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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 23, 2011 8:00 pm 
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gelatinbrain wrote:
I have a question about another totaly different puzzle.
The 3.7.6 is certainly the easiest of all my puzzles. If your goal is just solving, this is absolutely of no interest. But how about the optimum solve? Is it worth try again and again?
I ask this question because I'm thinking to make some simple puzzles for cell-phone.
Something enjoyable both for beginners and experienced players
and light enough to be played in the commutor train or waiting rooms.
I think even for the easiest of exiting twisty puzzles, the first hurdle is too high for beginners, and that obstruct twisty puzzles to be really popular...


I actually like 3.10.1 better than 3.7.6. I did try again and again to get the fewest move for that. In terms of difficulty I think they are comparable. But I don't know if Gliding Cube <http://www.glidingcube.com/> would complain it's their idea or not.

I think for cell-phone game, turning is a big issue. I have an iphone and have tried several twisty puzzles on it. The turning of some apps is really embarrassing. When there are too many possibilities of turning, I cannot let it do what I want. Fingers are very inaccurate compared with mouse. I think you need to find a puzzle that has less possibilities of turning, so that it can be handled with inaccurate operation. It's a completely different interface from the PC applet.

Making a puzzle for "normal people" (as Oskar said here: http://www.youtube.com/watch?v=vwnQJIZUvXI) is another challenge. Maybe you can simplify it using only two or three colors.

Are you making an app for Android or iPhone?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 23, 2011 8:50 pm 
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gelatinbrain wrote:
schuma wrote:
GB, I'm surprised that you implemented all three in such a short time! Awesome!

Just ask me. 8-)
On my program, I'm ignoring the collision. Physical versions would need some kind of pull-up mechanism. I've seen such a puzzle somewhere on this forum. But I don't remember exactly where...


I find that 1.2.25 is not working in the expected way. Scrambling produces some "impossible" edge pieces like a white-white edge or white-yellow edge. I think the reason is that the second layer move (***&2) is not defined in the right way. Now the second layer move is not the complement of two first layer moves and it tears some edge pieces apart. 1.2.26 & 27 don't have this issue. Thanks.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jun 29, 2011 1:34 pm 
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Many of the puzzles I have the records on I think are just from simply taking the time to get shorter set-up sequences, not because I have a particularly original solution. However, for 1.1.26, 1.1.31, and 1.1.35 I think I'm doing something different, so I thought I would post my outlines.

1.1.26 (Circle Starminx I)
Edges: (1,1) commutators
Circle-Edges: (3,1) commutator
Centers: (3,1) commutator
Ray Tips: (4,3) commutator
Circle-Rays: (4,5) commutator

1.1.31 is of course the same as 1.1.26 with the addition of megaminx-corners, which are solved in the beginning with the edges like a pyraminx crystal. For both puzzles, the difference I think is that I solve the circle-edges earlier instead of having to come up with a long commutator for it later.


1.1.35 (Circle Pentultimate)
Centers/Corners: Solve like Pentultimate...
Circle Pieces: (1,2) and (3,2) conjugates for which the results are pictured below

With this method, I know sub 500 is easily possible, because I wasted more than 50 moves on the pentultimate step alone (my total move-count was 551). The downside is that those conjugates are actually made up of pairs of 5-cycles (they appear to only swap a couple pieces because the other pieces are of the same color). This means I imagine it will be more difficult to implement this solution on 1.1.35c. I think this is considerably more efficient than solving corners last though.


Attachments:
1.1.35-2.JPG
1.1.35-2.JPG [ 45.9 KiB | Viewed 6982 times ]
1.1.35-1.JPG
1.1.35-1.JPG [ 45.89 KiB | Viewed 6982 times ]
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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jul 06, 2011 3:59 pm 
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GB, thank you for the new 3.3.* puzzles. I notice that there is no second layer turning for 3.3.21, 24, 25, 26, 27, 28, 29 and 30. It would be much more convenient if you could add it. Thanks a lot!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 14, 2011 3:08 pm 
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GB, in the downloadable Windows version, 1.1.35b is identical to 1.1.35 (pictures show it should be a color-changed version, but instead it appears still "plain"). I never got the online applet version to work on my computer, so I can't check if this is also the case there.

1.1.51

As Julian and schuma have alluded to, this puzzle is not as hard as it might appear, as it really only has 2 piece types, the edge-rays are actually just a visual for the orientations of the centers.

Center Permutation
: Mostly intuition, but (3,1) commutator for the last few (should only be about 15 moves total for this step)
Corners + Center Orientation: (6,1) commutator for corners with the side-effect of rotating two centers (one CW and the other CCW)... by keeping track of which centers need to turn and using additional set-up moves, you can solve the center orientations simultaneously.
Finishing Center Orientation: The previous step can only complete the puzzle if the sum of the rotations on the centers is a multiple of 5. (RUR'U)x21 can be used to finish the leftover center orientations (I'm sure there are better algorithms) but to avoid spending so many moves at the end, I just rescrambled after the center permutation step until I ended up with a multiple of 5.

1.1.57
I solved 1.1.64 first, which is the non-circle version of this puzzle. Solving this one was easy after realizing the circle pieces are functionally Pyraminx Crystal edges.

Circle Pieces: (1,1) commutators... can be done in less than 80 moves, but doing it "lazily" as I did during my solve takes more like 140 moves...
Non-Circle Centers: (3,1) commutator
Corners: (4,1) commutator (there may be a (3,1) that I didn't find)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 14, 2011 3:21 pm 
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DKwan wrote:
GB, in the downloadable Windows version, 1.1.35b is identical to 1.1.35 (pictures show it should be a color-changed version, but instead it appears still "plain"). I never got the online applet version to work on my computer, so I can't check if this is also the case there.


If your downloadable version contains the polyhedra.jar file, you may want to download the latest version at <http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/joglx/polyhedra.jar> and replace the old version. At least in my case, 1.1.35b is different from 1.1.35.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 14, 2011 3:48 pm 
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schuma wrote:
If your downloadable version contains the polyhedra.jar file, you may want to download the latest version at <http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/joglx/polyhedra.jar> and replace the old version.

Well, earlier I tried downloading the newest from the main page: http://users.skynet.be/gelatinbrain/App ... 20v1.1.zip
This does not seem to include the .jar file you linked. Maybe I'm missing something here?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 14, 2011 5:09 pm 
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DKwan wrote:
schuma wrote:
If your downloadable version contains the polyhedra.jar file, you may want to download the latest version at <http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/joglx/polyhedra.jar> and replace the old version.

Well, earlier I tried downloading the newest from the main page: http://users.skynet.be/gelatinbrain/App ... 20v1.1.zip
This does not seem to include the .jar file you linked. Maybe I'm missing something here?


No, you are not missing anything.
Schuma is talking of the executable jar version, and you are running the exe version. It was a bug and I just uploaded the fixed version... 8-)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 14, 2011 5:22 pm 
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gelatinbrain wrote:
It was a bug and I just uploaded the fixed version... 8-)

Ah, thanks for the quick fix =)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jul 27, 2011 6:22 pm 
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In [http://twistypuzzles.com/forum/viewtopic.php?p=262052#p262052] Brandon said:

bmenrigh wrote:
schuma wrote:
But I don't mind the current notation, because when I'm looking for algorithms, I twist the puzzle by clicking the mouse and then copy/paste the list of the moves. I never have to think which face is called what.

Sometimes I need to "mirror" an algorithm. When I do that I just swap F<->R, B<->L, clockwise <-> counterclockwise. This rule works for both the cube and the octahedron.

Yeah the current labels don't bother me either. I never have to think about the labels.

Regarding mirroring and inverting, etc, I have a series of perl scripts to help me:
Code:
gb_dodeca_rotate.pl
gb_dodeca_sequences.pl
gb_invert.pl
gb_mirror_cube.pl
gb_mirror_dodeca.pl
gb_pretty.pl
gb_update_check.pl


I have been planning on creating a simple web interface to these tools for people who want to mirror/rotate/invert/whatever the macros/notation.

Nan, when you're solving a puzzle with macros, do you pre-make the sequence, its inverse, its mirror, and its mirrored inverse? I only make the sequence and the inverse and sometimes I have to spend a bunch of time doing setup moves to make the sequence I need fit. Do you create a bunch of variants for each macro sequence?

I recently solved 1.2.28 and 1.2.29 and they took me ~50 minutes with macros and they only took you ~13 minutes. The majority of my time was with finding setup moves to cycle the center triangles. I was pretty amazed how much faster you were than me. I wasn't trying to be efficient. Did you have a lot more macro variants made for the triangles cycle?


Before I solve a GB puzzle with macros, I prepare all the necessary algorithms. Most of the time I premake at least two versions: original and inverse. If the pieces are in two chiral orbits, I have to make the mirror and mirror inverse. So for each type I usually premake two or four sequences. For some puzzles where setup moves are harder to find, I premake more sequences.

Finding setup moves can be very time-consuming. So I always pre-make a sequence that is friendly to setup.

Let me explain my algorithm for the triangle pieces in 1.2.28 as an example. I use a [3,1] commutator for this type. For example,
BFI',[ABC,AEF',ABC'],BFI,[ABC,AEF,ABC'],
is a 3-cycle. The effect of this [3,1] is as follows:
Attachment:
1.PNG
1.PNG [ 24.89 KiB | Viewed 6782 times ]

But I don't like this sequence. I added two setup moves in the beginning and at the end to make:

AFB,IJL,
BFI',[ABC,AEF',ABC'],BFI,[ABC,AEF,ABC'],
IJL',AFB',

The effect of this augmented sequence is as follows:
Attachment:
2.PNG
2.PNG [ 23.92 KiB | Viewed 6782 times ]

I solve at least and usually one piece at a time using this sequence. I move (setup) a destination piece to the top triangle in the back, and execute the sequence to bring the bottom triangle in front to the destination.

Why is the longer sequence setup-friendly?

(1) I can use whatever move in the back view in setup without affecting the other two positions in the 3-cycle.

(2) The destination position, upper triangle in the back, is symmetric to mirroring. So once I discover a setup routine from somewhere on the left side to it, I also have the mirror routine from somewhere on the right side to it.

(3) The two locations in the front face are both white. So, even if the top left triangle is solved, bringing it to the bottom doesn't ruin it. It remains solved. This property is particularly useful towards the end of the solution.

Because of the above nice features, I can find setup moves very fast. I can solve a puzzle like a machine because I don't have to think much. I find the experience much better, mentally more relaxed. And only if you are not tired of finding setup moves can you solve several puzzles in a day.

The drawback of the longer sequence is that it's inefficient. But when I'm not worrying about efficiency I just use algorithms of this style.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 01, 2011 5:45 pm 
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Hello everyone! I am back after a break.

schuma -- you continue to impress us with your speedy solves of all the puzzles.

Daniel -- congratulations on setting some amazing new records, especially for 1.1.35. I found similar 5-cycles, but I never thought they could be used to completely solve all the circle pieces.

Brandon -- nice 1.2.4 and 1.2.5 solves! I worked out new methods for them a while ago, finishing 1.2.4 with the small triangles touching the edges [5,1], and finishing 1.2.5 with the wide triangles touching the corners [6,1]. I estimated around 1700-1800 moves for these, which is what you got. :) (I won't be re-solving them as there are too many other puzzles to try and not enough time.) I haven't forgotten about 3.2.13, by the way; I still have no idea how you did it in 68 moves.

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

Last night I solved 3.12.3, which I posted about previously here. I tried to pair as many circle piece pairs as possible into quadruples using the [13,1] commutators, and I turned 32 pairs into 16 quadruples, which I then solved using the [7,1] commutators. Then I solved the remaining 16 circle piece pairs pure using the [17,1] commutators.

With the quadruples lined up as shown in the screenshot in my earlier post, existing quads are definitely preserved when setup sequences use only the F, U, B, and D faces (with x2 or z2 reorientations). However, I can't see a way of setting up pairs into "flipped" positions without also using R and L, which break up any quads that end up in the parts of the puzzle affected by the non-pure [13,1] algo after the setups. I think it is possible to build all 24 quads using my [13,1] algo, but it would be very difficult and confusing. While I am pleased with my solve of 1141 moves, if one used clever setups to pair all 24 quads, it would be possible to solve 3.12.3 in comfortably under 1000 moves.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 01, 2011 6:18 pm 
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Welcome back Julian! You've been missed.
Julian wrote:
Brandon -- nice 1.2.4 and 1.2.5 solves! I worked out new methods for them a while ago, finishing 1.2.4 with the small triangles touching the edges [5,1], and finishing 1.2.5 with the wide triangles touching the corners [6,1]. I estimated around 1700-1800 moves for these, which is what you got. :) (I won't be re-solving them as there are too many other puzzles to try and not enough time.)

You could beat my 1.2.4 and 1.2.5 records by at least 200 moves each. I was obscenely wasteful.

For 1.2.4 I solved the big triangles between the edges and center [5,1] (pure) and the small triangles next to the edges [3,1] pure. They are in two chiral orbits so you have to use the mirror too.

For 1.2.5 I solved the small triangles next to the edge [3,1] (non-pure) and the big triangles between the center and corner [5,1] (pure).

Overall they were very fun puzzles and I'm glad I finally tackled them. I remember the first time I played with 1.2.4 I had just solved 1.2.3 and I thought I'd give it a try. It was so different than 1.2.3 that I got intimidated and I never again tried it. It wasn't until this last week that I finally decided to go back and tackle it. I feel dumb that the fear of failure to solve a puzzle held me back from even trying.

Julian wrote:
I haven't forgotten about 3.2.13, by the way; I still have no idea how you did it in 68 moves.
I think 3.2.13 is the only fewest-moves record that I really earned. If you'd like I'd happily post my trick here. It can be solved sub-60 by somebody like you, Elwyn, or Daniel K.


After I solved 1.2.4 I opened up 1.2.7 and found some very short routines. I did a back-of-the-envelope calculation and think I could take the record on it. Unfortunately I didn't write them down and now I'm struggling to re-find them. I'm sure I'll get them again but I'm annoyed at myself.

You've always been the master of short-sequence finding but I have been developing a sequence construction "theorem" that is really helping me to find sequences that are as short and occasionally shorter than the ones you've described. I haven't sat down and actually worked it all out formally due to lack of time but I'm hoping to soonish. I'm not suggesting that I have any truly ground-breaking ideas but I'm hoping that even though surely everyone knows a bit of them, they haven't put them all together in the way I'm thinking. I'll post details when I've flushed all my ideas out.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 01, 2011 8:16 pm 
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bmenrigh wrote:
For 1.2.5 I solved [...] the big triangles between the center and corner [5,1] (pure).
Thanks, found it.

bmenrigh wrote:
Overall 1.2.4 and 1.2.5 were very fun puzzles and I'm glad I finally tackled them.
Me too. I also found it very satisfying to have the sequence solved from 1.2.2 through to 1.2.6. 1.2.7 to 1.2.9 seemed less daunting after that, except for their evil corners, and you and Stefan have made those corners less evil than they used to be!

bmenrigh wrote:
I think 3.2.13 is the only fewest-moves record that I really earned. If you'd like I'd happily post my trick here. It can be solved sub-60 by somebody like you, Elwyn, or Daniel K.
Thanks... I'll give myself the rest of August, then I'll beg for help if I still can't see it.

bmenrigh wrote:
After I solved 1.2.4 I opened up 1.2.7 and found some very short routines. I did a back-of-the-envelope calculation and think I could take the record on it. Unfortunately I didn't write them down and now I'm struggling to re-find them. I'm sure I'll get them again but I'm annoyed at myself.
Allowing for the fact that 1.2.7 has shift-click nowadays, I estimate 2800-2900 moves using my improved method that I posted a while back, which finishes with [6,1] pure for the small triangles. I'm sure you could comfortably take the record.

bmenrigh wrote:
I have been developing a sequence construction "theorem" [...] I'll post details when I've flushed all my ideas out.
I look forward to it!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 01, 2011 11:04 pm 
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Julian wrote:
Allowing for the fact that 1.2.7 has shift-click nowadays, I estimate 2800-2900 moves using my improved method that I posted a while back, which finishes with [6,1] pure for the small triangles. I'm sure you could comfortably take the record.

In the spirit of friendly competition I just re-found my 1.2.7 sequence and I worked hard to try to find the optimal solve order with them. I know you were working on finding sequences that would work on other puzzles besides 1.2.7 but for now I'm ignoring those puzzles and optimizing for 1.2.7 only.

Back in this post you advocated:
  • Corners [4:1] (20)
  • Big triangles [3,1] (60)
  • Edges [4,1] (30)
  • Kites [3,1] (60)
  • Edge triangles [6,1] (2x60)


I think the 30 edges with 10-move routines is pretty costly. Also, the 120 small triangles with 14-move routines is very costly.

Instead I would suggest:
  • Edges [1,1] (30)
  • Corners [4,1] (20)
  • Edge Triangles [3,1] (2x60)
  • Kites [3,1] (60)
  • Big triangles [6,1] (60)

Based on my 1.2.5 solve of 1750, I estimate 1.2.7 to be 2350-2450. I definitely wont have the time or stamina to tackle 1.2.7 for another two weekends.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 02, 2011 5:10 pm 
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1.2.7
bmenrigh wrote:
Instead I would suggest:
  • Edges [1,1] (30)
  • Corners [4,1] (20)
  • Edge Triangles [3,1] (2x60)
  • Kites [3,1] (60)
  • Big triangles [6,1] (60)
Excellent! I had a mental block against solving anything before the corners, even after your and Stefan's posts on how to avoid/deal with a single twisted corner, and there's obviously a huge gain when solving all those edge triangles your way. It was fun working out the algos from your outline; I didn't expect so many surprises from a puzzle I've known for nearly three years. When I eventually find the time and stamina, I'll try the dual puzzle 2.1.15 using your method.

P.S. Your first four stages work fine with 1.2.8.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 11, 2011 7:08 pm 
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So I want to solve 1.1.54 but the circle-bitten corners are giving me trouble.

My current solve order is:

* Corners
* Circle bitten corners [5,1]
* Big triangles [3,1]
* Petals [3,1]

I'm really trying to avoid that pesky [5,1] and my gut tells me it is possible but I can't find a way. Ideas?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 11, 2011 7:31 pm 
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I just thought I'd pop in and say I didn't get around to doing any solves at all over my holidays and I don't think I will for a while but I still check in here for anything interesting every now and then.

Keep solving :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Aug 12, 2011 6:37 pm 
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bmenrigh wrote:
So I want to solve 1.1.54 but the circle-bitten corners are giving me trouble.

My current solve order is:

* Corners
* Circle bitten corners [5,1]
* Big triangles [3,1]
* Petals [3,1]

I'm really trying to avoid that pesky [5,1] and my gut tells me it is possible but I can't find a way. Ideas?
The circle bitten corners can be cycled with [1:1, 1] = [3,1] algos.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Aug 12, 2011 6:48 pm 
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Julian wrote:
The circle bitten corners can be cycled with [1:1, 1] = [3,1] algos.
Brilliant. Apparently all I needed to be told is that the routine exists because I found it immediately :oops:

The variation I found has quite a few side-effects in the other pieces but it leaves the corners alone which is enough.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Aug 12, 2011 6:53 pm 
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Julian wrote:
1.1.39 & 1.1.40 -- Ctrl-click moves have been fixed! Thanks Gelatinbrain!

1.1.39: Solve the corners and edges like a Pyraminx Crystal, then kite pieces (3,1) non pure, trapezoid (3,1) non pure, and finish with large and small triangles in either order (3,1) pure.

1.1.40: Same as 1.1.39, then finish with the edge-circle pieces (5,1) pure, and corner-circle pieces (10,1) pure, in either order.

Edit: Fixed a goof with my suggested outline for 1.1.40.


Hey Julian, many months ago you did a basic outline for 1.1.40. I decided to look at it today and have a [3,1] for the circle-bitten edge wedges and a [6,1] for the circle-bitten corner wedges. Both are pure but I have a feeling if you make the circle-bitter corner wedges non-pure you might be able to do better than [6,1].

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Aug 12, 2011 7:55 pm 
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Elwyn wrote:
I just thought I'd pop in and say I didn't get around to doing any solves at all over my holidays and I don't think I will for a while but I still check in here for anything interesting every now and then.
I'm also on a break from solving at the moment. I have been solving some of the easier additions now and then, but I really don't feel like solving much. I still check the thread basically every day to maybe see if anything spikes my interest again.

Though I'm pretty much not interested in doing any solves, I have been working on a puzzle quite regularly without much success: 5.1.11. I have tried many ways to approach this puzzle but it seems that I'm missing out on something fundamental. Anyone care to share their order of solving for this puzzle?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Aug 12, 2011 9:34 pm 
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Katja wrote:
Though I'm pretty much not interested in doing any solves, I have been working on a puzzle quite regularly without much success: 5.1.11. I have tried many ways to approach this puzzle but it seems that I'm missing out on something fundamental. Anyone care to share their order of solving for this puzzle?


My method for 5.1.11 is basically as same as that for 5.1.10. (1) pair up the centers (2) pair up three edge pieces on each edge (one center + 2 close wings) (3) solve the paired pieces like the Halpern-Meier Pyramid, (4) solve the wings that are far from centers.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Aug 13, 2011 2:30 pm 
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bmenrigh wrote:
Hey Julian, many months ago you did a basic outline for 1.1.40. I decided to look at it today and have a [3,1] for the circle-bitten edge wedges and a [6,1] for the circle-bitten corner wedges. Both are pure but I have a feeling if you make the circle-bitter corner wedges non-pure you might be able to do better than [6,1].
Those are good algos! I can't find a way to avoid a [6,1] algo, but it's a lot better than the [10,1] I found earlier, so I'm happy.

To anyone who feels like trying an unusual cube puzzle, GB has recently added two more cubes with non-central circles: 3.12.7 and 3.12.8. I think 3.12.7 is the least difficult of the set and is a good one to start with. The restrictiveness of the puzzle helps, because there aren't many short sequences that leave the corners of one half intact. You can eliminate loads of possibilities just looking at what happens with the corners, before you look at the circle pieces. My method will be to solve the 2x2x2 (ignoring the little pieces), then cycle the little pieces with a [[3,1], 1] = [8,1] algo.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Aug 13, 2011 4:40 pm 
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Julian wrote:
To anyone who feels like trying an unusual cube puzzle, GB has recently added two more cubes with non-central circles: 3.12.7 and 3.12.8. I think 3.12.7 is the least difficult of the set and is a good one to start with. The restrictiveness of the puzzle helps, because there aren't many short sequences that leave the corners of one half intact. You can eliminate loads of possibilities just looking at what happens with the corners, before you look at the circle pieces. My method will be to solve the 2x2x2 (ignoring the little pieces), then cycle the little pieces with a [[3,1], 1] = [8,1] algo.


I was actually a little bit surprised when I saw GB made these asymmetric puzzles. And again I have to say your algorithms is much shorter than mine. :D


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 18, 2011 5:09 pm 
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Gelatinbrain has given us 4 more puzzles :D 5.1.20 - 5.1.23

I spent several minutes on 5.1.20 without much luck. The circle-bit-corner pizza slices are attached to the edges and solve themselves when you solve the edges.

The circle-bit-edge pizza slices come in pairs and they sorta act like the Circle FTO pieces but instead of 2 under each corner there are 3 under each corner. I did manage to 3-cycle them via a very long and ugly routine. I'm having trouble finding anything reasonable.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 18, 2011 6:04 pm 
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3.12.x
schuma wrote:
I was actually a little bit surprised when I saw GB made these asymmetric puzzles. And again I have to say your algorithms is much shorter than mine. :D
But what amazes me is just how fast you solved them! I found the small pieces of 3.12.2 and 3.12.3 especially difficult to set up. The only way I can solve these kinds of pieces is to take a break every few cycles to relax my brain and eyes. It can sometimes take me over 2 minutes to work out a setup for a single cycle. 3.10.3 is probably going to be the same way.

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

Thanks GB for 5.1.20-5.1.23, and Brandon for the notification!

5.1.20 seems to be the equivalent of a Skewb Ultimate, where the circle-edges are in groups of 3 and show the location and orientation of the 4 extra corners (the corners that are added to a Pyraminx to get a Skewb Ultimate). It's going to be very confusing to solve. I'll check out the others this weekend.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 18, 2011 9:38 pm 
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Julian wrote:
Thanks GB for 5.1.20-5.1.23, and Brandon for the notification!

5.1.20 seems to be the equivalent of a Skewb Ultimate, where the circle-edges are in groups of 3 and show the location and orientation of the 4 extra corners (the corners that are added to a Pyraminx to get a Skewb Ultimate). It's going to be very confusing to solve. I'll check out the others this weekend.


Although in principle I understand that the tetrahedral puzzles are equivalent to vertex-turning cubes, I really have a hard time to see the correspondence. For example, I feel that 5.1.22 should be equivalent to some slice-only 3.2.* puzzle. Eventually I'm looking for new algorithms rather than borrow algorithms from 3.2.*.

I noticed that GB increased the total number of puzzles by 6 (from 487 to 493). But I've found only 4 of them. I don't know where are the other two.

edit: GB just answered my question by adding 1.1.80 and 3.2.18. Thanks!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Aug 20, 2011 3:33 am 
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I started solving 1.2.7 today, but sadly the applet (downloadable) froze at this stage:
Attachment:
Før programmet klikka.png
Før programmet klikka.png [ 62.07 KiB | Viewed 6416 times ]
I had spent 4 hours getting there and I was doing pretty good regarding move count as well; I was at 1301 moves. I have never put so much effort into a solve before and losing it was pretty upsetting. I really like this puzzle, so I will try solving it again.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 21, 2011 4:24 pm 
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Katja wrote:
I started solving 1.2.7 today, but sadly the applet (downloadable) froze at this stage: I had spent 4 hours getting there and I was doing pretty good regarding move count as well; I was at 1301 moves. I have never put so much effort into a solve before and losing it was pretty upsetting. I really like this puzzle, so I will try solving it again.


It's so sad. I've seen frozen GB puzzles several times. Most of the time it occurred when I was dragging the puzzle. And most of the time it recovered by itself after several seconds. But I do remember one or two times that it didn't recover.

GB added three new puzzles, 5.1.24/25 and 3.3.34.

3.3.34 is breathtaking:
Attachment:
3334.PNG
3334.PNG [ 7.2 KiB | Viewed 6376 times ]

I don't know yet if it's related or equivalent to anything before or not.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 21, 2011 4:33 pm 
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schuma wrote:
It's so sad. I've seen frozen GB puzzles several times. Most of the time it occurred when I was dragging the puzzle. And most of the time it recovered by itself after several seconds. But I do remember one or two times that it didn't recover.

This used to happen to me once in a while and it turned to be a bug between the interaction of my video card driver and JOGL. It would happen during dragging the puzzle around. It resolved itself when I updated my video card drivers. It hasn't happened to me at all on Linux.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 21, 2011 8:25 pm 
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schuma wrote:
Although in principle I understand that the tetrahedral puzzles are equivalent to vertex-turning cubes, I really have a hard time to see the correspondence.
I find it hard to see tetrahedral puzzles as vertex-turning cubes, but I find it easier to see some of them as face-turning octehedra. I see the 4 corners of the tetrahedron as 4 other faces of an octahedron, and my way of seeing the moves and notating them is the same for both kinds of puzzle.

schuma wrote:
For example, I feel that 5.1.22 should be equivalent to some slice-only 3.2.* puzzle. Eventually I'm looking for new algorithms rather than borrow algorithms from 3.2.*.
I see 5.1.22 and 5.1.23 as "revenged" or "4x4x4-ed" Jing Pyraminxes (5.1.3) with circles and bandaging. So I will solve them a bit like a 4x4x4: fix the centers first, then pair the edges without messing up the centers, then solve the 5.1.3 with face moves only, then finally solve the small circle pieces*. I can't see any similar or equivalent 3.2.* puzzles.

GB, please could we have a puzzle like 5.1.22 but without the circles? I think it would make a nice addition: a plain "revenged" Jing Pyraminx.

* With 5.1.22 some moves could be saved by making the second-last stage to get the small circle pieces into valid equivalents of extra corners, then as the final stage solve the Skewb Ultimate equivalent puzzle using face turns only. But my brain would hurt too much relative to the number of moves saved. I already did this ending with 5.1.19.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 21, 2011 8:39 pm 
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schuma wrote:
3.3.34 is breathtaking... I don't know yet if it's related or equivalent to anything before or not.
Yes! My first reaction was: "Uh... what?!" I think it must be a unique puzzle, as "normal" cuts couldn't produce two edge pieces per edge with a single centre piece per face.

As far as I can see there are no orbitals or parities to worry about and it looks fairly simple to solve: center pieces first in a few moves, then cycle the edge pieces pure with [3,1] commutators. As with most edge-turning puzzles, it's going to be the setups that will slow me down.

Thanks for all the new puzzles, GB!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 22, 2011 3:46 am 
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schuma wrote:
It's so sad. I've seen frozen GB puzzles several times. Most of the time it occurred when I was dragging the puzzle. And most of the time it recovered by itself after several seconds. But I do remember one or two times that it didn't recover.
It happened when I hit the undo button to undo some setup moves. Then the program froze and it said "not responding". This has happened before, and I am starting to think it is more likely to happen if I run both the applet and Spotify (the music program) simultaneously. Next time I will listen to music on my iPod instead and hope it doesn't happen again :lol:

When I opened 3.3.34 I saw that it was different, due to the asymmetry, but then when I turned it I realized just how different! :shock: Thanks GB, I'm looking forward to figuring it out.


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 Post subject: Dino 3x3x3 - Gelatinbrain 3.4.5 parity
PostPosted: Mon Aug 22, 2011 4:21 am 
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Noah wrote:
After taking a couple days off, I can't for the life of me solve the super x anymore. I was trying to solve 3.4.5, and couldn't get the super x aspect of it. Even going back to the super x, I can't solve it. I always come to a point where I don't know how to commute it.


Anyways, the 3.4.5 solution.


Solve corners (Super x)
Solve edges (beware of permution parity, same as void cube)
Solve centers by turning a corner (dino move) then rotating a center to place the piece in (3x3 algorithms)
A few days ago, I have got a Dino 3x3x3 (V2) from TomZ (a great puzzle, BTW here is the thread).
I could solve it, but I find my parity handling annoyingly tedious. So, I have made a Google search for "Gelatinbrain 3.4.5 parity" and found this old post of Noah on page 1 of this thread.
I find the "beware of permutation parity" remark interesting. I do not see how to avoid parity very early in the game. I see it on a Void Cube and repair it (e.g. by R F' L2 F2 U' D R' F B' D' F2 D F' (13 moves)). I do not see how to beware of parity, otherwise? Or does the remark possibly mean exactly this " repair parity when you see it?

I do not assume that many people have a physical Dino 3, therefore I'm posting here and I'll make a reference in the Dino 3x3x3 thread.

I had a look at the "fewest move ranking" for 3.4.5 and find the fewest move count incredibly low for 60 moving pieces.
Would you guess that those are lucky solves (no parity involved; I mean no Super-X parity and no VOID parity) or have you found special short sequences for parity solving?
I would appreciate, if you can post such algorithms! :)

BTW, does everybody share Noah's opinion that it is better to do the corners first and centres last?
I have done the centres first until now. That makes parity handling longer but centre building shorter.
If you do centres last, you need to rotate them pure, not destroying any corners.

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 Post subject: Re: Dino 3x3x3 - Gelatinbrain 3.4.5 parity
PostPosted: Mon Aug 22, 2011 3:37 pm 
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Konrad wrote:
BTW, does everybody share Noah's opinion that it is better to do the corners first and centres last?
I have done the centres first until now. That makes parity handling longer but centre building shorter.
If you do centres last, you need to rotate them pure, not destroying any corners.

I would do the centers with a [3,1], than the edges with a 3x3 method, than the corners with a [1,1]. If that helps.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 22, 2011 4:17 pm 
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Katja wrote:
I run both the applet and Spotify (the music program) simultaneously. Next time I will listen to music on my iPod instead and hope it doesn't happen again :lol:

Does your music program shows animations too?
You'd better do not run two graphic programs simultaniously.
A driver-level deadlock is dangerous. In worst case, whole your computer will freeze.

In my part I will update my java compiler and recompile my applet.
I'm one of the last person still using version 1.4. Many bugs are fixed since, it looks....


Added three more puzzles! And I'm planning a really special one for the 500th.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 22, 2011 5:00 pm 
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gelatinbrain wrote:
Added three more puzzles! And I'm planning a really special one for the 500th.


Great! I'm waiting for the 500th.

btw, just now I tried to play 3.4.5. When I tried to move a slice by shift+clicking on a face center, the applet froze. This bug can be repeated. Can anyone else see it?

edit: this bug appears to be fixed in the lastest update.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 22, 2011 9:08 pm 
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schuma wrote:
3.3.34 is breathtaking
It's mind-bending too. Those were some really hard setups. I was trying to fix two wedges per cycle but I gave up and fell back to solving one at a time. For an "easy" puzzle it sure is hard...


Stefan Schwalbe: Welcome back!

gelatinbrain wrote:
I'm planning a really special one for the 500th.
I can hardly wait :twisted: .

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 22, 2011 11:14 pm 
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gelatinbrain wrote:
Does your music program shows animations too?
You'd better do not run two graphic programs simultaniously.
A driver-level deadlock is dangerous. In worst case, whole your computer will freeze.
Yes, it actually does show some animations and is an overall graphic program. And I had no idea :? But it seemed to cause the applet to crash. Usually when I solve hard puzzles that will take a long time, I only run the applet and Spotify, and so far my Mac has never completely frozen like you say it potentially could. But I do think I will listen to music from my iPod for sure next time. Thank you for the advise! :D

Can't wait for the 500th puzzle!! :D I was guessing you might want to make that puzzle a special one.
Stefan Schwalbe wrote:
I would do the centers with a [3,1], than the edges with a 3x3 method, than the corners with a [1,1]. If that helps.
I solve the centers like a 4x4x4 and then the rest is the same as Stefan's suggestion. I was able to do this in less than 300 moves, without the parity cases occurring, which I think is pretty good for not considering fewest moves. I have a pretty fast and easy (but probably not optimal) intuitively found parity fix for the super-x parity case, but for the other parity case, I don't yet have a specific algorithm.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 22, 2011 11:18 pm 
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Konrad wrote:
I find the "beware of permutation parity" remark interesting. I do not see how to avoid parity very early in the game. I see it on a Void Cube and repair it (e.g. by R F' L2 F2 U' D R' F B' D' F2 D F' (13 moves)). I do not see how to beware of parity, otherwise? Or does the remark possibly mean exactly this " repair parity when you see it?
I wasn't able to edit me previous post and quote this in, but I think what he meant was that you should beware that there is parity cases for the puzzle, not beware and therefore avoid. At least, I have no clever ways of avoiding parity ahead of time.


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 Post subject: Re: Dino 3x3x3 - Gelatinbrain 3.4.5 parity
PostPosted: Tue Aug 23, 2011 4:38 am 
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Katja wrote:
Konrad wrote:
I find the "beware of permutation parity" remark interesting. I do not see how to avoid parity very early in the game. I see it on a Void Cube and repair it (e.g. by R F' L2 F2 U' D R' F B' D' F2 D F' (13 moves)). I do not see how to beware of parity, otherwise? Or does the remark possibly mean exactly this " repair parity when you see it?
I wasn't able to edit me previous post and quote this in, but I think what he meant was that you should beware that there is parity cases for the puzzle, not beware and therefore avoid. At least, I have no clever ways of avoiding parity ahead of time.
Thanks Katja for this confirmation.
Stefan Schwalbe wrote:
Konrad wrote:
BTW, does everybody share Noah's opinion that it is better to do the corners first and centres last?
I have done the centres first until now. That makes parity handling longer but centre building shorter.
If you do centres last, you need to rotate them pure, not destroying any corners.

I would do the centers with a [3,1], than the edges with a 3x3 method, than the corners with a [1,1]. If that helps.
Thanks Stefan, that is quite doable. My question had been about the parity you will see in 50% of the cases at the very end of your step 3 ("corners with a [1,1]"). What do I do, if I need an odd number of permutations of the corner tips (wedges)?
I do it this way:
    1. Centres by [1,1] with setups (siilar to centres on a 444
    2. Corners by [1:1] as on a Super-X with the same handling of an odd permutation as on Super-X
    3. Solve the 3x3x3
    4. If there is a parity of the 3x3x3 edges, do a Void Cube parity sequence (13 moves) and repair four centres using a [1:12] conjugation; summing up to 96 moves; total 13+96 = 109 moves

My post had been asking "Is there a better way solving the parity situations" AND
"Do you guess that those low move counts in the Gelatinbrain statistics can include parity handling?"

I'm still debating with myself if I should resolve an odd permutation of step 2 at all. I could reduce the corners to the case where one pair only needs swapping, then solve the 3x3x3 and check for parity of the corner tips at the very end. If necessary I do the Void Cube sequence here.

EDIT: Here are the two parity situations I'm talking about;
Image
All invisible pieces are correct.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 23, 2011 9:02 am 
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Hi Konrad,

I just looked into 3.4.5.

Assuming you are reducing to a 3x3x3 by creating corner-groups of 3 wedges, you won't know about the edge parity until the end. If you run into a parity in the wedges you can pretend that the two swapped wedges are correct and that what's wrong is that the other two pieces in each bad corner group are swapped. You can fix that in 22 moves (possibly fewer):
[LUF, LFD, D, BRU', F', BRU, F, D', LFD', FLU', ULB', FLU, LFD, D, BRU', F', BRU, F, D', LFD', FLU', ULB]

This will have the effect of changing the parity of the edges in the 3x3x3 solving phase. Since you don't know if there was a parity already there or not it doesn't really matter. Solving the wedges in this way does not increase your chances of a parity later.

Then if you solve the reduced 3x3x3 and you have a parity in the edges, your void-cube-like strategy will work. By making use of slices moves I shortened your Void parity fix routine to 11 moves:
[B, D', F'2, D'2, R&2, D', F'&2, D', F'2, D, F']

Then using this sequence I was able to solve all of the centers:
[FUR, U&2, B'&2, U'&2, B'2, U&2, B&2, U'&2, B'2, URF']

In all I was able to solve the 3.4.5 edge parity in 83 moves. Certainly still too costly to compete for the fewest moves in this puzzle and still solve a parity case or two.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 23, 2011 10:23 am 
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Thanks a lot Brandon! :D This is quite an improvement compared with my sequences.
The 2 move difference between your Void sequence and mine are not the big deal.
The centre repair by a 10 move sequence compared with my 14 moves are more substantial, because they are needed multiple times.

All in all I've learnt a lot by playing with this puzzle and I appreciate your help!
The Dino 3x3x3 is probably one of the puzzles you underestimate easily, until you see the rotated corner (relatively easy to fix) and the parities.
And I'll use the word 'parity' more carefully, promised :lol:
bmenrigh wrote:
Hi Konrad,

I just looked into 3.4.5.

Assuming you are reducing to a 3x3x3 by creating corner-groups of 3 wedges, you won't know about the edge parity until the end. If you run into a parity in the wedges you can pretend that the two swapped wedges are correct and that what's wrong is that the other two pieces in each bad corner group are swapped.
In essence this expresses it similarly as saying "solve the corners as for the Super-X"
bmenrigh wrote:
You can fix that in 22 moves (possibly fewer):
[LUF, LFD, D, BRU', F', BRU, F, D', LFD', FLU', ULB', FLU, LFD, D, BRU', F', BRU, F, D', LFD', FLU', ULB]
I have done it thinking in 3-cycles and adding setups. Probably, your 22 moves are shorter than what I have been doing, so far.
bmenrigh wrote:

This will have the effect of changing the parity of the edges in the 3x3x3 solving phase. Since you don't know if there was a parity already there or not it doesn't really matter. Solving the wedges in this way does not increase your chances of a parity later.

Then if you solve the reduced 3x3x3 and you have a parity in the edges, your void-cube-like strategy will work. By making use of slices moves I shortened your Void parity fix routine to 11 moves:
[B, D', F'2, D'2, R&2, D', F'&2, D', F'2, D, F']

Then using this sequence I was able to solve all of the centers:
[FUR, U&2, B'&2, U'&2, B'2, U&2, B&2, U'&2, B'2, URF']

In all I was able to solve the 3.4.5 edge parity in 83 moves. Certainly still too costly to compete for the fewest moves in this puzzle and still solve a parity case or two.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 23, 2011 11:28 am 
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Konrad wrote:
Thanks Stefan, that is quite doable. My question had been about the parity you will see in 50% of the cases at the very end of your step 3 ("corners with a [1,1]")

I agree. And yes, for the centers in step 1 you'll need only a [1,1].
@Brandon: Thanks for your welcome.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 23, 2011 1:09 pm 
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Before I solve the last layer of Super-X, I used to trace the permutation of the corner pieces to find out the parity. This way I can avoid the parity issue in advance. For void cube I also do it sometimes. I don't remember what I did for 3.4.5, but probably I did the same thing. Anyway it's doable and not very hard. Its worth doing especially if one cares about the count.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 24, 2011 3:56 am 
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3.3.34

When I solved this puzzle I was (as I usually am) too lazy to find the inverse of my [3,1] to save moves. This obviously means that when I solved it, I sometimes had to repeat the [3,1] twice. I calculated that if I had used the inverse my move count would be less than or around 250. I see that Julian's move count is at 256, which leads me to believe since I pretty much suck at move count efficiency, that this puzzle can be solved with way less than 256 moves. Not trying to make Julian's move count sound bad or anything, but I'm quite curious as to how low the move count can get on this puzzle due to the confusing set ups.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 24, 2011 7:31 am 
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Katja wrote:
3.3.34

When I solved this puzzle I was (as I usually am) too lazy to find the inverse of my [3,1] to save moves. This obviously means that when I solved it, I sometimes had to repeat the [3,1] twice. I calculated that if I had used the inverse my move count would be less than or around 250. I see that Julian's move count is at 256, which leads me to believe since I pretty much suck at move count efficiency, that this puzzle can be solved with way less than 256 moves. Not trying to make Julian's move count sound bad or anything, but I'm quite curious as to how low the move count can get on this puzzle due to the confusing set ups.
Yes, the setups are tricky, aren't they! I found them close to 4.3.3 (octahedral Little Chop) in difficulty, just slightly easier because the less deep cuts leave more "hiding places".

I have been wondering about a realistic minimum too. If we do 12 cycles of [3,1] with an average of 5 setup moves and 5 undo moves either side, that's 216 moves. However, early on we could cycle pairs of pieces [1,1], provided the pairs don't include pieces that have already been solved, which would be confusing to track. If we could do [1,1] for the first 4 cycles that would save 16 moves, to give a total of 200 moves. If we could manage an average setup length of 4 moves instead of 5 moves, we would total 176 moves. I guess when Elwyn and DKwan solve this one, we'll have a better idea of what is humanly possible! :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 25, 2011 5:22 pm 
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Joined: Sun Aug 29, 2010 1:56 pm
Hello topic viewers,

I didn't play much with gelatinbrain's puzzle-simulations for the last few months. The reason is that I had always no time for it. So I had nothing to post here.

While I was away, Gelatinbrain has created a lot of new puzzles and schuma has solved them all - Good job! for both

3.3.34 has a really unexpected layout - I'm shocked. The setups seem to be tricky but it has only 6 + 24 pieces. I guess it's a good thing.

kind regards to all of you.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 28, 2011 4:46 am 
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Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
Hey guys,

The parity in this photo is the only parity that I could never understand and therefore never find a solution to. Normally I'd just scramble the puzzle and try again, but I'm getting pretty sick of doing that for every puzzle this occurs in. For the normal 4x4x4, I can solve the two other parities; the one where two edges need switching and when two edge pairs need switching (in the final stage of the last layer). But I just cannot solve this parity. I do understand why I get the parity, but I still can't use that knowledge to actually solve it. Does anyone know how to fix this and maybe also explain the logic behind how the fix was found?
Attachment:
Skjermbilde 2011-08-28 kl. 19.41.00.png
Skjermbilde 2011-08-28 kl. 19.41.00.png [ 22.26 KiB | Viewed 5875 times ]
EDIT: The puzzle is 3.1.21, but discard the fact that this is a circle puzzle. This just happened to be the latest puzzle I encountered the parity on, and I didn't want to start solving a standard 4x4x4 just to get a screenshot. I'm asking about the parity in general, not in relations to the puzzle in this photo.


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 Post subject: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 28, 2011 5:58 am 
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Joined: Tue Mar 24, 2009 12:52 pm
Try so:
(r U2)*2 (r' U2 r2 U2)*2 r' U' R' (r2 U' R U r' U' R' U) r' R U


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