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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Oct 30, 2011 4:59 pm 
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hi gelatinbrain,
I played with 3.9.2c and solved it (see picture). It didn't notice it. Is it a bug or are the inner cubies the reason?
Attachment:
3.9.2c.solved_without_recogn.png
3.9.2c.solved_without_recogn.png [ 122.09 KiB | Viewed 4982 times ]
Thank you, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Oct 31, 2011 8:10 am 
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Stefan Schwalbe wrote:
hi gelatinbrain,
I played with 3.9.2c and solved it (see picture). It didn't notice it. Is it a bug or are the inner cubies the reason?
Attachment:
3.9.2c.solved_without_recogn.png
Thank you, Stefan.
I got an idea, why this happend: because the cubies in the face-positions show only 2 colors, maybe the 3rd hidden color is checked by the program to get the solved state although it is not visible from outside. And thank you for adding the solve (in the picture) to the rankings :D Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 01, 2011 9:12 am 
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It seems like in today's version of the jar file, 1.1.84 and 1.1.85 are dropped. Also the total count in the ranking page is decreased by 2. Any problem with these two puzzles? I didn't attempt to solve them yet.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 01, 2011 10:26 am 
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schuma wrote:
It seems like in today's version of the jar file, 1.1.84 and 1.1.85 are dropped. Also the total count in the ranking page is decreased by 2. Any problem with these two puzzles? I didn't attempt to solve them yet.


I'm seeing
Code:
-1.1.84
-1.1.85
+1.2.51


I played with 1.1.84 and 85 yesterday and I had a solution mostly worked out. They were Penultimates but the centers had pentagon circles cut out that worked similar to 1.2.49 and 1.2.50 respectively.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 01, 2011 11:38 am 
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Yeah I know what 1.1.84 and 85 are. I'm even keeping that version of .jar that has them so I can still play with them if I'd like to. I'm just curious why GB dropped them. It doesn't seem to be a mistake. Maybe there are some bugs in that version of the puzzles.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 01, 2011 1:00 pm 
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schuma wrote:
Yeah I know what 1.1.84 and 85 are. I'm even keeping that version of .jar that has them so I can still play with them if I'd like to. I'm just curious why GB dropped them. It doesn't seem to be a mistake. Maybe there are some bugs in that version of the puzzles.

I dropped them because they are functionally 1.1.6 and 1.1.7 with additional trivial pieces. The center and the ring of the opposite face move always together.
I think there are many such duplicate puzzles, sometimes in a very complicated way that you don't see in a first glance.
But once someone solved and sent a score, it's too late to drop. :lol:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 02, 2011 11:18 am 
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gelatinbrain wrote:
I dropped them because they are functionally 1.1.6 and 1.1.7 with additional trivial pieces. The center and the ring of the opposite face move always together.
I think there are many such duplicate puzzles, sometimes in a very complicated way that you don't see in a first glance.
But once someone solved and sent a score, it's too late to drop. :lol:


Aha you are right. One can just ignore the inner centers and solve them as 1.1.6 and 1.1.7. I think some of the duplicate puzzles are quite interesting and deserve to be kept. For example the circle 3x3x3 is functionally nothing but a super 3x3x3, but most people will appreciate the correspondence. Another example is 3.2.10, it really take a while to spot the connection to another familiar puzzle. And during solving it's highly nontrivial to keep track of the correspondence. For this reason it's a great puzzle to solve, although it's a duplicate.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 03, 2011 9:57 am 
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I have solved the 3.9.6c. As in 3.9.2c it didn't notice the solve-state. Here is a picture of the solved puzzle:
Attachment:
3.9.6c.solved_didnt_notice.png
3.9.6c.solved_didnt_notice.png [ 115.41 KiB | Viewed 4818 times ]
Stefan Schwalbe wrote:
I got an idea, why this happend: because the cubies in the face-positions show only 2 colors, maybe the 3rd hidden color is checked by the program to get the solved state although it is not visible from outside.
...
Yes, but I solved 3.9.2c again and that was not the case. Maybe the permutation check is to exact. There is no difference between corner-cubies, edge-cubies, face-cubies and core-cubies in both puzzles. They are all corner cubies i.e. a face-cubie at a corner position looks like a corner cubie. They must only have the right 3 colors (and the right orientation). I hope, it is possible to find the correct solve-state routine.
Thank you, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 04, 2011 6:10 am 
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1.1.39:

1. Megaminx corners
2. Pyraminx Crystal edges
3. center triangles adjacent to edges [3,1]
4. center triangles adjacent to corners [3,1] (pure)
5. trapezoids [3,1] (pure)
6. little triangles [3,1] (pure)

And the best thing: I did it in 1758 moves. That's more than a third less than Sjoerd, who used to be 1st with 3081.
I needed to stop yesterday because it got to late and I still had work to do so I left the computer on throughout the night. It was worth it. :D
I hope this will be my first 1st place move count that I will have done with my own algs and that I will keep for longer than just a couple of days.

I needed 1. and 2.: 268 moves. Not really good I know. I was even thinking about starting over to get a better PC done because I knew I could actually beat 3081 but didn't then.
3.: 542 total. So I needed 274 for that part. Not bad. 60 pieces, 8 moves makes 480 moves, getting 2 pieces done everytime would be 240.
4.: 860 total. So 338 for that part. Could have been better.
5.:1145 total So 285 for that part. Ok. (Even though it is exactly the same cycle as the one for 4. just another slice move :? )
6.: 1758 total. So only 613 moves for 120 triangles. I was happy with that since it wasn't easy to set them up. Slice moves helped a lot but that part took soooo long. It helps to think of the fact that those pieces can be set up just like PC edges a bit. But again, slice moves are really better as set up moves for move count however took me long find.

No responsability is taken for the correctnes of the above sums of moves. I am done thinking for the time being. :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 04, 2011 7:40 am 
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alaskajoe wrote:
1.1.39:

1. Megaminx corners
2. Pyraminx Crystal edges
3. center triangles adjacent to edges [3,1]
4. center triangles adjacent to corners [3,1] (pure)
5. trapezoids [3,1] (pure)
6. little triangles [3,1] (pure)

And the best thing: I did it in 1758 moves.
..

Good job, alaskajoe, well done. Stefan. :shock: :D


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 04, 2011 5:07 pm 
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I solved 3.9.7c, it didn't notice. Here is a screen-shot:
Attachment:
3.9.7c.solved_didnt_notice.png
3.9.7c.solved_didnt_notice.png [ 125.93 KiB | Viewed 4758 times ]
Thank you for adding the score to the rankings. :D Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 04, 2011 8:06 pm 
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Stefan, congratulations on solving all the color-band puzzles!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 05, 2011 3:33 am 
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Oh my god, I just knew the real name of gelatinbrain. It was revealed by Oskar van Deventer in his lecture on the 2011 Dutch Cube Day:

http://www.youtube.com/watch?v=A2QdoKhu ... ure=relmfu


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 06, 2011 5:43 pm 
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Yes, after the presentation I asked Oskar if he knew GB, and whether he knew if he was present at the DCD, bu't he wasn't. If he was, I would've definetely shaken his hand and thanked him for all the work he puts into that masterpiece of a website :D

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 07, 2011 4:10 pm 
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1.1.39 and 1.1.81 got processed by gelatinbrain now. Thank's for that.
it seems that I infact got some numbers wrong. I did it in 1779 not 1785 moves but anyway.
Also 1.1.81 is the one I was talking about having beaten the record a few days ago. I used only Brandon's work with the corner sequence compilation because I couldn't resist trying that.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 09, 2011 10:45 pm 
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It has been a while since I posted. I'm still solving though :D In addition to solving various puzzles I have been working on some puzzle solving theory as well as some code to explore some of my ideas. With a lot of helpful ideas from GuiltyBystander I have written a pretty abstract "puzzle engine" that can simulate quite a few different puzzles. It currently has a few limitations and it's still a moderate amount of work to add a new geometry (such as adding edge-turning cubes or face-turning octahedrons, etc) but in general it is very flexible. It is only very loosely based on geometry and represents puzzles, pieces, and cycles as groups and operations on groups. Because of this it is trivial to handle complex pieces similar to how GuiltyBystander handles them.

The cool thing is that once a geometry is added, adding a new puzzle is just adding very compact definition of the piece types.

For example, here is the definition for 1.2.8:
Code:
add_piece_all_sym('11111111110000000000'); # Chopasaurus Corner
add_piece_all_sym('11111001110000000000'); # 1.2.7 edge
add_piece_all_sym('11111101110000000000'); # 1.2.7 right chiral edge
add_piece_all_sym('11111011110000000000'); # 1.2.7 left  chiral edge
add_piece_all_sym('11110011110000000000'); # 1.2.7 center kite
add_piece_all_sym('11111111000000010000'); # 1.2.8 center point
add_piece_all_sym('11110011110011000000'); # Chopasaurus Center

So with the aid of the program, I have made some progress on Julian's table:

Julian wrote:
With the shorter algos found recently by Elwyn, schuma, Brandon & Katja, there aren't many puzzles left that need longer than [8,1] commutators to solve, so I think it's time for an updated list that expands downward to x > 6. The same [7,1] can be used when solving the puzzles marked in bold, and it has been proven optimal by a computer program written by Brandon and discussed here.

If one solves the Gelatinbrain puzzles* entirely with [x-or-less, 1] commutators and setup moves, where the 1 is a regular move or a slice move, the following puzzles seem to have a minimum possible x > 6:

x = 7
1.1.32, 1.1.33, 1.1.34, 1.2.9, 1.2.15x, 1.4.12, 1.5.1, 1.5.2, 2.1.5, 3.3.7, 3.3.10, 3.3.15, 3.3.17, 3.3.19, 3.10.3x, 4.3.3

x = 8
1.1.26, 1.1.27, 1.1.31, 1.1.35x, 1.1.50, 1.2.8, 1.3.2, 2.1.8, 2.4.1, 3.3.11, 3.4.23, 3.6.5, 3.7.2, 3.7.5, 4.3.2, 4.5.1, 4.7.2

x = 10
1.4.3x, 1.4.7x, 2.3.1, 3.2.14, 3.5.1

x = 12
3.3.6, 3.4.24, 3.5.3, 4.3.4

* Excluding the spheres

  • Due to my work on the Complex 3x3x3 I have reduced 1.1.32 and 1.1.33 to [[1,[1,1]],1] == [6,1] commutators. R, U, B, U', B', R' isolates a pieces in an anti-D move. I have not worked on 3.1.34 because the mix of move-types is quite odd but I believe this applies just fine to it too.

  • With help from Katja I found a [[1:[1:[1,1]]],1] == [8,1] commutator for the points on 1.2.9 / 2.1.5 and I put a reasonable amount of effort trying to find what Julian described. I turned my program on the puzzle if you restrict the move sequences to ones made up of commutation, conjugation, and nesting with 1 move sequences then there is no [7,1] of that form but there are [8,1] sequences that have a canceling effect like what Julian described. Here is the X part it found with cancellation CDA, HIL', KED, HIL', KED', HIL', CDA'. Note that this is a [1:[2-gen]] sequence which is quite neat. This is not a proof that something better doesn't exist but if you exclude non-standard constructions, anti moves, re-orientation, and other such oddities than the shortest sequence is indeed [7,1]. This cancellation bugs be a bit and I'd prefer to think of it as a [8,1] with a cancellation rather than a [7,1]. Amazing find Julian!

  • Also, much to my surprise the tiny small center triangles on 1.2.8 can be done in [6,1] moves rather than [8,1]. As soon as my program spit out a [6,1] I went and looked instead of using the sequence my program found. It's quite embarrassing how easy the sequence is to find. Just do a typical [1,1] that looks like it's close to isolating one of those small triangles. Then find a setup move to add to make it a [1:[1,1]] and you will isolate a small triangle in a slice. The reason this was hard to find initially is that there is a "red herring" small triangle piece that is hard to isolate and there is a much easier to isolate piece that doesn't look very easy.

  • Also, speaking of the vertex turning dodecahedra, the best pure sequence I had for the big triangles on center triangles on 1.2.7 was [6,1]. Well it turns out there is a [5,1] and the 5 move X part is a 2-gen sequence! I look for [Z:[X:Y]] sequences where Z != Y but this sequence is [Y:[X:Y]]. I'm not surprised that nobody spotted that, it's hard to use setup moves that are also a part of your [1,1].

It is my hope that eventually I'll turn my program to some of the other puzzles on the list. The next geometry I need to add is the edge-turning dodecahedron (rhombic tricontrahedron) so that we can better understand the Big Chop.

It is a great amount of fun working on this chart so thank you Julian for all of the hard work you have put in to making it :P

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 09, 2011 11:59 pm 
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Brandon, nice work! I can see your program must have a great potential. Can it handle puzzles with multiple layers for each face, like Gigaminx? If currently not, how hard is it to add it?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 10, 2011 9:33 am 
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bmenrigh wrote:
[*]Also, much to my surprise the tiny small center triangles on 1.2.8 can be done in [6,1] moves rather than [8,1]. As soon as my program spit out a [6,1] I went and looked instead of using the sequence my program found. It's quite embarrassing how easy the sequence is to find. Just do a typical [1,1] that looks like it's close to isolating one of those small triangles. Then find a setup move to add to make it a [1:[1,1]] and you will isolate a small triangle in a slice. The reason this was hard to find initially is that there is a "red herring" small triangle piece that is hard to isolate and there is a much easier to isolate piece that doesn't look very easy.


I cared for this part first. Man it took long but I found it too. Actually In my eyes the piece that can be isolated by slice move with one additional set up move to the [1,1] actually was the one I would usually think about isolating first because it looked like it already was. The point is that the special required setupmove didn't look like it would do any good at first. Unless I actually found another [6,1] there but I doubt it. From your description I thought one of the triangles that are surrounded by other cycled stuff would have to be put to an unobvious position so I tried all triangles with all possible moves to than slice it away until I finally decided to go for the one that acutally looks so obvious but use an unobvious set up move.
I'll just post my way:

CHG', FJI, CHG, FJI', BIH', DGK'&2, BIH, FJI, CHG', FJI', CHG, BIH', DGK&2, BIH,

Honestly this is in the form of [4,3] still, as always with me. :roll:
The isolated triangle is the one on the very tip of the [1,1] cycled stuff. The only thing that prevents it from beeing isolated by slice move just right there already are some edgepieces and large triangles on the back of the cube. Hopefully that makes sense in words.

And now some questions:
1st When is a sequence called a 2-gen sequence?
Is that just a setupmove that's part of the [1,1]?
The basic idea of having setupmoves which are part of the [1,1] commutator just occured to me recently. Well it wasn't really my idea even. I just looked closely at the 9-move sequence for positioning corners on a 3x3x3, which is the last step in the beginners method I learned years ago. I found out that it is a [[1:1],3] however the 4th move of the [1,1] (180°) is just interfering with the first of the 3 moves. That's when I finally fully understood all the algos of the 3x3x3 beginners method I learned long ago.

you said:
Quote:
CDA, HIL', KED, HIL', KED', HIL', CDA'. Note that this is a [1:[2-gen]]

from this I would say it actually is a commutator that has one of the moves not "undone" but done a second time? That would mean those don't exist on puzzles that have 180° turns, so all edge puzzles?

2nd What is an anti move?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 10, 2011 3:54 pm 
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bmenrigh wrote:
With a lot of helpful ideas from GuiltyBystander I have written a pretty abstract "puzzle engine" that can simulate quite a few different puzzles.
...
Very interesting, Brandon. Is it using tree-searches?
It is very easy to add a new puzzle to it. Than you cycle 3 pieces and let it run to find the shortest solution, right?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 10, 2011 5:56 pm 
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Thanks for the comments all! I suppose I should say more about my program.

First, I wrote the program in perl because I thought that the rapid programming and ready-made datastructures available in perl would be a net win. Unfortunately the program is slow and memory hungry so the benefits of getting the program up and working seem to be outweighed by the limitations of the program.

Puzzles geometries are defined by what grips can be turned. A grip can be a edge, vertex, or face. To define the puzzle you describe which grips move and to which positions when you rotate the puzzle around a particular grip. For example, here is the U face twist definition on a cube:
Code:
   if ($grip == 0) { # White top face                                     
            # White and yellow don't move                                       
            $new_state[0] = $cur_state_ref->[0];
            $new_state[5] = $cur_state_ref->[5];

            $new_state[1] = $cur_state_ref->[4];
            $new_state[2] = $cur_state_ref->[1];
            $new_state[3] = $cur_state_ref->[2];
            $new_state[4] = $cur_state_ref->[3];
   }

After defining some rotations all of the orientations of the overall puzzle can be discovered and any grip twist can be mapped into a new state. A cube only needs two orientations deltas to be defined and then all 24 can be discovered. For a dodecahedron 2 re-orientations about a face defines all 60.

Then, once the puzzle geometry is defined, to add pieces to the puzzle you just define which grips can turn a piece. A corner on a cube can be defined by '111000'. By applying the symmetries of the geometry all of the other corners are discovered.

So when I add all of the pieces to 1.2.8 this is the program output:
Code:
Total orientation states: 60
Found 20 pieces of type 0 with twist freedom 3
Found 30 pieces of type 1 with twist freedom 2
Found 60 pieces of type 2 with twist freedom 1
Found 60 pieces of type 3 with twist freedom 1
Found 60 pieces of type 4 with twist freedom 1
Found 60 pieces of type 5 with twist freedom 1
Found 12 pieces of type 6 with twist freedom 5
There are 302 pieces in the puzzle state

The way routines are found is somewhat flexible. You define a pattern that the routine follows and then the program enumerate all sequences that fit into that pattern.

Here are the first few patterns in my program:
Code:
my @useful_sequences =
    ("0, 1, 0', 1'", # [1,1]
     "0, 1, 0', 2, 0, 1', 0', 2'", # [[1:1],1]
     "0, 1, 0', 1', 2, 1, 0, 1', 0', 2'", # [[1,1],1]
     "3, 0, 1, 0', 3', 2, 3, 0, 1', 0', 3', 2'", # [[1:[1:1]],1]
     "3, 0, 1, 0', 1', 3', 2, 3, 1, 0, 1', 0', 3', 2'", # [[1:[1,1]],1]
[...]


If you wanted to just brute force to a depth of 5 the pattern would be "0, 1, 2, 3, 4" and if you wanted to brute for the X portion of a [X,1] commutator you'd just do a pattern like "0, 1, 2, 3, 4, 5, 4', 3', 2', 1', 0', 5'".

Unfortunately the program is quite slow because all of the pieces in the puzzle are lists and with a puzzle that has 302 pieces, each with 20 list entries, one for each grip, even simple changes to the puzzle state are a lot of operations. The program would be several order of magnitude faster in C.

To search all [[1:[1,1]],1] == [6,1] sequences on 1.2.8 is about 3 hours. It would be a matter of seconds if I re-wrote the program for speed in C.

schuma wrote:
Brandon, nice work! I can see your program must have a great potential. Can it handle puzzles with multiple layers for each face, like Gigaminx? If currently not, how hard is it to add it?
The program can't currently handle multiple layer puzzles because the piece definitions are binary. To handle more layers I'd make each handle a bitmask so a piece that can be turned by the outer layer would have a grip entry of 1 and pieces that turn by the slice would have an entry of 2. Pieces that can be turned by both would have an entry of 3, etc. I suspect Gelatinbrain does something very similar to this with his &1 or &2 or &3 slice mask.

The trouble with adding slices is that there is an exponential increase in search time because of the additional possibilities that each entry in the sequence pattern can take. [Z:[X,Y]] takes at least 4x as long to search (more like 8x) due to the doubling of possibilities for each of X, Y, and Z.

Note though that the program does handle the "middle slice" of puzzles just fine because that's the same as turning the two opposite grips and then re-orienting the puzzle. The program also handles anti-moves just fine for the same reason.

Stefan Schwalbe wrote:
Very interesting, Brandon. Is it using tree-searches?
It is very easy to add a new puzzle to it. Than you cycle 3 pieces and let it run to find the shortest solution, right?
It is not however due to the time I spent programming the Pentultimate and my correspondence with GuiltyBystander on the subject, I know how to somewhat generically prune a brute-force tree-search so that whole branches of the tree can be abandoned because they aren't leading anywhere. This is not realistic to do in perl though because of the high memory usage.

As for figuring out the shortest solution, the current way the program searches for routines is based on a set of defined "invariants". That is, if I'm searching on the Master Pentultimate for pure corner routines then I want the twist and permutation of the centers, edges, and Starminx points to be invariant. If I'm searching for Starminx point routines and I don't care about the corners then I can just set the centers and edges to be invariant. In this way it is easy to find pure and non-pure routines by changing the invariant criteria.

In the "pie in the sky" dream program you'd be able to define a puzzle and it would tell you the optimal order and all of the cycles. I think I know how to do that but it's too slow to be realistic in my current program. Basically it would search for [1,1] commutators and then [3,1] and then [4,1] and so forth to find routines and their side-effects. Then it is a simple matter of solving a k-sat like problem. For puzzles without many unique piece types it doesn't matter that this is NP-complete.

Ultimately I would like to have an easy-to-use program (maybe even a web interface for it). My perl program isn't far away from being easy to use but it's way to slow to ever be useful to somebody else. I really need to re-write it in C for efficiency if I'm going to be able to answer good questions.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 12, 2011 8:55 pm 
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I programmed the geometry for edge turning dodecahedra and set my program loose on the Big Chop. The Big Chop is very difficult but I think knowing the shortest commutator is really telling about how difficult it really is.

Julian has stated that he knows a [10,1] based around a [X Y]x3 of the form [1:[1:[1 1]x3],1]. Katja knows a [12,1].

But how short can X be in a [X,1] commutator?

My program isn't currently fast enough to check for all X so I have restricted it to only "standard form" commutator construction. In brief, a "standard form" commutator is one based on commutation and conjugation where the argument to the conjugation or commutator operator is either a single move or a nested commutator or conjugate. That is, sequences that can be written entirely using '[', ']', ',', ':', '1'.

Here is my stab at a grammar for this:

SEQUENCE := OPERATOR_OR_MOVE | NULL
OPERATOR_OR_MOVE := OPERATOR | MOVE
OPERATOR := COMMUTATOR | CONJUGATE
COMMUTATOR := [OPERATOR_OR_MOVE,OPERATOR_OR_MOVE]
CONJUGATE := [OPERATOR_OR_MOVE:OPERATOR_OR_MOVE]
MOVE := 1

I have a hypothesis that the shortest useful 3-cycle for a piece is always of this "standard form" sequence but so far I have been unable to prove this. This is a topic of ongoing work :)

I had my program check all standard form commutators of X <= 8 and it did not find a sequence. I also had it check all standard form commutators of X = 10 and again no sequence was found.

This is a problem since Julian knows a X = 10 but X isn't of standard form. But, observe that the base of Julian's sequence is [1 1]x3 and if you truncate it to 5 moves it is standard form [1:[1:1]]. I had my program check for [9,1] sequences and indeed there is a pure 3-cycle 8-):
Attachment:
big_chop_9_1_commutator.png
big_chop_9_1_commutator.png [ 13.82 KiB | Viewed 4405 times ]

That is, the [9,1] is [[4:1],1] == [[3:[1:1]],1] == [[1:[1:[1:[1:1]]]],1]

The amazing thing to me is that Julian did find the shortest commutator on this puzzle except that he just included one extra unnecessary move because the [1 1]x3 can be truncated.

In my opinion finding this [9,1] is incredibly hard. If you're having trouble I'd suggest looking into [12,1] sequences that have nested commutators instead this horribly long commutated chained-conjugate sequence.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 12, 2011 9:16 pm 
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Brandon, this is amazing! :D A [9,1]! When I get more time I will try and search for a sequence of the form [[4:1],1]. Could you maybe post the sequence so I can look more closely at what it does exactly?

I'd also like to congratulate you on this. I hope you feel that all your hard work has paid off, because this is just breathtaking. I cannot believe we finally know a 20-move sequence for the Big Chop!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 12, 2011 9:23 pm 
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On the Big Chop / Gelatinbrain's 1.4.3:
Katja wrote:
Brandon, this is amazing! :D A [9,1]! When I get more time I will try and search for a sequence of the form [[4:1],1]. Could you maybe post the sequence so I can look more closely at what it does exactly?

I'd also like to congratulate you on this. I hope you feel that all your hard work has paid off, because this is just breathtaking. I cannot believe we finally know a 20-move sequence for the Big Chop!
Of course :D

[BC, EF, EK, AB, EK, AB, EK, EF', BC', AF, BC, EF, EK, AB, EK, AB, EK, EF', BC', AF']

Broken down into standard form:

[[BC:[EF:[EK:[AB:EK]]]],AF]

Note that EK is both the Y portion of the inner conjugate and the X part of the first outer-conjugate. This matches up with what Julian found: [AB EK]x3

It does feel good to have a program that can find these sequences but right now I feel like my program is only a shadow of what it can become. I have a lot of hard work ahead of me :twisted: .

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 13, 2011 8:08 am 
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Interesting work, Brandon.
bmenrigh wrote:
I have a hypothesis that the shortest useful 3-cycle for a piece is always of this "standard form" sequence but so far I have been unable to prove this. This is a topic of ongoing work
Here is an example for a [2,1] on the 3.9.10. Can you transform it to your standard form?
Attachment:
3.9.10_2-1-commutator.png
3.9.10_2-1-commutator.png [ 86.68 KiB | Viewed 4362 times ]
It goes:
/*000000*/URF,
/*000001*/DFR,
/*000002*/ULB2,
/*000003*/DFR',
/*000004*/URF',
/*000005*/ULB2,
This is [ [ URF DFR ], ULB2 ].
Thank you, Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 13, 2011 9:46 am 
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Awesome work with your programm. :shock: And a 9.1 for the big chop: I can't believe it. However I can't believe Julian had found a 10.1, let alone that it actually is the 9.1. I didn't look into Big Chop discussions ever. I don't really understand though how you can truncate the 10 into 9 without altering the effect of the further steps of the sequence. I mean there is just one move left away and this deep cut puzzle doesn't work like a shallow cut one where a conjugate sequence does the same as a full [1,1].
But anyway.
I recently found a sequence too, that doesn't behave like a normal commutator. I don't even fully understand it myself anymore. It appeared to me in my head kind of vaguely and perfectly worked:

The puzzle is 3.3.6, one step shallower cut than 24 cube and here is the sequence:

UR,DF,UR,DF,

BR&2,FU,RF&2,FU,BR&2,

DF,UR,DF,UR,

BR&2,FU,RF&2,FU,BR&2,

This cleanly cycles three of the (unregular) pentagonal pieces on the surface. It somehow is a [[1,1],5] or [[1,1],[2:1]].
I repeated it a lot and I don't think it cycles any other same-colored pieces which I missed. And again this was is some kind of open minded state or so. I know and remember why I did this [2:1] in there but still it is weird now.
Can this sequence be reduced to anything that makes sense as far as common commutator constructions are concerned?
And what is actually the shortest known routine for those pieces. I mean I don't even know if it makes sense to cycle them cleanly because I haven't found out a way to cycle the 24 pieces on this edgeturning cube. There are left.

Edit: uhm, so is that [2:1] maybe just considered a [1:[1:1]] ? :oops:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 13, 2011 12:29 pm 
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Stefan Schwalbe wrote:
Interesting work, Brandon.
bmenrigh wrote:
I have a hypothesis that the shortest useful 3-cycle for a piece is always of this "standard form" sequence but so far I have been unable to prove this. This is a topic of ongoing work
Here is an example for a [2,1] on the 3.9.10. Can you transform it to your standard form?
It goes:
/*000000*/URF,
/*000001*/DFR,
/*000002*/ULB2,
/*000003*/DFR',
/*000004*/URF',
/*000005*/ULB2,
This is [ [ URF DFR ], ULB2 ].
Thank you, Stefan.

Hi Stefan, thank you for this counter-example. I can't translate this into my standard form. I don't want to make excuses but this is is a troublesome puzzle.

I know I need to integrate both re-orientations and anti-moves into my standard notation but I haven't worked on that enough yet to say anything insightful about it.

The reason your 2-move [ URF DFR ] works so nicely is the overlap between the twists. I don't think my hypothesis applies to puzzles that have overlapping layers such as much of the 3.9.X series or puzzles like 1.8.1. You're canceling out the movement of the overlapped pieces so that you can isolate a piece on the surface.

There are puzzles that I think my hypothesis does apply to though that do sometimes require 2 moves. 1.1.35 for example. When you turn the top and bottom face what what you're actually doing is turning the middle layer which I would call 1 move. I'd argue that the applet should support shift+click to twist the two opposite middle circles.

Please keep the counter-examples coming, I need more things to think about :lol:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 13, 2011 12:34 pm 
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alaskajoe wrote:
[...]The puzzle is 3.3.6, one step shallower cut than 24 cube and here is the sequence:

UR,DF,UR,DF,

BR&2,FU,RF&2,FU,BR&2,

DF,UR,DF,UR,

BR&2,FU,RF&2,FU,BR&2,

This cleanly cycles three of the (unregular) pentagonal pieces on the surface. It somehow is a [[1,1],5] or [[1,1],[2:1]].
[...]
Edit: uhm, so is that [2:1] maybe just considered a [1:[1:1]] ? :oops:
Yeah you can turn a bunch of setups moves into a chain of [1:[1:[...]]]. This is somewhat of an annoying trivial case but it does emphasize that they are setup moves an not some other special sequence.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 13, 2011 2:09 pm 
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Stefan Schwalbe wrote:
[ [ URF DFR ], ULB2 ].


Nice example Stefan! I've never thought of this way to do a 3 cycle.

bmenrigh wrote:
There are puzzles that I think my hypothesis does apply to though that do sometimes require 2 moves. 1.1.35 for example. When you turn the top and bottom face what what you're actually doing is turning the middle layer which I would call 1 move. I'd argue that the applet should support shift+click to twist the two opposite middle circles.


I think Stefan's counter-example is similar to the counter-example involving middle layers: both have to do with two moves along the same axis. There might be a unified way to handle these cases.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 10:48 am 
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After Muffet's topic in the New Puzzles section about his "Solar Octahedron" puzzle I played with 3.3.6 a bit and I found some routines.

I won't post the algs here but what I can say is that I have a

-10 move sequence for 3-cycling edges (unpure: along with edge triangles and pentagonal pieces)
-16 move for changing orientation of two edges
-10 move for 3-cycling corners (also centers and edge triangles)
-4 move for changing orientation of two corners
-cheap 22 move for centers derived from the corners cycle
-18 move pure for triangles
-18 move pure for pentagonal pieces

I guess some of these aren't good at all and can be made better but the point of this post is the question if 3.3.6 should be solved by doing the 24-cube triangles first. That doesn't sound to weird because they are the 24-cube but actually it's quite unusual to solve some little triangle on the faces of a puzzle first and then the rest. I don't recall any puzzle where I would do that. Unless one where pairing centers is involved maybe (e.g. Gigaminx)
Did anyone ever look for a cycle of the face triangles on 3.3.6 that wouldn't break up centers, edges and corners?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 12:25 pm 
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alaskajoe wrote:
After Muffet's topic in the New Puzzles section about his "Solar Octahedron" puzzle I played with 3.3.6 a bit and I found some routines.

I won't post the algs here but what I can say is that I have a

-10 move sequence for 3-cycling edges (unpure: along with edge triangles and pentagonal pieces)
-16 move for changing orientation of two edges
-10 move for 3-cycling corners (also centers and edge triangles)
-4 move for changing orientation of two corners
-cheap 22 move for centers derived from the corners cycle
-18 move pure for triangles
-18 move pure for pentagonal pieces

I guess some of these aren't good at all and can be made better but the point of this post is the question if 3.3.6 should be solved by doing the 24-cube triangles first. That doesn't sound to weird because they are the 24-cube but actually it's quite unusual to solve some little triangle on the faces of a puzzle first and then the rest. I don't recall any puzzle where I would do that. Unless one where pairing centers is involved maybe (e.g. Gigaminx)
Did anyone ever look for a cycle of the face triangles on 3.3.6 that wouldn't break up centers, edges and corners?


My strategy for 3.3.6 is different from yours. But I'm not solving the 24-cube triangles first. I won't do that because there's a parity issue:

If one assumes a global orientation that is 90 degree away from the truth, he/she cannot solve it, because the permutation of edges is odd, and the total permutation of centers+corners is odd. One needs to either solve all the edges first, or solve all the corners and centers, to avoid this parity as soon as possible. Since there are too many duplicate 24-cube pieces, they tell nothing about the parity. So I won't solve them first.

When you are solving edges first, do you run into parity and fix it, or do you have a good way to avoid it?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 2:51 pm 
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I noticed that the total number of puzzles in the ranking page has increased by two, but the .jar file has not been updated yet. I hope this is a sign that two new puzzles are coming very soon.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 3:35 pm 
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schuma wrote:
Oh my god, I just knew the real name of gelatinbrain. It was revealed by Oskar van Deventer in his lecture on the 2011 Dutch Cube Day:

http://www.youtube.com/watch?v=A2QdoKhu ... ure=relmfu

Really... I need to go watch this when I get home. I've been curious who Gelatinbrain is for years and Oskar beat me again. LOL!!! The closest I've ever come to getting Gelatinbrain to introduce himself (or herself) was here.

Carl

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 5:18 pm 
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Continued from PM's...
(alaskajoe PM'd me pretty much the same as he asked here, but I thought I'd copy it in here so more people could follow the 3.3.6 discussion as it undoubtably is one of the trickiest puzzles. I'd write a separate post, but I'm too busy and I already spent a fair amount of time typing up this.)

Hey,

I wouldn't want to solve the little chop pieces first. The routine I have is a [7,1]:

UR, RF, LU, RF, UR, RF, LU, RF, UR, RF, LU, RF, UR, RF, LU, RF,

If you try pasting that in to 3.3.6, you'll see that it cycles too many pieces for it to be useful to do it first. The only pieces it does not move are the corners. That's too bad, because [7,1] is the shortest length routine for those pieces.
Me and Brandon spent a long time trying to work around this, finding routines that did the centers and not the little chop pieces etc, but it just wasn't convenient at all.

Therefore, I've decided on doing those pieces last, and the only pure routine I have for that is a [24,1] = 50 moves :? So that's why I haven't solve it yet, as it would take a minimum of 50 x 24/3 moves to cycle all of them, and that's if I got only perfect 3-cycles, which I know I can't from solving the normal little chop a few times.

However, yesterday, Brandon's new program (introduced in the thread recently) found a PURE [9,1] for the little chop pieces. It's hard to understand, because it doesn't isolate a pieces, it temporarily swaps it with another one, which due to (partly, I think) the symmetry of the 180 degree turns ends up in a pure 3-cycle and not 2 3-cycles. I discovered this way of cycling pieces not too long ago, and I've been calling it the temporary swap method. I'm planning to do an extensive post about it after I finish my exams. You might like to know that this swap method is also how Brandon's program found the optimal big chop routine. I'll save the details for later :D

I wish I knew how Julian solved it. He never mentioned how, or in what order. But his list (recently quoted by Brandon) states that he knows an x = 12 == [12,1] for 3.3.6, and that's the longest algo he has. It might be for the little chop pieces, but I have a gut feeling that he didn't do those last.

Katja


Edit: I should mention that I don't want to use the [9,1] Brandon's program found to solve it with. It would feel like cheating, almost. I didn't try the swap method on it yet, so when I get the time I will try searching for an x > 9 that allows for that.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 7:29 pm 
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A [9,1]! That is just too crazy. I would love to just check and see how that looks though.

But there's one basic thing again, I don't understand about your post. If your [7,1] messes up to many other pieces as well isn't that a reason to solve them first? As long as you don't have to care about them, you can ignore everything else and just do the little chop. Than cycle everything else.
Except for the parity you can run into. I didn't know there was one. If you did, I completely understand. :lol:

Also since there are only 6 centers I could bear having nothing better than 22 moves for a clean cycle. Of course there surely is a better way though.

schuma wrote:
My strategy for 3.3.6 is different from yours. But I'm not solving the 24-cube triangles first. I won't do that because there's a parity issue:

If one assumes a global orientation that is 90 degree away from the truth, he/she cannot solve it, because the permutation of edges is odd, and the total permutation of centers+corners is odd. One needs to either solve all the edges first, or solve all the corners and centers, to avoid this parity as soon as possible. Since there are too many duplicate 24-cube pieces, they tell nothing about the parity. So I won't solve them first.

When you are solving edges first, do you run into parity and fix it, or do you have a good way to avoid it?


I honestly haven't attempted a solve yet. Because I just don't know how to solve the 24-cube in a decent way in the first place. I just listed the algorithms I found so far. I guess this puzzle is even more difficult than I thought. I thought once I would be able to solve a 24-cube I could just do my described procedure with solving those 24 pieces first. But running into a parity with this puzzle would be a pain.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 15, 2011 7:51 pm 
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alaskajoe wrote:
But there's one basic thing again, I don't understand about your post. If your [7,1] messes up to many other pieces as well isn't that a reason to solve them first? As long as you don't have to care about them, you can ignore everything else and just do the little chop. Than cycle everything else.
Except for the parity you can run into. I didn't know there was one. If you did, I completely understand.

Also since there are only 6 centers I could bear having nothing better than 22 moves for a clean cycle. Of course there surely is a better way though.
I have been exploring other options, but I've been having a hard time finding routines for centers, edges, houses and chiral pieces that doesn't move any little chop pieces. Brandon used his program to look for routines that cycled the houses, allowing to break the chiral pieces, but that didn't cycle the little chop pieces, and the shortest for that was [17,1].
It's really hard to find anything that doesn't move the little chop pieces since you move 12 of them in each turn. So far I can do the chiral pieces without moving them, by commutating my [7,1] to make a [16,1]. I just don't think (with the routine I have) that doing little chop pieces first is optimal and I think it will make an already hard puzzle much harder.

If I do the little chop pieces last, I can solve most pieces with fairly short routines and making up for it by using a somewhat long routine at the end. If I could only find something shorter than [24,1], I'd be comfortable to solve it this way.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 16, 2011 1:28 am 
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3.3.6 / Fat Little Chop / Fat 24-cube / Master Little Chop:

Per Katja's comments above, I programmed the edge-turning-cube geometry and now I have answers :D

3.3.6 is a brutally difficult puzzle for sure but don't forget that it has slice moves. At first I forgot to allow slice moves and the routines my program was finding were extraordinarily long.

So first, lets name the pieces:
Attachment:
3.3.6_piece_numbers.png
3.3.6_piece_numbers.png [ 13.86 KiB | Viewed 4142 times ]


1) Edges (same edges that first appear in 3.3.2)
2) Corners (same corners as Helicopter Cube)
3) Centers (same centers that first appear in 3.3.2)
4) X-Centers (same as the small x-centers that first appear in 3.3.4)
5) Little Chop Triangles (same as the Little Chop / 24-cube / 3.3.7)
6) Left-Chiral Triangles (same as the ones that first appear in 3.3.2)
7) Right-Chiral Triangles (same as the ones that first appear in 3.3.2)

Figuring out a good solve older for these pieces is really hard. With the aid of my program though, we can figure out the lower and upper bounds for each piece type. That is, the lower bound for a piece is the shortest sequence to make a 3-cycle ignoring all other pieces. These are very non-pure sequences. The upper bound for a piece is the shortest pure 3-cycle that leave everything else on the puzzle untouched. These are usually too long to be useful.

Shortest non-pure 3-cycles for each piece (only "standard form" commutators considered):
Edges: [1,1] [UR, BR, UR', BR']
Corners: [1,1] [UR, BR, UR', BR']
Centers: [1,1] [UR, RF, UR', RF']
X-Centers [3,1] [UR, BR, UR', UB&2, UR, BR', UR', UB'&2]
Little Chop Triangles: [7,1] [UR, DF, UR, BR, UR', DF', UR', BR, UR, DF, UR, BR', UR', DF', UR', BR']
Chiral Triangles [3,1] [UR, RF, UR', LU, UR, RF', UR', LU']

Shortest pure 3-cycles for each piece (only "standard form" commutators considered):
Edges: [8,1] [LB, RD, UR, DF, UR', DF', RD', LB', UR&2, LB, RD, DF, UR, DF', UR', RD', LB', UR'&2]
Corners: [7,1] [BD, UB&2, UR, BR&2, UR', UB'&2, BD', BR&2, BD, UB&2, UR, BR'&2, UR', UB'&2, BD', BR'&2]
Centers: [7,1] [UR, RF&2, UR, BR, UR', RF'&2, UR', BR&2, UR, RF&2, UR, BR', UR', RF'&2, UR', BR'&2]
X-Centers [7,1] [UR, LB, UR, BR, UR', LB', UR', BR&2, UR, LB, UR, BR', UR', LB', UR', BR'&2]
Little Chop Triangles: [9,1] [RD, UB, BD, UR, BR, UR', BD', UB', RD', BR, RD, UB, BD, UR, BR', UR', BD', UB', RD', BR']
Chiral Triangles [5,1] [BR&2, UR, DF, UR', BR'&2, UB&2, BR&2, UR, DF', UR', BR'&2, UB'&2]


Now that the lower and upper bounds are known and playing with the solve order a whole bunch this is the best that I can come up with. Rather that start with the corners I start with the edges which resolves the parity issues up-front. Starting with the corners doesn't really shorten the solve.

Suggested solve order:
1) Edges: Place intuitively and then fall back on [1,1] commutators. Orient with [1,1] commutators.
2) Corners: Use [3,1] commutators for permuting and [1,1] for orienting.
3) Centers: [3,1] where the 3 is slice, edge, slice' and the 1 is edge.
4) Little Chop Triangles: [7,1] see above.
5) X-Centers: [5,1] commutators where the 1 is a slice move and the 5 is edge moves.
6) Chiral Triangles: [5,1] pure, see above.


Edit: I corrected the solve order. I had the Little Chop Triangles after the X-Centers with a [7,1] routine but that routine moves the X-centers. The [5,1] X-centers routine does not move the Little Chop Triangles. The new solve order is correct.

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Last edited by Brandon Enright on Wed Nov 16, 2011 9:27 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 16, 2011 9:19 am 
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Awesome Brandon.
So [9,1] infact. (I think in your summary where it says
Quote:
Little Chop Triangles: [7,1] see above.
it should be 9,1. :wink: )

Katja wrote:
Quote:
I have been exploring other options, but I've been having a hard time finding routines for centers, edges, houses and chiral pieces that doesn't move any little chop pieces. Brandon used his program to look for routines that cycled the houses, allowing to break the chiral pieces, but that didn't cycle the little chop pieces, and the shortest for that was [17,1].


Hmm. Maybe now his programm did a better job.^^
What I was also saying in my pm's is that I actually found a [4,[2:1]] clean 3-cycle for the houses (18 moves) and virtually the same to cycle the little edge triangles cleanly. I also have a [4,3] for 3-cycling the houses, allowing to break the chiral pieces, but that don't cycle the little chop pieces.

I'll post them if you want to look at them: (The one with the [2:1] is already somewhere above in a question I had.)

UR,DF,UR,DF,FU,RF&2,FU,DF,UR,DF,UR,FU,RF&2,FU, [4,3] for houses and chiral pieces

UR,DF,UR,DF,BR&2,FU,RF&2,FU,BR&2,DF,UR,DF,UR,BR&2,FU,RF&2,FU,BR&2, [4,[2:1]] houses clean

the one with the chiral triangles clean is essentially the same except that the [2:1] part is FL,FU,RF&2,FU,FL,

But as I said already since I don't know how to solve the 24 pieces this whole way of solving it that I suggested is not really well based. I was hoping to find a "dirty" way of doing the 24 cube already and prepared all this to then solve 3.3.6 too but I still couldn't except for a [24,1] and a derived [[24,1],1] that would make setup-moves a little easier. I never bothered pasting those into 3.3.6 to see how much stuff they mess up other than the 24 pieces.

Brandon wrote:
Quote:
4) X-Centers: [5,1] commutators where the 1 is a slice move and the 5 is edge moves.
5) Little Chop Triangles: [7,1] see above.
6) Chiral Triangles: [5,1] pure, see above.


These are invincible. :shock:

Also after shuma pointed out the possibility of edge and corner parities I don't think I will hold on to my way anyway. :?


Edit: sorry for missing names in quotes I added them manually.
Also: HA! :lol: I found your 4) Brandon. Really cool but crazy. I just tried around. After a certain [1:[1:1]] (that your 5 face moves had to be formed] the slice move really struck me. I wouldn't have found them logically and in a concieving way though.
Still thanks.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 16, 2011 9:37 am 
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alaskajoe wrote:
Awesome Brandon.
So [9,1] infact. (I think in your summary where it says
Quote:
Little Chop Triangles: [7,1] see above.
it should be 9,1. :wink: )
No I got the order wrong :? . I accidentally listed the Little Chop Triangles after the X-centers when they need to be done before. The [5,1] for the X-centers doesn't affect the Little Chop Triangles at all but it does make a mess of the chiral triangles which is why I have them listed last with a pure routine. I have fixed the ordering.

alaskajoe wrote:
Katja wrote:
I have been exploring other options, but I've been having a hard time finding routines for centers, edges, houses and chiral pieces that doesn't move any little chop pieces. Brandon used his program to look for routines that cycled the houses, allowing to break the chiral pieces, but that didn't cycle the little chop pieces, and the shortest for that was [17,1].


Hmm. Maybe now his programm did a better job.^^
I think the [17,1] is a bit out of context. I think what Katja is saying is that a [17,1] is the best she has for the pieces. I haven't used my program to search past a depth of [13,1]. It needs a re-write to be fast enough for that.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 17, 2011 11:13 pm 
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bmenrigh wrote:
I think the [17,1] is a bit out of context. I think what Katja is saying is that a [17,1] is the best she has for the pieces.
I'm probably mixing things up :?

I found a shorter routine for the little chop pieces, it's a non-pure [18,1]. Still a bit lengthy, but maybe I can find a shorter one if I try.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 20, 2011 2:02 pm 
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bmenrigh wrote:
3.3.6 / Fat Little Chop / Fat 24-cube / Master Little Chop:

Per Katja's comments above, I programmed the edge-turning-cube geometry and now I have answers :D

3.3.6 is a brutally difficult puzzle for sure but don't forget that it has slice moves. At first I forgot to allow slice moves and the routines my program was finding were extraordinarily long.
Your algos are amazingly short, especially the [7,1] non-pure and [9,1] pure for the Little Chop pieces, which a human would be unlikely to find because the puzzle looks so messy at the end of each main sequence!

My ancient solution to 4.3.4, which is piece equivalent to 3.3.6, is here. I finished with the Little Chop pieces using an algo I posted here. Written in reverse, it's [[3:1, 1], 1] = [[7,1], 1] = 32 moves due to move cancellations. Ages later I described a [12,1] pure algo I found for the Little Chop pieces here. My [12,1] algo is [[DL BR] : [UF:UL, DR], BD]. I'm amazed that a [9,1] pure algo is possible for these pieces.

By the way, I'm pretty sure that slice moves for 3.3.6 and 4.3.4 are a fairly recent development, because they didn't exist when I solved the puzzle in 2008, and they don't exist in the Java executable JAR I downloaded this year that's dated January 25th, 2011.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 20, 2011 2:16 pm 
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Brandon, thanks for describing your program and sharing your discoveries with us. While I did notice some recurring patterns with optimal length commutators, I was mostly fumbling around intuitively, and it's fascinating reading your combination of theoretical rigor and computational brute force to discover improved algos.

The [9,1] pure algo for the Big Chop is great! I would never have thought of chopping the last move off the inner back-and-forth sequence, though of course it makes sense when focusing on inner commutators or conjugates.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 20, 2011 5:40 pm 
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Ok so, I've been trying for a while now to solve the master pentultimate, and i've almost finished. THe only problem is I've now been stuck for about 2 weeks just on the last 2 corners :( .
Basically they are both twisted in place, and no amount of messing around is helping.
Can someone give me a hint please :oops: .

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 20, 2011 5:53 pm 
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MaeLSTRoM wrote:
Ok so, I've been trying for a while now to solve the master pentultimate, and i've almost finished. THe only problem is I've now been stuck for about 2 weeks just on the last 2 corners :( .
Basically they are both twisted in place, and no amount of messing around is helping.
Can someone give me a hint please :oops: .

I got stuck at this point for about 45 minutes the first time I solved it too. Basically the idea behind solving it is to build your twisting routine off of your 3-cycle routine.

So suppose your 3-cycle is this:
[A, E, F, E', F', A', H, A, F, E, F', E', A', H']
Then the inverse of it would be:
[H, A, E, F, E', F', A', H', A, F, E, F', E', A']

What you'd do is a 3-cycle which essentially "isolates" one of the corners for you. Then you change the orientation of the corner without affecting the other 2, then you undo the 3-cycle, then you undo the orientation change.

So in notation:

/* 3-cycle */
[A, E, F, E', F', A', H, A, F, E, F', E', A', H'],
/* change orientation */
[F2, I2, F2],
/* Undo 3-cycle */
[H, A, E, F, E', F', A', H', A, F, E, F', E', A'],
/* Undo orientation change */
[F'2, I'2, F'2]


This idea works on every twisty puzzle.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 20, 2011 6:05 pm 
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AHA
I finished the master pentultimate.

Thanks for the help Brandon, I really wouldn't have thought of doing it that way.

Time to move on to the pentultimate :lol:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 4:25 pm 
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OMG give me a break!! Or someone give me gallows.
i was just in the progress of breaking Julian's move count on 1.4.4 when I decided to take a break. I had everything except the little triangles done in a little less than 800 moves. I don't know if I could have beaten Julian with that but we won't know for some time because when I went for the gym I accidentally shut the computer down! OH MAN.

anyway:

1. face triangles like those on a normal helicopter dodecahedron [1,1]
mean because there is no centers and so you have to figure out the correct face for the 1st color. There is only one right face
out of twelve
2. corners [3,1]
I placed with orientation except for two corners because one of those was at the right place but orientated wrong from the
start.
3. kites [1,1]
4. edges [3,1]
5. small triangles [3,1]


Also I thought about 1.4.5

1. corners. takes about 80 moves only to solve them when they are first.
2. rhombic pieces [1,1]
3. centers [3,1]
4. small face triangles [5,1]
I don't know if 8 moves are possible when slice moves are allowed but I suppose not.
5. large triangles [3,1]
6. edges [5,1] pure

edges pure in the end sounds weird but it's much better to spend 12 moves per piece on 30 pieces plus 8 moves per piece on 120 pieces (giving 12*30 + 8*120 = 1320) than doing edges with 8 moves and triangles with 12 moves giving 1640 moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 4:38 pm 
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alaskajoe wrote:
1.4.4
[...]
1. face triangles like those on a normal helicopter dodecahedron [1,1]
mean because there is no centers and so you have to figure out the correct face for the 1st color. There is only one right face
out of twelve
2. corners [3,1]
I placed with orientation except for two corners because one of those was at the right place but orientated wrong from the
start.
3. kites [1,1]
4. edges [3,1]
5. small triangles [3,1]

You can do the stage 4 edges [1,1] (only moves the edges and small chiral triangles). Good find on the [3,1] for the small chiral triangles, that's not as obvious as some other [3,1] routines.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 4:46 pm 
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You're right with the edges. And you know what? I know that overlap of only edges and triangles and I did use it however I still remember using it as a [3,1] which is really dumb.
When will I stop embarrassing myself by missing things like that? :x I probably deserved forgetting the solve for a second and shutting down. :cry:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 4:52 pm 
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alaskajoe wrote:
You're right with the edges. And you know what? I know that overlap of only edges and triangles and I did use it however I still remember using it as a [3,1] which is really dumb.
When will I stop embarrassing myself by missing things like that? :x I probably deserved forgetting the solve for a second and shutting down. :cry:

Don't feel so bad, I forgot about the EXACT SAME overlap of the edges when I did my How to solve twisty puzzles (using Gelatinbrain's 1.4.14 as an example) video. Katja had to point it out to me.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 5:01 pm 
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In the applet I can't find this "Rex dodecahedron", the one on the top right corner in this photo. It's a vertex turning dodecahedron. Did I miss it or is it not there yet? This puzzle is close to mass production and I think it's a good idea to have it in GB. Thanks.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 5:13 pm 
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alaskajoe wrote:
1. face triangles like those on a normal helicopter dodecahedron [1,1]
mean because there is no centers and so you have to figure out the correct face for the 1st color. There is only one right face
out of twelve
2. corners [3,1]
I placed with orientation except for two corners because one of those was at the right place but orientated wrong from the
start.
3. kites [1,1]
4. edges [3,1]
5. small triangles [3,1]
I actually missed that [3,1]! I was so proud of my [5,1] for the triangles :P I started solving this puzzle about a year ago, but after an hour of solving, I realized that it was in a non-solvable state due to the invisible orientation. So I gave up on solving it. I need to get it solved soon though!
schuma wrote:
In the applet I can't find this "Rex dodecahedron", the one on the top right corner in this photo. It's a vertex turning dodecahedron. Did I miss it or is it not there yet?
You didn't miss it; it's not there. It is however, and I'm sure you already know this, a cubic transformation of one of the face turning icosahedron. I think it's 2.1.1, possibly? But I agree, it would make a nice addition.


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