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 Post subject: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Sun May 23, 2010 8:16 pm 
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Just got my Gear Cube yesterday and was frustrated with how easy it was so I decided to make it more difficult. 4 color face scheme is based on Waran's Turtle Cube. I made a 4 Color Face 3x3 with the same scheme when I made the Turtle Cube last year. The stickering isn't perfect but this is just a prototype.

4 Color Gear Cube Video


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File comment: 4 Color Gear Cube
4 Color Geary Cube 2.jpg
4 Color Geary Cube 2.jpg [ 1.5 MiB | Viewed 5411 times ]
File comment: 4 Color Gear Cube with a Turtle Cube and a 4 Color Face 3x3
4 Color Geary Cube 1.jpg
4 Color Geary Cube 1.jpg [ 2.25 MiB | Viewed 5411 times ]


Last edited by Sublime on Mon May 24, 2010 2:27 am, edited 2 times in total.
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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Sun May 23, 2010 10:25 pm 
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That's neat.I didn't think we'd see a gear cube mod(or sticker mod) for a little while.


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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Sun May 23, 2010 11:32 pm 
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I love that you stickered parts that weren't originally stickered!

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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 12:03 am 
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An oversight? Those pieces move!


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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 1:18 am 
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viewtopic.php?p=212350#p212350

Here is a regular gear cube from mefferts, without those parts stickered.

I don't even know what to call them.

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Last edited by theVDude on Mon May 24, 2010 2:47 am, edited 1 time in total.

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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 1:44 am 
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It's not a Geary Cube! Oskar originally called it the Caution Cube and Meffert renamed it Gear Cube, Geary Cube is the name of another of Oskar's puzzles, an anti-slice 3x3x3.

Does the sticker mod make it more difficult to solve? I've heard that the Gear Cube is rather easy to solve. Anyway, I can't wait till I receive mine.

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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 2:24 am 
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You're right. I must be losing my mind.

Yes, it is more difficult. How much more I don't know. Was close to solving it once. Almost trivial to solve with the original scheme.


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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 2:39 am 
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I want a Gear Mastermorphinx NOW!! :lol:

Can U make one plz?

:D Greg :D

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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 8:41 am 
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Sublime wrote:
An oversight? Those pieces move!


Not an oversight. They are too small to sticker in the factory and it was decided that rather than have a badly stickered puzzle they were best left alone.

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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 9:12 am 
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katsmom wrote:
Not an oversight. They are too small to sticker in the factory and it was decided that rather than have a badly stickered puzzle they were best left alone.


I got my Gear Cube over the weekend and I too have been wondering about those pieces. If they were stickered with the normal 6 color scheme do they add anything to the puzzle? I don't think its possible for those pieces not to be solved when all the others are. Can someone prove me wrong?

Carl

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 10:21 am 
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I originally put a piece of tape on one of the inner pieces and mixed and solved and it was not in the same place. The six color scheme would have been a lot easier to add to but I felt it would still be easy so I went with the four color face. I'm sure I would have figured the six color scheme by now.

The pieces could've been made so there was an ample stickerbed. The gears are novel but I would prefer the mechanism to be hidden.


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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 12:00 pm 
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wwwmwww wrote:
I got my Gear Cube over the weekend and I too have been wondering about those pieces. If they were stickered with the normal 6 color scheme do they add anything to the puzzle? I don't think its possible for those pieces not to be solved when all the others are. Can someone prove me wrong?

Carl
Those pieces move with the edges. The rotating edge pieces are attached to them.

edit: but it does seem that they can be rotated (probably in pairs) and the cube can be solved. For example, the pair around the red/blue rotating edge piece can be swapped.


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 Post subject: Re: 4 Color Geary Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 1:38 pm 
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Volitar Prime wrote:
edit: but it does seem that they can be rotated (probably in pairs) and the cube can be solved. For example, the pair around the red/blue rotating edge piece can be swapped.


Let's ask the question this way...

(1) How many states does the as produced Gear Cube have?
(2) How many states does the 6 color Gear Cube with stickered fixed edges have?

The 4 colored patern adds in face center orientation... so..

(3) How many states does the 6 color Gear Cube with stickered fixed edges and face center orientation have?

I was initially thinking the answer to (1) and (2) were the same... it now doesn't look that way.

Carl

P.S. How many states does this presented 4 color version have? It appears the centers can be swapped and maybe edges too so I expect its less then the answer to (3) above. Not sure... the 4 color patern confuses me.

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 2:23 pm 
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Regardless, solving the unstickered edges, if stickered, would be as trivial as turning one face of the cube until it rights itself.

Although much of the gear cube solves in that fashion, with some trivial center permutation here and there. :(

Edit: The edges and gears would "swap" four at a time due to the restrictions of the puzzle, so while it may have many more states then the original puzzle, it would not be even an inkling harder.

(assuming the edges and gears do "swap" in relation to eachother)


Anybody else consider the Gear Cube a very easy, but complexly(?) bandaged bandage cube?

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 3:18 pm 
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EMarx wrote:
Regardless, solving the unstickered edges, if stickered, would be as trivial as turning one face of the cube until it rights itself.

The unstickered edges don't rotate with single face twists. Unless I'm missing something.

Carl

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 3:28 pm 
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I don't think they are that restricted. I marked four on one face and was able to move them around pretty independently. I think they are bandaged more in pairs. I agree about the bandaging. It is sort of a 180 degree bandaged crazy 3x3 with no small corners but this doesn't address the outer gear edges. I don't want to think about it until I get a solution.

Just because it has a few permutations doesn't mean it is easy to solve. The Nightmare Cube is a good example of this. Also, the Dogic has many permutations and it is easy.

Stickering the six face would mean those pieces could be in any orientation on the face and the center would have four orientations. The 4 color face doesn't allow this. Just like the 4 Color Face or Turtle Cube, finding the correct center placement is difficult. I know the bandaging may correct for face and center orientations. But so far (an hour or two in) it has stumped me.


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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 3:50 pm 
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Carl, the unstickered edges are really the edges of a 3x3, with the gear built on top of it, so every unstickered edge is connected to the corresponding gear. So the only extra orientation would be flipping the gear in its respective edge.

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 4:09 pm 
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EMarx wrote:
Carl, the unstickered edges are really the edges of a 3x3, with the gear built on top of it, so every unstickered edge is connected to the corresponding gear. So the only extra orientation would be flipping the gear in its respective edge.
Exactly! Therefore, stickering those "inner edges" does not add any new challenge to the puzzle. You have to get the outer edges (=gears) to the right orientation, anyway.
@Sublime: Yes, relative to the core they move around, but they go always with the outer edge piece (=gear).

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 5:39 pm 
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EMarx wrote:
Carl, the unstickered edges are really the edges of a 3x3, with the gear built on top of it, so every unstickered edge is connected to the corresponding gear.


Agreed...

EMarx wrote:
So the only extra orientation would be flipping the gear in its respective edge.


Ok...

Nomenclature

face = face center on production gear cube
S-face = face center with orienation
corner = normal corners on production gear cube
edge = the un-stickered edges on the production gear cube that behave as edges on a 3x3x3
gear = the stickered edges on the production gear cube that are fixed to the edges (defined just above)

If we are talking about a 6 color cube...

Corners have a specific position and orientation in the solved state.
Edges have a specific position and orientation in the solved state.
Gears have a specific position and orientation in the solved state.

It's only the faces that just have a solved position, not an orientation. To fix that we could add S-faces somehow.

Now assume we are to super solve a gear cube from these two states (I'm not even sure both these are possible states).

State 1:
S-Faces are solved.
Corners are solved.
Edges are solved.
Gears are NOT solved.

State 2:
S-Faces are solved.
Corners are solved.
Edges are NOT solved.
Gears are solved.

To super solve the puzzle from state 1 is easy. Just rotate individual faces to rotate the gears into the correct orientation. We know they are already in the correct position as the edges are solved.

To super solve from state 2 may be easy too (assuming this state is even possible) but then the solution isn't jumping out at me. We know the edges are in the correct position as the gears are solved but they (or some of them) need their orientation swapped by 180 degrees.

You are correct that "flipping the gear in its respective edge" is easy but what about flipping an edge (or I assume that would need to be a group of atleast 4 edges)?

Using Oskar's names the Gear Cube is the Caution Cube. Then these "edges" are exactly the same edges as those seen on Oskar's Geary Cube. I'm now thinking the Geary Cube is a harder puzzle then the Caution Cube but you can take a production Gear Cube and make both (or the sum of the two) depending on how you sticker it.

Carl

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Last edited by wwwmwww on Mon May 24, 2010 6:10 pm, edited 1 time in total.

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 5:50 pm 
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konsassen wrote:
Exactly! Therefore, stickering those "inner edges" does not add any new challenge to the puzzle. You have to get the outer edges (=gears) to the right orientation, anyway.

Just because the gear is in the correct orientation how do you know the edge its attached to is? The edge itself could be flipped 180 degrees and still allow the gear to have the correct position and orientation.

Carl

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 5:57 pm 
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Orientation of the edges themselves is a non-issue.

Each set of four edges in the Gear Cube function as an essential 2x2x1, and each of the three 2x2x1's found on the Gear Cube keep their orientation in relation to the rest of the Gear Cube.

And the more I think about it, the less I think the Gears can flip in relation to the edges.


The Geary Cube and Caution Cube are equally easy puzzles, except the Caution Cube takes a few more turns on each face to orient the Gears.


Edit: Forgot to mention, do a few turns on the Gear Cube yourself, with the intent of trying to flip 2 edges in relation to the puzzle, and you'll see you can't do it.

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 6:09 pm 
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Ok... back on topic. Looking more at the 4 color mod this thread is about I think I see how each face center is unique due to the order the colors appear in. I now think this gives each piece a unique position AND orientation so this boils down to being able to super solve a Caution Cube and a Geary Cube combo. Add to that the confusion generated by using only 4 colors it makes it even a bit harder.

Question..
(1) Is each corner unique? Its possible as there are 8 corners there could be mirror image pairs each missing one of the 4 colors. I just can't tell from the pictures.
(2) Is each face unique? Again its possible. Going clockwise from the white portion you can have any of the 3 other colors. This leaves 2 ways to arrange the other 2 colors giving you 6 possibilities

Its not obvious to be that (1) and (2) can both be yes at the same time but I think it should be possible. And if (1) and (2) are both yes does that guarantee your edges (and gears) are unique as well?

Carl

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 6:26 pm 
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EMarx wrote:
Orientation of the edges themselves is a non-issue.

Each set of four edges in the Gear Cube function as an essential 2x2x1, and each of the three 2x2x1's found on the Gear Cube keep their orientation in relation to the rest of the Gear Cube.


Hmmm... that is what I was thinking at first until I read this:
Sublime wrote:
I originally put a piece of tape on one of the inner pieces and mixed and solved and it was not in the same place.


What you are saying if the gears are solved then the edges HAVE to be solved... correct? So Sublime's piece of tape should have returned to its starting position. I need to try this for myself. I've solved mine several times now but I haven't stickered my edges yet.

EMarx wrote:
And the more I think about it, the less I think the Gears can flip in relation to the edges.


They can... however I'm not sure the edge can be in the correct position and the gear be flipped at the same time.

EMarx wrote:
The Geary Cube and Caution Cube are equally easy puzzles, except the Caution Cube takes a few more turns on each face to orient the Gears.


I have yet to try a Geary Cube so I'll take your word for it.

EMarx wrote:
Edit: Forgot to mention, do a few turns on the Gear Cube yourself, with the intent of trying to flip 2 edges in relation to the puzzle, and you'll see you can't do it.


I will after I add some stickers to my puzzle. Personally, I was thinking that IF it could be done then 4 edges would have to be flipped at once

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 6:50 pm 
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EMarx wrote:
Edit: Forgot to mention, do a few turns on the Gear Cube yourself, with the intent of trying to flip 2 edges in relation to the puzzle, and you'll see you can't do it.

I haven't made it home yet but here is a 3 move sequence that flips 4 edges on a Geary Cube:
http://www.randelshofer.ch/cube/rubik/?LRUDFB
Here is a 4 move sequence that flips 8 edges on a Geary Cube:
http://www.randelshofer.ch/cube/rubik/?LRUDFBUD
Granted in these examples the corners and other edges aren't in the solved position but it makes it hard for me to understand your statement:
EMarx wrote:
Each set of four edges in the Gear Cube function as an essential 2x2x1, and each of the three 2x2x1's found on the Gear Cube keep their orientation in relation to the rest of the Gear Cube.

Carl

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 7:22 pm 
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I repeated Sublime's tape experiment by placing a piece of tape on the red side of the red/blue edge (not the gear, the unstickered edge). I scrambled and solved only to find the tape on what seemed to now be the blue side. I'm assuming that 1 or 3 other edges are also flipped when this happened.


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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 7:24 pm 
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In the video I mark four center edges and label them to the corresponding center color. When I brought them back to one face only the center needs to be flipped. But, this is not solved. Originally I marked the piece closest to Oskar on the yellow side and it ended up on the green face when I solved it.

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Mon May 24, 2010 7:58 pm 
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It appears I've been horrendously wrong.

I'll just sit by the wayside instead of making false assumptions.

Carl, is after all the most knowledgable person when it comes to understanding new puzzles :D

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Tue May 25, 2010 3:44 am 
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wwwmwww wrote:
konsassen wrote:
Exactly! Therefore, You have to get the outer edges (=gears) to the right orientation, anyway.

Just because the gear is in the correct orientation how do you know the edge its attached to is? The edge itself could be flipped 180 degrees and still allow the gear to have the correct position and orientation.

Carl
I was not talking about a Gear Cube with S-Faces. I thought of something as your state 1 above:
State 1:
Faces are solved.
Corners are solved.
Edges are solved.
Gears are NOT solved.

Starting with this state, the orientation of the gears is trivial. Therefore, I said
Quote:
stickering those "inner edges" does not add any new challenge to the puzzle.
I'm not sure about the S-Faces, though.

EDIT1: One might ask, is it not harder to achieve this state 1 above (edges solved, correct place, correct orientation)?
I have not stickered the edges but have simulated the Gear Cube moves on an ordinary 3x3x3. It turned out that any scramble could be solved pretty easy. On top of that, the gears are solved trivially.
My conclusion is: With stickered edges you would avoid flipped edges during the solution and not end up with flipped edges that need to be flipped at the very end of the solution.

EDIT2: As always, it depends a lot from where you are coming when judging the difficulty of a puzzle. I had started with a normal 3x3x3 simulating the Gear Cube moves. On this it is quite natural to solve the edges. This did not seem really difficult. On a real Gear Cube without stickering the edges, the solution is even a bit easier. So, my final verdict is: Yes, stickering the edges makes the puzzle a bit harder, but not so much.

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 Post subject: Re: 4 Color Gear Cube and 4 Color Face 3x3
PostPosted: Thu Jun 03, 2010 3:40 am 
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konsassen wrote:
EDIT2: As always, it depends a lot from where you are coming when judging the difficulty of a puzzle. I had started with a normal 3x3x3 simulating the Gear Cube moves. On this it is quite natural to solve the edges. This did not seem really difficult. On a real Gear Cube without stickering the edges, the solution is even a bit easier. So, my final verdict is: Yes, stickering the edges makes the puzzle a bit harder, but not so much.


I agree, it makes a little bit harder.
After scrambling and solving it several times, I have only ever come across a state like this (aside from the fully solved state) where the 8 "inner edges" on one middle slice are in the correct location while the other 16 are not. In this case the orange/green/yellow/blue middle slice:
Image

However, with a fairly simple sequence, it can be turned into this:
Image

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