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 Post subject: Fudging and jumbling Dayan's Gem II
PostPosted: Sat Apr 16, 2011 9:46 am 
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Last Thursday, Dayan’s Gem 2 arrived. I had great fun solving it. In the end I needed to add two alg’s to my gem-1 repertoire (a 3-cycle for the pieces with pentagonal faces, and a 3-cycle for the rectangular centre pieces). When scrambling I accidently made a fudging move like on the 1st photo. I didn’t pay much attention, continued scrambling, solved the puzzle and ended in the jumbled situation of the 2nd picture. I fudged back and was able to solve it using only ‘legal’ moves.

Image

Image

My intuitions tells me the 2nd picture isn’t possible without fudging. Can anyone prove that?

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sat Apr 16, 2011 1:15 pm 
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That isn't fudging. Fudging is a technique used to remove jumbling via the making of space where there would be an infinite number of pieces.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sat Apr 16, 2011 11:49 pm 
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The definitions I found on the forum are not conclusive: does it include making otherwise illegal moves or is it restricted to pieces being in illegal places. If anyone can clarify, please do (in a dictionary thread).

Enough semantics: can somebody explain if the shape with the ears is possible with only legal moves? (with the color scheme shown that is!)

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun Apr 17, 2011 2:38 am 
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Yes, but this puzzle isn't fudged. It jumbles. And fudging is in the building process of the puzzle; "I fudged the puzzle to allow so and so pieces to move".

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sat Apr 30, 2011 3:27 pm 
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The case shown is possible without the illegal potentially puzzle-damaging move. I have encountered it on my Dayan Gem II adventures.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 5:45 am 
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Emile wrote:
The case shown is possible without the illegal potentially puzzle-damaging move. I have encountered it on my Dayan Gem II adventures.
If you define "legal moves" as 180 degree turn of the edges, only (you could call them Helicopter moves), the shown situation is certainly not poosible. 180 degree edge turns will never change the shape of the Gem II and the shown situation is shapeshifted.
Any other moves of edges can only be jumbling moves. Or how do you define "legal"?

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 6:54 am 
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I want to know if jumbling can cause a situation where the cube is only solvable by completing more jumbling moves, or if once the jumbling is unpacked and the cube shape restored if the solve is straightforeward `as always`? Because I believed it might create a `type of parity`, but I haven't come across it yet. (For the Dayan Gem 1 or 2).
*EDIT Sorry, I meant: I get it all the time in the Gem 1, why not in the Gem 2.. You answered my question with intuition regardless Konrad, so thanks. :wink:
Cheers,
Burgo.

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Last edited by Burgo on Mon May 02, 2011 2:36 am, edited 1 time in total.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 8:14 am 
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Emile wrote:
The case shown is possible without the illegal potentially puzzle-damaging move. I have encountered it on my Dayan Gem II adventures.

Great, how? Can you give an alg, I never stumbled on this situation legally, can be a concidence ( not very probable considering the number of solves).

I think the puzzle can be solved without jumbling, please see my comment in the solving forum.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 12:20 pm 
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maarten wrote:
Emile wrote:
The case shown is possible without the illegal potentially puzzle-damaging move. I have encountered it on my Dayan Gem II adventures.

Great, how? Can you give an alg, I never stumbled on this situation legally, can be a concidence ( not very probable considering the number of solves).

I think the puzzle can be solved without jumbling, please see my comment in the solving forum.

I'm really confused: How on earth can you achieve something like the situation in your picture
Image
by "legal" moves? The two pieces sit at their right location , but they are flipped.
I define legal moves as 180 degree turns of edges (the pieces with four stickers are equivalent to the edges of the 3x3x3. I would not call them "corners") How do you define "legal" moves????
Your picture shows clearly a jumbled situation. How can that be seen differently?

BTW, can you make a turn of the square U face in your picture, if there is a jumbled piece in it (sitting flipped in that square face.) I cannot do that, but maybe I have an especially tight version. (See my post here).

BTW, why do we have three threads in the solving forum about this one puzzle?
(the other from April 27th
the first from April 13th)

I think it is a nice and easy puzzle:
1. unjumble
2. cross
3. edges of the 3x3x3 (pieces with four stickers)
4. pieces with two stickers (=Helicopter centres, but much easier, due to the missing Helicopter corners)

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 12:44 pm 
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Burgo wrote:
I want to know if jumbling can cause a situation where the cube is only solvable by completing more jumbling moves, or if once the jumbling is unpacked and the cube shape restored if the solve is straightforeward `as always`? Because I believed it might create a `type of parity`, but I haven't come across it yet. (For the Dayan Gem 1 or 2).

Cheers,
Burgo.
I think that the Gem I can be seen as a Helicopter like puzzle, centres only, no corners.
The moving pieces (24) live in 4 orbits
By jumbling you can switch pieces between orbits and you cannot reverse this by "legal" moves.
On the Gem II this is different because you have the additional square turns. I cannot prove it mathematically, but I share maarten's assumption that any situation can be solved by legal moves only, after you have achieved its ordinary shape.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 4:51 pm 
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Konrad wrote:
Emile wrote:
The case shown is possible without the illegal potentially puzzle-damaging move. I have encountered it on my Dayan Gem II adventures.
If you define "legal moves" as 180 degree turn of the edges, only (you could call them Helicopter moves), the shown situation is certainly not poosible. 180 degree edge turns will never change the shape of the Gem II and the shown situation is shapeshifted.
Any other moves of edges can only be jumbling moves. Or how do you define "legal"?


Oh I obviously agree! When I said "legal" I meant moves that are possible without making parts of the mechanism cry. I might be unfamiliar with official terminology... Are any jumbling moves "illegal" even though they do not strain the puzzle?

Anyway, here's a link to me fixing the case by unjumbling, then doing a simple 3-cycle. It really isn't a bad case:
http://www.youtube.com/watch?v=YOPfOO_XsKI

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 4:52 pm 
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Hi Konrad,

I achieved the situation in the picture by forcing an illegal move ( see photo in 1st post). I did loosen the tension of the screws a bit since the puzzle was a bit stiff making the illegal move possible. The sound is not good though :roll: . My question in the original post was: can anyone make this legally or prove that's impossible?

Your other post
I'm working on the math but can't get it right. Thank you for adding the shape-clause.

Thank you for your thoughts.
Maarten

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 4:55 pm 
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Hi Emile,

Jumbling moves are legal.

I confess I made the mechanism cry.

Puzzle still is working fine though.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Sun May 01, 2011 5:00 pm 
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Ho Emile,

Just managed to view your vid, you answered my question!
Thanks! :D

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Mon May 02, 2011 3:26 am 
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maarten wrote:
Hi Konrad,

I achieved the situation in the picture by forcing an illegal move ( see photo in 1st post). I did loosen the tension of the screws a bit since the puzzle was a bit stiff making the illegal move possible.
....

Thank you for your thoughts.
Maarten
Aaaah, I see now what you mean by illegal moves. My puzzle does not allow them (it is too stiff) and therefore I had misinterpreted "illegal" as "jumbling" moves.

Can we agree on the terminology and notation? (Because the puzzle is so easy, we will probably not need much notation of algorithms, but it can be confusing if different people use different notations.)

My proposal:

- Gem II is a combination of an edges only 3x3x3 and a Helicopter without corners.

- we have three piece types:
o the rectangles can be named as "outer centres" (They are part of the 3x3x3 centre and can be done very easily in the first steps. No algorithms needed.) They build the square faces of a 3x3x3, which can be named as on a 3x3x3 by U, D, F, B, L, R
o The pieces with the four stickers correspond to the 3x3x3 edges. They can be named like edges on a 3x3x3 by the two face names they are sitting in, e.g. FU, RU. Non jumbling moves can be named - as somebody has proposed - by [FU], [RU] etc
o the pieces with two triangular stickers correspond to the centres of a Helicopter. It would be confusing to call them "Helicopter centres", we could call them just"triangular pieces". I do not think they need to be named further, but if that is ever necessary, we could name them after the two intersecting moves they can be turned by, e.g. {[FU], [RU]}

- Jumbling moves could be named like j[FU] , describing a clockwise move of [FU] to the next jumbling position and
j'[FU], the same thing anticlockwise.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Thu May 12, 2011 11:26 pm 
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maarten wrote:
Last Thursday, Dayan’s Gem 2 arrived. I had great fun solving it. In the end I needed to add two alg’s to my gem-1 repertoire (a 3-cycle for the pieces with pentagonal faces, and a 3-cycle for the rectangular centre pieces). When scrambling I accidently made a fudging move like on the 1st photo. I didn’t pay much attention, continued scrambling, solved the puzzle and ended in the jumbled situation of the 2nd picture. I fudged back and was able to solve it using only ‘legal’ moves.
[...images snipped...]
My intuitions tells me the 2nd picture isn’t possible without fudging. Can anyone prove that?
Hi maarten, this situation does not require any fudging moves. It can be done in two 3-cycles. I have put my puzzle in the same position:
Attachment:
dayan_gem_edges_flipped_small.png
dayan_gem_edges_flipped_small.png [ 247.51 KiB | Viewed 1686 times ]
I have created a demonstration video showing how I put my puzzle into this position. As you can see no fudging is required. The only jumbling comes in the last 4 moves.

Edit: My apologies to Emile who figured this out and posted a video before me. I had not seen your post.

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 Post subject: Re: Fudging and jumbling Dayan's Gem II
PostPosted: Fri May 13, 2011 3:46 am 
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Hi bmenrigh,

Thank you for your post, it's double but still a nice vid!

The next question is: how many pairs can you flip without torturing the mechanism? Would love to see a photo!

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