edges lined up, but once I get there, I can get the remainder done...

Fun puzzle! Best challenge I've had with a cube in quite some time...

-D


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 Post subject: Re: Latch cube by okamoto
PostPosted: Thu Sep 02, 2010 4:35 pm 
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I have two questions for the mathematical experts:
- Can all patterns of a normal 3x3x3 be created by legal moves on a Latch Cube? (My guess is "yes", but I have no clue how this could be proved - or am I wrong?)
- Any ideas in which range we can locate God's number for the Latch Cube? (I would assume that it is incredible hard to find a proof as for the normal 3x3x3.)

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 Post subject: Re: Latch cube by okamoto
PostPosted: Thu Sep 02, 2010 5:40 pm 
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konsassen wrote:
- Can all patterns of a normal 3x3x3 be created by legal moves on a Latch Cube? (My guess is "yes", but I have no clue how this could be proved - or am I wrong?)


My answer to this question is NO. Consider the superflip pattern. It is the state where all the edge pieces are flipped but still in the original locations, and all the corner pieces are completely unchanged. This pattern is reachable on a normal 3x3x3 by 20 moves. But if someone disassembles a Latch Cube and re-assembles it to the superflip state, he will find that all six faces are locked, because there are two contradicting arrows on each face. Therefore superflip is not reachable on a Latch Cube from the solved state. In fact superflip is an isolated state for Latch Cube. You can go nowhere from superflip, and you cannot come from anywhere to superflip.

If we define an "orbit" as the set of states that can be reached by legal moves from a certain state, then a classical result shows that a normal 3x3x3 has 12 different orbits. We have to dissassemble it to jump from one orbit to another. I wonder how many orbits does a Latch Cube have. Apparently there is a single-element orbit, that is, the superflip. Since an orbit of a Latch Cube must be contained in an orbit of a normal 3x3x3, the number of orbits of a Latch Cube is definitely more than 12.

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 Post subject: Re: Latch cube by okamoto
PostPosted: Fri Sep 03, 2010 5:52 am 
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schuma wrote:
konsassen wrote:
- Can all patterns of a normal 3x3x3 be created by legal moves on a Latch Cube? (My guess is "yes", but I have no clue how this could be proved - or am I wrong?)
My answer to this question is NO. ...
That makes completely sense. Thanks! :)
It will not be easy to compute the number of possible permutations for the "Okamoto" orbit (the one in which it comes preassembled), right?

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 Post subject: Re: Latch cube by okamoto
PostPosted: Fri Sep 03, 2010 7:02 am 
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Has anyone met the situation that only one face can be turned? Though I've never seen, I cannot rule out the possibility.


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 Post subject: Re: Latch cube by okamoto
PostPosted: Wed Sep 08, 2010 6:05 pm 
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I got mine yesterday. I'm still trying to solve it. I believe I ended up in a situation where only one face could turn. However, if I turned the face to other positions it freed up other faces to turn. I don't know if that counts.

Right now I'm still having trouble getting the edges positioned. I have all of the edges oriented, but I have two adjacent edges that need to be swapped. I haven't been able to find a way to do this yet. It's been challenging for me just making it this far.


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