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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 8:05 pm 
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Julian wrote:
Stefan Schwalbe wrote:
Gelatinbrain: the 3.10.3 has a piece-type with 192 members. You need great endurance to solve that. I used: F, B,U4,B', R,F',R',F, B, F',R,F,R', U'4, R,F',R',F, B', F',R,F,R', F', to solve the 192 pieces one by one.
That is a clever algo. I couldn't find a pure algo to cycle smaller pieces on 3 different faces but I have found a pure commutated commutated commutator :) where 2 pieces are on the same face: (((L3, F), R'), U2). Setups are going to be tricky.


Interesting, my algo is

F2, R,B,U4, L',R,/*setup moves*/
L,[B,R,B',R,B,R'2,B'],L',[B,R2,B',R',B,R',B'],/*commutator*/
R',L,U'4,B',R',F'2,/*reverse setup moves*/

The core is only the second line. The first and third lines are setup moves. Among the three locations, two are on the back face in a single quadrant, which are very compact. The third is on the front face, far away from the other two. Every time I can use any combination of F, U, R to setup. I found setups pretty easy. But I can solve only one piece at a time.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Sep 10, 2010 12:58 pm 
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Julian wrote:
That is a clever algo. I couldn't find a pure algo to cycle smaller pieces on 3 different faces but I have found a pure commutated commutated commutator where 2 pieces are on the same face: (((L3, F), R'), U2). Setups are going to be tricky.

My algo (F, [B,U4,B'], [[R,F',R',F], B, [F',R,F,R']], U'4, [R,F',R',F], B', [F',R,F,R'], F',) is a commutated commutated commutator too :o :

-I started with (R,F',R',F): that cycles 3 center-pieces on the down face (DRB->DFR->DLF->) and the 3 center-pieces (FUR->URF->RFU->).
-Now I needed a good modificaton-move and than I would do the reverse of the first 4 moves.
-B seemed to be a good modification move. So I tried: (R,F',R',F),(B),(F',R,F,R'),(B').
-It gave a good result: The center pieces were all back. It cycled 6 corner-pieces on the down-face and 1 corner-piece on the right-face.
-That 1 corner piece must now be changed, without changing the other 6 corner-pieces. That does (B,U,B').
-The ready move sequence with (A and B swaped)looks now: [B,U,B',] [(R,F',R',F,) B, (F',R,F,R',), B'] [B, U', B'] [B, (R,F',R',F,) B', (F',R,F,R',)] (26 moves).
-Accidental some B moves in the middle combine and make it 4 moves shorter. It's not so easy, to see the commutator structure in it.
-I finally changed [B,U,B'] into [B,U4,B'] and enclosed all with F [...] F' to make it more convenient.
-For the setup moves I can use U, F, L without changing position1 or position2. Especially L at the end of the setup is usefull.
-My move-count was 4671. For a better move-count I could solve two pieces at once.
How would my move-sequence look in your kind of writing? Maybe: F,[([B,U4,B'],((R,F'),B))],F'
Your (((L3, F), R'), U2) is not bad.

schuma wrote:
F2, R,B,U4, L',R,/*setup moves*/
L,[B,R,B',R,B,R'2,B'],L',[B,R2,B',R',B,R',B'],/*commutator*/
R',L,U'4,B',R',F'2,/*reverse setup moves*/
...
Among the three locations, two are on the back face in a single quadrant, which are very compact. The third is on the front face, far away from the other two. Every time I can use any combination of F, U, R to setup. I found setups pretty easy. But I can solve only one piece at a time.

The way of it is interesting. 28 moves is okay. My first approach was 50 moves. I forgot it. I agree: setups are easy. Maybe I can think into your solving way. I would like to know, how this alg. was build.

bmenrigh wrote:

I want to hear about your 2.1.1 solve strategy and solve order. Are your routines more efficient than mine posted here:

Julian wrote:
I'd like to read about your methods for 4.3.1 and 4.5.2, please.

Ok, I will write that into separate posts as soon as possible. Julian, can you in return tell me your Pentultimate-approach wich got the fascinating move-count of 123. I suppose you're using a layer-method.

That's it for now, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Sep 10, 2010 3:15 pm 
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bmenrigh wrote:
I want to hear about your 2.1.1 solve strategy and solve order. Are your routines more efficient than mine posted here: http://www.twistypuzzles.com/forum/view ... 8&p=211229?

That is: center diamonds ((1,1), 3), center triangles ((1,1),1) and small two-color triangles ((1,1),3), where the (1,1) can sometimes be shortened to just 3 moves? Those 60 tiny 2-color triangles take me forever. Sometimes I have to use 8-10 setup moves to get them in the right position and orientation.


Here it is:

"Gelatinbrain 2.1.2" - Solution (single cut, face turning icosahedron)

Attachment:
File comment: corner-letter-notation
GB2.1.2.jpg
GB2.1.2.jpg [ 27.96 KiB | Viewed 6889 times ]


2.1.2 has all piece-types from 2.1.1 as well as 2.1.3. So you can solve all three puzzles with a 2.1.2 strategy.

The piece-types are:
-1. edge (30)
-2. face-corner (60) "kite"
-3. face (20)
-4. corner (12) with 5 orientations
-5. corner-edge (60) "butterfly"

The solving order is like given. Solve all pieces of one type, and than continue with the next type.
-prepare a color scheme, and a letter-notation scheme.

Algs:

-1. edge (30):
commute any pair of level-1-relation face-moves.
-use move-sequences like: [ABC, FBA, ABC', FBA',]. Do that from all angles.

That cycles 3 edges and scrambles a lot of other pieces wich does'nt matter.

-2. face-corner (60) "kite":
commute any pair of level-2-relation face-moves.
-use move-sequences like: [ABC, CDG, ABC', CDG',]. Do that from all angles.

Additional move-sequences to get the last pieces solved:
-a ring-cycler: [KEG', LJK, KEG, LJK, KEG', LJK, KEG,]
-two locations on one face: [[FBA', DCB, FBA], AIF, [FBA', DCB', FBA], AIF',]. Do that from all angles.

That cycles 3 face-corners, does'nt change any edge, and scrambles 3 other piece-types, which does'nt matter.

-3. face (20):

-move-sequence: [[LGD, KEG', LGD'], BHD, [LGD, KEG, LGD'], BHD',], use this move-sequence with appropriate setup-moves.
(You can vary BHD to BHD' or KEG' to KEG on need.
This move-sequence cycles 3 face-pieces, and scrambles no other piece.

-4. corner (12):

-move-sequence: [[LJK', HJL, LJK], KEG', [LJK', HJL', LJK], KEG], use this move-sequence with appropriate setup moves.
Solve the orientation too!
-for twisting a target use [CGE, EAC,] or [CGE, EAC,]2 or [EAC',CGE',] or [EAC',CGE',]2 or similar moves.
This cycles 3 corner-pieces and scrambles some corner-edges, wich does'nt matter.

-5. corner-edge (60) "butterfly":

-move-sequence: [[GLK', LGD, [LDH,] LGD', GLK,] KIE, [GLK', LGD, [LDH',] LGD', GLK,] KIE',], use this move sequence or bacic variations (for instance: KIE' instead of KIE), with appropriate setup moves.
This cycles 3 corner-edges and doesn't change other pieces.
A hint for finding setup moves:
-Find all moves, that change the target location.
-Remember all locations that you got.
-All that locations are 1 move afar from the target location.
-Draw a scheme with a "1" on all that locations.
-You can repeaet that and find all locations that are 2 moves afar and so on.
-Use only moves, that do not change the other 2 locations of the 3-cycle.


That is my solution for the 2.1.2.
I hope I have nothing forgotten. If not, please tell me.

Stefan.

P.S.
bmenrigh wrote:
Sometimes I have to use 8-10 setup moves to get them in the right position and orientation.


Note that the corner-edges have only one orientation!


Last edited by Stefan Schwalbe on Sun Sep 12, 2010 6:35 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 6:18 am 
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Julian wrote:
I'd like to read about your methods for 4.3.1 and 4.5.2, please.


Here is my approach for the 4.3.1:

I used a one letter per face notation. A, B, C, D, a, b, c, d.
I used a color scheme:

Attachment:
File comment: color and face-letter scheme
GB4.3.1a-.gif
GB4.3.1a-.gif [ 6.55 KiB | Viewed 6865 times ]



The piece-types are:
1. face-corner (4 groups of 6 pieces)
2. face (8) (odd permutation parity possible)
3. corner-edge (24)
4. corner (6) (odd permutation parity possible)

Solve piece-type by piece-type in the given order.

1. face-corners (4 groups of 6 pieces)

Attachment:
File comment: groups
GB4.3.1b-.gif
GB4.3.1b-.gif [ 1.42 KiB | Viewed 6858 times ]

The picture shows the 4 groups of face-corners.

Start with red. Look for the 3 red face-corners. Remember the 3 groups they are in. Look into the scheme for a face with that 3 groups. Solve them into that face.
Rotate the whole puzzle to get the red face on A (face: left view, up).
Look for the yellow pieces in the same way and solve them to the right face, adjacent to the red face. Now get red and yellow where they belong on your color scheme, in rotating the whole puzzle.
Moves like (CB,AB)2 cycle 3 face-corners of one group, don't scramble any other face-corners, scramble some other pieces wich doesn't matter.

1b. face-corners (4 groups of 6 pieces) parity fix

You can solve all of them, or end up with two odd groups.
In that case, find an edge with that two groups, and twist that edge. Now the groups are all even, and you can solve the face-corners.

2a. faces (8) parity-fix
Check the parity of the face-pieces without doing one move. If it is odd you can get it even with the following:
Do a single move on a "1"-"4"-edge. Groups 1 and 4 are now odd and the faces are even. Take a third group "3" into. Do a move on a "3"-"1"-edge, and a move on a "3"-"4"-edge. All groups are now even. Than you must solve some face-corners again.
That parity fix would look so: [Bd,AB,BC],(Bd,BC)2,(BC,AB)2,(Bd,AB)2.
Enhancement: You may solve the parity of the face-corners and the faces together, and save some moves.

2b. faces (8)
move-sequence: (DA,AB,BC,AB)2 cycles 3 face-pieces and doesn't change the allready solved face-corner-pieces.

So the face-corners and the faces are now all solved.

3: corner-edge (24)
use the following move-sequences with appropriate setup moves.
forward: ((AB,DC,AB)Ac,)2
backward:(Ac,(AB,DC,AB))2
left->right-reflection, forward: ((DA,BC,DA)Ac,)2
left->right-reflection, backward: (Ac,(DA,BC,DA))2

Solve one piece at once.

Set-up:

Attachment:
File comment: setup
GB4.3.1c.gif
GB4.3.1c.gif [ 1.84 KiB | Viewed 6865 times ]


The picture shows the depth of the locations. 0 are the target locations. x are the loc.1 and loc.2 for the 3-cycles. location-1,2,3 - pieces you can get into the targets without moving any x piece. Not so with 4 and 5- depth locations.
depth 5 pieces you must first get into depth 4 locations with one move.
To get depth 4 pieces into the targets you must first save one of the x - pieces with a setup, wich looks so:
For DA -> Bd : (moves:) dc, [AB,Bd], dc
For AB -> bD : (moves:) cb, [DA,bD], cb
The depth-4 pieces on the right view are set into the targets in a similar way.

4. corners (6)

The corners must now be even in permutation-parity, because of the solved face-corners and faces.
For the corners I use that (moves): [(AB, DC)2, (BC,DA)2, (DC, AB)2, (DA,BC)2]
That does a clean 3-cycle of corner-pieces: (ABCD->aCBd->BAcd->)
I solve the permutation and orientation at once.
Twist the aCBd target clockwise with (moves): [aC,ab,ad]. Counterclockwise with [aC,ab,ad]'. double- twist with [aC,ab,ad]2.
Twist target BAcd similar.

finished,
Stefan.

P.S.
Julian can you tell me wich part of it has helped you enhancing your own solve for I don't believe, I had to tell you all that.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 11:45 am 
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4.5.2 solve:

Julian wrote:
I'd like to read about your methods for 4.3.1 and 4.5.2, please.


my notation + color scheme

Attachment:
File comment: My notation and the color scheme
4.5.2a.gif
4.5.2a.gif [ 5.1 KiB | Viewed 6857 times ]


piece-types:

1. edge-wing (24)
2. left corner-face (24)
3. right corner-face (24)
4. corner (24)

solve order:
1. pair up edge wings
The piece in Ca we bring with one move to its other part. This move is Db. We need to setup the other part to Ac. We use only face-moves for that. If the other part is on cA, because we can not get it with face-moves to Ac, we do one edge-move (Ac). This breaks the edge-pairs Db and Bd. So bevore we do Ac we must setup unsolved edge pieces on both Db and Bd. At the end we may have no unsolved pieces to setup at Db and Bd. This is, when only two unsolved edge-pairs are left, and they are wrong twisted.
Here is a fix for that:
Bring one edge-pair to AB and the other to DA. Now do:
gelatinbrain-moves-notation: [DR, DBL, DB, UBR, URF, UBR', URF', DF, URF, UBR, URF', UBR', DF, DB, DBL', DR,]
Now all edges are paired.

2. solve all edge-pairs (12)
Use only face moves for that, because the edge- moves break edge-pairs
You may need to twist edges:
do (gelatinbrain-moves-notation): UFL', ULB, BL, ULB', UFL, URF', UFL', ULB, BL, ULB', UFL, URF,
This twists both the DA and AB edge-pairs.
You may need a swap for fixing the odd parity of edge-pairs.
do (gelatinbrain-moves-notation):
[DR, DBL, DB, [DF, [UBR, URF, UBR', URF'], DF, [URF, UBR, URF', UBR']], DB, DBL', DR],
[DF, DBL', DL, [[UFL', URF', UFL, URF], DR, [URF', UFL', URF, UFL], DR], DL, DBL, DF],
This swaps DA with AB.

3. pair up the corner-faces (24)
We bring a left corner-face to a right corner-face of the same color.

Do (gelatinbrain-moves-notation): [FL, UBR, FL, UBR'], DBL', [UBR, FL, UBR', FL], DBL,
backward : DBL', [FL, UBR, FL, UBR'], DBL, [UBR, FL, UBR', FL],
This cycles three left corner-faces. Use the location on the b-face for the target. This can be accesed in several ways without changing loc. 1 and loc. 2.

The left and right corner-faces should now be paired.

4. solve the corner-face-pairs (24):
Use (gelatinbrain-moves-notation): [UBR, UFL', UBR', UFL], BL, [UFL', UBR, UFL, UBR'], BL,
and the reverse of it. That cycles 3 corner-face-pairs.

5. corner-quarters (24)
Use (gelatinbrain-moves-notation):

FL, BRU, FL, BRU',
UL, BDR, UL, BDR',
BRU, FL, BRU', FL,
BDR, UL, BDR', UL,

and the backward of it:

UL, BDR, UL, BDR',
FL, BRU, FL, BRU',
BDR, UL, BDR', UL,
BRU, FL, BRU', FL,

That cycles 3 corner-quaters. Best-target is cA.

(With cA I mean the left corner-quater-piece on the left view. The right piece I would call Ac)

That's it
Stefan.

Thank you for your request.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 1:01 pm 
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Stefan Schwalbe wrote:
4.5.2 solve:

...snip...

5. corner-quarters (24)
Use (gelatinbrain-moves-notation):

FL, BRU, FL, BRU',
UL, BDR, UL, BDR',
BRU, FL, BRU', FL,
BDR, UL, BDR', UL,
I haven't played with 4.5.x enough to comment on your solution outline other than to say your routines are very complicated! Interestingly, the above routine seems to trigger a bug in the Applet with the Undo button. If I paste in what you've listed above, I do get a corner piece 3-cycle but when I press the Undo button moves aren't undone correctly and even removing all 16 moves leaves the 3-cycle in place. Did you experience trouble with the Undo on this puzzle too?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 1:57 pm 
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bmenrigh wrote:
Stefan Schwalbe wrote:
4.5.2 solve:

...snip...

5. corner-quarters (24)
Use (gelatinbrain-moves-notation):

FL, BRU, FL, BRU',
UL, BDR, UL, BDR',
BRU, FL, BRU', FL,
BDR, UL, BDR', UL,
I haven't played with 4.5.x enough to comment on your solution outline other than to say your routines are very complicated! Interestingly, the above routine seems to trigger a bug in the Applet with the Undo button. If I paste in what you've listed above, I do get a corner piece 3-cycle but when I press the Undo button moves aren't undone correctly and even removing all 16 moves leaves the 3-cycle in place. Did you experience trouble with the Undo on this puzzle too?


Yes, I know that bug. That happens only when you use the Input-Text-Area on some puzzles. You can't undo the "Input"-Moves.


Do you know how to link to a special post?

Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 3:49 pm 
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Stefan Schwalbe wrote:
Yes, I know that bug. That happens only when you use the Input-Text-Area on some puzzles. You can't undo the "Input"
Oops, je m'en occupe... :(

I updated the standalone version
You can now send your scores from the standalone program.
When you quit the program the current session is automatically saved and resumed when you restart.
So you don't have to keep your computer on during the night(more ecologic :) ).
It's only for Windows. Sorry for mac and linux users(not that I particularly like Windows :wink: ).

P.S.
Stefan, is there any signification in your stage name?
So far, I know that Agamemnon is a Greek mithological figure and Harmagedon a biblical term for the end of the world. But the combination of the two...??? :roll:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 4:55 pm 
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I finally solved the Circle FTO but I'm not particularly happy with my understanding of the puzzle and move count. It seems my attitude towards solving puzzles has changed a lot in my several month solving hiatus because previously I would have been happy that I solved it and that I didn't get the worst move count.

I recognized that the middle circle pieces show the orientation of the centers. I also observed that circle pieces under the corners were paired. Unfortunately I don't understand what those paired pieces represent. I was able to come up with a 3-cycle for them but I couldn't relate them to pieces from any other puzzle I'm familiar with. With 3-cycles to move the paired pieces and the virtual centers I solved all of the circle pieces in about 150 moves. From there, I solved like a super-FTO which took me about 400 moves to get to here:
Attachment:
circle_fto_center_twist.png
circle_fto_center_twist.png [ 15.67 KiB | Viewed 6987 times ]
I spent about an hour trying dozens of things before I figured out how to put an excess twist in the center without also putting an excess 3-cycling in the edges. My resulting fix that that case is about 100 moves.

As far as I can tell, the only way to sub-500 this puzzle is if you have a better understanding of the circle pieces. What am I missing? Is there some trick to approaching this puzzle?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 5:33 pm 
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Stefan Schwalbe wrote:
Do you know how to link to a special post?
Yeah but phpBB doesn't make it easy.

If you mouse-over the post's quote button or the report ! button you'll get the post number from the link:
Code:
http://twistypuzzles.com/forum/posting.php?mode=quote&f=8&p=228893

The to link to that post you'd do:
http://twistypuzzles.com/forum/viewtopic.php?f=8&p=228893#p228893

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 5:49 pm 
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3.10.3
schuma wrote:
L,[B,R,B',R,B,R'2,B'],L',[B,R2,B',R',B,R',B'],/*commutator*/

I found setups pretty easy. But I can solve only one piece at a time.
I really like that algo -- "sliding Sune" for a pure cycle of just (7,1). Hmmm, I'm going to have to go with more difficult setups but solving 2-3 pieces every time. My setup method will be "choose homeboy and homeboy's neighbor" -- then get the neighbor into a circle, spin him around until he is 45 degrees twisted away from homeboy, then slot him into position. Then setup the other piece. I was going to set myself a target of 2500 with my (10,1) cycle but now I'll set myself a target of <=2000 moves, when I get around to solving it.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 6:18 pm 
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Stefan Schwalbe wrote:
P.S. Julian can you tell me wich part of it has helped you enhancing your own solve for I don't believe, I had to tell you all that.
Here is my original 4.3.1 solution. Because I solved the corners first, my later algos were much less efficient. I also finished with a (7,1) pure algo where I see now that there is a (5,1). I knew about the orbitals and parity issues, but it has been very helpful to see your solving order and algos. I have just used your method (I solved most of the face-corners intuitively before cycling) to do a solve in 296 moves: face-corners in 40, centers in 24, edges in 162, and corners in 70. Thanks!

Your 2.1.2 solution is very interesting too. Some of us found a (9,1) pure algo for the corner-edges, then later we were pleased to find (6,1), but you found (5,1)! I was starting with the edges but then I did the corners before the kites (not sure why now), which was costing extra moves. I'll read your 4.5.2 solution tomorrow, and I'll also reply about my Pentultimate method.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 12, 2010 9:21 pm 
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Stefan Schwalbe wrote:
schuma wrote:
F2, R,B,U4, L',R,/*setup moves*/
L,[B,R,B',R,B,R'2,B'],L',[B,R2,B',R',B,R',B'],/*commutator*/
R',L,U'4,B',R',F'2,/*reverse setup moves*/

I would like to know, how this alg. was build.


In order to construct a clean 3-cycle, I tried some routines. I tried this: [R, U, R', U, R, U'2, R'], which is a 3x3x3 last layer algorithm. Of course, the definition for R is turning by 45deg rather than 90deg like in 3x3x3. But I found this routine and a D-turn form a great commutator. But the 3 positions in the 3-cycle turn out to be too close to each other, so that the setup is a little bit hard. Therefore I intentionally added some setup moves to separate one location away from the other two, so that I have more freedom to setup. I also re-oriented the cube to let me easier to think.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 1:07 am 
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bmenrigh wrote:
Stefan Schwalbe wrote:
Do you know how to link to a special post?
Yeah but phpBB doesn't make it easy.

If you mouse-over the post's quote button or the report ! button you'll get the post number from the link:
Code:
http://twistypuzzles.com/forum/posting.php?mode=quote&f=8&p=228893

The to link to that post you'd do:
http://twistypuzzles.com/forum/viewtopic.php?f=8&p=228893#p228893

There's a quicker/better way. See that white/orange page next to the text "Posted: Sun Sep 12, 2010 3:18 pm?" It has a link to that post.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 2:56 pm 
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Seeing Drewseph's amazing Choposaurus made me go back to Gelatinbrain 1.2.9, to try to find a shorter pure algorithm for the triangles. Here is a symmetrical (8,1) algo:

DCG,IJL, /* Setup moves */
HIL,ACD,HIL',ACD', /* Central (1,1) sequence using cutting planes as far apart as possible while still intersecting */
IJL',DCG', /* Undo moves */

KGL', /*Replace the isolated swapped piece with another */

DCG,IJL,ACD,HIL,ACD',HIL',IJL',DCG',

KGL

--------------------------------------------------------------

Then I noticed that the 6th and 7th move of the above algo are exactly opposite each other, so I fused them into a single move with a puzzle rotation, and here is the resulting (7,1) algo:

CGD,IJL,HIL,ACD,HIL',IJL,DEA',
EJF',
DEA,IJL',HIL,ACD',HIL',IJL',CGD',
GLK

Image

This algorithm also cycles three edge pieces of the dual puzzle 2.1.5 pure. Now I wonder if it is possible to solve these puzzles in under 1000 moves?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 3:27 pm 
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Julian wrote:
Stefan Schwalbe wrote:
P.S. Julian can you tell me wich part of it has helped you enhancing your own solve for I don't believe, I had to tell you all that.
Here is my original 4.3.1 solution. Because I solved the corners first, my later algos were much less efficient. I also finished with a (7,1) pure algo where I see now that there is a (5,1). I knew about the orbitals and parity issues, but it has been very helpful to see your solving order and algos. I have just used your method (I solved most of the face-corners intuitively before cycling) to do a solve in 296 moves: face-corners in 40, centers in 24, edges in 162, and corners in 70. Thanks!
...


Thank you! 296 is better than my move-count. :D I like that.
Thank you for showing me your own 4.3.1 solution.

gelatinbrain wrote:
Oops, je m'en occupe... :(

I am sorry. Your programm is still the greatest for me.

gelatinbrain wrote:
Stefan, is there any signification in your stage name?
So far, I know that Agamemnon is a Greek mithological figure and Harmagedon a biblical term for the end of the world. But the combination of the two...??? :roll:

Don't worry about that. I found it joky, when it came into my mind. :oops:
bmenrigh wrote:
As far as I can tell, the only way to sub-500 this puzzle is if you have a better understanding of the circle pieces. What am I missing? Is there some trick to approaching this puzzle?


As I remember, I have solved all the middle circle pieces first.


schuma wrote:
In order to construct a clean 3-cycle, I tried some routines. I tried this: [R, U, R', U, R, U'2, R'], which is a 3x3x3 last layer algorithm. Of course, the definition for R is turning by 45deg rather than 90deg like in 3x3x3. But I found this routine and a D-turn form a great commutator. But the 3 positions in the 3-cycle turn out to be too close to each other, so that the setup is a little bit hard. Therefore I intentionally added some setup moves to separate one location away from the other two, so that I have more freedom to setup. I also re-oriented the cube to let me easier to think.

Thank you for the reply. I was amazed that [R, U, R', U, R, U'2, R'], which I also know from the cube works on the 3.10.3 :o .


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 4:30 pm 
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Stefan, thanks for sharing your clever 4.5.2 method. Almost fully reducing to a Face-Turning Octahedron, with just broken corners left at the end. :idea: (Apart from the first few edge pieces, I cycled everything: edges then corners then center pieces.)

I like the way you find efficient non-commutator algos. For example, the best I can do solving the corners pure with a commutator is (8,1):

RF,DLF', /* Setup moves */
UBR',FL,UBR,FL, /* Face and edge back and forth to cycle groups of 4 pieces */
DLF,RF, /* Undo moves */
URF, /* Replace swapped corner piece with another */
RF,DLF',FL,UBR',FL,UBR,DLF,RF,
URF'

Which is of course 2 moves longer than your "4x4":

FL, BRU, FL, BRU',
UL, BDR, UL, BDR',
BRU, FL, BRU', FL,
BDR, UL, BDR', UL


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 5:09 pm 
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Stefan Schwalbe wrote:
Julian, can you in return tell me your Pentultimate-approach wich got the fascinating move-count of 123. I suppose you're using a layer-method.
Here is my Pentultimate solution from around a year ago, which I have improved slightly since then. You are right, it is essentially a layer-by-layer method. Nowadays I try to completely finish one half before solving the last 6 centers. Of corners 6-10, sometimes the first one or two can be solved in 4 moves (not counting a rotation of the unsolved half to set up the corner), otherwise in 6 or 7 moves, if the corners are not in the adjacent layer. If the corners are in the ring adjacent to where they need to go, they are much harder to solve. To solve a corner adjacently takes me 9 moves and can only be done by pushing a neighboring corner out of position. (I have recently found that by adding a setup move to an algo Brandon found, a corner can be solved adjacently from 2 out of 3 orientations in 10 moves.)

My record of 123 moves was very lucky. At the time I said:

"Crazy luck solving the Pentultimate (1.1.7)! I solved one half of the puzzle in 70 moves, which is nothing special. But, when I checked the other half:

* The other 6 centers were already solved
* 2 of the last 10 corners were already solved
* 3 of the other 8 corners were sitting in a perfect 3-cycle (including orientation)

I calculate the odds of all these happening at 1 in 1,944.

So I had 5 corners left to solve after 88 moves; 3 corners left after 106 moves; and finished at 123 moves."

Brandon has written a program that has proved the last 6 centers can be solved from any permutation with no effect on the solved half, in a maximum of 10 moves, including a twist to roll them into place relative to the solved half. He has also found pure corner cycles of 10 and 11 moves. This is so efficient that there is only point in solving corners 6-10 one by one as long as they are in convenient positions, then we switch to solving the last 6 centers and cycling the remaining corners. I think we could soon be looking at an average solution length of around 140 moves!


Note to Brandon: Sorry, I will try to get that list of Pentultimate corner cycle possibilities to you later this week. :oops:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 5:24 pm 
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Stefan -- copying your approach but making a slight change, I have found that we can cycle three corners of 4.3.1 pure in 14 moves:

FL,BL,FL,
UF,DF,UF,DF,
FL,BL,FL,
DF,UF,DF,UF


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 6:05 pm 
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Julian wrote:
Note to Brandon: Sorry, I will try to get that list of Pentultimate corner cycle possibilities to you later this week. :oops:
No problem at all! I'm really enjoying the conversation about algorithms between you and Stefan. I wish I had more to contribute; the puzzles Stefan is best at I've hardly touched. New thoughts and approaches are great to read about though.

I understand how long it takes to classify the algs I've already posted -- it took me a long time just to pop them in and spot their pattern -- looking at the orientations of the corners is going to take twice that time.

When I realized I wasn't using all my CPUs efficiently with my 11-move searching I started up my 12-move searching at a lower priority to keep the CPUs saturated. The 12-move search is already 1/16th completed and 56 algs have been found. I think it will be done in only two months. Several new patterns have come up already. I'm only going to post the new patterns until you've had a chance to check the orientations on the patterns I've already posted that don't cover all of the possible corner orientations. That way I don't flood the forum with dozens of routines that are already covered by the 10 or 11 moves routines.

As for moves, I think the first center, the 5 corners around it, and then the other 5 centers around that can be placed in 45 moves or so. After that the remaining centers can be done in 9 moves for a total of 54 moves. Then, supposing 2.5 corners are cycled into place in an average of 15 moves for each cycle, were looking at another 90 moves. That comes to 144 moves total 8-) A lucky solve like your 123 moves should drop into the sub-100 range. Once we've cataloged all the routines I'd love to see what you can do with them.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 13, 2010 11:14 pm 
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This post is meant to catalog all of the useful pure Pentultimate/1.1.7 corner 3-cycles of length 12.

I have already posted all length 10 cycles and all length 11 cycles. Rather than post all length 12 routines I will only post the patterns that aren't covered by the 10 or 11 move routines. Once the corner orientations of those routines have been cataloged I will update this post with routines that fill in gaps.

These sequences will take my computer 2-3 months to finish finding. I will keep updating this post even if it is pushed several pages back in this thread.


Skinny Tall Triangle:
Attachment:
skinny_tall_triangle.png
skinny_tall_triangle.png [ 56.84 KiB | Viewed 6873 times ]
[A1, B1, C3, B4, F1, C3, B4, E2, F1, B4, E2, A4]
[A1, B1, D3, B4, C1, D3, E4, A2, E1, C4, D2, A4]
[A1, B2, F4, E1, B2, A4, B3, A1, E4, B3, F1, A4]
[A1, B2, F4, E1, B2, E4, B3, F1, C4, A3, C1, A4]


Left Askew:
Attachment:
left_askew.png
left_askew.png [ 55.58 KiB | Viewed 6873 times ]
[A1, B1, D2, A4, D3, A1, B4, D3, C1, D2, C4, A4]
[A1, B1, D3, B4, F2, B1, C4, F2, B1, D3, C4, A4]
[A1, B1, C3, B4, C2, F1, A4, C2, A1, C3, F4, A4]
[A1, B1, C2, F4, E3, B1, F4, E3, F1, C2, F4, A4]
[A1, B2, A4, B3, A1, E4, B3, F1, B2, F4, E1, A4]
[A1, B2, D4, B3, A1, E4, B3, E1, B2, A4, D1, A4]


Counter-Clockwise Ninja Star:
Attachment:
ccw_ninja_star.png
ccw_ninja_star.png [ 55.96 KiB | Viewed 6873 times ]
[A1, B1, D2, B4, D3, C1, E4, A3, E1, D2, C4, A4]
[A1, B1, C2, B4, E3, B1, F4, E3, B1, C2, F4, A4]
[A1, B1, C3, D4, A2, D1, B4, C2, F1, C3, F4, A4]
[A1, B1, D3, C4, F2, B1, C4, F2, C1, D3, C4, A4]
[A1, B2, F4, B3, F1, C4, A3, F1, A2, F4, C1, A4]
[A1, B2, F4, D3, F1, E4, D3, F1, B2, E4, F1, A4]


StarTrek Communicator:
Attachment:
startrek_communicator.png
startrek_communicator.png [ 56.68 KiB | Viewed 6614 times ]
[A1, B3, F4, B2, E1, A4, B2, A1, B3, E4, F1, A4]
[A1, B3, D4, B2, D1, C4, B2, F1, A3, F4, C1, A4]


Length 13 move sequences are out of reach. It would take a distribute effort and many months to find them all. If somebody is willing to donate "nice -n 19" CPU time on a cluster, it would need about 920,000 CPU hours. On 256 nodes each with 8 cores that's less than 3 weeks.

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Last edited by Brandon Enright on Sat Sep 18, 2010 8:46 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 12:12 pm 
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It seems I'm not able to open 3.1.24. I only get this when I try:
Attachment:
3.1.24.jpg
3.1.24.jpg [ 26.61 KiB | Viewed 6860 times ]


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 2:12 pm 
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Katten wrote:
It seems I'm not able to open 3.1.24. I only get this when I try: [...snip...]
3.1.21-3.1.24 aren't linked from the main page. You can only get to them via the "File" menu inside of the applet.

I did notice the scores page is truncated though so maybe Gelatinbrain ran out of disk space?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 4:05 pm 
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bmenrigh wrote:
Katten wrote:
It seems I'm not able to open 3.1.24. I only get this when I try: [...snip...]
3.1.21-3.1.24 aren't linked from the main page. You can only get to them via the "File" menu inside of the applet.

I did notice the scores page is truncated though so maybe Gelatinbrain ran out of disk space?


Looks OK. Maybe you just accessed at very critical moment...
3.1.24 was once removed, because I noticed it is functionally equivalent to simple 2x2x2. All who solved this should know it. But as it looks so popular, I restored it.
Added 300th puzzle (3.3.12). 8-)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 4:37 pm 
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Yes, I noticed when I just solved it. Not hard at all, though I'm not feeling too secure with circle puzzles just yet.
gelatinbrain wrote:
Added 300th puzzle (3.3.12).
I really think that's a fascinating puzzle, thanks!


Last edited by Katja on Wed Sep 15, 2010 1:36 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 6:14 pm 
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gelatinbrain wrote:
Added 300th puzzle (3.3.12). 8-)


(3.3.12) is an interesting puzzle. I have to confess that I don't deserve the record of 2:54 and 102 moves. It seems that it was caused by a bug.

Here is the reason. The first time I scramble it, the second layers were not moved at all. I didn't realize the second layers could be moved. It was exactly a helicopter cube for me, and I solved it like a helicopter cube. I was just wondering what was the difference between this thing and a helicopter cube.

The second time I played it, it works properly. I would like to solve it again. Gelatinbrain, can you remove my record with 2:54 and 102 moves? It shouldn't be that easy.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 6:25 pm 
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I got the same problam, but to me it didnt get fixed..

It still acts like a helicopter cube.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 14, 2010 6:35 pm 
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Sharon Avidor wrote:
I got the same problam, but to me it didnt get fixed..

It still acts like a helicopter cube.
Java probably cached your applet. You should clear your Java "Temporary Internet Files" and try again.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 15, 2010 1:40 am 
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Sharon Avidor wrote:
The second time I played it, it works properly. I would like to solve it again. Gelatinbrain, can you remove my record with 2:54 and 102 moves? It shouldn't be that easy
This happened to me as well, so it's only fair that mine be removed too.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 15, 2010 1:11 pm 
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Hello,
I solved 1.1.4 and 1.1.6. For the face-corners I used an alg., I used too, when I first solved 1.1.5.
It is (14 moves):
F, C', F', C,
A'2, E'2&2, A2,
C', F, C, F',
A'2, E2&2, A2,

The 1.1.6 corners I solved with my old Pentultimate corner-cycler (18 moves):
F', C, F, C',
J', G, L, G', J,
C, F', C', F,
J', G, L', G', J,
This was the best alg. I found for the Pentultimate-corners. I tried first one of Brandons 10 move-algorithms, which worked on the Pentultimate, but on the 1.1.6 it scrambled a lot of pieces.
I will continue with the 1.1.x-puzzles.

I have found a mechanic version of the 1.1.5. It's called Starminx.

gelatinbrain wrote:
Added 300th puzzle (3.3.12).

gelatinbrain: I really would like to know, how you can achieve this - creating so many puzzles. This must be a lot of hard work. Especially how you construct your models. I expect, you're using splitting algorithms.

Julian wrote:
Stefan -- copying your approach but making a slight change, I have found that we can cycle three corners of 4.3.1 pure in 14 moves:

FL,BL,FL,
UF,DF,UF,DF,
FL,BL,FL,
DF,UF,DF,UF


Yeah, thats good, thank you. :D
Julian wrote:
Here is my Pentultimate solution ...

Thank you, for explaining your Pentultimate solution.
I tried the old one, but I couldn't do some moves. For instance "f". I would like to enhance my own Pentultimate-solution - I will try again. 8-)


Julian wrote:
Stefan, thanks for sharing your clever 4.5.2 method. Almost fully reducing to a Face-Turning Octahedron, with just broken corners left at the end. (Apart from the first few edge pieces, I cycled everything: edges then corners then center pieces.)
...


I took pleasure in it. Ask for more!!

GuiltyBystander wrote:
bmenrigh wrote:
Stefan Schwalbe wrote:
Do you know how to link to a special post?
Yeah but phpBB doesn't make it easy.

If you mouse-over the post's quote button or the report ! button you'll get the post number from the link:
Code:
http://twistypuzzles.com/forum/posting.php?mode=quote&f=8&p=228893

The to link to that post you'd do:
http://twistypuzzles.com/forum/viewtopic.php?f=8&p=228893#p228893

There's a quicker/better way. See that white/orange page next to the text "Posted: Sun Sep 12, 2010 3:18 pm?" It has a link to that post.


Thank you! Bye.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 15, 2010 4:52 pm 
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Stefan Schwalbe wrote:
gelatinbrain: I really would like to know, how you can achieve this - creating so many puzzles. This must be a lot of hard work. Especially how you construct your models. I expect, you're using splitting algorithms.

I think I found a good algorithm to cover a fairly wide range of twisty puzzles. So adding a new puzzle is just a question of a few lines of data.
So, 3.2.8 Circle Dino, 3.4.22 Circle Super X
Someday I will make my source public...

BTW, how is it called the puzzle in your new avatar? :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 15, 2010 6:28 pm 
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Gelatinbrain, I sincerely appreciate your hard work. You are updating puzzles so frequently. Only because of you, I have the opportunity to play the various complicated puzzles created by Drewseph, TomZ etc, for FREE. And I am pretty sure that a great portion of puzzles they will create in the near future has been covered by your applets. Thank you very much.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 15, 2010 6:33 pm 
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schuma wrote:
Gelatinbrain, I sincerely appreciate your hard work. You are updating puzzles so frequently. Only because of you, I have the opportunity to play the various complicated puzzles created by Drewseph, TomZ etc, for FREE. And I am pretty sure that a great portion of puzzles they will create in the near future has been covered by your applets. Thank you very much.
Well said. I love seeing new puzzles being made that I have either already solved or have the opportunity to play with on your applet. Twisting your applet feels as real to me as owning the puzzle. Your hard work to bring us new puzzles is very appreciated!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 16, 2010 2:23 am 
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Stefan Schwalbe wrote:
I tried first one of Brandons 10 move-algorithms, which worked on the Pentultimate, but on the 1.1.6 it scrambled a lot of pieces.
The (6,1) algo in my Pentultimate solution works with 1.1.6 too, so you can leave the corners of 1.1.6 to the end if you like. But there is also a (3,1) algo to cycle the center-corner pieces of 1.1.4, 1.1.5 and 1.1.6 pure. Hint: The "3" are face moves and the "1" is a slice (shift-click) move.

Stefan Schwalbe wrote:
Thank you, for explaining your Pentultimate solution. I tried the old one, but I couldn't do some moves. For instance "f".
The moves in lower case are puzzle rotations. For example, with "f" you rotate the whole puzzle clockwise 72 degrees around the F face. I did this so I could leave the main part of the algorithm the same for every orientation case.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 16, 2010 2:34 am 
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bmenrigh wrote:
schuma wrote:
Gelatinbrain, I sincerely appreciate your hard work. You are updating puzzles so frequently. Only because of you, I have the opportunity to play the various complicated puzzles created by Drewseph, TomZ etc, for FREE. And I am pretty sure that a great portion of puzzles they will create in the near future has been covered by your applets. Thank you very much.
Well said. I love seeing new puzzles being made that I have either already solved or have the opportunity to play with on your applet. Twisting your applet feels as real to me as owning the puzzle. Your hard work to bring us new puzzles is very appreciated!
I'll third that -- your prog has brought great pleasure to my life.

Gelatinbrain -- I know you have already added an amazing variety of puzzles, but I have remembered a category of puzzles that is missing! I was going to say something a long time ago, then I forgot, and TomZ's recent physical Helicopter Skewb has reminded me.

Could you please add a category for vertex + edge turning cubes? Some combinations of Dino Cube/Master Skewb/Skewb + 3.3.1/3.3.3/3.3.5/3.3.7 would probably make good puzzles.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 16, 2010 3:04 am 
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Julian wrote:
But there is also a (3,1) algo to cycle the center-corner pieces of 1.1.4, 1.1.5 and 1.1.6 pure. Hint: The "3" are face moves and the "1" is a slice (shift-click) move.
The (3,1) i use is different, the three is face, slice, face and the 1 is a face move. I posted it back on page 36, as i said there i always thought you used the same one hahaha apparently not.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 16, 2010 3:08 am 
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Julian wrote:
Could you please add a category for vertex + edge turning cubes? Some combinations of Dino Cube/Master Skewb/Skewb + 3.3.1/3.3.3/3.3.5/3.3.7 would probably make good puzzles.
I agree. Then we won't have to use 3.2.3 to simulate a Dino Cube solve anymore (like I did last night :lol: ) etc. I believe these puzzles would be greatly appreciated in your vast collection of virtual puzzles.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 16, 2010 2:39 pm 
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I haven't been on GB for a while and now I'd like to go back on it, but I'm just getting a blank area where the puzzle should be; does anyone know what's going on? :?

Alex

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Sep 17, 2010 4:28 pm 
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Elwyn wrote:
Julian wrote:
But there is also a (3,1) algo to cycle the center-corner pieces of 1.1.4, 1.1.5 and 1.1.6 pure. Hint: The "3" are face moves and the "1" is a slice (shift-click) move.
The (3,1) i use is different, the three is face, slice, face and the 1 is a face move. I posted it back on page 36, as i said there i always thought you used the same one hahaha apparently not.

Thank you Elwyn for the (3,1). I didn't even think, that this is possible. :o . Julian, can you tell me the (6,1), for the Pentultimate-corners or at least another hint? :D

gelatinbrain wrote:
Stefan Schwalbe wrote:
gelatinbrain: I really would like to know, how you can achieve this - creating so many puzzles. This must be a lot of hard work. Especially how you construct your models. I expect, you're using splitting algorithms.

I think I found a good algorithm to cover a fairly wide range of twisty puzzles. So adding a new puzzle is just a question of a few lines of data.
So, 3.2.8 Circle Dino, 3.4.22 Circle Super X
Someday I will make my source public...

BTW, how is it called the puzzle in your new avatar? :)


Thank you. I expected something like this. Great thing. Don't stop.

bmenrigh wrote:
schuma wrote:
Gelatinbrain, I sincerely appreciate your hard work. You are updating puzzles so frequently. Only because of you, I have the opportunity to play the various complicated puzzles created by Drewseph, TomZ etc, for FREE. And I am pretty sure that a great portion of puzzles they will create in the near future has been covered by your applets. Thank you very much.
Well said. I love seeing new puzzles being made that I have either already solved or have the opportunity to play with on your applet. Twisting your applet feels as real to me as owning the puzzle. Your hard work to bring us new puzzles is very appreciated!


Your words really moved me. I feel the same.

gelatinbrain wrote:
BTW, how is it called the puzzle in your new avatar? :)

It is your words, that made it a puzzle - funny Idea. For me it was just a visualization of the commutator principle.
:|

P.S. I recently solved the 1.1.8 and the 1.1.9 "gigaminx". For the 1.1.8 corner-faces i used a (3,1) and for the edge-halfs i used a (7,1). I guess there is a better alg. With my 1.1.9 solve i will not appear in the rankings, for it was too bad. :oops:

Bye, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Sep 17, 2010 4:48 pm 
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Stefan Schwalbe wrote:
P.S. I recently solved the 1.1.8 and the 1.1.9 "gigaminx". For the 1.1.8 corner-faces i used a (3,1) and for the edge-halfs i used a (7,1). I guess there is a better alg.
It seems like most of us had a hard time with 1.1.8 so good job.

For the "edge-halves" I too used a (7,1) when I first solved it. I just revisited it though and this (5,1) popped out at me as easy and kinda obvious. I wonder why I didn't spot it before :?

[F'2,C',B'2,C,F2], [E&2], [F'2,C',B2,C,F2], [E'&2]

Note that by modifying the commutated E&2 slice you can vary what gets cycled rather easily.

Elwyn came up with a brilliant reduction to Megaminx trick for this puzzle. He wrote about it here. See the posts after that one too for more discussion about 1.1.8.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Sep 18, 2010 5:36 pm 
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1.2.9 (physical version = Drewseph's Chopasaurus)

New solution outline

Stage 1 - Solve 8 corners using intuitive sequences: 5 corners around a face, then 3 adjacent corners in the next layer/ring. This stage should only take around 30 moves. With the last 3 of these corners, the idea is to get the corner in a place to spin it around to the correct orientation without disturbing other pieces, then set it up, and finally put it in place with a simple 2-gen sequence.

Stage 2 - Solve the remaining corners, permuting and orienting at the same time, mostly a pair at a time, using (4,1) commutators.

Stage 3 - Two thirds of the time you will end up with a single twisted corner. If you do, twist it to its correct orientation and then re-solve the other 9 corners in 3 cycles.

Stage 4 - Solve the centers using (6,1) commutators.

Stage 5 - Solve the triangles using (7,1) pure commutators.

Algos for stages 4 and 5 can be found by experimenting with (1,1) commutators using two corners that are far apart. The stage 4 algo has a single setup and undo move either side of a (1,1), and the stage 5 algo has two setup and undo moves, but a move overlap (consecutive moves on the same axis) allows the sequence to be reduced from 8 to 7 moves.

Solved today in 752 moves using this method. :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Sep 18, 2010 5:46 pm 
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Stefan Schwalbe wrote:
Julian, can you tell me the (6,1), for the Pentultimate-corners or at least another hint? :D
The 6 moves are the sequence called P (or Pm for the mirror image) in my solution. Another way of looking at it is to take three faces that all touch each other and call them F, U, and R, like a Rubik's cube. F U R U' R' F' isolates a single swapped corner in half of the Pentultimate.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 20, 2010 2:50 am 
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I was laying in bed, unable to sleep thinking about the center-twist "parity" I got on the Circle FTO and how all the fixes I tried didn't come out pure. I got to thinking about what is required for a orientation parity twist to be pure and I realized that it is easy to find twists on 1.2.2 that meet those requirements:
Attachment:
1.2.2_parity_pure.png
1.2.2_parity_pure.png [ 92.48 KiB | Viewed 6674 times ]
The routine is:
[[[EDK,AEF,EDK'],[AFB,ADE,AFB']],[[EDK,AEF',EDK'],[AFB',ADE,AFB]]]x2
...and it's pure (24 moves).

I suppose this isn't such an amazing thing for 1.2.2 but I think I'm pretty close to adapting it to 1.2.3 and deeper cut vertex turners such as 1.2.9. The principal works for all modulo-3 puzzles but finding short sequences that meet the right conditions seems non-trivial for the deeper cut puzzles.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 20, 2010 1:10 pm 
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bmenrigh wrote:
I was laying in bed, unable to sleep thinking about the center-twist "parity" I got on the Circle FTO and how all the fixes I tried didn't come out pure. I got to thinking about what is required for a orientation parity twist to be pure and I realized that it is easy to find twists on 1.2.2 that meet those requirements. The routine is:
[[[EDK,AEF,EDK'],[AFB,ADE,AFB']],[[EDK,AEF',EDK'],[AFB',ADE,AFB]]]x2
...and it's pure (24 moves).

I suppose this isn't such an amazing thing for 1.2.2 but I think I'm pretty close to adapting it to 1.2.3 and deeper cut vertex turners such as 1.2.9. The principal works for all modulo-3 puzzles but finding short sequences that meet the right conditions seems non-trivial for the deeper cut puzzles.
Genius! :D Believe it or not, you have solved annoying corner orientation problems for 1.2.2-1.2.9.

With 1.2.3, the most efficient solving order I know is wide triangles, corners, centers, thin triangles, so the algo doesn't need to be pure, just not to affect wide triangles. It does the job perfectly for 1.2.3.

It is natural to solve 1.2.4 and 1.2.5 corners first so no problem there anyway, just a single twist if necessary before solving the centers.

1.2.6 has no corners so that leaves 1.2.7-1.2.9, where again it is natural to solve them corners first, so all we care about is that we can twist a single corner without affecting any other corners. I tried the same pattern as your algo but spacing the 4 turning points further apart, and here we are:

[DCG,JEK,DCG',
IJL,EAD,IJL',
DCG,JEK',DCG',
IJL',EAD,IJL,]x2


You have just made solving 1.2.2-1.2.9 a lot more fun -- thanks! (Now I need to take some time to understand exactly how your magic algo works...)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 20, 2010 3:39 pm 
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Hello again, it's great to be here :D
bmenrigh wrote:
The routine is:
[[[EDK,AEF,EDK'],[AFB,ADE,AFB']],[[EDK,AEF',EDK'],[AFB',ADE,AFB]]]x2
...and it's pure (24 moves).

That is an amazing approach. It's great.

My moves for it were (30):
ADE,
[AEF', AFB, AEF,] ADE,
[AEF', AFB', AEF,] ADE,
[AEF', AFB, AEF,] ADE,
[AEF', AFB', AEF,]
EDK', ADE', AFB,[
[ACD, EDK, ACD'], AEF, [ACD, EDK', ACD'], AEF',
]AFB',ADE, EDK,

Your (12)x2 is really impressing.

Julian wrote:
Stefan Schwalbe wrote:
Julian, can you tell me the (6,1), for the Pentultimate-corners or at least another hint? :D
The 6 moves are the sequence called P (or Pm for the mirror image) in my solution. Another way of looking at it is to take three faces that all touch each other and call them F, U, and R, like a Rubik's cube. F U R U' R' F' isolates a single swapped corner in half of the Pentultimate.

Thank you, Julian :D. Your 1.2.9 solve has impressed me very much.

bmenrigh wrote:
It seems like most of us had a hard time with 1.1.8 so good job.

For the "edge-halves" I too used a (7,1) when I first solved it. I just revisited it though and this (5,1) popped out at me as easy and kinda obvious. I wonder why I didn't spot it before

[F'2,C',B'2,C,F2], [E&2], [F'2,C',B2,C,F2], [E'&2]

Note that by modifying the commutated E&2 slice you can vary what gets cycled rather easily.

Elwyn came up with a brilliant reduction to Megaminx trick for this puzzle. He wrote about it here. See the posts after that one too for more discussion about 1.1.8.


Thank you Brandon. The (5,1) is good. Elwyn's solve of the 1.1.8 has also impressed me as it saves many moves. It seems to be hard to me, to pair the edges in his way. I tried the idea to write down the 2 colors of the 30 edge-pairs on a sheet of paper and tick off the solved edges but there must be a better way and I didn't really do that. Elwyn, if you want, you can tell me how you did that. :D

Stefan. :scrambled:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 20, 2010 7:56 pm 
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1.2.9 is too hard for me. :( One day I WILL SOLVE IT.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 21, 2010 12:38 am 
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Julian wrote:
Believe it or not, you have solved annoying corner orientation problems for 1.2.2-1.2.9.

With 1.2.3, the most efficient solving order I know is wide triangles, corners, centers, thin triangles, so the algo doesn't need to be pure, just not to affect wide triangles. It does the job perfectly for 1.2.3.
It is quite a privilege to be able to work with, and sometimes even contribute to such talented solvers. I spent another hour today trying to do better that what I came up with last night in my head in 30 minutes and no computer. No success though... I can't figure out how to mask of the extra thin triangle on 1.2.3 to make the routine pure. Even if I do come up with a solution, it will probably be 18 x 2 moves which hardly seems worth it.

But, much to my amazement, I don't need to adapt my routine to 1.2.9 because you already have :mrgreen:. Individually we come up with good routines and solutions. Collectively our solutions are brilliant. It really feels great to interact with such good solvers.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 21, 2010 1:54 am 
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Interesting, gelatinbrain has done something new. I went to look at the records for 1.2.9 and found an odd "help" link above it which lead right to this thread, specifically to Julian's recent solutions outline.
Stefan Schwalbe wrote:
I tried the idea to write down the 2 colors of the 30 edge-pairs on a sheet of paper and tick off the solved edges but there must be a better way and I didn't really do that. Elwyn, if you want, you can tell me how you did that.
You did just as i did, wrote them down and crossed them off. I think i might be able to do it without writing them down now because of how well i know the colour scheme but it would be hard.
Stefan Schwalbe wrote:
With my 1.1.9 solve i will not appear in the rankings, for it was too bad.
Did you use reduction? If you want you should try solving it again like This I've always liked the gigaminx :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 23, 2010 12:09 pm 
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Julian wrote:
1.2.9 (physical version = Drewseph's Chopasaurus)
...
Stage 3 - Two thirds of the time you will end up with a single twisted corner. If you do, twist it to its correct orientation and then re-solve the other 9 corners in 3 cycles


Here is a way to fix the orientation-parity early. Check the parity without doing one move. Than fix it with one move if it is 1 or 2.

The orientation parity of all corners is computed in adding the orientation-state of each of the 20 corners, wich can be 0: correct, 1: clockwise twisted, 2: counterclockwise twisted. The summ is than taken modulo 3. 1 is fixed with a single counterclockwise move. 2 is fixed with a single clockwise move. 0 is allready correct.
The corners are divided up into 4 groups as indicated in the picture.
Attachment:
1.2.9-o-parity.jpg
1.2.9-o-parity.jpg [ 20.09 KiB | Viewed 6551 times ]

1: corners with a white facelet
2: corners with a yellow facelet
3: corners with one left color and two right colors
4: corners with one right color and two left colors

So each corner-piece has a 0-facelet, and each corner-location has a 0-facelet-location. Go through the 20 corner-locations and look where the 0-facelet of the corner-piece is in relation to the 0-facelet-location. Add the numbers that you get together. When you are through take it modulo 3 and fix the corner-orientation-parity with one single move. :mrgreen:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 23, 2010 2:02 pm 
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Julian: Today I checked your new 1.2.9 outline (posted on this page), and I solved it in 900 moves, thanks to this brilliant method. :D Especcially the (7,1) for the face-edges is half as short as my alg. would have been. The solve of the corners at the beginning is very good, except I would fix the parity earlier as I have explained in my last post. I need not to say that the 1.2.9 method will also solve the 2.1.5. The only difference will be the orientation of the corner pieces and the face pieces. I'm always happy, when I solve a puzzle for the first time. :D

Elwyn: I solved the gigaminx again with your method, and this time I reached into the fewest move rankings. Your method is clever in saving moves, and it is a fun to do it in your way. 8-)

Stefan.


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