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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 07, 2010 5:38 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

konsassen wrote: My technical problems are back and the situation is worse than ever: I have now three different Windows computers in my house and Gelatinbrain applets do not run on one of them. I have Windows 7 x64, Vista Home Premium 32 bit and XP SP3 32bit. I had reported that after a complete new installation of Java, I could run Gelatinbrain applets on IE32 with Java 32. A few days later, nothing works anymore. Other JOGL applets run without problems. I have given up!!!! Konsassen, I just tried the applet on Windows XP SP2 32bit + Java 1.6.0.21 and you're right, it doesn't work. I also tried my test applet and it too doesn't work. This is what the Java console reports: Oct 7, 2010 10:12:47 PM org.jdesktop.applet.util.JNLPAppletLauncher displayError SEVERE: Class not found: jzzz.CMainApplet I took a packet trace and confirmed that everything is fine from that standpoint. Of course I cleared every darn cache there is and tried several times without it working. I tracked the issue down to a Java security setting. Namely, no option works except: Attachment:
java_sec.png [ 22.44 KiB  Viewed 6265 times ]
This was discussed before and Gelatinbrain rightly pointed out that this isn't really a good idea from a security standpoint. I agree. I tried the other 3 options (clearing the caches between tries) and no dialog or other warning popped up and the applet always failed to load. The console always reported "Class not found: jzzz.CMainApplet". I find it strange that a security setting is not reporting a security violation in the console. Reporting that a class can't be found is really reporting the sideeffect of a security setting rather than the cause of the issue. I tried signing the polyhedra.jar file since Java treats signed jars as more trusted. That didn't make any difference either. The default security settings must be different for the Linux JRE since I don't have to adjust any settings to get it to work.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 08, 2010 2:39 am 

Joined: Thu May 31, 2007 7:13 pm Location: Bruxelles, Belgium

I don't know why my applet doesn't work in the sandbox. But until I find a solution, I recommend to do not use my applet, and never chose the "disable verification" option. It's dangerous because this policy is applied to all applets. I guess "mixed code" means that JOGL is signed but my code is not. But I don't understand why that causes a security problem. My code is safe exactly because my applet is not signed, because JAVA blocks all security violating operations of an unsigned applet. On the contrary, if my code is signed and once you accept my sign, it's really dangerous for you. If I like I can do anything on your computer, reading and transfering your personal infos, writing on your disk, etc. If my code is considered suspicous simply because it is not signd, The "securtiy" here shoud mean a totally different thing, for example an applet showing a fake "password please" window. Oh no! There's no remedy for people that credulous...
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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 08, 2010 5:51 am 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

Katten wrote: 5.2.5 solution outline Thanks Katja, your solution worked out fine for me except for one thing I'd like to add... when pairing the edges, this can happen: Attachment:
GB 525 edge problem.jpg [ 19.04 KiB  Viewed 6229 times ]
I use an 8 move fix [CB&2,CD], [AC&2,CD]x2, [CB&2,CD]. You were slightly lucky not to get this during your one solve, because it probably happens the majority of the time. Katten wrote: For some reason I find the 5.2.x puzzles easier than the 5.1.x puzzles. I have gotten the feeling that it's mostly the other way around I see most of 5.1.x as octahedral puzzles in the form of tetrahedra. The way I think about them and the way I write down algos, I always think of the 4 corners and 4 faces as a collection of 8 "faces", and the puzzles feel as familiar as face turning octahedra. On the other hand, 5.2.x are equivalent to 180degreeturnsonly face turning cubes or vertex turning octahedra, which I found weird and difficult to get used to, especially with 5.2.4 and 5.2.5.


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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 08, 2010 10:40 am 

Joined: Tue Feb 16, 2010 12:15 pm Location: Sandnes, Norway

Hi Julian, I'm glad you got something out of it. The case you are describing did not happen to me on my first solve. Just now I solved it 5 times in a row, and it happened 3/5 times. Thanks for adding that part, I will go back and edit my original post. Would it be OK if I use your illustration image for that? To fix this situation I used this: CB&2, AB, CB&2, DB&2, AB,DB&2, CB&2, AB, CB&2, Which is one move longer than yours. Also, I realize I left something else out as well: when pairing up the edges, make sure you do this at the edges correct place. For instants: don't pair up the greenyellow edge next to the bluered centers. Because this puzzle is limited to 180 degree turns, the place where you put it is the place where it will stay. But I suppose that's quite obvious, but I'll still add it in case. Julian wrote: I see most of 5.1.x as octahedral puzzles in the form of tetrahedra. The way I think about them and the way I write down algos, I always think of the 4 corners and 4 faces as a collection of 8 "faces", and the puzzles feel as familiar as face turning octahedra. On the other hand, 5.2.x are equivalent to 180degreeturnsonly face turning cubes or vertex turning octahedra, which I found weird and difficult to get used to, especially with 5.2.4 and 5.2.5. That's a clever way to look at it. I find the octahedra very hard, so this would definitely explain why I'm having a rough time with them.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 08, 2010 2:22 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

5.2.5 Katten wrote: Would it be OK if I use your illustration image for that? Sure, no problem. I've been doing a run of tetrahedra today. 5.2.65.2.8 turned out to be easier than I expected. 5.3.1 and 5.3.2 are weirder and harder but I've got the hang of them now.


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Konrad

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 08, 2010 6:03 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

gelatinbrain wrote: I don't know why my applet doesn't work in the sandbox. But until I find a solution, I recommend to do not use my applet, and never chose the "disable verification" option. ... I can confirm that it works with bmenrigh's security configuration. (Java 6.21 32 bit AND 64 bit on W7) Very strange and I hope, gelatinbrain, that you'll find a solution. Another question for you: How much work is it to create a "Compy Skewb" as designed by TomZ (with nontrivial tips)? Could you possibly provide it to us? Thanks Konrad
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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 08, 2010 6:15 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

konsassen wrote: gelatinbrain wrote: I don't know why my applet doesn't work in the sandbox. But until I find a solution, I recommend to do not use my applet, and never chose the "disable verification" option. ... I can confirm that it works with bmenrigh's security configuration. (Java 6.21 32 bit AND 64 bit on W7) Very strange and I hope, gelatinbrain, that you'll find a solution. What I don't understand is that I signed a copy of the applet and it failed the same way. Signed applets are supposed to run with elevated privileges. I also don't understand why the applet is failing considering it didn't in the past. Also, I'm surprised the Java console doesn't print a sandbox access violation or the Java equivalent. It just seems to fail silently and not load the main polyhedra.jar class.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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APJ

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 09, 2010 3:18 pm 

Joined: Sat Jul 11, 2009 1:09 pm Location: My House

GB was working for me before, but isn't working now, I just get the blank screen. I am on Firefox 3.6.10 and have Java 6.0.21. Alex
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Elwyn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 10, 2010 2:13 am 

Joined: Tue Sep 08, 2009 8:41 am Location: The Blue Mountains, Australia

I'm in the same boat, having to switch the security to the dangerous setting otherwise i get the "class not found" error. Katten wrote: A 907 move Gigaminx solve! Actually, I think I would be able to get my move count down even more, so a sub900 is my next attempt. I used Elwyn's Gigaminx method, slightly altered to fit my solving preferences. I just did my first FM gigaminx solve in a while and beat Michael's record with a 572 move solve only 23 moves off my last record but that means i beat his by 20 so i'm happy. I think the fact i got better at the megaminx step at the end might have been what helped. I'd say i could beat the 1.1.11 record as well
_________________ Some PBs 3x3x3 :20.7 seconds, 5x5x5 2:33, gigaminx 16:40, 7x7x7 9:48, pyraminx crystal 3:42


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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Oct 11, 2010 7:14 pm 

Joined: Thu Jul 23, 2009 5:06 pm Location: Berkeley, CA, USA

I just found two new puzzles that GB had recently added: 3.11.1 and 3.11.1b. I wonder if they are inspired by any puzzle in the real world. I've never seen such things.
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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Oct 11, 2010 7:46 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

schuma wrote: I just found two new puzzles that GB had recently added: 3.11.1 and 3.11.1b. I wonder if they are inspired by any puzzle in the real world. I've never seen such things. I noticed them an hour ago during my daily beforebed check for new puzzles. There is also a nice update to the File menu from the applet, now showing images of the puzzles along with their names. Thanks Gelatinbrain, for the new puzzles and the continual refinements. I think I see how 3.11.1 works: when making a 90 degree turn, each ball is first pushed over 90 degrees "forwards" by the ball "behind" it, i.e. about to replace its position; then each ball is pushed over 90 degrees in the direction it is about to move to arrive at its new position. It's the first face turning cube I've seen where a 360 degree turn does not take us back to exactly the same situation: we have to do three full turns for that. I can see a (4,1) commutator that affects 3 adjacent balls while leaving the other 5 balls intact, and I think the puzzle should be solvable using that one algo (plus its inverse and/or mirror). It's going to be tricky though. I think the same movements happen with 3.11.1b too, but I find it much more difficult to visualize.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Oct 11, 2010 7:58 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

schuma wrote: I just found two new puzzles that GB had recently added: 3.11.1 and 3.11.1b. I wonder if they are inspired by any puzzle in the real world. I've never seen such things. Really cool! Visually they remind me of electron orbitals. I tried solving 3.11.1 using intuition and I got down to just two balls/corners twisted. They were more inverted than twisted though which is a problem I've only ever seen on the 4dimensional puzzles. I think 3.11.1 can be solved with a bit of luck and intuition. A fewest moves solve is going to require insight. I love the imagebased menu too! Thanks Gelatinbrain! Edit: I have only seen this happen on the 3x3x3x3 cube (any N^4 tesseract actually): Attachment:
damn_parity.png [ 44.24 KiB  Viewed 6071 times ]
I don't have any idea how to handle this case just yet... Gelatinbrain, you're an evil genius Edit 2: If you twist the top face in the above parity by 1 quarter turn and then resolve the face it does change the parity. I'm certain the parity can eventually be fixed in this way. The number of quarter turns required is going to take some more analysis. Edit 3: I have figured out how to fix the above parity with a strange X, Y, Xmirror Y' routine. This sequence shouldn't do anything but it does. On a regular 2x2x2 this Y routine is a nooperation. On this puzzle it is magical. Using this fix I solved it in 108 moves. With a better understanding of the puzzle I'm sure it can be solved in 40 or so since I was able to solve the first 4 spheres in 10 moves.
_________________ Prior to using my real name I posted under the account named bmenrigh.
Last edited by Brandon Enright on Tue Oct 12, 2010 2:16 am, edited 1 time in total.


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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Oct 12, 2010 1:38 am 

Joined: Thu May 31, 2007 7:13 pm Location: Bruxelles, Belgium

schuma wrote: I just found two new puzzles that GB had recently added: 3.11.1 and 3.11.1b. I wonder if they are inspired by any puzzle in the real world. I've never seen such things. I'm sure you will beat them quite soon. This puzzle is not inspired by any existing puzzle(except 2x2x2) but not purely conceptual either. There are analogues in the nature. E.g. ,planets or electrons(as Brandon pointed) spinning on itself while rorating around a common axis. How many possible patterns this puzzle have? I'm not very good at this kind of calculation. Each ball has 12x8 orientation, compared with 3x8 of a 2x2x2 corner. So far, that's what I know...
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Jared

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Oct 12, 2010 1:50 am 

Joined: Mon Aug 18, 2008 10:16 pm Location: Somewhere Else

Gelatinbrain, if you're going to make puzzles based on grids of spheres, do you think you could make a 3D analogue to the Cmetrick/Cmetrick Junior puzzle?


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Oct 12, 2010 2:41 am 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

Single rotated sphere of 3.11.1 bmenrigh wrote: I have only seen this happen on the 3x3x3x3 cube (any N^4 tesseract actually). I have figured out how to fix the above parity with a strange X, Y, Xmirror Y' routine. This sequence shouldn't do anything but it does. On a regular 2x2x2 this Y routine is a nooperation. On this puzzle it is magical. A similar thing happens with the Trajber's Octahedron (4.2.1), where you can have the puzzle completely solved except for one corner. Because each move of 3.11.1 involves an even number of 90 degree rotations, and any reorientation of the whole puzzle is an even number of rotations, I'm fairly sure that whenever there is only one sphere left to solve, it must be an even number of 90 degree rotations from solved. So I don't think we would ever see a single sphere just 90 degrees away from solved.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Oct 12, 2010 2:45 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: Single rotated sphere of 3.11.1 bmenrigh wrote: I have only seen this happen on the 3x3x3x3 cube (any N^4 tesseract actually). I have figured out how to fix the above parity with a strange X, Y, Xmirror Y' routine. This sequence shouldn't do anything but it does. On a regular 2x2x2 this Y routine is a nooperation. On this puzzle it is magical. A similar thing happens with the Trajber's Octahedron (4.2.1), where you can have the puzzle completely solved except for one corner. Because each move of 3.11.1 involves an even number of 90 degree rotations, and any reorientation of the whole puzzle is an even number of rotations, I'm fairly sure that whenever there is only one sphere left to solve, it must be an even number of 90 degree rotations from solved. So I don't think we would ever see a single sphere just 90 degrees away from solved. Yeah I came to the same conclusion while solving them. The last sphere is restricted to just 180 degree rotation about one of the 3 axis. I'm trying to get my move count down on 3.11.1b right now. I'm starting to get a better intuition about these puzzles Edit: it seems it can have the 180 degree parity in more than one axis based on the solve I just did. Maybe I'm too blearyeyed tired to understand the puzzle right now... Edit again: scratch that, it was 90 degrees in 2 different axes. My parity fix can only handle 180 degrees in one axis. I'll have to play with this some more tomorrow.
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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Oct 12, 2010 6:49 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

3.11.1  a tough puzzle! I finally did a first solve in 50 moves. I don't know how lucky I was and if there are significant gaps in my method, but here it is in outline:
1. Solve 4 adjacent spheres (around a face) using a mixture of intuition, observation, and trial and error.
2. Permute the remaining 4 spheres to valid positions, so that each sphere is an even number of 90 degree rotations from solved.
3. Using a slightly modified Rubik's last layer edge ('A') perm of 10 moves that does yz' and y'z to UFR and DFR, and another algo of 8 moves that I found using a Rubik's cube that does xz and xy, get the spheres so they are all either solved or 180 degrees from solved.
4. Using (1,1) commutators to do y2 to two spheres or z2 to one and x2 to another, complete the solve.
5. If you reach one unsolved sphere twisted 180 degrees, this can be fixed in 12 moves: y2 to two spheres in 4 moves, then 2 setup moves to push the twisted sphere to a different adjacent position, then the double y2 algo again (in the new, rotated position) and finally undo the 2 setup moves.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Wed Oct 13, 2010 8:55 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: 3.11.1  a tough puzzle! I finally did a first solve in 50 moves. I gave it another go and this time I got all the way to a single sphere with a 90 degree twist in two different axes in only 21 moves . Unfortunately I tried a few sequences to fix it. When they didn't work I undid and eventually I lost my spot. I was able to get back but it cost me moves. I finally solved it in 53 which is frustrating. I'm sure I can solve it in 35 moves with a bit more experimentation. I bet you could do 30 if you were careful. Edit; just got a 41 move solve in 1:40 The solve didn't submit though so I have a certificate that I'll email to Gelatinbrain. With a bit of luck this puzzle can be done in under 30 moves. With a lot of luck it could be done in under 20.
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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 1:22 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

I'm more comfortable with this puzzle now so I understand your solution outline well enough to comment. Julian wrote: 3.11.1  a tough puzzle! I finally did a first solve in 50 moves. I don't know how lucky I was and if there are significant gaps in my method, but here it is in outline:
1. Solve 4 adjacent spheres (around a face) using a mixture of intuition, observation, and trial and error. I do the same. I can usually get 4 spheres solved in a face in less than 10 moves. Julian wrote: 2. Permute the remaining 4 spheres to valid positions, so that each sphere is an even number of 90 degree rotations from solved. I don't understand why this step is needed. Are you trying to reduce the number of times you have to apply step 3? I have been twisting this face until one of the remaining spheres is solved. If it isn't solved, usually I can twist it around until two adjacent spheres can both be solved is a single step sequence in step 3. Julian wrote: 3. Using a slightly modified Rubik's last layer edge ('A') perm of 10 moves that does yz' and y'z to UFR and DFR, and another algo of 8 moves that I found using a Rubik's cube that does xz and xy, get the spheres so they are all either solved or 180 degrees from solved. If you apply Sune you can do a y'z and y'x' in 8 moves. There is a ((1,1),1) sequence that will do y'z' in both spheres. The more sequences we have for this step the easier it is to shave off moves in the solve. Julian wrote: 4. Using (1,1) commutators to do y2 to two spheres or z2 to one and x2 to another, complete the solve. I combine step 3 and 4 into one step. I think we have the same sequences for this step. Very useful and only 4 moves! Julian wrote: 5. If you reach one unsolved sphere twisted 180 degrees, this can be fixed in 12 moves: y2 to two spheres in 4 moves, then 2 setup moves to push the twisted sphere to a different adjacent position, then the double y2 algo again (in the new, rotated position) and finally undo the 2 setup moves. I found this too but then I realized you only need 1 setup move. The whole sequence can be done in 10 moves. By changing the orientation on the puzzle before you start you can put the 180 degree twist into any axis. Unfortunately you can wind up with a single sphere twisted 90 degrees in two different axes. I don't know how to solve this case cleanly. I have to go back to steps 3 and 4 to resolve it. I've played with different setup moves for the 180 degree twist to get 90 in two axes but I haven't had any luck. Earlier when I was going for fewest moves I just started over when I ended up with this situation.
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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 1:47 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

gelatinbrain wrote: How many possible patterns this puzzle have? I'm not very good at this kind of calculation. Each ball has 12x8 orientation, compared with 3x8 of a 2x2x2 corner. So far, that's what I know... EDIT: These calculations are WRONG. There are only 12 possible orientations but more orientations are available when the permutation of the puzzle is odd. Calculating the possibilities seems quite hard.For 1.11.1 Each sphere can be in 24 orientations, the orientation of the last sphere is restricted to only 12 orientations, and the overall orientation of the puzzle (24) doesn't matter. That brings us to 24^6 * 12 = 2,293,235,712 total unique states. That's more than 624 times the number of states in a normal 2x2x2 Rubik's cube. For 1.11.1b there are 8 spheres to be arranged for 8! total permutations. The rest of the calculation is the same. That comes to 8! * 24^6 * 12 = 92,463,263,907,840 That's more than 25,000 times the number of states in a normal 2x2x2 Rubik's cube. I'm a bit shaky about this 1.11.1b calculation though because the freedom of twists available might be tied to the parity of permutation. The calculation might need to take into account a small factor of unreachable twists because each sphere is unique so it's obvious when they switch places.
_________________ Prior to using my real name I posted under the account named bmenrigh.
Last edited by Brandon Enright on Thu Oct 14, 2010 3:11 pm, edited 1 time in total.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 1:17 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

gelatinbrain wrote: schuma wrote: I just found two new puzzles that GB had recently added: 3.11.1 and 3.11.1b. I wonder if they are inspired by any puzzle in the real world. I've never seen such things. I'm sure you will beat them quite soon. This puzzle is not inspired by any existing puzzle(except 2x2x2) but not purely conceptual either. There are analogues in the nature. E.g. ,planets or electrons(as Brandon pointed) spinning on itself while rorating around a common axis. I like the "optical" nature of the color scheme too! gelatinbrain wrote: How many possible patterns this puzzle have? I'm not very good at this kind of calculation. Each ball has 12x8 orientation, compared with 3x8 of a 2x2x2 corner. So far, that's what I know... That's the way I see them too. To make things simple, I first assume that each puzzle is in a fixed cage and that we only consider visually unique patterns from a fixed orientation/viewpoint. With 3.11.1b there are 12^8 orientations and 8! permutations because the spheres are unique and so their permutation does matter. If we want to count only unique patterns when viewing 3.11.1b from any one of the 12 even orientations, we can just divide by 12 to give 12^8 * 8! / 12 = 1,444,738,498,560. [Edit: Thanks to Brandon for pointing out an error in my original calculation.] With 3.11.1 we have two problems making the calculation trickier: 1. The permutation does matter even though the spheres are identical in appearance. They come in two groups of 4 spheres each, like the orbitals of the corners of a Skewb. Each sphere can reach 12 orientations when it is in one orbital and the other 12 orientations when it is in the other orbital. So we need to consider the distinct ways in which "even" and "odd" spheres are distributed. I believe there are 8! / (4! * 4!) possible permutations of the two types of sphere. 2. Because the pieces are all identical, we cannot assume that we have counted every unique pattern 12 times too often, and if we simply divide by 12 we will be undercounting. So if a pattern is unique from every orientation we count it once, if it looks the same from 2 orientations we count it twice, and so on, and then we can take that total and divide by 12 to give the answer. Ignoring the second factor gives us: (12^8 * 8!) / (4! * 4! * 12) = 2,508,226,560. As this is a slight undercount, I'll just say that I think there are approximately 2.5 billion possible patterns for 3.11.1.
Last edited by Julian on Thu Oct 14, 2010 4:01 pm, edited 3 times in total.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 1:52 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

bmenrigh wrote: Julian wrote: 2. Permute the remaining 4 spheres to valid positions, so that each sphere is an even number of 90 degree rotations from solved. I don't understand why this step is needed. Edit: I think the spheres can be considered as having "odd" and "even" positions. I'll illustrate in another post. bmenrigh wrote: If you apply Sune you can do a y'z and y'x' in 8 moves. Good find! bmenrigh wrote: The more sequences we have for this step the easier it is to shave off moves in the solve. Very true. I'll try and build up a decent collection over the next several days then I'll post it. bmenrigh wrote: Julian wrote: 5. If you reach one unsolved sphere twisted 180 degrees, this can be fixed in 12 moves: y2 to two spheres in 4 moves, then 2 setup moves to push the twisted sphere to a different adjacent position, then the double y2 algo again (in the new, rotated position) and finally undo the 2 setup moves. I found this too but then I realized you only need 1 setup move. The whole sequence can be done in 10 moves. By changing the orientation on the puzzle before you start you can put the 180 degree twist into any axis. I like! I didn't think about 360 degree moves as possible setups. bmenrigh wrote: Unfortunately you can wind up with a single sphere twisted 90 degrees in two different axes. I don't know how to solve this case cleanly. I have to go back to steps 3 and 4 to resolve it. I've played with different setup moves for the 180 degree twist to get 90 in two axes but I haven't had any luck. Earlier when I was going for fewest moves I just started over when I ended up with this situation. True; it turned out that I was lucky with my first solve. I don't see any way of visualizing it in advance, due to the complexity of the puzzle. One minute you're puzzling, the next, you have a single sphere twisted in two axes. Maybe the solution will be a quick algo that affects 3 spheres, solving the one and leaving the other 2 in an easily solvable position? If I find anything I'll post it here.
Last edited by Julian on Thu Oct 14, 2010 2:42 pm, edited 1 time in total.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 1:55 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: That's the way I see them too. To make things simple, I first assume that each puzzle is in a fixed cage and that we only consider visually unique patterns from a fixed orientation/viewpoint. With 3.11.1 there are 12^8 such patterns  because each sphere is identical, the permutation is irrelevant, it only matters which one of the 12 even orientations each sphere is in. With 3.11.1b we need to multiply this by 7! because the spheres are unique and so their permutation does matter (not 8! because the position of the last sphere is determined by the other 7).
If we want to count only unique patterns when viewing 3.11.1b from any one of the 12 even orientations, we can just divide by 12 to give 12^8 * 7! / 12 = 180,592,231,230. Hi Julian, please excuse me if I'm being dumb but I'm pretty sure each sphere except the last has 24 orientations available to it. See: Attachment:
1.11.1_quarter_turn.png [ 62.29 KiB  Viewed 5764 times ]
If you can twist a sphere by only 90 degrees in only 1 axis while only affecting one other sphere doesn't that mean that all but the last sphere can be in 24 possible orientations? That's how I got (24^7 * 12) / 24. Regarding your 1.11.1b calculation, I think you are accounting for the orientation of the puzzle twice. The 8th sphere that is uniquely defined by the previous 7 can be thought of uniquely defining part of the orientation of the puzzle. This is how Jaap does his 2x2x2 calculation.
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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 3:06 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

bmenrigh wrote: If you can twist a sphere by only 90 degrees in only 1 axis while only affecting one other sphere doesn't that mean that all but the last sphere can be in 24 possible orientations? I think it shows that the spheres must have swapped places  I've remembered why my solution has a stage 2. If you don't swap those spheres back, you will never be able to solve them. One is 1 quarter turn from solved, the other is 3 quarter turns from solved. 1 or 3 turns = wrong position; 0 or 2 turns = right position. The corners of 3.1.11 come in the same orbitals as the two sets of corners of a Skewb. The spheres have to be in the orbital they started in to be solved, and wherever they are, they can only be in one of 12 orientations. But of course talking about this makes me realize that the permutation of the spheres of 3.1.11 does matter! Ach, these are complicated puzzles... bmenrigh wrote: Regarding your 1.11.1b calculation, I think you are accounting for the orientation of the puzzle twice. The 8th sphere that is uniquely defined by the previous 7 can be thought of uniquely defining part of the orientation of the puzzle. This is how Jaap does his 2x2x2 calculation. Of course you're right. My total was 8 times too low. I think it's correct to divide by 12 instead of 24, because we won't get any new patterns with odd reorientations. Similarly to the Skewb, if we do a 90 degree rotation we're merely looking at a position that could never be reached except with such a reorientation, due to the orbitals the corners are in.


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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 6:00 pm 

Joined: Tue Feb 16, 2010 12:15 pm Location: Sandnes, Norway

1.4.2  solved Attachment:
Skjermbilde 20101015 kl. 00.33.41.png [ 74.13 KiB  Viewed 5740 times ]
This was a real pain to solve, mostly because it took a lot more time than I originally thought. As for my method; I hardly think it's worth giving a detailed outline, but here's a summary: 1.) Solve centers  no commutators 2.) Solve edges  one commutator: (BC, AC, AB, AC, BC, AC, AB, AC) x2 3.) Solve triangle pieces  one commutator: HG, BH, HG, BH, CD, BH, HG, BH, HG, CD, I may resolve this puzzle sometime, so I'll welcome any suggestions and pointers from those with better move counts (which is basically everyone )


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 6:39 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

3.11.1  Twisting a single corner in two axes. The following sequence twists the FUR sphere xz with a harmless side effect that it also swaps places with BDR, which does not change orientation: U'3,R'3,F'3,R3,F3,U3,R'3, /* Rubik's edge flipping algo with 270 degree turns  twists 3 corners */ D,R,D',R,D,R'2,D',R'2, /* Sune to solve one corner and leave the other two twisted in one axis */ U'4, /* Setup move */ R'4,F4,R4,F'4, /* (1,1) for twisting two corners y2 y2 */ U4, /* Undo move */ 21 moves is too long for my taste, but I submit it as an opening bid. Ideally I'm looking for a <10 move algo to twist 3 spheres, fixing the single corner and leaving a pair that solve easily.


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Elwyn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Oct 14, 2010 6:50 pm 

Joined: Tue Sep 08, 2009 8:41 am Location: The Blue Mountains, Australia

Katten wrote: I may resolve this puzzle sometime, so I'll welcome any suggestions and pointers from those with better move counts (which is basically everyone ) Haven't solved it yet but i have a method. I would solve edges before centres with intuition and a (1,1) commutator then centres dirty (3,1) then thin triangles (3,1) CD, HG, CD, AB, DC, GH, DC, AB, I looked at this puzzle a long time ago but never actually solved it but i'd say this method could beat the FM record by around 100 if enough effort was put in.
_________________ Some PBs 3x3x3 :20.7 seconds, 5x5x5 2:33, gigaminx 16:40, 7x7x7 9:48, pyraminx crystal 3:42


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 15, 2010 3:47 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: 3.11.1  Twisting a single corner in two axes. The following sequence twists the FUR sphere xz with a harmless side effect that it also swaps places with BDR, which does not change orientation: U'3,R'3,F'3,R3,F3,U3,R'3, /* Rubik's edge flipping algo with 270 degree turns  twists 3 corners */ D,R,D',R,D,R'2,D',R'2, /* Sune to solve one corner and leave the other two twisted in one axis */ U'4, /* Setup move */ R'4,F4,R4,F'4, /* (1,1) for twisting two corners y2 y2 */ U4, /* Undo move */ 21 moves is too long for my taste, but I submit it as an opening bid. Ideally I'm looking for a <10 move algo to twist 3 spheres, fixing the single corner and leaving a pair that solve easily. This is complicated, thanks for breaking it down! I made what I hope is a useful observation. If you twist the top face 180 degrees and then resolve 3 of the spheres without allowing them to change places you end up with one sphere with twists in two axes. Using that trick, this sequence is a bit shorter: R2, /* move the top */ B', /* setup */ [R',B',R],F'4,[R',B,R],F4, /* twist two adjacent spheres in two axes (solves one sphere) */ B, /* undo */ [R',U',R],D'4,[R',U,R],D4 /* twist the remaining two adjacent spheres in two axes (solves both) */ It's 19 moves which is still too long. Perhaps the R2 trick will help you? Also, I'm in the process of building up a repertoire of sequences to handle various twist of two adjacent spheres. I'll post them this weekend.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 15, 2010 2:50 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

bmenrigh wrote: I made what I hope is a useful observation. If you twist the top face 180 degrees and then resolve 3 of the spheres without allowing them to change places you end up with one sphere with twists in two axes. Using that trick, this sequence is a bit shorter:
R2, /* move the top */
B', /* setup */ [R',B',R],F'4,[R',B,R],F4, /* twist two adjacent spheres in two axes (solves one sphere) */ B, /* undo */
[R',U',R],D'4,[R',U,R],D4 /* twist the remaining two adjacent spheres in two axes (solves both) */
It's 19 moves which is still too long. Perhaps the R2 trick will help you? This occurred to me on the train ride to work this morning. I was thinking about the fact that it doesn't matter if we swap pairs of 3.11.1 spheres around a face provided they are diagonally apart from each other, then I thought, "Hey, what about making a 180 turn and proceeding from there?" Then I laughed because I realized there was a high probability that you had already thought about the same thing, found a shorter algo, and would post it before my lunchtime. And so it proved! I just got lucky though; I tried something else on impulse and it worked. I tried the first part of a Rubik's commutator to twist two corners: R' D R F D F', and followed it with a D' twist to leave only two corners swapped with each other. Then I thought, "What would happen if I flipped the puzzle upside down around the FR edge and made the same 7 moves again?" The answer is exactly the fix we want, which does not permute any spheres so is useful for both 3.11.1 and 3.11.1b. Twisting the FUR sphere x'z' by itself: F',U,F,R,U,R',U', B',R,B,U,R,U',R' 14 moves Attachment:
GB 3111b single corner twist in two axes.jpg [ 75.17 KiB  Viewed 5645 times ]
Last edited by Julian on Fri Oct 15, 2010 3:06 pm, edited 1 time in total.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 15, 2010 3:03 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: :D This occurred to me on the train ride to work this morning. I was thinking about the fact that it doesn't matter if we swap pairs of 3.11.1 spheres around a face provided they are diagonally apart from each other, then I thought, "Hey, what about making a 180 turn and proceeding from there?" Then I laughed because I realized there was a high probability that you had already thought about the same thing, found a shorter algo, and would post it before my lunchtime. And so it proved!
I just got lucky though; I tried something else on impulse and it worked. I tried the first part of a Rubik's commutator to twist two corners: R' D R F D F', and followed it with a D' twist to leave only two corners swapped with each other. Then I thought, "What would happen if I flipped the puzzle upside down around the FR edge and made the same 7 moves again?" The answer is exactly the fix we want, which does not permute any spheres so is useful for both 3.11.1 and 3.11.1b. Twisting the FUR sphere x'z' by itself:
F',U,F,R,U,R',U', B',R,B,U,R,U',R'
14 moves Great job, beautiful routine! It was bugging me this morning that both our proposed fixes wouldn't work on 1.11.1b which limits usefulness. It kills me that you started with R' D R F D F' because I tried dozens of variants of that commutator last night with no luck. Your sequence makes complete sense. I'm glad you spotted it . 14 is really short. I want to digest this some more and then see if I can come up with a shorter sequence that will work with this puzzle flipping idea  if you don't beat me to it .
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 15, 2010 5:21 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

1.4.2 Elwyn wrote: Katten wrote: I may resolve this puzzle sometime, so I'll welcome any suggestions and pointers from those with better move counts (which is basically everyone ) Haven't solved it yet but i have a method. I would solve edges before centres with intuition and a (1,1) commutator then centres dirty (3,1) then thin triangles (3,1) CD, HG, CD, AB, DC, GH, DC, AB, I looked at this puzzle a long time ago but never actually solved it but i'd say this method could beat the FM record by around 100 if enough effort was put in. That's the way I solved it. I thought I did a good job until Michael solved it 110 moves faster, and it is humbling that you reckon you could beat even Michael's solve by a good margin! I found the setups tricky with this one.


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Elwyn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 15, 2010 7:43 pm 

Joined: Tue Sep 08, 2009 8:41 am Location: The Blue Mountains, Australia

Julian wrote: That's the way I solved it. I thought I did a good job until Michael solved it 110 moves faster, and it is humbling that you reckon you could beat even Michael's solve by a good margin! I found the setups tricky with this one. Oh, that makes me think perhaps i was being rather optimistic hahaha. I'll probably have to use a lot more moves as setup moves than i thought, i suppose i won't know till i solve it.
_________________ Some PBs 3x3x3 :20.7 seconds, 5x5x5 2:33, gigaminx 16:40, 7x7x7 9:48, pyraminx crystal 3:42


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Oct 15, 2010 7:49 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Elwyn wrote: Julian wrote: That's the way I solved it. I thought I did a good job until Michael solved it 110 moves faster, and it is humbling that you reckon you could beat even Michael's solve by a good margin! I found the setups tricky with this one. Oh, that makes me think perhaps i was being rather optimistic hahaha. I'll probably have to use a lot more moves as setup moves than i thought, i suppose i won't know till i solve it. I used very close to the same technique that you propose and Julian used. I was expecting the puzzle to take me an hour but the setups were brutal. I really struggled to use setups that would put the edges in place with the correct orientation. I'm sure you'll do great but I think the puzzle is deceptively hard.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Elwyn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 12:27 am 

Joined: Tue Sep 08, 2009 8:41 am Location: The Blue Mountains, Australia

bmenrigh wrote: I used very close to the same technique that you propose and Julian used. I was expecting the puzzle to take me an hour but the setups were brutal. I really struggled to use setups that would put the edges in place with the correct orientation. I'm sure you'll do great but I think the puzzle is deceptively hard. Yes the setups for the edges were a little odd but orientation was by far the easiest part, they are far enough away (at least with my commutator) that you just twist the individual edge if it is wrong, i now have 470 moves to cycle 55 triangles with a (3,1) alg i have never used before... i actually don't know how this will turn out with these stupid setup moves. Attachment:
1.4.2 after steps 1 and 2.jpg [ 130.08 KiB  Viewed 7034 times ]
Attachment:
1.4.2.jpg [ 115.24 KiB  Viewed 7029 times ]
Two hours and another 340 moves later and i beat Michaels record by 130 moves, turns out i wasn't being optimistic with my guess of beating it by 100 Julian wrote: That's the way I solved it. I thought I did a good job until Michael solved it 110 moves faster, and it is humbling that you reckon you could beat even Michael's solve by a good margin! I found the setups tricky with this one. I'm not going to lie, set up moves on this thing are horrendous, far harder than i expected, but it's very nice to know i wasn't being over confident for my move count estimate.
_________________ Some PBs 3x3x3 :20.7 seconds, 5x5x5 2:33, gigaminx 16:40, 7x7x7 9:48, pyraminx crystal 3:42
Last edited by Elwyn on Sat Oct 16, 2010 2:35 am, edited 1 time in total.


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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 2:34 am 

Joined: Tue Feb 16, 2010 12:15 pm Location: Sandnes, Norway

bmenrigh wrote: I was expecting the puzzle to take me an hour but the setups were brutal. I really struggled to use setups that would put the edges in place with the correct orientation. I'm sure you'll do great but I think the puzzle is deceptively hard. Brandon, I absolutely agree with what you're saying. My last 3cycle, I had to use about 15 setup moves. And I assumed that it would be a relatively quick solve, but yet I spent over 3 hours solving it. That surprised me a lot. As for my move count: I could easily have gotten it sub2000 if I weren't so sloppy. I basically just threw away moves by not undoing unnecessary moves. Elwyn, good job on getting so far using so few moves! I'll be excited to see what you're final move count will be. EDIT: you just edited your post with your completed solve, haha. Good job on beating the record! Second edit: I didn't have any trouble with the orientation of the edges: I did exactly what Elwyn did here and it worked fine. The issue was the other setup moves. Maybe because I insisted on not writing any of them down and also because they were hard in general. But it made me feel better that I'm not the only one who experienced that.
Last edited by Katja on Sun Oct 17, 2010 4:30 am, edited 1 time in total.


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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 5:14 pm 

Joined: Tue Feb 16, 2010 12:15 pm Location: Sandnes, Norway

I decided to give 1.1.19 a second try tonight, and just as last time: I got stuck with the same situation I didn't manage to solve before: Attachment:
Skjermbilde 20101017 kl. 00.08.24.png [ 268.64 KiB  Viewed 7004 times ]
This time though, I was more optimistic about finding a solution to the problem. Until I accidentally hit the "go back one page" button! Arg, now I've lost my motivation to try for a third time. I'm only 4 puzzles away from getting my name on the leader board, so I though 4 challenging puzzles would be most fitting. Maybe this just has to wait. This puzzle really hates me, I'm sure


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 5:16 pm 

Joined: Sun Aug 29, 2010 1:56 pm

Gelatinbrain: I find your "rolling spheres cubes" beautifull. The spheres have 12 orientations. That is new and it is a real challange to solve the puzzle. There is one thing I dont understand. Maybe you can help me. How do the spheres change orientation, when I do one move. Is it like they would roll physically on the outline of a circle? I tried to get the ball at the uprightfore location into other orientations and found that I can only get 11 other orientations. 6 cases I reached by one move, 2 cases I reached by 3 moves and 3 cases I reached by 4 moves. With reversing the moves with an other ball it is possible to solve the puzzle all but one ball, and never need more than 6 moves for one ball. For the last ball I use 8, 13 or 15 moves. Some cases of two remaining balls I can solve at once. When solving the ball before the last ball it might be possible, to get the last ball into a good case or solve it even. But two balls make a lot of possibilities. I also wonder, if an U6 move for instance can be counted as one move. In the half turn metric a doublemove is counted as one move, because it performs in time nearly as a single move. Now can you say that about a move that is repeated 6 times? The answer is clearly not. I have read all the recent posts about this puzzle from Brandon and Julian. I guess they are on the same level than me. Stefan.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 6:04 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Katten wrote: I decided to give 1.1.19 a second try tonight, and just as last time: I got stuck with the same situation I didn't manage to solve before: [...snip...] This time though, I was more optimistic about finding a solution to the problem. Until I accidentally hit the "go back one page" button! Arg, now I've lost my motivation to try for a third time. I'm only 4 puzzles away from getting my name on the leader board, so I though 4 challenging puzzles would be most fitting. Maybe this just has to wait. This puzzle really hates me, I'm sure It hurts to put a bunch of time into a puzzle and then lose the progress. As was said before, that isn't any sort of parity case and just requires you to swap two identically colored triangles in a threecycle. Here is a 16move fix for that case: /* Setup first triangle */ F2, /* Setup second triangle */ [H'2&2,K',D2], /* Perform (3,1) commutator */ [F&2,A',F'&2],K&2,[F&2,A,F'&2],K'&2, /* Undo second triangle setups */ [D'2,K,H2&2], /* Undo first triangle setups */ F'2The heart of the routine is the 3cycle [F&2,A',F'&2],K&2,[F&2,A,F'&2],K'&2. The setups just move the right pieces into place so that we get orange 1> orange2 > red1 > orange1.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 7:12 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: Stefan Schwalbe wrote: The spheres have 12 orientations. That is new and it is a real challange to solve the puzzle. There is one thing I dont understand. Maybe you can help me. How do the spheres change orientation, when I do one move. Is it like they would roll physically on the outline of a circle? [...] With each 90 degree move, each ball first rotates 90 degrees as if being "pushed" by the ball "behind" it (about to take its position); then each ball rotates 180 degrees in the same axis as the move. So when you make a U move, each sphere finishes with y2: UFR moves to UFL and spins x'y2; UFL moves to UBL and spins z'y2; UBL moves to UBR and spins xy2; and UBR moves to UFR and spins zy2. I have been imagining a gearing mechanism on the spheres where there is a floating point above the center of the face I'm about to turn and 4 axles descend from that point down through the diagonal of each for the 4 spheres about the face. Then I can look at a face and see how each of the spheres will turn without thought but mechanical intuition. Stefan, you said you have a 8move sequence to solve for the last sphere? I've only been able to find a 10 move sequence. I got a special case of Julian's 14 move routine down to 13 moves. I'm working on screenshots for these cases for a post I hope to do tomorrow. Stefan's low move counts motivated me to try harder. It hasn't hit the scoreboard yet but I got a 17 move solve . Edit: fixed to properly quote Julian.
_________________ Prior to using my real name I posted under the account named bmenrigh.
Last edited by Brandon Enright on Sat Oct 16, 2010 7:21 pm, edited 2 times in total.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 7:16 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

Edit: Brandon, I immediately deleted my post because I realized it had an important mistake in it and I wanted to avoid confusing anyone with incorrect info. My corrected response is below... Stefan Schwalbe wrote: The spheres have 12 orientations. That is new and it is a real challange to solve the puzzle. There is one thing I dont understand. Maybe you can help me. How do the spheres change orientation, when I do one move. Is it like they would roll physically on the outline of a circle? Hi Stefan. I noticed yesterday that you have joined the cubespheres party! Very low move counts from you. If it helps, here is the way I see the way the spheres rotate: With each 90 degree move, each ball first rotates 90 degrees as if being "pushed" by the ball "behind" it (about to take its position); then each ball rotates 180 degrees in the same axis as the move. So when you make a U move, each sphere finishes with y2: UFR moves to UFL and spins x'y2; UFL moves to UBL and spins z'y2; UBL moves to UBR and spins xy2; and UBR moves to UFR and spins zy2. That's why each ball can only be in one of 12 orientations wherever it is, because it has always rotated through an even number of quarter moves if it is in the same Skewb corner orbital that it started, and it has always rotated through an odd number of quarter moves if it is in the different Skewb orbital.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Oct 16, 2010 7:38 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

3.11.1 state counting attempt 2:
There are 8 spheres divided into 2 groups of 4. Spheres in each group are indistinguishable but the orientation of a sphere reveals which group it is in. Therefore, there are 8! / (4! * 4!) ways to order the spheres.
Each sphere can be in 12 different orientations independently of all other spheres. This allows for 12^8 possible orientations.
The overall orientation of the puzzle doesn't matter which reduces the number of possibilities by 24.
That results in (8! * 12^8) / (4! * 4! * 24) == 1,254,113,280 possible positions.
The reason the orientation of the puzzle is a factor of 24 rather than 12 is that you could solve the puzzle into a state where all of the even spheres and odd spheres have swapped position. You wouldn't know this and each sphere would have a quarterturn in the same axis.
_________________ Prior to using my real name I posted under the account named bmenrigh.
Last edited by Brandon Enright on Mon Oct 18, 2010 12:23 am, edited 1 time in total.


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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 4:36 am 

Joined: Tue Feb 16, 2010 12:15 pm Location: Sandnes, Norway

bmenrigh wrote: The heart of the routine is the 3cycle [F&2,A',F'&2],K&2,[F&2,A,F'&2],K'&2. The setups just move the right pieces into place so that we get orange 1> orange2 > red1 > orange1. Brandon, that's such an easy fix! I cannot believe I didn't figure this out by myself I was really frying my brain with a fix for it last night and this crossed my mind, but I didn't find the right way to execute it. Anyways, thanks a lot for sharing; tonight this puzzle is going down!


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 12:40 pm 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

bmenrigh wrote: 1.11.1 state counting attempt 2: Psst... it's 3.11.1. bmenrigh wrote: That results in (8! * 12^8) / (4! * 4! * 24) == 1,254,113,280 possible positions.
The reason the orientation of the puzzle is a factor of 24 rather than 12 is that you could solve the puzzle into a state where all of the even spheres and odd spheres have swapped position. You wouldn't know this and each sphere would have a quarterturn in the same axis. Of course! Thank you; now I have seen the light. This is the closest answer yet. It is a slight undercount though, because some scrambles look the same from different orientations. For example, if you spin FUR, FDR, BUL, BDL all y2, then the puzzle looks exactly the same from 2 different orientations, so you would need to count this state twice before dividing by 24. This is a pesky situation that doesn't come up often  identical pieces with distinct orientations. I don't know how many rotationally symmetric states there are with this puzzle. It could well be a trivial number compared to the scale of 1.25 billion, and not enough to push the exact result up to 1.26 billion to 3 sig figs. P.S. 17 moves?!


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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 1:54 pm 

Joined: Thu May 31, 2007 7:13 pm Location: Bruxelles, Belgium

Stefan Schwalbe wrote: There is one thing I dont understand. Maybe you can help me. How do the spheres change orientation, when I do one move. Is it like they would roll physically on the outline of a circle? The amazing thing is you solved it nevertheless,and even broke the record. Maybe the animation is not smooth enough or too fast to follow the movement. The balls rotate simulatniously around itself and a common center. Just like the earth turning around the sun or the teacups in an attraction park. The axis of selfrotation is the line connecting the center of each ball and the face center of the circumscribing cube. The balls spin 120Âº while turning 90Âº around the common axis so that they settle down in their original orientation after 3 rounds. In fact the resulting orientation is as same as Julian explained. Katja, thank you for help links. Be careful to do not click "go back". The area outside the gray rectangle is the browser's territory. The applet cannot show a warning for clicks outside its own area. Check new puzzles: 3.1.27 ~ 3.1.30 & 3.2.11(TomZ's "Compy Skewb" compatible, I think...)
_________________ Virtual Magic Polyhedra Applet(Online) Executable Jar Installer Win32 Executable(Download) troubleshooting


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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 2:08 pm 

Joined: Tue Feb 16, 2010 12:15 pm Location: Sandnes, Norway

gelatinbrain wrote: Be careful to do not click "go back". The area outside the gray rectangle is the browser's territory. The applet cannot show a warning for clicks outside its own area. Yes, I blame only myself for that happening. I was really tired and didn't pay attention to where the pointer was before I pressed the button and then it was too late. gelatinbrain wrote: 3.2.11(TomZ's "Compy Skewb" compatible, I think...) I'd say yes, except for one thing: when you do a Dino Cube rotation, the corners won't move. Check out Tom's video. As for the other new puzzles: they look like hard puzzles!


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TomZ

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 3:09 pm 

Joined: Fri Feb 08, 2008 1:47 am Location: near Utrecht, Netherlands

On my Compy Skewb, there are tips that are fixed to the inner skewb. When you make a skewb rotation they rotate with it, but they're stationary when you do a compy/dino move. The tips show the orientation of the internal skewb corner, making the puzzle yet a little harder. Maybe you could include the puzzle's name under it? Or have you stopped doing that? I remember that for instance, the megaminx was properly labeled (the nxnxn cubes still bear labels). If that's not the case, a link would be really, really nice
_________________ Tom's Shapeways Puzzle Shop  your order from my shop includes free stickers! Tom's Puzzle Website
Buy my mass produced puzzles at Mefferts:  4x4x6 Cuboid for just $38  Curvy Copter for just $18  3x4x5 Cuboid for just $34


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 3:40 pm 

Joined: Sun Aug 29, 2010 1:56 pm

Thank you for explaining the 3.11.1 spheres behavior to me. Now I understand. I admire the new puzzles (3.1.27 ~ 3.1.30 ). Another new idea. The circle pieces turn 45 deg while the other pieces turn 90 deg. Dont know how to solve it. Maybe I find some time for it.
Last edited by Stefn on Sun Oct 24, 2010 2:53 pm, edited 1 time in total.


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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Oct 17, 2010 5:32 pm 

Joined: Thu May 31, 2007 7:13 pm Location: Bruxelles, Belgium

TomZ wrote: On my Compy Skewb, there are tips that are fixed to the inner skewb. When you make a skewb rotation they rotate with it, but they're stationary when you do a compy/dino move. The tips show the orientation of the internal skewb corner, making the puzzle yet a little harder. Maybe you could include the puzzle's name under it? Or have you stopped doing that? I remember that for instance, the megaminx was properly labeled (the nxnxn cubes still bear labels). If that's not the case, a link would be really, really nice So, tips are not trivial as I thought. Then this oneshould come close. I stripped names of puzzles for two reasons First, I thought it's better to avoid using possible trademarks or something of that sort. No complaint so far,just for a precaution. Second reason is that personally I don't like those arbitrary names like brabrabraminx. It's just a question of taste, but I think someone should elaborate a mathematically correct naming convention applicable to all possible twisty puzzles. If you want links to your site, then PM me. Maybe not everyone appreciates such an initiative. So I will do only for demand.
_________________ Virtual Magic Polyhedra Applet(Online) Executable Jar Installer Win32 Executable(Download) troubleshooting


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Oct 18, 2010 12:51 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Julian wrote: bmenrigh wrote: 1.11.1 state counting attempt 2: Psst... it's 3.11.1. Damn, thanks for pointing that out. My brain has an aggressive autocorrect for these sorts of things. I would have never caught that. I never see mistakes like if/of, or/on/of, if/it an/on, etc. In general a single replacement of a letter of a transposition of letters gets me every time. The other day I even misspelled Elwyn as Elywn ... twice! Believe it or not, I actually proofread my posts 23 times to try to reduce these sorts of mistakes and I still fail. It's really a wonder I can solve any twisty puzzles at all! Julian wrote: bmenrigh wrote: That results in (8! * 12^8) / (4! * 4! * 24) == 1,254,113,280 possible positions.
The reason the orientation of the puzzle is a factor of 24 rather than 12 is that you could solve the puzzle into a state where all of the even spheres and odd spheres have swapped position. You wouldn't know this and each sphere would have a quarterturn in the same axis. Of course! Thank you; now I have seen the light. This is the closest answer yet. It is a slight undercount though, because some scrambles look the same from different orientations. For example, if you spin FUR, FDR, BUL, BDL all y2, then the puzzle looks exactly the same from 2 different orientations, so you would need to count this state twice before dividing by 24. This is a pesky situation that doesn't come up often  identical pieces with distinct orientations. I don't know how many rotationally symmetric states there are with this puzzle. It could well be a trivial number compared to the scale of 1.25 billion, and not enough to push the exact result up to 1.26 billion to 3 sig figs. Okay I'm pretty sure I see what you're saying and this seems like a hard problem to tackle. I think we're actually overcounting though, not undercounting. I'm not positive on this but here's my argument for why: Take any scramble that looks identical from two different orientations. The reason we still need to divide by 24 on that scramble is that there are still 24 different orientations that we could make that scramble. By shuffling the pieces around we could create 24 identical scrambles that we need to cancel to 1. The trouble with the scramble is that if it is indistinguishable from two different orientations then that means there will be two "different" scrambles that will result in the same visual scramble. I think my calculation counts those twice but we need to cancel one and only count it once. I suppose I could be thinking about this the totally wrong way though... My gut tells me that there are only a few hundred to a thousand different patterns like this? I'm not sure. Julian wrote: P.S. 17 moves?! Yeah I was really happy with it too. I should just fess up though and say it was mostly luck. I partially solved about 50 scrambles, getting to the last 14 spheres. If it took me more than 12 moves to get there I just rescrambled. Eventually I got lucky and hit on a scramble where two adjacent spheres were already in the same orientation. turning another face a few times placed a third sphere in the correct orientation right next to them. I then played with a simple 3move sequence that put the 4th sphere on the face in place. I solved half the puzzle in 4 moves. Then I was even luckier on the top  three spheres were already in the same orientation and a few quarter turns reoriented them the same way as the bottom four. I got to the last sphere which had twists in two different axes in 5 moves. I used a 13move version of your 14move fix to solve it. I worked it out so that the first move of the fix nicely canceled with the 5th move of the solve. 17 moves of pure luck. It only took about 50 tries.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Oct 18, 2010 6:42 am 

Joined: Mon Jul 21, 2008 4:52 am Location: Brighton, UK

bmenrigh wrote: It's really a wonder I can solve any twisty puzzles at all! I'm the same way with proofreading my own posts, so no worries! bmenrigh wrote: Julian wrote: bmenrigh wrote: That results in (8! * 12^8) / (4! * 4! * 24) == 1,254,113,280 possible positions.
The reason the orientation of the puzzle is a factor of 24 rather than 12 is that you could solve the puzzle into a state where all of the even spheres and odd spheres have swapped position. You wouldn't know this and each sphere would have a quarterturn in the same axis. Of course! Thank you; now I have seen the light. This is the closest answer yet. It is a slight undercount though, because some scrambles look the same from different orientations. For example, if you spin FUR, FDR, BUL, BDL all y2, then the puzzle looks exactly the same from 2 different orientations, so you would need to count this state twice before dividing by 24. This is a pesky situation that doesn't come up often  identical pieces with distinct orientations. I don't know how many rotationally symmetric states there are with this puzzle. It could well be a trivial number compared to the scale of 1.25 billion, and not enough to push the exact result up to 1.26 billion to 3 sig figs. Okay I'm pretty sure I see what you're saying and this seems like a hard problem to tackle. I think we're actually overcounting though, not undercounting. Here's an illustration of why I say it's an undercount. I always like to take extreme cases for illustrative purposes so here's a very extreme case... let's say that a cube puzzle has just two overall states: black and white. When you make a move the whole of the outside turns from black to white, or from white to black. If we take the 2 states and divide by 24, we get 1/12, which is clearly incorrect. The allblack state looks the same from 24 orientations so we must count it 24 times, and the same with the white. Then 48/24 = 2, resulting in the correct answer. The same logic applies but obviously in a less extreme way with this and other puzzles. The example I gave above, where four corners are twisted y2, is only counted 12 times in the part of the calculation before we divide by 24. Our count of possible states is effectively paired/fused by a y2 rotation of the whole puzzle when we are oriented to see the four spheres spun y2 from solved. I find it quite confusing to think and write about, but I remember that Burnside's Lemma is relevant to the logic. Julian wrote: My gut tells me that there are only a few hundred to a thousand different patterns like this? I'm not sure. I agree, I don't think there are that many.


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