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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 12, 2011 7:40 pm 
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schuma wrote:
Hi Brandon, I have a few selfish requests about this app.

No problem. I figure if it's useful for you then it will be useful to lots of others too :D . I have added all three.

There is a quirk with the reset button and checkboxes which is probably browser dependent. If it doesn't reset the checkboxes the way you want I'm not sure there is anything I can do about it without adding JavaScript to the page.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 13, 2011 1:41 am 
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bmenrigh wrote:
There is a quirk with the reset button and checkboxes which is probably browser dependent. If it doesn't reset the checkboxes the way you want I'm not sure there is anything I can do about it without adding JavaScript to the page.


The reset button seems to work well on my computers. Thanks for adding these functions.

Gelatinbrain, I'd like to propose a puzzle as follows:

Can you make a cubic puzzle that looks just like 3.5.2, but make it face-vertex-edge turning? That is, the face turning is like in 3.5.2. The edge turning is only 180 deg (let's make it classical). The vertex turning affects three 90-deg sectors around a corner. I think it should be a neat puzzle to play with.

The original idea belongs to Roice Nelson, who made this beautitful hexagonal puzzle in MagicTile v2:
Attachment:
Image 000.png
Image 000.png [ 113.74 KiB | Viewed 6497 times ]

This is also a face-vertex-edge turning puzzle, where all the circles are of the same size, just like in 3.5.2 all the circles share the same radius. He also made the corresponding hyperbolic {7,3} puzzle and {5,3} dodecahedron (projected on to a plane).

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 13, 2011 8:04 am 
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bmenrigh wrote:
I have written a simple script to help pretty-print Gelatinbrain's macro move-sequences as well as invert and mirror routines. You can see it here: http://www.brandonenright.net/cgi-bin/gb_util.pl

Eventually it will be able to deconstruct your routine if it follows "standard form" and tell you what the form is. In the future it may also support []xN notation such as [A, B, A', B']x3.

If the program needs more features let me know.
Good idea, Brandon. Thank you, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 24, 2011 8:07 am 
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Merry Christmas to all of you. Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 24, 2011 12:32 pm 
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Merry Christmas to you too, Stefan :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 24, 2011 12:35 pm 
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Merry Christmas to all of GB solvers!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 28, 2011 10:43 am 
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Long time no post :D

I haven't solved these puzzles in a long time, but I wanted to get back into it for fun/ goofing off while I'm not programming. Unfortunately I cannot figure out how to load these applets any more. I have the latest version of Java and have tried on several different operating systems, but they refuse to load. Can anyone help me out?

Percy


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 28, 2011 1:00 pm 
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Percy wrote:
Long time no post :D

I haven't solved these puzzles in a long time, but I wanted to get back into it for fun/ goofing off while I'm not programming. Unfortunately I cannot figure out how to load these applets any more. I have the latest version of Java and have tried on several different operating systems, but they refuse to load. Can anyone help me out?
Hey Percy, it's always good to have old names come back. Due to changes in the way Java handles the signing of native code as well as changes in how browsers interact with plugins, the program no longer works very well as an applet. You need to download a local copy and run the jar directly, bypassing the browser altogether.

The easiest way to setup the local environment is to use Gelatinbrain's installer.jar. Make a directory somewhere on your computer. Download installer.jar and put it in that directory. Then from the command prompt (or the terminal on OS X) change to the directory you made and run java -jar installer.jar. On OS X the installer window draws really small and you can't see any of the buttons so you first have to expand the window before you can click anything.

Once everything is downloaded you can launch the program by running java -jar polyhedra.jar from the command prompt / terminal.

If you want to stay up to date with the latest puzzles, you only have to download the latest copy of polyhedra.jar and replace the downloaded one: http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/joglx/polyhedra.jar

Also, the images zip that gets pulled down by the installer isn't kept very up-to-date so if you want more images in the menu, I've written a program to maintain a fresh copy of the full images directory. http://www.brandonenright.net/~bmenrigh/gb_images.zip. Just replace the images directory that gets downloaded with the one in that zip. Note, the puzzles missing images aren't a bug, Gelatinbrain doesn't make images for every puzzle. I'm sure it is a lot of work to do so and making images doesn't help bring new and amazing puzzles into the world :D .

If you have any trouble getting the local copy running there is a troubleshooting thread Gelatin Brain's Applet Problem. Post there and somebody will be able to help.


In other news, Gelatinbrain has given us a somewhat shallow-cut vertex-turning tesseract (8.2.1)! The projection used to explode out the cells on the tesseract makes for some rather distorted looking twists (DGFA) for example.

Also, DGFA and EGAF are inverses of each other but the way the program counts moves, it is 2 moves so be careful.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 28, 2011 7:16 pm 
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SO, it's the holidays and I have very few excuses not to solve puzzles, except for moving out, but that is taken care of now.

I watched Brandon's first video on solving the 3x3x3x3. It was very understandable, so I downloaded the applet and started twisting around, but didn't get too far. I then decided to have a go at the easier 2x2x2x2, which is also on GB. Here's the only sequence I have come up with so far:
Attachment:
2x2x2x2.PNG
2x2x2x2.PNG [ 11.78 KiB | Viewed 6265 times ]

So it's a 3-cycle of the 4-color 'corners.
I think I may need an algorithm for the orientation as well, so that's the next step. The 2x2x2x2 just crunches my brain a bit too much.

That is why I moved on to some organisational tasks. My collection of algorithms for difficult puzzles has always been a mess. It is just a big word file, with groups of algorithms and corresponding pictures. They were in chronological order, so in the order that I solved the puzzles.

So, I decided to clean that up and expand it in way more organised files. I started this at the beginning, so dodecahedra. I just started with the first puzzle, 1.1.1, and am working my way up.
I don't put down an entire solution, just the algorithms and explanatory pictures. Per puzzle the algorithms get numbered. So every algorithm will have a specific code to describe it, like 1.1.6-Alg2, which is a corner orienting algorithm for 1.1.6.
Later on in the file, for instance with 1.1.7, I can refer back to 1.1.6-Alg2 for solving the same piece on different puzzles. Here's a preview:
Attachment:
preview.PNG
preview.PNG [ 263.47 KiB | Viewed 6265 times ]


Of course I don't have every algorithm needed for every puzzle, so this will also motivate me in finding methods for puzzles I haven't solved yet. Everything is the same format, so if people want to help with this they may of course do so! However that will prevent me from learning new methods.

I will try to get as far as I can with this, but I already anticipate this to be a literally endless process. This evening I only got through about 9 puzzles, and I already knew all about these!

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Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 30, 2011 12:15 am 
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bmenrigh wrote:
In other news, Gelatinbrain has given us a somewhat shallow-cut vertex-turning tesseract (8.2.1)! The projection used to explode out the cells on the tesseract makes for some rather distorted looking twists (DGFA) for example.


I call 8.2.1 an edge turning tesseract. I do have solved a shallow cut edge turning tesseract before, using MPUlt by Andrey Astrelin. But this not-so-shallow cut version looks much neater, partly because some cuts meet, and partly because some one-color pieces are dropped. According to MPUlt, there should be some one-color pieces in the interior of the cells. But these pieces are not visible in the GB puzzle. I assume we don't have to worry about them because we cannot see them. With the two-color pieces in GB 8.2.1, it's already hard enough. I appreciate the current form of this puzzle.

I haven't solved it yet. I find that in 4D I'm so spoiled by the automatic features in MPUlt, such as automatically undoing setup and piece tracking (not to mention, game saving). As a result, I'm not good at remembering complicated setup moves in 4D. I have tried to solve it in GB and I found my current method too slow. Before the next formal attempt, I need to develop some ways to avoid memorizing long setup moves.

Gelatinbrain, thank you for making this puzzle and also 8.2.2, and 8.2.3. They also look really nice. Thank you for taking your time debugging 8.2.1 for several rounds.

--schuma

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 02, 2012 9:49 am 
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Hi all, and a happy new year to you.
I started solving all of the 3.4.* puzzles. It just came to 3.4.24 and I had failure. :evil: I need some move-sequences, for I have found nothing. :oops: I hope that Julian, schuma or Brandon (maybe with his algorithm-finder) can help me.
In a post on page 39
schuma wrote:
Puzzle 3.4.24 also has many multiple appearance-pieces. I had to do a thorough analysis for the movement of all kinds of pieces. The basic principle is that if two pieces can be moved by the same set of turns, they belong to one multiple appearance-piece.

For example, I wrote down: each curved isosceles triangle can be moved by three face-turns (the three faces are around a vertex, call it vertex-A) and four vertex-turns (the four vertices are those vertices that are far away from vertex-A). The set of such three faces and four vertices has a three-fold rotational symmetry with respect to the line connecting vertex-A and the center of cube. Therefore, this set of turns will not only affect one curved isosceles triangle, but also two more triangles. These three triangles have a three-fold rotational symmetry with respect to the same line. Therefore they are actually one multiple appearance-piece.

I think this is a systematic method to recognize multiple appearance-pieces. I used this analysis a lot for 3.4.24. Eventually 3.4.24 cannot be reduced to any puzzle I'm familiar with. So I have to find some commutators to solve it.
So, the X-faces inside the circles build groups of 3, they are like 2x2x2-corners but harder to see. After some trying I could solve them: (First I had to care for the orientation-index-sum of the corners and fix it if necessary to avoid ending with a single twisted inner X-face group.)
Attachment:
3.4.24_Stage1solved.png
3.4.24_Stage1solved.png [ 30.62 KiB | Viewed 6214 times ]
Julian gave an outline to 3.4.24 on page 41:
Julian wrote:
3.4.24 Solution Outline



Stage 1: The bigger circle pieces come in groups of 3, each associated with a 2x2x2 corner. Solve them like a 2x2x2, making a single Skewb move if faced with a single twisted group.

Stage 2: The smaller circle pieces come in groups of 4, each associated with one of the 24 Skewb cut lines on the faces. Their logical location is right on the border between the bitten pieces and the corners. As they occupy zero area in their logical locations, they can only be seen as groups of 4 small circle pieces spilling out elsewhere. These piece groups can be solved with ((3,1),1) = (8,1) commutators, where the 3 is made of distant corner and face moves back and forth.

Stage 3: Solve the corners with ((3,1),1) = (8,1) commutators. The sequence of 3 in the (3,1) is exactly the same as with stage 2.

Stage 4: Solve the bitten pieces pure with (1+(4,1)+1,1) = (12,1) commutators. The (4,1) is a Skewb algo to twist two corners.


As a guide, my solve using this method took 42 + 302 + 68 + 274 = 686 moves.
The two kinds of groups are:
-stage 1
Attachment:
3.4.24_InnerXFaceGroups.png
3.4.24_InnerXFaceGroups.png [ 29.06 KiB | Viewed 6214 times ]

-stage 2
Attachment:
3.4.24_EdgeSideGroups.png
3.4.24_EdgeSideGroups.png [ 29.39 KiB | Viewed 6214 times ]

This puzzle I would call a hard puzzle.
I hope someone can help me with the missing move-sequences, for Julian's outline is not enough for me to find them. :oops: Some hints would be very welcome. 8-)
Thank you, Stefan. :scrambled:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 02, 2012 12:35 pm 
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Gelatinbrain was updating the applet earlier today. Although there seems to be no new puzzle, he is adding the "save"/"open" feature. In the current version, when a pop-up dialog asks me to specify the location of a file to open or to save, I can't see the existing files and directories. But I can indeed save a puzzle in the default directory and open it (only because I remember the file name). So although a bit buggy, this feature is working now. I think it is going to be very very useful in solving complicated puzzles.

I also notice that in the latest version I cannot access 2.4.1. It's in icosahedra->mixed, but the number is changed to "FV1".

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 02, 2012 4:53 pm 
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Hey Stefan, I tried 3.4.24 a bit too and it is a hard puzzle. I haven't found routines for all of the pieces yet. Also, I haven't programmed the face + vertex geometry yet but with 14 turnable grips it'll take me a while. Congrats on taking 2nd in solves :D .

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 02, 2012 7:29 pm 
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Stefan Schwalbe wrote:
Hi all, and a happy new year to you.

3.4.24
This puzzle I would call a hard puzzle.
I hope someone can help me with the missing move-sequences, for Julian's outline is not enough for me to find them. :oops: Some hints would be very welcome. 8-)
Thank you, Stefan. :scrambled:
Happy New Year, Stefan and all!

Yes, I think 3.4.24 is very confusing and is one of the hardest puzzles in Gelatinbrain.

Stage 2: [[3,1], 1] = [8,1] "where the 3 is made of distant corner and face moves back and forth" ==> [[LUF : R, F], URF]

Stage 3: [[LUF : R, F'], URF]. Note that this is the same as the previous algo except for the move in bold.

Stage 4: [1 : [4,1], 1] = [12,1]. "The [4,1] is a Skewb algo to twist two corners." ==> [? : [[RBD',FDL], DFR], ?]. To keep a bit of mystery, the first ? represents a face move and the second ? represents a vertex move.


Last edited by Julian on Tue Jan 03, 2012 4:21 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 02, 2012 9:12 pm 
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schuma wrote:
Gelatinbrain was updating the applet earlier today. Although there seems to be no new puzzle, he is adding the "save"/"open" feature. In the current version, when a pop-up dialog asks me to specify the location of a file to open or to save, I can't see the existing files and directories. But I can indeed save a puzzle in the default directory and open it (only because I remember the file name). So although a bit buggy, this feature is working now. I think it is going to be very very useful in solving complicated puzzles.


After checking the latest .jar file I have to say the reason why I didn't see the existing files and directories in the file selection dialog was because I didn't turn the "Files of Type" to "All Files". After doing that I can freely browse and select any file in any folder.

I'm really excited about this feature, because we can share the whole solutions here.

As an example, I saved a 2x2x2 solution and attached it in this post. If you want to see my method, you can do the following:

(1) Save 2x2x2.zip on your computer
(2) Unzip it to get "2x2x2.zzz". (Since this forum doesn't allow .zzz as an attachment, I have to zip it)
(3) Open the latest version of Gelatinbrain. Click File -> Open
(4) Change "Files of Type" to "All Files"
(5) Navigate to the directory where you saved "2x2x2.zzz" and open it
(6) Now you can see a solved 2x2x2 cube, with the list of moves shown explicitly.
(7) You can copy the list of moves to somewhere else, then undo the moves and re-apply the moves according to the list to re-enact my solution. I used the Ortega method.

The last part would be much easier if there is a "Redo" button. I wonder if that's convenient to implement or not.

I can imagine many other situations where this saving feature is useful. For example if you get stuck by a weird parity issue, you can save the game and post it here and ask for help. Other people can do experiment from exactly where you got stuck. Once you know how to solve the issue you can go back and resume the solution.

For some exotic puzzles, the applet fails to recognize the solved state. In that case, you can save the puzzle and post it here. That's a perfect proof that you have solved it.

When people share these save files, we should all be honest about the ownership of a solution. If someone shares a partial solution, anyone can resume and complete it and submit his/her own name. But I think we have already shown that we are an honest and friendly community so that this kind of things won't happen.

On an unrelated subject, does anyone know the two un-numbered records at the top of the ranking page, between the leaders board and 1.1.1? One guy called "=01David" solved an un-numbered puzzle in 4 min 6 sec using 89 moves. What is this puzzle? Another guys called "?????Gw?????" solved another puzzle using negative moves, which must be an error probably due to a broken certificate code.


Attachments:
2x2x2.zip [587 Bytes]
Downloaded 129 times

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 02, 2012 11:22 pm 
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I really like the idea of being able to share puzzle states, it'll open up a whole new way to do collaborative solves and share how we solve.

With regard to cheating, I think us in the core group of solvers aren't at risk of cheating. There is a technical means of preventing somebody from cheating and "solving" a puzzle with some nearly-solved state we post here. Ask the user to enter a password/key/token, hash it, and stuff it in the header to the saved state. Then others can load that state and play with the puzzle and see the moves done but they can't resume solving and submit the solve unless they enter the password to unlock the resumeability. Basically until you re-enter the password that was given on save, the save is only good for viewing and toying with but not good for submitting as a solve. If you want to restore your own saves just enter the password and keep solving.

A scheme like hash = password; for i in (1 .. 1000) { hash = sha1(hash + salt + i)}; should do just fine for a hash code.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 6:19 am 
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Julian wrote:
Stefan Schwalbe wrote:
Hi all, and a happy new year to you.

3.4.24
This puzzle I would call a hard puzzle.
I hope someone can help me with the missing move-sequences, for Julian's outline is not enough for me to find them. :oops: Some hints would be very welcome. 8-)
Thank you, Stefan. :scrambled:
Happy New Year, Stefan and all!

Yes, I think 3.4.24 is very confusing and is one of the hardest puzzles in Gelatinbrain.

Stage 2: [[3,1], 1] = [8,1] "where the 3 is made of distant corner and face moves back and forth" ==> [[LUF : R, F], URF]

Stage 3: [[LUF : R, F'], URF]. Note that this is the same as the previous algo except for the move in bold.

Stage 4: [1 : [4,1], 1] = [12,1]. "The [4,1] is a Skewb algo to twist two corners." ==> [? : [[RBD',FDL], DFR], ?]. To keep a bit of mystery, the first ? represents a face move and the second ? represents a vertex move.
Thank you, Julian. This will help me. :D Stefan.

schuma wrote:
When people share these save files, we should all be honest about the ownership of a solution. If someone shares a partial solution, anyone can resume and complete it and submit his/her own name. But I think we have already shown that we are an honest and friendly community so that this kind of things won't happen.
I fear it will lead to cheats, but not from us.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 9:19 am 
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bmenrigh wrote:
Hey Stefan, I tried 3.4.24 a bit too and it is a hard puzzle. I haven't found routines for all of the pieces yet. Also, I haven't programmed the face + vertex geometry yet but with 14 turnable grips it'll take me a while. Congrats on taking 2nd in solves :D .
I couldn't resist, although I'm a bit ashamed of it. :?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 12:29 pm 
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1.1.51 has a very scary way of turning. I tried to solve it, and my first step was of course to figure out how the pieces actually move. What I found out was that it just has two pieces, not three. The little triangles are connected to the centers, like this:
Attachment:
1.1.51pieces.PNG
1.1.51pieces.PNG [ 28.28 KiB | Viewed 6161 times ]


So the same colored pieces are actually connected. The following picture just shows one of these, to avoid confusion:
Attachment:
1.1.51pieces2.PNG
1.1.51pieces2.PNG [ 28.05 KiB | Viewed 6161 times ]

Of course the red center isn't part of the pieces, but is there to demonstrate where the triangles end up.

This means the triangles are actually the pieces that show the orientation of the centers. So the puzzle is ALMOST the exact same as 1.1.7b, the super-pentultimate. The corners act the exact same as pentultimate corners, but the centers act a bit different.

It took me quite some moves to solve this one, because I used my insanely long nested commutators.

There is just one problem I have with both this one and the super-pentultimate: one center can be twisted by 1/5 of a turn. This can also be seen as twisted by -4/5 of a turn. I have an algorithm to twist two centers by 1/5 of a turn in different directions, but I have no clue how to use it to twist just one center. Does anyone have any hints on that subject?

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Olivér Nagy wrote:
43,252,003,274,489,856,000. Or the full number in Hungarian is:
Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 1:26 pm 
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Sjoerd wrote:
There is just one problem I have with both this one and the super-pentultimate: one center can be twisted by 1/5 of a turn. This can also be seen as twisted by -4/5 of a turn. I have an algorithm to twist two centers by 1/5 of a turn in different directions, but I have no clue how to use it to twist just one center. Does anyone have any hints on that subject?
I've put a lot of effort into this particular area and spent some time exploring these types of routines with the various programs I've written. My current solver isn't fast enough to explore very deeply so until I re-write it in C some of my efforts are on hold.

With regard to changing the overall twist of a piece type, a commutator can never do it (simple proof). The best way to change the orientation of a piece is with a conjugate [N:M] because a conjugate can change the overall twist. It is M in the conjugate that changes the overall twist and N is just used to try to reduce the side-effects. Usually you can't find a [N:M] that is pure but if you can find one with few side-effects (such as a 3-cycle) you can attempt to cancel the 3-cycle by applying the conjugate 3 times.

The issue with [N:M]xQ is that N M N' N M N' ... causes all of the N's to cancel and you wind up with N MxQ N' which is not useful. The trick is generally to do something like changing the orientation of the puzzle between each application or apply another move between each application.

For a non-trivial example see http://twistypuzzles.com/forum/viewtopic.php?p=229974#p229974 and the conversation that follows through to http://twistypuzzles.com/forum/viewtopic.php?p=230353#p230353

On the of the Pentultimate, the shortest routine I know is [[3:1] 1]x3 == 24 moves. It's pure on most of the face-turning dodecahedra (but the twist of the centers on the Pentultimate is tied to the twist of the centers on the Megaminx so it's as pure as can be on the Multi-Dodecahedron).

More specifically the 1 portion of the conjugate and the 1 move that separates the application of the conjugate is the same move. In my programmatic searches for these sorts of routines this is always the case but I'm not sure if there is some deep underlying reason why just yet.

I have included the Pentultimate routine below:

"[B, A'2, E', A, E, A2, B', A]x3 or broken down [[B:[A'2:[E':A]]] A]x3"

Of course you will have to translate this into center piece variants that appear in 1.1.51.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 2:32 pm 
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I didn't really understand the concept of conjugates just yet, but what I gather from your post it seems [N:M] = N,M,N', where the lack of the M' causes the overall twist. So I think in [N:M], where the N part is reversed, N will be multiple moves, whereas M will be 1 or maybe even a pure commutator in most cases?

In any case, your hidden routine works like a charm! Too bad it is a conjugate inside a conjugate inside a conjugate, while I don't even completely understand the use of conjugates! :lol:

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Olivér Nagy wrote:
43,252,003,274,489,856,000. Or the full number in Hungarian is:
Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 3:12 pm 
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Sjoerd wrote:
I didn't really understand the concept of conjugates just yet, but what I gather from your post it seems [N:M] = N,M,N', where the lack of the M' causes the overall twist. So I think in [N:M], where the N part is reversed, N will be multiple moves, whereas M will be 1 or maybe even a pure commutator in most cases?

In any case, your hidden routine works like a charm! Too bad it is a conjugate inside a conjugate inside a conjugate, while I don't even completely understand the use of conjugates! :lol:
Conjugates are just setup moves that you undo. If you setup moves don't commute then you must undo them in reverse order which means than [5:1] can be decomposed into a chain of 1-move setups [1:[1:[1:[1:[1:1]]]]]. The only reason you'd ever want to decompose the setups in this way is that often each setup move serves a purpose somewhat independently of the other setup moves so you don't always want to group them together.

The workhorse of a conjugate is the middle part (M) of N M N'. The setup moves in N just change what pieces M affects.

In the case of the Pentultimate center twist, the workhorse conjugate is "B, A'2, E', A, E, A2, B'" which performs a 5-cycle of the large outer blocks (it's easiest to see on a Megaminx) and also leaves a twist in the center. The A all by itself also performs a 5-cycle of the large outer blocks, the three setup moves just change which of the outer blocks are involved in the cycle.

The magic is that rotating 4 of the 5 blocks that are being cycled by twisting A after each conjugate allows the 5-cycle to be undone when applied 3 times. An excess twist of 2 is left in A each time and when applied three times 2 * 3 mod 5 = 1 so the routine changes the twist by 1.

In trying to understand this routine I'd suggest taking a look at the inverse (just turn both A moves into A' moves). Also, turn the routine into a commutator by inverting the trailing A (which results in B, A'2, E', A, E, A2, B', A') and apply it to the Megaminx.

I find this Pentultimate center-twist routine quite hard to understand when viewed on a Pentultimate but somewhat easier on a Megaminx. Also, I find my pure corner twist on 1.2.2 much easier to understand overall. Also, my 1.2.2 twist routine can be made pure on 1.2.3 by adding an additional setup move to one of the sub-components. I have tried (without success) to add more setup moves to the various sub-components to make pure twist routines on the deeper-cut vertex-turning Dodecahedra without much luck. I have been searching because I want to understand the structure / form these routines better.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 3:15 pm 
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Sjoerd wrote:
There is just one problem I have with both this one and the super-pentultimate: one center can be twisted by 1/5 of a turn. This can also be seen as twisted by -4/5 of a turn. I have an algorithm to twist two centers by 1/5 of a turn in different directions, but I have no clue how to use it to twist just one center. Does anyone have any hints on that subject?


My solution to single-center rotations was (RUR'U)*21, which meant that at the end of solving the rest of the puzzle, I would have to spend up to 168 additional moves to rotate the last center. However, knowing that in theory I had come up with a true solution to this problem, I was satisfied enough to just avoid this issue in my actual solve by rescrambling after the center-permutation step until the sum of the twists on the centers was a multiple of 5.

I should note that I don't actually have a clue of what makes that algorithm work... I just stumbled upon it because I know (RUR'U)*5 and (RUR'U)*12 are single-center rotation algs for the 3x3 and megaminx respectively.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 3:41 pm 
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DKwan wrote:
[...]I just stumbled upon it because I know (RUR'U)*5 and (RUR'U)*12 are single-center rotation algs for the 3x3 and megaminx respectively.
These work for the same reason and are of the same form except that instead of a complex 3 setup moves (B, A'2, E'), only one (R) is used.

On the Megaminx R U R' U is a 4-cycle + a 1-1 swap so if you apply it 4 times there will be an excess twist in the center and the corners will be cycled back correctly. Unfortunately the corners also undergo a twist so you have to apply 4 * 3 = 12 times to cancel both the permutation and orientation changes. Since 12 mod 5 != 0 the routine leaves an excess twist.

This [[R:U] U]xN trick is what I built my 1.2.2 and 1.2.3 pure corner twist routine around.

When I was trying to find Doug's routine I managed to find something on 2.2.3 that resulted in a 7-cycle and a 3-cycle that I also had to apply 21 times to cancel both. Unfortunately it had some other side effects that require executing it another large factor of times. It was almost pure after something like 300 moves.

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Last edited by Brandon Enright on Wed Jan 04, 2012 1:10 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 03, 2012 4:53 pm 
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Thanks for the expanation Brandon, I think I understand it a bit better now :mrgreen:

To GB: 1.1.35b recognises my almost-solve as a solve:
Attachment:
1.1.35b wrong.PNG
1.1.35b wrong.PNG [ 122.97 KiB | Viewed 6113 times ]

As you can see I just needed to turn two opposite sides to solve it, but it was recognised prematurely, so the center orientation doesn't matter when it should.

And while I have your attention: Do you have anything special planned for puzzle #600? I personally would love to see a Multi Dodecahedron, it seems feasible with TomZ's implementation, using turns like on 1.1.82 and 1.1.83. Just a suggestion :D

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43,252,003,274,489,856,000. Or the full number in Hungarian is:
Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 12:42 pm 
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regarding Julians's 3.4.24 outline:
Stefan Schwalbe wrote:
Thank you, Julian. This will help me. Stefan.
And it did!!
Attachment:
3.4.24 solved against the movecount.PNG
3.4.24 solved against the movecount.PNG [ 120.39 KiB | Viewed 6054 times ]
Earlier I solved it against the time and I got a 19min solve with 1200 moves (also with Julian's method).

This time I solved it against the movecount, and I needed:
-corner orientation sum: 1 move
-stage 1 (inner x-face groups): 25 moves, 4:20min
-stage 2 (edge-side groups): 264 moves, 43:10min
-stage 3 (corners): 86 moves, 17:00min
-stage 4 (x-faces): 219 moves, 07:32min
for stage 2,3 and 4 I needed more time with the setup moves, because I had to solve 2 or 3 pieces at once to save moves. It's amazing that a solve with double of the moves took only a quater of the time. For me it means, that the move-count is not so important if the time is ok.

Beautiful method, Julian. The algorithms are far from ordinary. It's a real admirable find.
And sorry, that I took your move-count record with your own method.

I feel not sad, that I couldn't find an own method, for then I would not have known your method and schuma's method (wich he has pm'd me)!

Thank you, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 5:37 pm 
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I just spent an hour on 1.1.66, then putting my laptop to sleep so I could attend something else, and when I woke it up the applet screen was blank, which has happened every time, but it slipped my mind this time. Bottom line: I REALLY want to know how the save function works. Just clicking on them doesn't work for me, ctrl+s and ctrl+o don't work for me.. Do more people have this problem or is it just me. It would be really useful..

Regarding 1.1.66: It is actually pretty easy, it's surprising only schuma has solved it so far. the eye pieces are connected and function like megaminx edges. So hard to recognise, but after recognising, very easy.

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Olivér Nagy wrote:
43,252,003,274,489,856,000. Or the full number in Hungarian is:
Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 5:48 pm 
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Sjoerd wrote:
I just spent an hour on 1.1.66, then putting my laptop to sleep so I could attend something else, and when I woke it up the applet screen was blank, which has happened every time, but it slipped my mind this time. Bottom line: I REALLY want to know how the save function works. Just clicking on them doesn't work for me, ctrl+s and ctrl+o don't work for me.. Do more people have this problem or is it just me. It would be really useful.
Saving and opening seems to work just fine for me.

Gelatinbrain is adding the ".zzz" extension to the files but the file picker dialog doesn't filter for just these so you first have to choose "All Files" in order to be able to pick your save. It stores the puzzle number, the time, the scramble, the moves done, etc. It seems like perfect save and resume to me.

The "Save As" dialog box has a button labeled "open" even though you're saving a file. It works just fine though.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 5:59 pm 
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Yeah it seems like perfect save and resume to me too, but no windows pop up. I think another browser might work, but I don't want to risk downloading another version of java and not being able to play at all anymore.. I'll see what I come up with.

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Olivér Nagy wrote:
43,252,003,274,489,856,000. Or the full number in Hungarian is:
Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 6:14 pm 
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Sjoerd wrote:
Yeah it seems like perfect save and resume to me too, but no windows pop up. I think another browser might work, but I don't want to risk downloading another version of java and not being able to play at all anymore.. I'll see what I come up with.
Hmm, we might want to take this to the problems thread rather than this one.

One question though, are you running the program via the applet launcher inside of the browser? I can imagine a scenario where the security model inside of the browser would prevent save and open from working, possibly even where a security exception is raised if you try to open a file dialog rather than actually presenting a dialog.

Executing the stand-alone jar with Java 1.6.0_29 on a 64 bit Linux system is working fine for me. If you haven't transitioned to a local copy yet you really should, it solves many issues.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 6:35 pm 
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The applet cannot access your local disk without your permission.
You have to modify the ".java.policy" file. See the troubleshooting thread quoted above.
Or you should use the executable java version.
Then you will have no problem. The current session is automatically saved when you quit and reloaded the next time you launch..

On my computer, file filtering works fine.
By default I'm filtering only "zzz" files. I don't have to change to "all files". :(

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 7:14 pm 
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gelatinbrain wrote:
The current session is automatically saved when you quit and reloaded the next time you launch.

I really like the sound of this feature but it isn't working on my system. I tracked it down to a hard-coded reference to "Magic Polyhedra" in my home directory. Namely:

Code:
open("/home/brenrigh/Magic Polyhedra/sessions/.default.zzz", O_WRONLY|O_CREAT|O_TRUNC, 0666) = -1 ENOENT (No such file or directory)


I have the local copy stored elsewhere on disk. Perhaps there could be a reference to "." (the current working directory) too? I could make a sessions directory within the CWD for ".default.zzz" to be stored? Another option would be to add a command line switch to specify the path to the default save file.

Thanks again for the save/load feature, I'm much more likely to solve the big long puzzles now! Also, for the 3.4.X series there were a number of times when I'd write down the move-count, then explore one way to finish the reduction, have it not work out well, and then undo back to what I wrote down to try a different way to do the reduction. Save and load will make that a bit safer and easier to do.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 04, 2012 8:41 pm 
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Since I'm completely useless when it comes to code, 'advanced' use of computer, and those kind of things, I will let this rest for now. I use the applet on the website, and not the separate program.

I managed pretty well without the save option the past couple of years, so I'll just continue doing without.

If I have any further questions/comments like this I'll post them in the problems thread.

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Olivér Nagy wrote:
43,252,003,274,489,856,000. Or the full number in Hungarian is:
Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jan 08, 2012 1:48 am 
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Hi Gelatinbrain,

In the older versions of your applet, I use "ctrl + A" a lot in the text boxes to "select all" the input moves or the executed moves. But in the latest version, "ctrl + A" becomes "save as..." Could you please change the shortcut for "save as" as something else so that I can continue to use "select all"? Thanks!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jan 08, 2012 7:59 am 
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3.4.24
Stefan Schwalbe wrote:
I got a 19min solve with 1200 moves
That's amazingly fast! If my life depended on it, I couldn't solve just the little pieces in that amount of time, because I find the groups so hard to recognize.

Stefan Schwalbe wrote:
Beautiful method, Julian. The algorithms are far from ordinary. It's a real admirable find.
And sorry, that I took your move-count record with your own method.
No problem about the record -- under 600 moves is really tight. I enjoy sharing methods, and efficient algos are only part of doing a tight solve. I remember that I found fairly quickly a way of isolating a group of little pieces pure with a repeated algo [8,1]*3, but not only did [54,1] seem long, but I couldn't find the other algos I needed to solve the puzzle in that order. The order I ended up using was the only way I could solve the puzzle.

I often find that selecting two moves the appropriate distance apart (especially as far apart as possible while intersecting) and moving them back and forth often leads to useful algos. I try each form of 1:1 and 1,1 with those two moves and then I try to find a move to make a commutator and/or setup moves to push the cleanest parts of the puzzle into the same area. With hybrid puzzles (like this one with face moves and vertex moves) I also try algos that have a small effect on the pure version of the puzzle (in this case, twisting two corners of a Skewb), and see what happens to the hybrid.

Off topic -- one of the piece types of 3.4.24 reminds me of the spinning top important to Leonardo DiCaprio's character in the movie Inception.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 09, 2012 10:36 am 
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Julian wrote:
3.4.24
Stefan Schwalbe wrote:
I got a 19min solve with 1200 moves
That's amazingly fast! If my life depended on it, I couldn't solve just the little pieces in that amount of time, because I find the groups so hard to recognize.


Sorry, I forgott to tell you of the macro-moves, it was actually a 18:49 min + 1026 (macro-moves) solve wich is 35:55 min and you didn't use macromoves for your solve.

Stage 1 (the bigger circle pieces) I practised about 10 times or more when I had no clue for the rest of the solve.
After you told me your solution,
for stage 2 (the smaller circle pieces), stage 3 (the corners) and stage 4 (the bitten pieces) I used a solve-one-piece-at-once strategie. The advantage of it is, that you only use setup moves, wich doesn't change the first and the second position of the 3-cycle, the number of setup moves never exceed 3 moves or so. That 3 moves you can keep in mind for a short time. Also you can prepare the move sequence so, that position 1 and 2 are as close as possible, so that you have plenty free moves for the setups. Once one of the positions 1 or 2 get solved, you can continue by turns with forward and backward of the 3-cycling move-sequence and you don't lose the solved piece. If position 1 and 2 need a swap, push one of the pieces into an unsolved position and continue with solving the new piece. If both position 1 and 2 is solved, it's time to rotate the whole puzzle to get position 1 or/and 2 unsolved again.
I did that lots of times with many puzzles and it works well until all pieces are solved. It reduces the stress while solving and is very fast, often faster than solving two/three pieces at once. You never really lose time for hesitation - there is nothing to think about.
I hope you understand this method, wich turned out to work well for me.

Thank you, Stefan :solved:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jan 11, 2012 1:08 am 
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Score +1 for save files (and Skype screen sharing). I was able to collaborate with a fellow solver to work on the setups on a edge-turning cube. Having been on the solving side of things and unable to find the setups for the last 3-cycle for 30+ minutes it's great to be able to discuss strategies for this sort of thing with fellow solvers. This thread has given us all a great way to share overall strategies and even commutator construction but the ability to discuss strategies for finding setups is a whole new area of collaboration enabled by save files. :D

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jan 12, 2012 5:12 pm 
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bmenrigh wrote:
I have written a simple script to help pretty-print Gelatinbrain's macro move-sequences as well as invert and mirror routines. You can see it here: http://www.brandonenright.net/cgi-bin/gb_util.pl

Eventually it will be able to deconstruct your routine if it follows "standard form" and tell you what the form is. In the future it may also support []xN notation such as [A, B, A', B']x3.

If the program needs more features let me know.
Per a minor epiphany yesterday about how to really easily deconstruct routines using recursion I have implemented a sequence disassembler. If your sequence is in "standard form" it will be able to disassemble it without changing any options. More complicated sequences may require allowing concatenation. I've built a backtracking heuristic in for the concatenation so that the results are pretty good (but to limit CPU, not necessary optimal).

For example, if you enter "r, a, c, e, c', a', r'" the disassembled notation is "[r:[a:[c:e]]]".

Now if somebody provides a really long and complicated sequence (for example on the Starminx) like:
[F'2, C, F2, C', F'2, C, F2, C', F'2, C, F2, C', H'&2, L, H&2, C, F'2, C', F2, C, F'2, C', F2, C, F'2, C', F2, H'&2, L', H&2]

The disassembler will search for structure and report to you that the routine is:
[[F'2,C]x3,[H'&2:L]] or [[1,1]x3,[1:1]]

Since the program doesn't really "understand" the notation you give it, if the moves are cube faces and F2 is the same as F'2 you'll need to tell the program that. The same goes for edge turn moves.

Of course I'm interested in bugs, feature requests, and unexpected results so if anything comes up please let me know!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jan 16, 2012 10:53 am 
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@Brandon: thanks for your sequence-transformer script. I use it since it came out.

Yesterday I solved 3.5.1, 3.6.1 and 3.5.4.
For 3.5.1 Julian wrote on page 29:
Julian wrote:
3.5.1 (2x2x2 + Little Chop)

1. The pieces are in two orbitals. Choose the "left-handed" or "right-handed" pieces to solve first, and make some intuitive moves to solve as many as possible.

2. Solve the remaining pieces in your chosen orbital using non-pure (8,1) cycles. Hint: Try to isolate a piece in a Little Chop half of the puzzle with a (3,1) commutator, not caring if one or two pieces from the other orbital stray into the same half.

3. Solve the pieces in the other orbital using pure (12,1) cycles. Hint: Try making a couple of face moves either side of a mirror image of the same (3,1) commutator you used in stage 2, to see if you can isolate a single piece in a Little Chop half of the puzzle without any pieces from the other orbital straying into the same half.

I took 362 moves using this method.
I used Julian's method but not with that short move-sequences. The [8,1] for the left pieces I have found, but I didn't find the [12,1] for the right pieces and so I had to use an over 40 moves alg.. I'm envious of your move-counts.

For 3.6.1 I developed my own outline:

3.6.1 outline

I. Wings in layer, let unsolved two neighbor corners (6 wings)
with a [1,1], something like: [LUF,UR]
II. wings parity (if odd, solved with a single edge-move)
III. last two corners (6 wings) (setups might get tricky)
IV. ESr (edge-sides, right) with a [1,[1:1]] URF, DF, RD, DF, URF', DF, RD, DF,
V. ESl (edge-sides, left) similar like IV.

For 3.5.4 I used my own outline:

3.5.4 outline

I. edge ori sum (because 50% of the configurations have a single twisted edge)
II. corner + edge parity sum (because 50% of the configurations have a different corner and edge parity. this is important for solving the face centers right)
III. I+F: [1:1] (inner + faces) something like [UR:U]
IV. IxF: [1,1] (inner x faces) something like [UR,FU]
V. xF to C: [1:1] (x-faces to corners) something like [UR:F']
VI. ESr (edge-side, right) to edge: reduced [3,3] move-seq to 7 moves [3:1]
/*UF->FL->RB*/
UR', R2, U, L', U', R2, UR',
/*
after the move sequence
UF is at BL
FL is at UF
RB is at RB
*/

VII. ESl to E: similar to ESr
VIII. 3x3x3

I got good results with it:
3.05.01 0969 00:05:10 +0908 (good time, but the 908 seconds for the macro-moves make it bad, if I had shorter move-sequences..)
3.05.04 0438 00:26:50 (first place in time and move-count)
3.06.01 0307 00:22:14 (first place in time)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 17, 2012 2:51 am 
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Stefan Schwalbe wrote:
@Brandon: thanks for your sequence-transformer script. I use it since it came out.
Sure, I'm glad others find it useful!

Stefan Schwalbe wrote:
3.5.4 outline

I. edge ori sum (because 50% of the configurations have a single twisted edge)
II. corner + edge parity sum (because 50% of the configurations have a different corner and edge parity. this is important for solving the face centers right)
III. I+F: [1:1] (inner + faces) something like [UR:U]
IV. IxF: [1,1] (inner x faces) something like [UR,FU]
V. xF to C: [1:1] (x-faces to corners) something like [UR:F']
VI. ESr (edge-side, right) to edge: reduced [3,3] move-seq to 7 moves [3:1]
[...]
VII. ESl to E: similar to ESr
VIII. 3x3x3

I got good results with it:
3.05.04 0438 00:26:50 (first place in time and move-count)
Hey Stefan, when I first solved 3.5.4 I cycled piece-by-piece. After solving the 3.4.X series via reduction I decided I'd go back and develop a reduction method for 3.5.4 but I didn't get around to actually doing a solve. Your post motivated me to go ahead and solve it though and I got 338 moves (in 1 hour 14 min). I'm looking and your outline and it is slightly more efficient than mine.

I did:
1) + centers and edge parity and edge orientation free form
2) Outer X centers to corners with [1:1] conjugates
3) Inner X centers in a truncated [3:1] conjugates (7 moves)
4) Right chiral edge triangles with [1:3] conjugates (5 moves)
5) Left chiral triangles same way
6) Solved reduced 3x3x3

Your solve order seems better because it avoids the 7-move routine for the inner X centers but my chiral triangle routine is shorter. If we combined our strategies we'd probably break 300 moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 17, 2012 11:48 am 
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bmenrigh wrote:
Your post motivated me to go ahead and solve it though and I got 338 moves (in 1 hour 14 min).
Congratulations on your solve 8-) . I didn't thought that this is possible.
bmenrigh wrote:
4) Right chiral edge triangles with [1:3] conjugates (5 moves)
Good find, Brandon. I will surely use that on my next solve.
bmenrigh wrote:
If we combine our strategies we'd probably break 300 moves.
Maybe, you can reach that, good luck.
Stefan


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jan 17, 2012 5:46 pm 
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I tried to solve 3.5.3. I came to that point:
Attachment:
3.5.3_progres.PNG
3.5.3_progres.PNG [ 117.91 KiB | Viewed 5426 times ]
The left and right corner-faces are like 3.5.1. It's a real hard puzzle. The setups for the inner circle pieces are not easy. I hope I can solve it. My move-sequences are somtimes more than 50 moves long. :evil: After my first solve I try to reduce them.
Stefan

Edit:
Attachment:
3.5.3_progres2.PNG
3.5.3_progres2.PNG [ 92.13 KiB | Viewed 5416 times ]
Attachment:
3.5.3_progres3.PNG
3.5.3_progres3.PNG [ 117.47 KiB | Viewed 5416 times ]
Attachment:
3.5.3_progres4.PNG
3.5.3_progres4.PNG [ 174.93 KiB | Viewed 5416 times ]
Now I'm finished!! :solved:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jan 19, 2012 5:43 pm 
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Hi Stefan!

3.5.1 -- I found a [10,1] pure algo after I wrote my outline, which is [UR : [UL : R2, U'], D].

3.5.3 -- I think the trick is to experiment with simulated slice moves, for example, we could call U' D y => u, a sliced face move, or FL BR and clicking the up or down arrow twice => fl, a sliced edge move.

My method solves the larger face-central pieces non pure with [U RD : [u', FL], FD], then the smaller face-central pieces pure with [[F2 : fl, L], B]. Both of these are [10,1] algos.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jan 20, 2012 7:45 am 
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Hi Julian,
Thank you very much for your tips regarding 3.5.1 and 3.5.3.
Such great algorithms you found! :shock: I will consult you again.
Julian wrote:
3.5.1 -- I found a [10,1] pure algo after I wrote my outline, which is [UR : [UL : R2, U'], D].
How it separates one piece - magic!

Julian wrote:
3.5.3 -- I think the trick is to experiment with simulated slice moves, for example, we could call U' D y => u, a sliced face move, or FL BR and clicking the up or down arrow twice => fl, a sliced edge move.
Nice idea to compile such moves ('u' and 'fl') and handle them like normal moves. The U' D and the FL BR I found myself and used them in my solution.

And here is another issue, I would ask you, it is about 3.6.5. On page 45 you wrote:
Julian wrote:
3.6.5 (Skewb + Little Chop)

Solution Outline

Step 1 - Make some intuitive moves to solve as many square pieces as possible.

Step 2 - Complete the square pieces with non-pure (6,1) commutators. The 6 moves are 1 + (1,1) + 1: a setup move, then alternating corner and edge turns as far apart as possible, then an undo of the setup move.

Step 3 - Use Skewb moves to permute and twist Skewb corners to quickly solve as many triangle pieces as possible.

Step 4 - Cycle the triangle pieces pure with (8,1) commutators. The pieces come in two distinct sets/subgroups/orbitals/orbits. When you have an algo to cycle pieces of one set, the mirror image of the algo will cycle pieces of the other set. The 8 moves are a (3,1) commutator where the 3 moves are again alternating corner and edge turns as far apart as possible.

Highly recommended -- it only has 72 pieces, so it doesn't take a very long time to solve. Setups are tricky but short -- perhaps 80% of the time you won't need to use more than 3 moves to set up cycles to solve 2 pieces at a time.
For step 1, 2 and 3 I could follow you. But I found no sequence for the 'triangle pieces'. Can you please give me one hint more? :wink:

Thanks, Stefan - undiminished fun!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jan 20, 2012 12:41 pm 
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Stefan Schwalbe wrote:
On page 45 you wrote:
Julian wrote:
3.6.5 (Skewb + Little Chop)

Solution Outline

...

Step 4 - Cycle the triangle pieces pure with (8,1) commutators. The pieces come in two distinct sets/subgroups/orbitals/orbits. When you have an algo to cycle pieces of one set, the mirror image of the algo will cycle pieces of the other set. The 8 moves are a (3,1) commutator where the 3 moves are again alternating corner and edge turns as far apart as possible.
For step 1, 2 and 3 I could follow you. But I found no sequence for the 'triangle pieces'. Can you please give me one hint more? :wink:

Thanks, Stefan - undiminished fun!
My algo for step 4 is [[LUF' : RD, ?], ?]. We're aiming to cycle 3 strips of pieces with the [3,1] commutator so that almost all of the moved pieces are in one half of the puzzle, with just one moved triangle in the other half.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jan 20, 2012 3:27 pm 
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Julian wrote:
My algo for step 4 is [[LUF' : RD, ?], ?]. We're aiming to cycle 3 strips of pieces with the [3,1] commutator so that almost all of the moved pieces are in one half of the puzzle, with just one moved triangle in the other half.
I got it. Thanks Julian.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Feb 15, 2012 1:24 am 
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I started solving again this past month. Thanks to Brandon's suggestion and prodding, I've completed the flat-cut 2-3 layer 3.3.x's (and taken all the fewest move counts except 3.3.1, for which Ethan has a ridiculous count on). Here are my outlines for 3.3.2-7:


3.3.2: 528 moves
1. Solve the corners and xcenters as for a regular helicopter cube (3.3.1)
2. +centers via [3,1] --> 2-2 swap: [RF,FU,RF,RD&2,RF,FU,RF,RD&2] 3-cycle: [FU,RF,BR,RF,FU,RF,BR,RF]
3. Centers via [5,1] --> 3-cycle: [LU,FU,DF,RD,DF,FU,LU,FU,DF,RD,DF,FU]
4. Edges via [1,1] --> 3-cycle: [UR,FL,UR,FL]
5. Chirals via [5,1] --> 3-cycle: [LU,UB,RF&2,UB,LU,RF,LU,UB,RF&2,UB,LU,RF]

Note: Steps 3 and 5 can be reduced by careful planning in steps 2 and 4 respectively to solve/maintain as many of those pieces as possible.


3.3.3: 423 moves
(same as 3.3.2 without the xcenters)


3.3.4: 599 moves
1. Solve the pieces from 3.3.3
2. New xcenters via [7,1] --> 2-2 swap: [UB,RF,BD,UB,FU,UB,BD,RF,UB,RF,BD,UB,FU,UB,BD,RF]

Note: Step 2 can be significantly reduced (or even completely eliminated actually) with careful planning in the previous step.


3.3.5: 452 moves
(same as 3.3.4 without the +centers)


3.3.6: 623 moves
1. Solve the new +centers from 3.3.7 (see below)
2. Corner permutation via [1,1] --> 3-cycle: [BR&2,UR,BR&2,UR]
3. Corner orientation via [1,1] --> opposite corners: [RF&2,FU&2,RF&2,FU&2]
4. Centers via [4,1] --> 3-cycle: [FL&2,FU,FL&2,FU,RD,FU,FL&2,FU,FL&2,RD]
5. Edges via [4,1] --> 3-cycle: [FL&2,DF,UR,DF,UR,FL&2,UR,DF,UR,DF]
6. Chirals (first orbit) and xcenters via [5,1] --> 3-cycle: [LU,UB,RF&2,UB,LU,RF,LU,UB,RF&2,UB,LU,RF]
7. Chirals (second orbit) via [3,1] --> 2-2 swap: [BR,UR,BR,FU&2,BR,UR,BR,FU&2]

Note: Setting up for the step 7 algorithm is particularly difficult I think. In my actual solve, I used the step 6 algorithm to fully solve both chiral orbits and the xcenters simultaneously through a lot of planning and extra setup moves, so I didn't have to do step 7 separately. I know there are pure 3-cycles out there for this step as well, but I didn't bother to find/use one.


3.3.7: 43 moves
My method for this doesn't use commutators. I use a short/simple 5-move conjugate to fully swap 2 adjacent faces: [UB,BR,RF,BR,UB]
This algorithm also shuffles around some of the individual pieces on some faces as well, which helps for it's intended purpose of setting up for pairing pieces together with plain moves.
1. Reduce the puzzle to pairs of pieces, so that each face is split on a diagonal with 2 colors.
2. Pair the pairs into full faces.
3. If the relative positions of the colors matter like in 3.3.6, swap faces around as necessary.

Note: With this method, I average around 70 moves. I felt it was good enough to take the record from fusion with some luck, so I solved it about 5 or 6 times to get the 43 move solve.


Last edited by DKwan on Fri Apr 13, 2012 1:25 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Feb 28, 2012 5:40 pm 
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DKwan wrote:
Here are my outlines for 3.3.2-7:
They make fascinating reading! When most of us solved 3.3.2-6, those puzzles didn't have shift-click, so we were more limited in our approach and our algorithms. But of course that only accounts for part of the dramatic difference between the previous records and your new ones! In general, the way you use algorithms other than 3-cycles (such as double swaps and 5-cycles) extensively in your solves brings something very new to our collective Gelatinbrain solving manual, as does the extent to which you are able to minimize or eliminate stages. I was also amazed to see that you start 3.3.6 with the 3.3.7 pieces. Thanks for sharing your methods.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 05, 2012 1:52 pm 
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Haven't posted here in a while so I have a few questions.

First of all, I'm interested in finding out how many of the people on the to 20 chart still actively use this app. I've just sneaked into 5th place on the puzzles solved chart, and I have a personal goal to break 300 solves by the end of the year. I'm wonder does anyone else have any goals for the app.

I Also have two questions directed towards Gelatin Brain. Are the chart's case sensitive, I've wondered this for a while since I switch between a capital and lowercase B all the time. Also I've managed to misspell my own name :oops: on the last solve I did of 3.1.10, If you could fix this I would greatly appreciate it.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 05, 2012 2:16 pm 
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boublez wrote:
First of all, I'm interested in finding out how many of the people on the to 20 chart still actively use this app. I've just sneaked into 5th place on the puzzles solved chart, and I have a personal goal to break 300 solves by the end of the year. I'm wonder does anyone else have any goals for the app.


Congratulations!

At least I'm still active, whenever there are new puzzles. For example, I just solved three new puzzles 2.8.1, 2.8.1b, and c last night. And I think I will solve 2.8.2* today or tomorrow.

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