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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Oct 28, 2010 3:07 am 
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Katten wrote:
So yesterday I came up with all the missing commutators for 1.1.39 and I actually managed to find pure (3,1)'s for most of them. However, my pure (not (3,1)) cycle for the thin triangles kinda backfired a little on me. Here's the pieces it cycles:
Attachment:
Skjermbilde 2010-10-27 kl. 18.47.43.png
It only works for the pieces in those exact spots and as far as I experienced, getting the other pieces into those spots turned out not to work at all. This surprised me a lot as I didn't think this would occur. I'd like your thoughts on this; is there anything extremely obvious that I'm not seeing here?
Those pieces are in two different orbitals. That is, there are left-handed thin triangles and right-handed thin triangles.

The triangles in your cycle are all left-handed. No amount of setup moves is ever going to get a right-handed thin triangle into those spots. What you need to do is apply the mirror of your algorithm. If you mirror your routine horizontally across the puzzle then it should cycle the right-handed ones instead.

For example, if right-handed Sune is [R, U, R', U, R, U'2, R', U'2] then left-handed Sune is [L', U', L, U', L', U2, L, U2]. You will probably find mirroring your routine pretty intuitive and easy.

When I solved 1.1.39 I only barely knew they were different. I didn't realize they were in orbitals or anything like that. Now ever though I feel like I have a much better grasp of puzzle fundamentals puzzles don't seem much easier.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Oct 28, 2010 3:27 am 
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I thought of this 5 minutes after submitting my post and tada:
Attachment:
Skjermbilde 2010-10-28 kl. 10.16.18.png
Skjermbilde 2010-10-28 kl. 10.16.18.png [ 60.63 KiB | Viewed 4025 times ]
So now I feel like an idiot for posting a relatively obvious question like this, realizing after hitting the submit button that the solution was that simple :lol: But thanks a lot for replying, Brandon. Fully understanding how a puzzle works is not easy. I feel that I'm well on my way, but just like you, I feel I'm not there just yet. But I do believe this is the first time I've come across identical looking pieces that needed two different cycles due to the fact that they're in different orbitals. I will keep this in mind and hopefully it will be more obvious if I come across it again.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Oct 29, 2010 4:57 am 
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1.1.39 Solution Outline - Reduction to Pyraminx Crystal

1.) Place the trapezoids (the pieces underneath the corners) using a non-pure (3,1) commutator. Actually, I found a pure (4,1) commutator for these pieces just a few hours after submitting my solve, making it possible to swap this step with step 4a and 4b (as my non-pure (3,1) for the trapezoids also moves two thin triangles). I suggest doing this for fewest moves.

2.) Place the large triangle pieces, making the reduction of the Pyraminx Crystal corners complete. I used a pure (4,1) here. No parity here either.

3.) Place the diamond-looking pieces using a non-pure (3,1) commutator. This is the first step in making the Pyraminx Crystal edges. No parity.

4a.) In this step, I placed the left-orbited thin triangles using a way too long routine; 32 moves, pure. I actually didn't realize that these pieces came in two different orbits at first. This means that you cannot use only one commutator to cycle them; you will need the mirror image of it to cycle the right-orbited triangles. As no matter the set-ups, you will never be able to move a right orbit-piece into the left orbit. No parity.

Thank you Brandon, for making me aware of this.

4b.) Last step before the reduction is complete: placing of the right-orbited thin triangles. As I said above, you need to use the mirror image of a routine that cycles the pieces in the left orbit. No parity.

5.) At this stage, the puzzle looks like this:
Attachment:
Skjermbilde 2010-10-29 kl. 11.38.16.png
Skjermbilde 2010-10-29 kl. 11.38.16.png [ 66.16 KiB | Viewed 4088 times ]
Now all that's left is solving it like the Pyraminx Crystal/1.1.3. No parity.

I won't include commutators, unless anyone requests it. Feel free to comment on my outline :)

Also, this is without a doubt my new favorite puzzle. It's a lot of fun to solve and I recommend solving it :D


Last edited by Katja on Fri Oct 29, 2010 8:05 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Oct 29, 2010 6:40 am 
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Katten wrote:
1.) Place the trapezoids (the pieces underneath the corners) using a non-pure (3,1) commutator. Actually, I found a pure routine for these pieces just hours after submitting my solve. But that's actually a (4,1), so if you solve trapezoids first, you might as well use the non-pure routine. No parity for this step.
This is where i'd think "pure, do them last" because instead of your "way too long routine; 32 moves" for the small triangles you can use a nice (3,1) and hence all algs are (3,1) except for the last (4,1). That's how i plan on solving it.

With reduction it's also useful to look for commutators that use only the outer most layer turns for the larger part of the commutator, as in the 3 of the (3,1) as that means you can do the 1 first and only have to do the 3 once for a total of 5 moves! For example [K&2, E', B, E, K'&2,] looks like it messes things up but really just pyra-crystal moves left to do and they aren't needed. (that is what i'd use to cycle diamonds)
If this can't be done make the 1 a shallow cut and leave it off the end.

So i would solve large triangles around the corners first with 5 moves then diamonds 5 moves small triangles 7 moves and trapezoids 9 moves

So really not too different to your solution, just move trapezoids to the end and shorten the small triangles alg.



On a different note i just solved the rex cube and the master skewb with reduction to a cubic pyraminx and a skewb respectively. The latter made me realize i'm really bad at the normal skewb, i found the finishing part of the solve the hardest :lol:
Both are similar to solving an FTO with reduction to octaminx but the master skewb added something with the corners.

And someone beat my megaminx record and it wasn't Michael :shock: That's going to be hard to get back!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Oct 29, 2010 8:00 am 
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Elwyn wrote:
This is where i'd think "pure, do them last" because instead of your "way too long routine; 32 moves" for the small triangles you can use a nice (3,1) and hence all algs are (3,1) except for the last (4,1). That's how i plan on solving it.
You are absolutely right. The reason I didn't do it in that order, is that I didn't come up with the pure routine for the trapezoids before after submitting my solve. I'll definitely do a re-solve of this and do it in the order you explained. Though using a 32 move routine I still managed to keep my solve under 4000 moves, which makes me think that with practice and patience I may sub-3000 it. But I imagine that you may be able to sub-1000 it :lol:
Elwyn wrote:
And someone beat my megaminx record and it wasn't Michael :shock: That's going to be hard to get back!
I noticed that a few days ago and I was really surprised that someone actually could lower that record even more! As for me, I'm still at 270 something moves :lol:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 01, 2010 4:54 am 
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All this Pentultimate business made me decide to have a solve using one of Brandon's algorithms. I only used one of the 10 move ones. [A2, D', F, E2, D', E'2, D, F', A'2, D] to be precise.

I did three solves and got 127 then 125 then 122, pretty consistent hey.

Up for another little competition Julian? I only beat your count by 1 move :roll: That was with the old corner cycle and having a 10 move cycle rather than a 14 one managed to knock around 40 moves off my solves.
Katten wrote:
using a 32 move routine I still managed to keep my solve under 4000 moves, which makes me think that with practice and patience I may sub-3000 it. But I imagine that you may be able to sub-1000 it
Hahahaha i doubt it, i'd say around 1700 is what i'd aim for. There are 120 of those small triangles after all :shock:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 01, 2010 3:39 pm 
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Hello forum, members and guests,
since I have noticed it, some years and a half before, I'm a big admirer of Jaap Scherphuis' Sphere Applet. This is such a nice idea and it's pretty mighty. One can visualize (as it seems to be) an infinit number of symmetric regular puzzles with it. Even mixed axle-sets, x-cut puzzles and a lot more for instance anchor-systems for puzzles. No boundaries - amazing, incredible!
If Jaap reads that, I would like to ask you, how you got the idea of it? Came it from the "Cubic Circular" or else? I'm taking the chance to say a big thank you to you for the Sphere Symmetries Applet.
Let's start with a single cut. Maybe on the "icoset" (regular icosahedron face set). Here is my approach of working with the Sphere-Applet. If you don't know, what to do with it, it may help. It also contains exercices for you, in case you want to discover things by yourself. It's too big for one post, and maybe it fits not exactly into this forum, so I attach it as a pdf file. I hope it creates some interest in you, or maybe you start loving it, like me.
Gelatinbrain made a big effort, to simulate a big bunch of puzzles for us. The singlecut icoset is 2.1.x and 1.2.x in Gelatinbrains Virtual Magic Polyhedra Applet. There are even some more puzzles on the Sphere as you may notice. But I don't cry for new puzzles here, for I didn't solve all 1.2.x puzzles until now, and there are a lot of other puzzles that I didn't solve. It's only for the imagination.
Attachment:
icoset.singlecut.1.pdf [1.37 MiB]
Downloaded 85 times

edit: here is an update (I recommend loading this instead of the old file)
Attachment:
icoset.singlecut.2.pdf [1.47 MiB]
Downloaded 108 times

it contains a new section on calculating touchpoints, and a puzzle table for the icosahedron-face-set
Links: Sphere-Applet


Last edited by Stef-n on Wed Nov 10, 2010 12:26 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 01, 2010 4:06 pm 
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Elwyn wrote:
All this Pentultimate business made me decide to have a solve using one of Brandon's algorithms. I only used one of the 10 move ones. [A2, D', F, E2, D', E'2, D, F', A'2, D] to be precise.

I did three solves and got 127 then 125 then 122, pretty consistent hey.

Up for another little competition Julian? I only beat your count by 1 move :roll: That was with the old corner cycle and having a 10 move cycle rather than a 14 one managed to knock around 40 moves off my solves.
Amazing job, this has me convinced that occasional sub-100 solves are possible with the right catalog of moves.

Earlier today my search for 12-move sequences finished. Instead of taking 2.5 months it only took 1.8 or so. Hooray for L1 and L2 caches giving my code an execution locality boost :D

Julian sent me a list of all corner permutation+orientation patterns so now I just need to get to tagging sequences. I think I'm going to write a program to rotate/mirror all of the sequences and identify where they fit in Julian's list. I'm expecting this to be about 8 hours of work. It'll take me a couple of weeks before I have the time.

13-moves sequences are out of my reach. Somebody would have to donate significant cluster time. In a few months I'll write a proposal and present it to various cluster operator/owners I know around here.

Using setup moves for the 10, 11, and 12 move sequences will be required to make all the patterns until somebody searches all of the 13 move sequences. Once I have a program to rotate/mirror and classify routines adding setup moves is easy.

If somebody wants to play with the length-12 sequences in their unclassified form, I uploaded them to: http://noh.ucsd.edu/~bmenrigh/pent_12.txt

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 01, 2010 6:05 pm 
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Elwyn wrote:
Hahahaha i doubt it, i'd say around 1700 is what i'd aim for. There are 120 of those small triangles after all :shock:
I was just giving you a compliment, but I'm sure you're right; sub-1000 was maybe a bit optimistic :lol: What do you reckon your move count for the circle version of 1.1.39 (1.1.40) would be? I just solved it using more than 8000 moves! Basically I screwed up one of the algorithms. I did a horrible job bulletproofing if it was pure or not.

Also, new puzzles: 3.6.1, 3.7.6, 3.7.6b, 3.7.6c, 3.7.7, 3.7.8.

3.7.6 - 3.7.8 are a new "branch" I'd say and they look very very interesting!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 01, 2010 7:15 pm 
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Elwyn wrote:
Pentultimate ... Up for another little competition Julian? I only beat your count by 1 move :roll:
Congratulations! I will enjoy seeing if you or anyone else can get sub-100, but I won't be competing myself. In a few weeks I will own a physical Pentultimate :D , so I will be focussing on physical solves and improving my recognition, short-term memory, and fluency. I put quite lot of work into my corner orientation cases and setups, so if I switched to computer algos I'd feel like Kasparov resigning to Deep Blue, and I'm too stubborn to resign! :lol:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 01, 2010 7:33 pm 
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bmenrigh wrote:
13-moves sequences are out of my reach. Somebody would have to donate significant cluster time. In a few months I'll write a proposal and present it to various cluster operator/owners I know around here.
well if you aren't going to do them how about looking for some 2-2 swaps? They too could be useful (this is how i got the Icosimate record as 2-2 swaps are easier to use if there's no orientation) because otherwise if two corners need swapping you need to solve just one corner with a cycle to fix it. I used to know one but i can't remember it, it's written in this thread but you might be able to find different ones.
Katten wrote:
What do you reckon your move count for the circle version of 1.1.39 (1.1.40) would be?
Far too high hahaha, i don't know if I'll solve it any time soon just because it would take so long.
Julian wrote:
Congratulations! I will enjoy seeing if you or anyone else can get sub-100, but I won't be competing myself. In a few weeks I will own a physical Pentultimate , so I will be focussing on physical solves and improving my recognition, short-term memory, and fluency.
Colour me jealous!
TomZ's i assume, i wish i could afford it and will hopefully get one eventually. When solving for speed i'll still use the old commutator even on gelatinbrain.

... i think i need to practice speed anyway, i just tried then and it took me 10:53 when i used to be able to get 6 minutes hahaha my new aim is to just beat my old time.

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3x3x3 :20.7 seconds, 5x5x5 2:33, gigaminx 16:40, 7x7x7 9:48, pyraminx crystal 3:42


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 02, 2010 7:54 am 
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Yesterday I started working on the edge-turning cubes, however when I opened 3.3.8 to solve it earlier today, I was not able to twist the puzzle. It's like this for all the 3.3.x puzzles, but not for any of the others. Does anybody know how I can fix this?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 02, 2010 2:50 pm 
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I really wished the applet would work on Windows 7 (64bit), since Julian went past me in numbers! And there are so many new ones to try out....

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 02, 2010 6:39 pm 
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Sjoerd wrote:
I really wished the applet would work on Windows 7 (64bit), since Julian went past me in numbers! And there are so many new ones to try out....

32/64 compatibility problem is only for the exe version and not for the applet.
If your browser and JAVA runtime support 64bit mode, there's no problem.
If you see "class not found" things on java console,
it's another problem. For a makeshift solution,see Brandon's post on page 42.
Katten wrote:
Yesterday I started working on the edge-turning cubes, however when I opened 3.3.8 to solve it earlier today, I was not able to twist the puzzle. It's like this for all the 3.3.x puzzles, but not for any of the others. Does anybody know how I can fix this?

Yes it was a bug but it's now fixed. 8-)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 02, 2010 7:36 pm 
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Elwyn wrote:
Julian wrote:
In a few weeks I will own a physical Pentultimate :D , so I will be focussing on physical solves and improving my recognition, short-term memory, and fluency.
Colour me jealous!
TomZ's i assume, i wish i could afford it and will hopefully get one eventually. When solving for speed i'll still use the old commutator even on gelatinbrain.
I ordered RubixFreakGreg's Pentultimate one day before TomZ's was advertised in TP! With the Pentultimate I'm not bothered about how the puzzle is held together, just as long as it turns okay, and I'm happy to save some money by going with Greg's.

(Physical puzzles digression: My favorite puzzle this year is TomZ's 3x4x5. I've solved it a few times, but in a very fumbling, bumbling way and never in a single sitting. I'm enjoying being mystified by it and trying to figure out a "proper" solution. So far I am doing 180 degree scrambles and solves only. A couple of years ago I made a shortlist of puzzles that I particularly wanted to own, if they were ever made: FTO, 3x4x5, Pentultimate, and Little Chop. It's amazing that soon I will only be one dream puzzle away from a full set! I have also been enjoying the Gear Cube Extreme recently as a fun and tricky change of pace.)

Gelatinbrain: thanks for starting a cubic vertex/edge hybrid family with 3.6.1! :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 03, 2010 12:21 pm 
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Julian wrote:
In a few weeks I will own a physical Pentultimate

Congratulations! :D I would want to have that too. It's amazing, that this is even possible.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 05, 2010 4:46 pm 
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Elwyn wrote:
bmenrigh wrote:
13-moves sequences are out of my reach. Somebody would have to donate significant cluster time. In a few months I'll write a proposal and present it to various cluster operator/owners I know around here.
well if you aren't going to do them
I'm determined to do them but I don't have the resources (yet). I'm going to slice the job up into small work-units so that I can farm out jobs to tons of machines and/or volunteers. I have a really deep queue of programming projects though so it's going to be a few months before I get to it.
Elwyn wrote:
how about looking for some 2-2 swaps? They too could be useful (this is how i got the Icosimate record as 2-2 swaps are easier to use if there's no orientation) because otherwise if two corners need swapping you need to solve just one corner with a cycle to fix it. I used to know one but i can't remember it, it's written in this thread but you might be able to find different ones.
This is a good idea and I'm surprised I didn't think of it. I did think of it for the Little Chop (but haven't implemented it yet. Surprisingly, baring some stupid mistake on my part, there aren't any 2-2 corner swaps on the Penultimate of length 11 or shorter :!: Can you dig up a sequence you know results in a 2-2 swap so that I can test to make sure my code is correct?

Checking for 2-2 swaps is no more work than checking for a 3-cycle if done at the same time. Unfortunately I didn't think to add that to the code when I did the 12 move search so if there are any 12 move 2-2 swap sequences I'll have to re-do the search to find them.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 05, 2010 6:17 pm 
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@bmenrigh
Your program sounds very impressive. Any chance of sharing the source? I don't have a cluster, but I'd love to help in any way I can, even if it's just 8 cores/night if you end up doing a highly distributed system.
I'm curious, what kind of system did you run your 12-sequence search on?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 05, 2010 7:14 pm 
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GuiltyBystander wrote:
@bmenrigh
Your program sounds very impressive. Any chance of sharing the source? I don't have a cluster, but I'd love to help in any way I can, even if it's just 8 cores/night if you end up doing a highly distributed system.
I'm curious, what kind of system did you run your 12-sequence search on?

Sure, I believe source code, like information, is meant to be free. Understand though that this code is pretty awful because I've spent so much time hacking on things as they come to mind. That should be apparent given the amount of commented out code.

My Pentultimate sequence finder is available at:
http://noh.ucsd.edu/~bmenrigh/dodeca_solver/

And my Little Chop sequence finder is available at:
http://noh.ucsd.edu/~bmenrigh/edge_cube_solver/

Right now both are *nix only because of the heavy use of fork() for parallelism and POSIX+glibc+gcc only because of the use of some of the IPC stuff.

The Little Chop code is cleaner than the Penultimate code because I wrote it later and had a slightly cleaner design in mind.

My plan is to clean up and better comment the code and remove the cruft that has crept in. To tackle big jobs like 13 moves on the Pentultimate I'll move to a work-unit model where anyone can retrieve a work unit, process it, and submit it back. Of course I'll add command line switches to choose how many threads to run and such as well as print statistics to the user. I suppose I'll have to make it support Windows too. I would clean up the source and released it so that people wouldn't have to trust some binary client.

To search all 12-move Pentultimate machines I ran it for ~2 months on a 16-core (4 quad-core) Intel Xeon X5560. The machine has 48GB of ram but that doesn't matter since the program uses less than a meg of memory per thread. The memory is clocked at 1333MHz. I was running 20 threads across the 16 cores.

Adding another turn to do 13 moves increases the amount of work by a factor of 20. I've noticed though that I only need to search half the space I have been because the second half of the space just finds mirrors of the routines found in the first half. That means to do 13 moves I need 10x the computing power of my 12 move search. I have several more machine just like the one I used and with a few volunteers like yourself I think we could easily get 13 moves done in less than 6 months.

The hard work is in getting the program ready to be used by others in a way that is easy for them.

Since most of the work is in doing the twisting, I'm going to add checking for 2-2 swaps and 5-cycles too. I'll also look for super-penultimate face twist sequences. All of this will add less than 1% overhead to the existing 3-cycles checks.

In a month or two I'll start a new thread soliciting volunteers.

Okay, time to stop talking about coding and start actually coding :lol:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 05, 2010 8:40 pm 
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OK i found the 2-2 swap. I found it in the Noah's pentultimate writings thread. Using gelatinbrain notation it is
[C2, F3, C3, F2]x3

12 moves. Last time i tried to use it though i remember it being hard to find setups for especially to get the right orientation.

Also gelatinbrain added 1.5.1 and 1.5.2 pentultimate+bigchop and pyraminx crystal+bigchop respectively.
Both might be able to be reduced to the face turning part of the puzzle (actually reduction to pentultimate would be stupidly difficult) to save moves but that would introduce paritys on both.

The pyraminx crystal bigchop was suggested by Girgr a long time ago and is a nice looking puzzle. I can cycle the edge face triangles pure in 14 moves but the corner ones are a little harder to find a 3 cycle for.

Alright the ones around the corner in 22 moves impure (edge ones move to but the can be solved after)
I'm pretty sure there will be shorter algs for both.

Also pairing the edge triangles means you cycle half of them with the longer alg then pair those pairs to make whole edges in only three moves per cycle if you pair them like this. hence you only have to use the longer alg half as many times.
Attachment:
1.5.2 edge halves..jpg
1.5.2 edge halves..jpg [ 52.53 KiB | Viewed 3789 times ]

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 06, 2010 4:31 pm 
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Elwyn wrote:
gelatinbrain added 1.5.1 and 1.5.2 pentultimate+bigchop and pyraminx crystal+bigchop respectively. Both might be able to be reduced to the face turning part of the puzzle (actually reduction to pentultimate would be stupidly difficult) to save moves but that would introduce paritys on both.

The pyraminx crystal bigchop was suggested by Girgr a long time ago and is a nice looking puzzle. I can cycle the edge face triangles pure in 14 moves but the corner ones are a little harder to find a 3 cycle for.

Alright the ones around the corner in 22 moves impure (edge ones move to but the can be solved after)
I'm pretty sure there will be shorter algs for both.

Also pairing the edge triangles means you cycle half of them with the longer alg then pair those pairs to make whole edges in only three moves per cycle if you pair them like this. hence you only have to use the longer alg half as many times.
Well spotted! Thanks Gelatinbrain.

I am tempted to reduce 1.5.2 (Pyraminx Crystal + Big Chop) to a Big Chop. I would do this with 3 move algos to reduce one orbital and 11 move algos to reduce the other orbital (moving the edge pieces to join the relevant corner pieces all the way), then solve the Big Chop. The 11 moves are just a shortening of a (1 + (1,1) + 1, 1) = (6,1) = 14 move algo which is probably just like the one you've found to cycle 3 edge pieces pure.

1.5.1 (Pentultimate + Big Chop) -- a possible method

1. Solve one orbital of big triangles non-pure with (1 + (1,1) + 1, 1) = (6,1) cycles.

2. Solve the other orbital of big triangles non-pure with (1 + 2*3 + 1, 1) = (8,1) cycles.

3. Solve one orbital of small triangles non-pure with (2 + (1,1) + 2, 1) = (8,1) cycles.

4. Solve the other orbital of small triangles pure with (3 + (1,1) + 3, 1) = (10,1) cycles.

The inner (1,1) bits are made from distant face and edge turns, and the inner 2*3 is two edges back and forth. The algo for stage 4 is the same as stage 3 apart from an extra setup and undo move on the outside.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 06, 2010 9:00 pm 
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I thought about reduction to bigchop because then you don't have to move the corner triangles. I decided against it not because it's a bad idea but i can't solve the bigchop :lol: That and 200 move pyraminx crystal solve seemed easier than a 2000 move bigchop one but i'd need a shorter alg for the corner triangles.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 07, 2010 3:50 am 
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Is there even a bigchop on Gelatinbrain?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 07, 2010 3:58 am 
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Katten wrote:
Is there even a bigchop on Gelatinbrain?


Yes, the Bigchop is 1.4.3

-Mark- :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 07, 2010 7:41 pm 
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1.5.2
Elwyn wrote:
I thought about reduction to bigchop because then you don't have to move the corner triangles. I decided against it not because it's a bad idea but i can't solve the bigchop :lol: That and 200 move pyraminx crystal solve seemed easier than a 2000 move bigchop one but i'd need a shorter alg for the corner triangles.
Since my recorded solve I've found that the Big Chop should be solvable in around 1500 moves: 15-20 pieces intuitively from one orbital, finish the orbital with (8,1) cycles, then solve the mirror image orbital with (12,1) pure cycles. So maybe 2200-2300 moves total for me if I use that method. Reducing to a Pyraminx Crystal could give a similar total.

The first orbital of corner pieces can be cycled with (5,1) reduced to 11 move algos, and the second orbital can be cycled with (7,1) reduced to 14 move algos. Commutators in invisible ink:

K, /* Setup move */
IF,C2,IF, /* Distant edge and face moves back and forth */
K', /* Undo move */
IF, /* Replace the swapped group of pieces, including one corner piece from each orbital */
K,IF,C'2,IF,K',
IF

D'2,K2, /* Setup moves */
IF,C,IF, /* Distant edge and face moves back and forth */
K'2,D2, /* Undo moves */
JI, /* Swap one corner piece and a bunch of unimportant edge pieces */
D'2,K2,IF,C',IF,K'2,D2,
JI


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 10, 2010 12:49 pm 
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here is an update to my icoset.singlecut.1.pdf:
icoset.singlecut.2.pdf [1.47 MiB]
it contains the following puzzletable, and a new section on calculating touchpoints
Attachment:
icoset.singlecut.puzzletable.1.jpg
icoset.singlecut.puzzletable.1.jpg [ 194.29 KiB | Viewed 3642 times ]

I believe that the puzzletable is natural to the icoset, except the varialbe slider values between the touchpoints. Of course I'm not 100% sure. If you want to know, how I have created the puzzletable, take a look into the icoset.singlecut.2.pdf.
Please post or pm any comments!! I need some feedback. :)
Especially, I am unsure, wether this fits into the Gelatin Brain's Applet Solutions Discussion Thread. If this is not tolerated here, I will completely erase the posts, and maybe post it somewhere else. Please tell me, wether you tolerate this here!!
Thank you.
Of course I will continue posting gelatinbrain solution related posts here.
Links:
Jaap Scherphuis' Sphere Applet


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 11, 2010 11:56 am 
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Hi everyone,

this morning I was playing around with the Face-Turning Octahedron a bit and I was very pleased with what I got out of it: my first pure 3-cycle for the triangle pieces! Now, this isn't really that much of an accomplishment by itself, but the FTO was my first "hard" puzzle solved before I even started using Gelatinbrain. Back then I wasn't able to find any pure cycles for it, and that's why it feels so good to finally have found one. When I first got this puzzle, I spent so much time finding a solution to it and I was never happy with the one I used, until now :D This find has made the FTO my favorite non-virtual puzzle of the ones I own. I even brought it with me on the bus to work today :lol:

The cycle's a bit long for now; 20 moves, but I'm just happy to have one at all, as least for the time being. This is what it does:
Attachment:
Skjermbilde 2010-11-11 kl. 17.46.51.png
Skjermbilde 2010-11-11 kl. 17.46.51.png [ 32.35 KiB | Viewed 3611 times ]
EDIT: I didn't have time before, but here's the notation:

(BRU, LUF', BRU', LUF,
ULB', BRU, LUF', BRU', LUF,
ULB,) x2


Last edited by Katja on Sun Nov 14, 2010 3:32 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 11, 2010 3:10 pm 
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Katten wrote:
This find has made the FTO my favorite non-virtual puzzle of the ones I own.

Hi Katten, you fall in love with a puzzle, after you have got your first good solve on it. That has also happend a few times to me.
I remember, the FTO (4.1.2) I solved some time bevor. I first solved the edges, then the triangular face pieces and at last the corners. The edges are really easy. For the face pieces I used a (3,1), but it scrambles the corners. For the corners I used a pure (4,4), thats 16 moves but you have only 6 corner pieces to solve. Have fun with your FTO.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Nov 11, 2010 4:42 pm 
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Hello Gelatinbrain. Your 3.7.6 series is totally nice. I love it.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 12, 2010 7:59 pm 
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I'm working on some code that could potentially help bmenrigh's program. I had a quick question about the limitations of the pentultimate since I've never actually played with or solved one. Can you ever switch two adjacent faces? I don't care if it screws up corners or not. If I coded it right, it seems like you can't, but I wanted to double check with the pros here.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 12, 2010 8:11 pm 
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GuiltyBystander wrote:
I'm working on some code that could potentially help bmenrigh's program. I had a quick question about the limitations of the pentultimate since I've never actually played with or solved one. Can you ever switch two adjacent faces? I don't care if it screws up corners or not. If I coded it right, it seems like you can't, but I wanted to double check with the pros here.
You're correct, it isn't possible swap two faces without affecting another face somewhere -- irregardless of what happens to the corners. This is because a twist on the Penultimate is a 5-cycle of face centers which is an even permutation.

I'm still working on your PM and your int -> uchar suggestion gives me a 10% performance boost :D The reason I chose to use ints is that simple arithmetic on an int and a char takes the CPU the same number of cycles and I thought having 4-byte aligned memory accesses would be faster than no alignment. The program puts the CPU under cache pressure though so reducing the size of the data increases the chances of a cache hit. Your 40% boost in performance is all thanks to better use of your L1/L2 cache. The bigger the cache the less difference moving from int -> char makes. 10% is still really good though, thanks! If I get volunteers to help crunch 13 moves, many people will see your ~40% performance boost which is awesome.


Edit: After a bit more thought on this, I should be more specific:

If you have swapped the position of two faces then you must have swapped the position of two other faces. A 2-2 swap is an even permutation.

If you have moved some piece A to some other location B but not B -> A (they didn't swap) then there must be some other location, C, that is involved in the cycle. A 3-cycle is also an even permutation.

Of course this means that if we were to make a face twist cache, instead of a cache size of 11! it only needs to be 11! / 2.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 12, 2010 8:48 pm 
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bmenrigh wrote:
You're correct, it isn't possible swap two faces without affecting another face somewhere -- irregardless of what happens to the corners. This is because a twist on the Penultimate is a 5-cycle of face centers which is an even permutation.
Thanks. This should help me if I can quickly identify which ones are unreachable...
bmenrigh wrote:
<paraphrase>L1/L2 cache = win</paraphase>
Ah cool. I didn't fully know why. I wish I new a little more about fine tuning code based on how CPU's work. Sometimes it feels like just trial & error. Everyone should see a slight boost from the memcpy regardless of cache size right?
bmenrigh wrote:
Of course this means that if we were to make a face twist cache, instead of a cache size of 11! it only needs to be 11! / 2.
Exactly, but only if we can quickly identify which ones are which. It looks like it takes 8 moves max (maybe 7 if you don't pick one color to be a "core" that everything is relative to) to solve the centers. I'm not sure if that's helpful to people racing for fewest moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 12, 2010 9:13 pm 
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GuiltyBystander wrote:
bmenrigh wrote:
<paraphrase>L1/L2 cache = win</paraphase>
Ah cool. I didn't fully know why. I wish I new a little more about fine tuning code based on how CPU's work. Sometimes it feels like just trial & error. Everyone should see a slight boost from the memcpy regardless of cache size right?
In theory yes but in practice no. On x86/x86_64 memcpy() gets compiled to a "repz mov..." which is basically a super-fast for() loop in the CPU microcode. You have to copy about a page (4kb) of memory before the size of the copied data matters.

There are so many crazy gotchas to getting code to go fast on modern CPUs that optimization is really an art rather than a science. For example, I found that if I changed:
Code:
if (dodeca[i][1][j] != i) {
    bad++;
}
To:
Code:
bad += (dodeca[i][1][j] != i);
The speedup was huge (1000x faster). The trouble was that the branch wasn't predicable so there was a pipeline stall 50% of the time.

GuiltyBystander wrote:
bmenrigh wrote:
Of course this means that if we were to make a face twist cache, instead of a cache size of 11! it only needs to be 11! / 2.
Exactly, but only if we can quickly identify which ones are which. It looks like it takes 8 moves max (maybe 7 if you don't pick one color to be a "core" that everything is relative to) to solve the centers. I'm not sure if that's helpful to people racing for fewest moves.
Back in this post I looked at useful center cycles and found that 1 case (A <--> B, C <--> E) required 9 moves. It would be great if you could sanity check my numbers from that post.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 13, 2010 4:10 am 
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bmenrigh wrote:
Back in this post I looked at useful center cycles and found that 1 case (A <--> B, C <--> E) required 9 moves. It would be great if you could sanity check my numbers from that post.
That post also tries to keep half the puzzle solved. I'm completely ignoring corners so I end up screwing up a lot of stuff. Here's the algorithm though if you still want it.
[F3, E1, A1, E4, F1]
Here's a short table showing the number of states and their distance from solved.
Code:
depth     count
0             1
1            24
2           480
3         9,570
4       182,620
5     3,109,532
6    15,773,531
7       882,637
8             5

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 13, 2010 1:40 pm 
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Here is a (10,1) pure cycle for the Big Chop (1.4.3):

CH,AC, [FJ,AD]x3, AC,CH,
HG,
CH,AC, [AD,FJ]x3, AC,CH,
HG

The key sequence is in bold. Turning 2 precisely spaced edges back and forth 3 times results in 2 groups of 12 pieces being flipped/reversed, and the 2 setup moves cut away a single piece from the end of one of the groups. This algo can be used with 1.4.3x, 1.4.7x (solving the circle pieces after the regular pieces), and 2.3.1.
Attachment:
Big Chop (10,1) pure cycle.jpg
Big Chop (10,1) pure cycle.jpg [ 34.12 KiB | Viewed 3484 times ]


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 13, 2010 2:04 pm 
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Katten wrote:
this morning I was playing around with the Face-Turning Octahedron a bit and I was very pleased with what I got out of it: my first pure 3-cycle for the triangle pieces! The cycle's a bit long for now; 20 moves, but I'm just happy to have one at all, as least for the time being.
Well done! You are in good company, because the first or second person to solve over 100 Gelatinbrain puzzles (Noah) initially used a 24 move algo to cycle the FTO triangles pure. Here's a hint to finding a short algo, which I didn't think about when I was new to the FTO: remember to check middle/slice layers as well as faces. Try making 3 face moves and then look carefully for a single swapped triangle in a middle layer somewhere. If 4.1.2 and 4.1.3 had shift-click then we could make a (3,1) pure cycle, but instead we can make a (3,2) cycle, simulating a slice move by making two opposite face moves combined with a puzzle rotation.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 13, 2010 5:18 pm 
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Julian wrote:
Here's a hint to finding a short algo, which I didn't think about when I was new to the FTO: remember to check middle/slice layers as well as faces. Try making 3 face moves and then look carefully for a single swapped triangle in a middle layer somewhere. If 4.1.2 and 4.1.3 had shift-click then we could make a (3,1) pure cycle, but instead we can make a (3,2) cycle, simulating a slice move by making two opposite face moves combined with a puzzle rotation.

This is a good trick, wich I add to my repertory. It is not easy, to do the right moves after an imagined puzzle rotation. And it is not easy, to see a commutator in a move sequence, that contains a puzzle rotation. But virtual slice moves are a good thing.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 13, 2010 8:08 pm 
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In addition to all of the other interesting puzzles that Gelatinbrain has added recently, I have just noticed another 5 new cubes:

3.3.14 = circle 3.3.3
3.3.15 = circle 3.3.5
3.3.16 = shallow cut Helicopter Cube (3.3.1) + 3.3.6

3.6.2 = slightly deeper cut Master Skewb (3.2.2) + 3.3.3
3.6.3 = Master Skewb (3.2.2) + 3.3.5

I especially like the new circle edge turners. Thanks again Gelatinbrain!


Edit: Corrected "shallow" to "slightly deeper" in my description of 3.6.2. Also I have a request for two puzzles that I think would make nice additions:
Attachment:
DinoChop or SkewbChop.jpg
DinoChop or SkewbChop.jpg [ 13.98 KiB | Viewed 3428 times ]

The DinoSkewb (Dino Cube 3.2.4 + Skewb 3.2.1) and SkewbChop (Skewb 3.2.1 + Little Chop 3.3.7) look the same, as above. The latter would be the dual of 4.5.1 (Skewb Diamond 4.2.1 + OctaChop 4.3.3), which is a fun and very tricky puzzle.


Last edited by Julian on Sun Nov 14, 2010 3:42 am, edited 2 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 13, 2010 8:14 pm 
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Julian wrote:
In addition to all of the other interesting puzzles that Gelatinbrain has added recently, I have just noticed another 5 new cubes:

3.3.14 = circle 3.3.3
3.3.15 = circle 3.3.5
3.3.16 = shallow cut Helicopter Cube (3.3.1) + 3.3.6

3.6.2 = shallow cut Master Skewb (3.2.2) + 3.3.3
3.6.3 = Master Skewb (3.2.2) + 3.3.5

I especially like the new circle edge turners. Thanks again Gelatinbrain!
I agree, great to see!

A few weeks ago I built up all the routine needed to solve 3.3.2 - 3.3.5 and then I gave 3.3.2 a try. I got stuck on the last edge 3-cycle and I couldn't find the setups to get it done. I closed the applet after about an hour of work. I need to revisit the edge turners when I have more time and patience so that I can then tackle the circle versions.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 3:29 am 
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More edge-turners --> my favorites :D I especially like 3.3.14 and 3.3.16. Thanks a lot Gelatinbrain!
bmenrigh wrote:
I got stuck on the last edge 3-cycle and I couldn't find the setups to get it done.
When it comes to edge-turners, I feel that the set-ups is the hard part, though I feel that all you need is practice and patients. When it comes to finding algorithms for these puzzles, I find it surprisingly "easy". Maybe because after two turns you're back where you started - meaning counter clockwise moves + R2, U2 etc are out as well. Which gives the algorithms a lot of restrictions and therefore are a lot easier to find.
Julian wrote:
Try making 3 face moves and then look carefully for a single swapped triangle in a middle layer somewhere. If 4.1.2 and 4.1.3 had shift-click then we could make a (3,1) pure cycle, but instead we can make a (3,2) cycle, simulating a slice move by making two opposite face moves combined with a puzzle rotation.
Thanks, Julian! This is genius! I haven't been playing around with my FTO yet, but I'm pretty sure I know just how to find this cycle. Also I'm quite baffled that a (3,1) is possible for these pieces. I spent some time finding my 20 move routine for them :lol: I didn't have time to post it before, but here it is:

(BRU, LUF', BRU', LUF,
ULB', BRU, LUF', BRU', LUF,
ULB,) x2


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 11:10 am 
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Katten wrote:
More edge-turners --> my favorites :D I especially like 3.3.14 and 3.3.16. Thanks a lot Gelatinbrain! When it comes to edge-turners, I feel that the set-ups is the hard part, though I feel that all you need is practice and patients. When it comes to finding algorithms for these puzzles, I find it surprisingly "easy". Maybe because after two turns you're back where you started - meaning counter clockwise moves + R2, U2 etc are out as well. Which gives the algorithms a lot of restrictions and therefore are a lot easier to find.


Talk about setups, I should say that 3.3.14 is tricky. In the beginning I found some 3-cycle algorithms and though they were sufficient. But later I found it impossible to set-up a certain type of pieces. Then I realized that there was a constraint that limited that kind of pieces in orbits. So the first thing to do is to use the orbits to determine the orientation.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 3:07 pm 
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schuma wrote:
In the beginning I found some 3-cycle algorithms and though they were sufficient. But later I found it impossible to set-up a certain type of pieces. Then I realized that there was a constraint that limited that kind of pieces in orbits. So the first thing to do is to use the orbits to determine the orientation.
Kinda like on 1.4.8? Because when I first tried solving it, I found it impossible to get some of the pieces cycled into place. At first I though I'd made some kind of mistake. But later on I realized that I would have to place the triangle pieces first to determine the correct face for each color and then I'd be able to start working on the edges. If that's the case, I'll have to save 3.3.14 for later. I'm still in need of some practice with my 1.4.8 technique.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 3:44 pm 
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Katten wrote:
schuma wrote:
In the beginning I found some 3-cycle algorithms and though they were sufficient. But later I found it impossible to set-up a certain type of pieces. Then I realized that there was a constraint that limited that kind of pieces in orbits. So the first thing to do is to use the orbits to determine the orientation.
Kinda like on 1.4.8? Because when I first tried solving it, I found it impossible to get some of the pieces cycled into place. At first I though I'd made some kind of mistake. But later on I realized that I would have to place the triangle pieces first to determine the correct face for each color and then I'd be able to start working on the edges. If that's the case, I'll have to save 3.3.14 for later. I'm still in need of some practice with my 1.4.8 technique.


Yeah, it's like 1.4.8. According to my notes, 1.4.4, and 4.3.1 also share similar properties. They are all edge-turning puzzles, indeed. But I think 3.3.14 is easier than 1.4.8. Once you figure out how pieces move, it takes no more than one minute to find which face is for which color.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 5:07 pm 
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schuma wrote:
But I think 3.3.14 is easier than 1.4.8. Once you figure out how pieces move, it takes no more than one minute to find which face is for which color.
It's usually that way with circle puzzles, I've experienced. That's also why they're so much fun: you get to really figure out how all the pieces interact :D

On a different note;
Attachment:
Skjermbilde 2010-11-14 kl. 22.52.58.png
Skjermbilde 2010-11-14 kl. 22.52.58.png [ 61.99 KiB | Viewed 3368 times ]
I FINALLY solved the Pentultimate :D I was planning on saving it for my 100th puzzle, but how could I resist solving it when I just found my first 3-cycle for the corners! I used a very similar approach to finding this commutator as I did with my newly discovered 3-cycle for the triangles on the FTO. It's 20 moves, pure:

(F, C', F', C,
K',
C', F, C, F',
K,) x2

The hardest part with this puzzle I'd say was getting the set-ups for the corners which allowed the pieces to get both cycled into the desired spots and simultaneously get correctly oriented. Regardless, I think this is one of the most fun puzzles I've ever solved. Now I'm really tempted to give into temptation and get TomZ's Pentultimate :lol:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 5:17 pm 
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schuma wrote:
Talk about setups, I should say that 3.3.14 is tricky. In the beginning I found some 3-cycle algorithms and though they were sufficient. But later I found it impossible to set-up a certain type of pieces. Then I realized that there was a constraint that limited that kind of pieces in orbits. So the first thing to do is to use the orbits to determine the orientation.
Not only that, but during my attempt this evening I had those pieces in their correct orbitals, but I came across odd perms within those orbitals, and I didn't know how to resolve the issue. :? Unlike the Helicopter Cube, we can't just move a pair of edges back and forth 3 times and carry on. I had to give up and experiment from a solved position, and since then I've found a weird algo of 10 moves that swaps 2 pairs of these pieces, each pair in a different orbital, without disturbing... certain other pieces. :lol: (It's funny talking about these things indirectly.) My fix algo could be described as "almost make a snake pattern all the way around the orbit, but stop slightly short and go back." It can also be seen as P Pm, where P is a sequence of 5 moves and Pm is its mirror image. Hmmm... I will try 3.3.14 again tomorrow.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 5:57 pm 
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Julian wrote:
Also I have a request for two puzzles that I think would make nice additions:
Attachment:
DinoChop or SkewbChop.jpg

The DinoSkewb (Dino Cube 3.2.4 + Skewb 3.2.1) and SkewbChop (Skewb 3.2.1 + Little Chop 3.3.7) look the same, as above. The latter would be the dual of 4.5.1 (Skewb Diamond 4.2.1 + OctaChop 4.3.3), which is a fun and very tricky puzzle.

3.2.13 & 3.6.4
I will upload pictures later.


Brandon, in your place, I will assign separate memory areas for corners and centers
32 bytes(one byte for each corner and center) is enough because each piece has only 60 states (12 location x 5 orientation for centers, and 20x3 for corners).
You don't have to use stack either. One byte swap area is enough.
I suppose you are first copying all to the stack for cache efficiency, but no memory access at all is still better, IMHO.
Core optimization is as adictive as twisty puzzles. :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 6:17 pm 
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Not sure this is the right place to ask, but what limits are there on the types of puzzles the Gelatin Brain app can simulate?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 7:08 pm 
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logan wrote:
Not sure this is the right place to ask, but what limits are there on the types of puzzles the Gelatin Brain app can simulate?

I support only 3 types of symmetry correponding 5 platonic solids(dodeca-icosaghedral, cube-octahedral & tetrahedral)
Prisms(square one,masterball,etc) need a different interface, so difficult to support.
Jumbable puzzles too.
And I don't want to add functionally same puzzles with only different appearances.
Another criteria is my taste, of course. But it's difficult to explain.

I think your inner cube is very interesting. But I don't fully understand how pieces move.
Unfortunately I don't have enough time to answer to each PM. But any suggestion is welcome.
:)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 7:35 pm 
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logan wrote:
Not sure this is the right place to ask, but what limits are there on the types of puzzles the Gelatin Brain app can simulate?
Logan, I don't understand your Inner Cube description either but it sounds like it is similar in idea to Gelatinbrain's 3.9.1 or his 3.11.1 puzzles.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 14, 2010 7:50 pm 
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gelatinbrain wrote:
Brandon, in your place, I will assign separate memory areas for corners and centers
32 bytes(one byte for each corner and center) is enough because each piece has only 60 states (12 location x 5 orientation for centers, and 20x3 for corners).
You don't have to use stack either. One byte swap area is enough.
I suppose you are first copying all to the stack for cache efficiency, but no memory access at all is still better, IMHO.

My implementation is sticker-based rather than piece-based. The reason is that when I was trying to figure out how to best handle representing the penultimate in my program so that twisting would be easy to implement, I couldn't figure out how piece twist worked. GuiltyBystander has shared with me an implementation that is piece based with 12x5 states for centers and 20x3 states for corners (32 bytes total). He even made a fancy diagram for me to help me understand how to track piece twist. His code is quite compact and makes mine look quite clunky and dumb.

He also came up with a brilliant pruning idea involving caching all the possible center permutations and then abandoning parts of the search tree by looking up the center permutation in the table and determining if there is enough depth left in the search tree to get the centers back to a solved state. This eliminates a huge amount of work that has no chance of yielding a pure corner routine.

Long story short, after implementing it, I did all length 12 sequences in about 20 seconds, all length 13 in about 5 minutes, and all length 14 in 100 minutes. The only thing left to do is to rotate/mirror all the found routines and then categorize them. There is probably only 20 hours of work left until I can post a master list of routines.

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