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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Mar 05, 2012 2:21 pm 

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

For a while I was going for 300 solves but I got distracted with programming projects and I haven't done a solve in a few months. I'm certainly not done, I plan on resuming solving at some point. The program I'm working on will (hopefully) answer a lot of outstanding questions myself and others have about solving these puzzles. Also, I think I have a few new ideas about how to define the difficulty / complexity of a puzzle and code will help automate the analysis. I was also going for fewest moves records and got quite a few. Lately Dan (DKwan) and I have been talking a lot about solving and fewest moves strategies and I have been challenging Dan to beat some of my records (which he has had no trouble doing...). I'd certainly like to get back to putting up competitive solves, especially after Dan has claimed so many records I had. Of the top 20, these folks are either not active at all or barely active: 11 Doug Cube 148 12 Daniel Devitt 141 15 Campbell 120 16 Elwyn Holloway 119 17 Noah Hevey 114 19 fusion 105 20 Percy 101 Some of us haven't been active in much lately (Brandon, Michael, Julian, Sjoerd). Speaking for myself, I'm not done solving by a long shot . Ultimately I'd like to solve most of the puzzles. There are probably 20 puzzles that I'm not interested in. I suppose when I do all the ones I am interested in I'll feel the completionist need to push through and solve the remaining ones. Hopefully I get there some day. The more folks that solve the more it fosters competition which I think brings the best out of all of us.
_________________ Prior to using my real name I posted under the account named bmenrigh.


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Mar 05, 2012 3:02 pm 

Joined: Sun Aug 29, 2010 1:56 pm

boublez wrote: I'm wonder does anyone else have any goals for the app. Yes me  I try to complete 3.3.* (edgeturning cubes). These are left: 3.3.11, 3.3.14, 3.3.15, 3.3.16, 3.3.18, 3.3.23, After that, maybe I do the 4.3.6  4.3.10 (edgeturning octahedron). I'm having much fun with it  I hope you too. Stefan.
Last edited by Stefn on Fri Jan 31, 2014 1:45 pm, edited 2 times in total.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Mar 05, 2012 3:55 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

boublez wrote: First of all, I'm interested in finding out how many of the people on the to 20 chart still actively use this app. I've just sneaked into 5th place on the puzzles solved chart, and I have a personal goal to break 300 solves by the end of the year. I'm wonder does anyone else have any goals for the app. I didn't make it onto the top 20 list for puzzles solved until the last week or so, so it's safe to say I'm actively solving right now. As for personal goals, I don't have any immediate goals for quantity of puzzles solved, but my total slowly accumulates automatically as I aim for more fewest move count records.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Mar 05, 2012 9:18 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

Julian wrote: When most of us solved 3.3.26, those puzzles didn't have shiftclick, so we were more limited in our approach and our algorithms. Yeah, I'm not sure how my methods would have evolved without slice moves on these. They definitely make some things a lot easier. Julian wrote: I was also amazed to see that you start 3.3.6 with the 3.3.7 pieces. Thanks for sharing your methods. I decided to start with the 3.3.7 pieces because I had a very easy and efficient method for them without commutators, and I hadn't yet figured out a commutator for them anyway. I therefore designed my 3.3.6 method around the premise of having to solve the 3.3.7 pieces first. I was happy to find the rest of the solution worked out quite well. ___________________ So now to post about another series which Brandon has urged me to try... the 3.4.x series. So far, I have finished up through 3.4.10, and they have been a lot of fun. These puzzles I feel open up to a much greater variety of different strategies than normal puzzles because of the reduction possibilities. It's not all about commutators, which is a bit refreshing. Here are some outlinenotes on my strategies (I have left out information on the parities and some of the more "obvious" algorithms): 3.4.1: 62 moves 1. Use skewb moves to pair corners to their respectively colored centers (a single skewb turn can almost be treated like a double 3cycle of center piece pairing). Setup for each skewb turn freely with 2x2 turns. 2. Solve the reduced 2x2 3.4.2: 32 moves 1. Use dino turns to pair up the 3 pieces that make up each corner (a single dino turn is like a 3cycle for this). You can also use simple 3move truncated [1,1] commutators for this. 3. Solve the reduced 2x2 Note: My first strategy for this was a reduction to dinocube, but reduction to 2x2 is easier and shorter. 3.4.3: 320 moves 1. Pair centers to corners (same as 3.4.1) 2. Pair Xcenters to corners (same as previous, except using slice moves to pair) 3. Solve the notquitereduced 2x2 4. Pair edges: Use a [3,1] 3cycle to move edges around, and pair with plain 2x2 moves along only one cut, similar to pairing edges of a 4x4 cube 5. Orient edge pairs: As dinoedges, these have set orientations that cannot be changed with masterskewb turns. 5a. Put half of the incorrect edges on one side of the puzzle (via [3,1]) 5b. Make a quarter turn on the side with these edges 5c. Swap the first half with the second half of incorrect edges (via [3,1]) 5d. Undo the quarter turn from 5b 6. Permute edges via [3,1] 3cycle Note: Although I was able to take the record with this method, a better method should be to pair the edge pieces with their respective corners after step 2 via a 7move, truncated [3,1], then finish the reduction by solving the Xcenters with another 7move, truncated [3,1]. Then just solve the reduced 2x2. I will have to go back and see how much lower I can get the move count for this puzzle at some point. 3.4.4: 276 moves 1. Pair center pieces into diamondshaped pairs: Most of this is intuitive (setup with corner turns, pair with 2x2 turns), but you can use a [3,1] to help move around the diamonds near the end of the pairing. 2. Solve the centers: Move the diamonds around via [3,1] 3cycle 3. Solve edge/corner pieces via [3,1] pure 3cycle 3.4.5: 92 moves 1. Solve the centers intuitively 2. Reduce the corners, similarly to 3.4.2 3. Solve the reduced 3x3 Note: I first took the record for this with a 109 solve using a much more original reduction to dino cube method, but Brandon has been fighting me for this record, and I have since concluded that reduction to 3x3 has more potential for a lower record despite having more parity problems. 3.4.6: 290 moves 1. Pair corners with their respective Xcenters: 3x3 turns to setup, corner turns to pair 2. Fix center permutation via [1,1] 22 swap 3. Pair chirals to edges via 7move truncated [3,1] 3cycle: [URF',U'&2,URF,D',URF',U&2,URF,D] 4. Pair +Centers to edges via 9move truncated [4,1] double 3cycle: [BRU',URF,BRU,URF',D',URF,BRU',URF',BRU,D] 5. Solve the reduced 3x3 Note: Similarly to when I was working with the 3.3.x series, step 4 can be reduced by careful planning in step 3. I only had to use the algorithm for step 4 once. 3.4.7: 244 moves 1. Solve centers intuitively 2. Pair corners with their respective Xcenters: 3x3 turns to setup, corner turns to pair 3. Pair chirals to edges via 7move truncated [3,1] 3cycle (same as 3.4.6 step 3) 4. Solve the reduced 3x3 3.4.8: 129 moves 1. Reduce as many full edges as possible via intuition: Form +center/edge pairs, and combine pairs to form full edges... 3x3 turns to setup, skewb turns to pair. 2. Use the algs from 3.4.6 for steps 3 and 4 to finish reducing the last few edges. 3. Solve the reduced 3x3 3.4.9: 257 moves 1. Solve centers intuitively 2. Reduce corners mostly intuitively similarly to 3.4.2 (with the corner turning being somewhat in reverse) 3. Reduce edges same as in 3.4.8 4. Solve the reduced 3x3 3.4.10: 217 moves 1. Pair and solve edges: By doing both steps for each edge as you go, you can carefully avoid edgeorientation problems. The easiest way to do this is to do all white and yellow ones first, and then the 4 around the equator. Use basic [1,1] commutators to move edges around as necessary. 2. Reduce centers: Move centers around with [1,1] commutators and pair with 2x2 turns 2a. Start by forming pairs of pieces so each center is only split down the middle 2b. Pair the pairs together to form full faces 3. Permute the reduced centers via [1,1] 4. Permute the rexcube tips via [3,1] Yikes, sorry for this post being so long =O


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Mar 08, 2012 3:22 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

I've been solving a whole bunch more of the 3.3.x series, and found the littlechoplike puzzles from 3.3.2630 to be very entertaining. Puzzles 26 and 29 were relatively easy, as the slice move makes it "simple" to construct a [3,1] 3cycle on the edges. Puzzle 28 was also "straightforward" as it was just little chop with centers that are solved easily at the end. Then I got to puzzles 27 and 30 and found myself utterly stuck. Looking at the move counts of the other solvers (all in the doubledigits for 3.3.27), I was sure I was missing something... Turns out it may not have been so obvious afterall though...
Here's my story for this strange puzzle, 3.3.27:
There are various ways to do a 22 swap on this puzzle, for example: [RU,FL,RU,FL,RU,FL]
I couldn't find a nice short 3cycle (there might be one, I just didn't find it), so I decided to see if I could solve it with just the 22 swap anyway. However, part way through a solve I found my 22 swap very difficult (almost impossible) to setup for. At that point, I gave in and nested my 22 swap into a [6,1] 3cycle just for the sake of trying to finish the puzzle: [RU,FL,RU,FL,RU,FL,UL,RU,FL,RU,FL,RU,FL,UL]
To my extreme surprise, I discovered that not only is this 3cycle "difficult" to setup for, it is actually IMPOSSIBLE to setup for. What I mean by this is no combination of turns on the puzzle can change the symmetry/arrangement of the 3 pieces being cycled. There are no "connected" pieces, and each piece is capable of being moved to any other position on the puzzle (implying no orbits), so how was this possible? I consulted Brandon, and he was equally confused by this property of my 3cycle. At first I thought it was just an unfortunate coincidence of how my 3cycle interacts with the geometry of the puzzle, but it turns out I had stumbled upon what I now believe to be moveable orbits. The 24 pieces are broken into 6 orbits of 4 pieces each, but unlike the orbits of a helicopter cube which are stationary, these orbits can be moved in relationship to the other orbits on the puzzle. With this in mind, it now makes sense why my previous attempts with the 22 swap were failing... basically I had not positioned the orbits correctly on the global scale before swapping around the pieces within the orbits.
Each orbit goes around a "belt" of 4 cubefaces, including one piece for each face around that belt. The cube has 3 belts, and each belt has 2 orbits. This means there are for example, 2 orbits with the colors Red/White/Orange/Yellow, and that there are no orbits that contain the colors Red/White/Blue because those 3 faces do not exist in the same belt. In order for the puzzle to be solvable by 22 swaps and/or 3cycles, the orbits must first be paired with their identically colored orbits into each belt of the cube.
With this new understanding of the puzzle, solving it wasn't so bad. I broke it down like so: 1. Solve 1 face intuitively, making sure that the 4 orbits that include this face are correctly paired into their 2 belts. (Note that by simply completing one face, there is a 50/50 chance that those 4 orbits will just happen to be correct... but also completing one face can be rather difficult in itself depending on the scramble.) 2. Since you know the other 2 orbits are automatically paired correctly around the belt that does not include the first face, you can complete the solve with the 6move 22 swap and the [6,1] 3cycle I mentioned earlier.
With this method, I have managed to get move counts of 36 and 39 for 3.3.27 and 3.3.30 respectively. I found them to be a very tough challenge to figure out... something the move counts clearly do not reflect. I am curious to know how the others who solved this puzzle worked around these orbits... (I'm looking at you Stefan, because I know you solved these two puzzles yourself only a week ago =P)
Attachments: 
File comment: This is an "orbit" map of the puzzle...
3.3.27orbitmap.PNG [ 6.63 KiB  Viewed 6314 times ]

File comment: The 4 pieces that have been moved comprise one "orbit".
3.3.27orbit.PNG [ 6.58 KiB  Viewed 6318 times ]



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Katja

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Mar 09, 2012 12:58 am 

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

bmenrigh wrote: Of the top 20, these folks are either not active at all or barely active: 11 Doug Cube 148 12 Daniel Devitt 141 15 Campbell 120 16 Elwyn Holloway 119 17 Noah Hevey 114 19 fusion 105 20 Percy 101 I'm not sure why I'm not on that list, but I haven't been active on the applet for months, so I should probably be labeled as one of the "top 20 folks that are neither active or barely active" :S. I really don't know why, but I don't want to solve on the applet anymore. I wish I did, but I really don't. Not sure if I'll be wanting to solve again in the future, but currently, I don't see that happening


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Mar 09, 2012 3:14 pm 

Joined: Sun Aug 29, 2010 1:56 pm

DKwan wrote: With this method, I have managed to get move counts of 36 and 39 for 3.3.27 and 3.3.30 respectively. I found them to be a very tough challenge to figure out... something the move counts clearly do not reflect. I am curious to know how the others who solved this puzzle worked around these orbits... (I'm looking at you Stefan, because I know you solved these two puzzles yourself only a week ago =P) Hi Daniel, congratulations on your recent move count records. I'm really astonished and ask myself how you did it, in many cases. I'm planning to follow your trace in some puzzles, not sure if I'm able, but I have not decided it for now  a maybe later thing. Now to your question regarding 3.3.27. I first found a 22swap, than a 3 cycle (all the same than you). I found that there were no setups possible and it had to be some kind of orbits  exactly like you. 6 permutable orbits  maybe also called 6 orbits of pieces, not of piecepositions, 6 sets of 4 pieces, where two sets can be swapped completely, something like that. Here is my outline as pdf for your comparison: Attachment:
3.3.27 outline.pdf [44.44 KiB]
Downloaded 132 times
Thank you for asking, Stefan.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Mar 10, 2012 2:55 pm 

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

DKwan wrote: Here's my story for this strange puzzle, 3.3.27:
I am curious to know how the others who solved this puzzle worked around these orbits... Thanks for your interesting post, which brought me out of semiretirement to try 3.3.27! I found your orbit "map" very useful. Like you and Stefan, I can't find any faster way of cycling 3 stickers than a [6,1] commutator. I view the puzzle as having 6 compound pieces, each of which shows one of 12 possible orientations via its 4 stickers. Each move of the puzzle swaps two pairs of compound pieces and leaves the other two compound pieces alone. With each move, one of the swaps is a "bad" swap in that it prevents the puzzle from being solved with purely 22 swaps or 3cycles of the stickers of each compound piece, while the other swap makes no difference. Edit/correction: If we call the compound pieces without a red sticker R, those without a white sticker W, and those without a blue sticker B, I think the worst that can happen to the permutation of the compound pieces is that they can be 2 moves away from a solvable position via 22 swaps or 3cycles of the stickers. My reasoning is that there are only three varieties of "bad" swap: R<=>W, W<=>B, B<=>R. If two swaps have happened, a third swap involving the last two compound pieces will result in an overall reorientation of the puzzle as if no swaps had happened, while a third swap including an alreadyswapped piece will just change or undo an existing swap. My method is to jot down R, W, and B for all the stickers on a pencil sketch of the puzzle, then it's obvious which move or moves need to be made to fix the compound pieces. When fixed, there are always two opposite RW faces, two opposite WB faces, and two opposite BR faces, showing the possible valid orientations of the puzzle to finish with 22 swaps and 3cycles of stickers. I think the worst case scenario with this method is 86 moves: 2 moves to swap the compound pieces or orbitals around, then a 3cycle of 14 moves for every compound piece or orbital. Maybe around 60 moves on average. My solve of 43 moves was using your method, Dan: a lucky scramble with a single move to solve a face with 3 orbitals already solved, then 3 cycles of 14 moves each. But I find it incredibly confusing to solve a face unless it's within 2 moves of solved, which is why I worked out an alternative method.


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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Mar 13, 2012 10:34 pm 

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

bmenrigh wrote: Of the top 20, these folks are either not active at all or barely active: 11 Doug Cube 148 12 Daniel Devitt 141 15 Campbell 120 16 Elwyn Holloway 119 17 Noah Hevey 114 19 fusion 105 20 Percy 101
Talking about the active solvers of the top 20, one of my Chinese friends, "honglei", recently made it into this list. He has been playing gelatinbrain for only ~ 1.5 months. He has shown strong ability of solving many complicated puzzles on the mf8 forum, using Bo Hu's simulator.
_________________ Check out some virtual puzzles I created at http://nan.ma


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Mar 19, 2012 6:22 pm 

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

DKwan wrote: 3.3.7: 43 moves My method for this doesn't use commutators. I use a short/simple 5move conjugate to fully swap 2 adjacent faces: [UB,BR,RF,BR,UB] This algorithm also shuffles around some of the individual pieces on some faces as well, which helps for it's intended purpose of setting up for pairing pieces together with plain moves. 1. Reduce the puzzle to pairs of pieces, so that each face is split on a diagonal with 2 colors. 2. Pair the pairs into full faces. 3. If the relative positions of the colors matter like in 3.3.6, swap faces around as necessary.
Note: With this method, I average around 70 moves. I felt it was good enough to take the record from fusion with some luck, so I solved it about 5 or 6 times to get the 43 move solve. Please can you give some more hints/details? I can build 89 pairs in stage 1 then I can't see how to finish without using commutators. Then in stage 2, I assume the idea is to use just 3 of the 6 axes to avoid splitting up existing pairs, but I've noticed that if we do this, we have 6 quadruple pieces in 2 orbitals of 3 pieces each that must have their colors paired correctly to be solvable, and I have struggled to find routines to swap pairs between or within orbitals. And what do we do if we end up with a single flipped quadruple piece at the end? Here is my latest saved solve at the end of stage 1: Attachment:
Little Chop paired pieces.jpg [ 25.01 KiB  Viewed 6049 times ]
What would you do next, please? I am looking forward to resolving 3.5.1 and 3.7.2, both of which will finish with a reduced 3.3.7, so I need to get good at 3.3.7. Thanks!


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Mar 19, 2012 7:45 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

Ok, so the tricky part I think lies in the fact that the 5move conjugate I mentioned shuffles the pieces within some of the faces. You have to manipulate the use of this to arrange the pieces within the faces to allow the pairing to work. Another simple move to help with the arrangements is the 3move conjugate [RF,FL,RF] (which swaps 2 opposite faces), although all cases can be resolved with the 5move conjugate. I think the only way to show this is with some examples of situations and how to fix them. Here are the 3 simplest cases: Matched Parallelogram Case: This is the most basic case, and only requires a single faceswap. [(BD,DR,RU,DR,BD), UR] will fix this case. All other cases rely on obtaining this case, and then fixing it with those 6 moves. Attachment:
File comment: Matched Parallelogram Case
3.3.7parallelogram.PNG [ 8.33 KiB  Viewed 5994 times ]
Matched Triangle Case: [(RD,UR,RD), (BU,UL,LD,UL,BU), UR] (2 face swaps, 9 moves total) Attachment:
File comment: Matched Triangle Case
3.3.7matchedtriangle.PNG [ 8.46 KiB  Viewed 5994 times ]
Unmatched Triangle Case: [(UL,LB,BR,LB,UL), (BL,LD,DR,LD,BL), UR] (2 face swaps, 11 moves total) Attachment:
File comment: Unmatched Triangle Case
3.3.7unmatchedtriangle.PNG [ 8.35 KiB  Viewed 5994 times ]
When applying these algs, I always use the faceswapping algorithm from the same orientation (for me, with the U and F faces being the ones getting swapped), so I reorient the puzzle midsequence. This helps me understand/remember the combinations better. My actual application of the unmatched triangle case would look like this: [Y, (UB,BR,RF,BR,UB), Z', (UB,BR,RF,BR,UB), FL] From your image, I can see you could start by solving the white face with the matched parallelogram case, or the blue face with the matched triangle case for example. There are only 3 other possible cases, the unmatched parallelogram, and the 2 cases with opposing faces, and all 3 of them should require 3 face swaps. They should be easy enough to figure out with some trial/error. If you can understand how to apply this stuff for "phase 2", "phase 1" should hopefully make more sense. In "phase 1" you should be able to find a decent amount of pairs that can be made with plain moves, and there is more freedom to make turns without breaking any pairs, so some of this step is intuitive/freeform. Also, if you get to the end of "phase 1", but the cases for the last bunch are unfortunate, you can skip ahead and start doing "phase 2" for a while until the last bits of "phase 1" are more convenient (line up for the matched parallelogram case for example). As for movecount, it takes a certain amount of luck to get as many parallelogram cases as possible and not get stuck with any of the cases requiring 3 faceswaps at the end. However, I have applied this method many times on various puzzles with this piece type, and even with the worst luck I have never had to spend more than 90 moves on these pieces. EDIT: Btw Julian, on an unrelated note, I just saw a post of yours from a few pages back wondering how low of a movecount is possible on 3.3.34. I solved this one 2 weeks ago, with a count of 120. Here's a breakdown of my moves from that solve: Moves 119: Intuitively solving a full face Moves 2022: Solve the centers Moves 23120: Solve the remaining edges with 8 3cycles with a total of 17 setup moves I would say that with some luck, sub100 is certainly within reach.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Mar 20, 2012 6:41 pm 

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

Dan (DKwan), thanks for the useful tips and routines for 3.3.7, and the info on 3.3.34. I just made a first successful solve of 3.3.7 using your method in 101 moves, and I should be able to reduce that move count with later solves. (My previous PB for 3.3.7, finishing with [10,1] commutators, was 130 moves.) I had a tricky final swap that I eventually figured out. With all the faces complete except for F and U, and the FL and UR pieces still needed swapping, and I managed to pair them in 13 moves, but while splitting up the faces. I'll recreate this situation tomorrow and experiment some more. Thanks again. And congratulations on taking first place for least moves solves as of yesterday's leaderboard update!


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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Mar 20, 2012 7:01 pm 

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

Julian wrote: And congratulations on taking first place for least moves solves as of yesterday's leaderboard update! DKwan, congratulations! You totally deserve this record! Great job!
_________________ Check out some virtual puzzles I created at http://nan.ma


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Mar 20, 2012 10:00 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

schuma wrote: Julian wrote: And congratulations on taking first place for least moves solves as of yesterday's leaderboard update! DKwan, congratulations! You totally deserve this record! Great job! Thanks guys =) Although it's been a long journey so far, there's so much farther to go!


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Wed Mar 28, 2012 12:01 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

GB, there is a bug with the solverecognition for 1.1.35b. It prematurely recognized the puzzle as solved before I fixed the center orientations. Attachment:
1.1.35bsolverecognitionbug.PNG [ 48.46 KiB  Viewed 5842 times ]
It recognized the puzzle as solved at this point (scramble not unlocked because I took the screenshot later by loading a save file for this point)... Attachment:
1.1.35bsolved657.PNG [ 48.89 KiB  Viewed 5842 times ]
It took me this many moves to actually complete the puzzle. If possible, can you manually edit my movecount to the one in this screenshot (657 instead of 578)? Also, while on the topic of 1.1.35, it would be great if you could also implement slicemoves for the 1.1.35 series. My solution method in particular uses slice moves extensively. Also, thanks GB for the new puzzles! ___________ As is probably obvious from my posting of this bug, my method for solving this puzzle was to solve it as 1.1.35 first (using 8move double5cycle conjugates), then orient the centers at the end. Half of the centers can be fixed with simulated slicemoves, and the other half I fixed using a 24move algorithm (can be truncated to 21 moves with move cancellations) that twists 2 nonopposite centers. There may be a shorter algorithm for this but it only has to be applied a maximum of 6 times in the worst case scenario so it's not so bad. Unfortunately, this alg won't work for 1.1.35c because it does some scrambling amongst the identical circlepieces on 2 of the faces.


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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Mar 29, 2012 2:02 am 

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

Among the new puzzles that Gelatinbrain added lately, 5.8.1 interests me the most. It looks very simple: Attachment:
Image 000.png [ 7.85 KiB  Viewed 5817 times ]
It's an "edgeturning" (actually "sliding" not "turning") tetrahedron. There are six axes, just like the faceturning cubes. It's a deep cut puzzle: each turn affects half of the pieces. Turning around each axis four times and then the puzzle is back to the solved state. Looking at the above properties, one may think this is equivalent to 2x2x2. Surprisingly, it is not true. It has 16 pieces rather than 8. All 16 pieces move independently and are in one orbit. I'd call it a "fake"2x2x2. This puzzle reminds me of the discussion about "complex puzzles". In that system the pieces are classified by the axes that move them. GB 5.8.1 obviously doesn't fit into that systematic definition. But it is indeed a mathematically well defined, neat puzzle, which is related to 2x2x2. I wonder if there's a way to generalize the definition of "complex puzzles" to include GB 5.8.1. Anyhow it's an interesting thing to think about. Gelatinbrain, thank you for inventing this puzzle!
_________________ Check out some virtual puzzles I created at http://nan.ma


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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Mar 29, 2012 2:11 pm 

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

schuma wrote: This puzzle reminds me of the discussion about "complex puzzles". In that system the pieces are classified by the axes that move them. GB 5.8.1 obviously doesn't fit into that systematic definition. But it is indeed a mathematically well defined, neat puzzle, which is related to 2x2x2. I wonder if there's a way to generalize the definition of "complex puzzles" to include GB 5.8.1. Anyhow it's an interesting thing to think about.
In another word they are classified by the groups having compositons of rotations as elements? face turning cubes > S4 vertex turning cubes > A4 Icosaddodecahedrons > A5 5.8.1 > ? Like 2x2x2, you can move the entire puzzle by twisting two halves in opposite directions. So I think that the compositions of these overall orientations form a group. Maybe we can find an isomorphism among wellknown small groups. So far I can say, as the S4, it contains the Klein group as subgroup, but not the supergroup of S4. This is not that evident with 4.9.1 & 2.8.1, because with these puzzles you canot reorient the entire puzzle. With each axis, there are always unaffected pieces. I fixed the macro bug too.
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boublez

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Apr 03, 2012 4:59 pm 

Joined: Sun Dec 06, 2009 9:00 am

Very excited to take a solve at these 2. GB just added 1.1.88 Master Starminx and 1.1.89 Royal Pentultamate.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Wed Apr 04, 2012 12:13 am 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

boublez wrote: Very excited to take a solve at these 2. GB just added 1.1.88 Master Starminx and 1.1.89 Royal Pentultamate. Indeed! Thank you GB for both of them. I have today just finished the last of the 23 layer 1.1.x puzzles. This is the first GB "category" I've managed to complete (even though it's not all of 1.1.x, it's still a subdivision in GB). This has been a longterm goal of mine, and I'm proud to say I currently have the fewestmoves records on all 61 of them. A lot of the puzzles 1.1.50+ are visually very intimidating. Many of them involve circles and sliceonly turns, which results in many nonintuitive piecetypes. The result of these many circle/sliceonly puzzles are a combination of difficulttosolve pieces, and pieces made up of nonadjacent stickers/surfaces that makes this series rich with variety and difficulty, both theoretically and visually. Just as examples... The circlestarminxtip piece (BCDE) cannot be solved via a shorter commutator than [5,1] when it's completely on it's own. It is present in many many of these puzzles, and in all cases the [5,1] is way too dirty to be useful (the nature of this piece generally places it later in the solve order), so it always requires at least a [6,1]. On the visualdifficulty side, the stickers on 1.1.83 that are at the union of the centercircles and the outercircles are actually virtually joined in groups of 4 which are quite spread out... although these pieces are super easy to solve theoretically based on the grip pattern, the actual solve is very very confusing because of the difficulty in recognition (also this is not the only piece with disjointed stickers in this puzzle). __________________ Anyway, I thought I would post my outlines for the last 2 puzzles in the series that I solved. I think that not only are they 2 of the hardest of the 23 layer 1.1.x's, but my solutions for them are representational of some of the tactics I tried to use for some of the 50+'s to avoid using lengthy commutators. (Technically 1.1.61 was my 2ndtolast, but since it's a subset of 1.1.63 I'm not counting it) 1.1.72: This is one rough puzzle... aside from the centers, it has 3 60piece types which all seem to require at least a [6,1] regardless of the solve order you choose. If you do some quick math, 180 pieces at 7moves per piece (solving 2 at a time with 0 setups) gives a rough estimate of 1260 moves plus centers and setups. My solve method however, makes sub1k possible (my solve took 1053). Centers: Intuition, [1,1] 22 swap, [3,1] 3cycle, yada yada... same as 1.1.5 centers Xcenters: Circlepentultimate pieces. I used the same double 5cycle conjugates as with my solves on the 1.1.35 set (except with the advantage of slice moves being available)... Intuitive [1:1] > [F,E&2,F'] for almost 1hemisphere worth and [3:1] > [F'2,C2,F2,C'2&2,F'2,C'2,F2,C2&2] for the rest. Edges & +centers Reduction: Reduce them into 4piece macroedge groups. I used a [4,4] for this > [F',C,F,C',J&2,E'&2,J'&2,E&2,C,F',C',F,E'&2,J&2,E&2,J'&2]... however, since it is being used in a reduction method, I can truncate the last 4 slice moves and there is also a move cancellation in the middle (C'+J&2=J'+reorient), shortening it to this 11move alg > [E',C,E,J',E'&2,J'&2,E&2,C,F',C',F]. The last 3 macroedges are very difficult, but not impossible to reduce with this one alg, so I should note that I would suggest finding a pure alg for one of the pieces to be used once or twice at the very end of the reduction. (See EDIT below) Macroedges: Solve about 10 of them with intuition (slice moves) and [1,1] > [F'&2,B&2,F&2,B'&2], and 3cycle the rest with [3,1] > [F'&2,B&2,F&2,B',F'&2,B'&2,F&2,B]... There is one caveat, in that you may run into a macroedge swap "parity". I ran into this on my actual solve and it cost me 46 moves at the end. 1.1.63: I think but haven't checked that this puzzle holds the records for both the most piece types and the most pieces in total of any 23 layer 1.1.x puzzle... it was also very clearly my highest movecount of the series (1637). It was a great puzzle to end this set on. Reduce/Pair the wide triangles: These groups are made up of 3 pieces each, one 2sticker pyracrystal edge and two 1sticker pieces that are each 1grip shy of being a pyracrystal edge. Pairing is done with a regular turn, and setups for the pairing are done by shuffling around these macropieces with standard pyracrystal [1,1]s. PCedge groups: Because of the way they are reduced, solving these must be done solely with [1,1] commutators and with careful setups soas not to break up the pairings. Corners: [4,1] > [C',F,C,F',E',F,C',F',C,E] Reduce/Pair the starpoints: Pairing is done with a regular turn (which must be eventually turned back). Tip groups are moved onto the "pairingface" 2atatime with [3,1] > [F',C,F,J,F',C',F,J'] and when it gets harder, 1atatime with [1:[3,1]] > [B,F',C,F,J,F',C',F,J',B']. Special care must be made to make sure to not accidentally break up alreadypaired tips, which I believe I did a few times in my actual solve unintentionally (this happens if you break a tippair in the setup moves, and it gets cycled in the placementcommutator). Centers: [3,1] > [F',C,F,J,F',C',F,J']... just like with solving 1.1.5, it helps the move count dramatically if you use this as a double 3cycle for about half of the tips before completing the centers with it (the difference is even greater in this case because the startip commutator is longer than on 1.1.5). Startip pairs: [4,3] > [C',F,C,F',L,G,L',F,C',F',C,L,G',L'] Circlecorners: [6,1] > [B,A,F,A',F',B',L',B,F,A,F',A',B',L] Note: The reduction method to form pyracrystal edgegroups is applicable to ~10 puzzles in the series. It is applicable for not only true PCedges, but also 2grip pieces that are functionally similar. EDIT: I just realized that for 1.1.72, I can use this even shorter 9move alg, truncating from a [3,4] base rather than a [4,4] > [F',D',G,C&2,G&2,C'&2,F',C,F]... This alg is less "pure" than the 11move one, but it doesn't matter because it is being used in a reduction method. I would say this means a move count less than 900 is "easily" possible.


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GuiltyBystander

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Apr 05, 2012 10:05 am 

Joined: Wed May 13, 2009 4:58 pm Location: Vancouver, Washington

I found someone who is taking up a bunch of slots on the records page for 3.2.4 that prevent us some of us from seeing where we are on the list. If it's not against any unwritten policy to do this, okay, but if the duplicates could be renamed to the best one, that'd be great. Code: billy 3.2.4 20100614 moves Billy .C 3.2.4 20100618 moves,time billy.c 3.2.4 20100712 moves billy 98 3.2.4 20100722 moves billy98 3.2.4 20100722 moves billy 1998 3.2.4 20100724 moves billy1998 3.2.4 20100724 moves,time billy.c1998 3.2.4 20100727 moves billy .c 1998 3.2.4 20100729 time billy.c 1998 3.2.4 20100729 time,moves billy . 1998 3.2.4 20100822 time,moves billy . 1998 . c 3.2.4 20100822 moves billy . 1998 . c 9 8 3.2.4 20100823 time billy . 1998 . c 98 3.2.4 20100823 time,moves billy Clemens 1998 3.2.4 20100831 moves,time
_________________ Real name: Landon Kryger


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Apr 09, 2012 4:28 pm 

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

3.5.1 (2x2x2 + Little Chop)
This can be solved by reducing the puzzle to a Little Chop (3.3.7) and then solving the 3.3.7 using DKwan's method posted higher up on this page. During reduction we save moves by cycling 3.5.1 pieces without caring that some complete Little Chop pieces get moved around as well, and importantly we only have to cycle up to 24 of the pieces, not caring where the other 24 go as long as they are paired.
Edit: I have since found a routine of just 11 moves to reduce 3.5.1 to 3.3.7: L',FL,R,FL,L,RF,L',FL,R',FL,L repairs the FL, RU, and BD 3.3.7 pieces. My original description of longer 15 and 17move routines is below in small font. A suitable sequence for reduction can be found by putting the appropriate face move either side of a Little Chop routine to swap two faces: [face move] : [BU BR FR BR BU]. Because face moves break up so many Little Chop pieces, this 7 move sequence needs to be used with an edge move as [7:1] or [7,1] (the last move to make a commutator is only needed when doing inverse cycles). If you use only edge setup moves, they do not need to be undone afterwards, saving many moves. Another possible reduction algo, slightly longer, is of the form [face move]: [two edges back and forth 3 times]. You can use whichever is easier to set up each cycle.
Also make sure to look around for some 2x2x2 moves to make at the beginning to quickly build as many Little Chop pieces as possible. I look at each axis in turn, and sometimes permuting or twisting 2x2x2 corners is worthwhile to get extra pairs for a small number of moves. I took 217 moves, but I hope to do a resolve sometime in around 180 moves, say 115 moves to get to 3.3.7 and then 65 moves to solve the 3.3.7.
3.7.2. (2x2x2 + Skewb + Little Chop)
I love this puzzle! It's special because the only other GB puzzle with every type of deep cut (around faces, vertices, and edges) is a dodeca one with hundreds of pieces. 3.7.2 has just 96 pieces so it doesn't take a really long time to solve.
My new method is to reduce to a 3.5.1, then solve the 3.5.1 as above. At the beginning, look at the puzzle as a Skewb Ultimate (because the centers have visible orientation) and make some Skewb moves to build as many 3.5.1 pieces as possible. Then use a 10 move sequence to cycle 3 outer pieces while shuffling some other 3.5.1 pieces around: [vertex move, face move] : [two distant edges back and forth 3 times]. You'll be able to make half of the 3.5.1 pieces with this sequence, and you'll be able to make the other half with its mirror image. Make sure to use only face and edge setup moves, which you won't need to undo.
I will try sometime to do a sub400 solve. I don't expect to be able to beat haru's amazing record of 352 moves but I'll try to get as close as I can. With my second attempt of 404 moves I took 203 moves to reduce to 3.5.1, then 115 moves to reduce to 3.3.7, then 86 moves to solve a tricky 3.3.7.
Last edited by Julian on Sat Apr 14, 2012 8:32 am, edited 1 time in total.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Apr 13, 2012 1:43 am 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

Julian, congrats on your improvements on those two puzzles! I still have to work out good methods for them myself. I think they are deceptively difficult. When I first pulled up 3.5.1 while scanning through the 3.4+.x puzzles, I thought it would be easy but that turned out to not be the case, let alone 3.7.2! With regards to Haru's amazing score on 3.7.2, I'm curious to know if he used the exact same approach as you did or if he came up with something cleverer.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sat Apr 14, 2012 9:18 am 

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

DKwan wrote: Julian, congrats on your improvements on those two puzzles! I still have to work out good methods for them myself. I think they are deceptively difficult. When I first pulled up 3.5.1 while scanning through the 3.4+.x puzzles, I thought it would be easy but that turned out to not be the case, let alone 3.7.2! Thanks. 3.5.1 is a very tricky puzzle. Whatever one's method, I don't see a way of building a useful algo without testing various face moves as setups, and it's surprising how destructive a single 2x2x2 move can be when attached to what looked like a promising sequence. It took me quite a while to find a pure cycling algo to solve it the first time. DKwan wrote: With regards to Haru's amazing score on 3.7.2, I'm curious to know if he used the exact same approach as you did or if he came up with something cleverer. I've been wondering the same thing. Adding to the mystery of course is that Haru hasn't put a 3.3.7 or 3.5.1 solve onto the leaderboard! I played around with 3.5.1 some more today and found an 11move sequence to repair three 3.3.7 pieces; I've edited my earlier post with the details. This will save quite a few moves compared to the 15 and 17move sequences I've been using. If we assume 6 pairing cycles to reduce 3.5.1 to 3.3.7 at a saving of 5 moves per cycle, that would knock my PB down to 374, which is only 22 moves from the record. Hmmm... I've been wondering if Haru might have reduced 3.7.2 to 3.3.7 without the 3.5.1 stage in the middle, but that would be incredibly difficult. Skewb moves are so damaging in the middle of the solve, the way they break up every face and half of the 3.3.7 pieces, and my instinct is to be rid of them as soon as possible.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Apr 26, 2012 2:28 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

For my 200th puzzle I wanted to do something special, so I decided to do Big Chop (1.4.3) as a nice landmark puzzle. Here's the 3cycle I found/used: [5,5] > [IF,CH,IF,CH,IF, DE,CH,DE,CH,DE, IF,CH,IF,CH,IF, DE,CH,DE,CH,DE] nice and simple, only 3 grips in an easytoremember pattern =) The way the geometry of the cuts are on this puzzle allows you to split up the puzzle into "orange slices" in 3 different ways, 10 slices around a facecentered axis, 6 slices around a cornercentered axis, and 4 slices around an edgecentered axis. My plan was that for a commutator I could use a sequence of moves that shuffled slices along one axis for the X part, and then a sequence that shuffled slices along a different axis for the Y part. 6move algs like (IF,CH)x3 and (DE,CH)x3 are applications of an alg used in some other puzzles, each of which results in flipping the orientation of 2 slices in their respective axis (facecentered for the former, cornercentered for the latter), and they seemed like the best candidates for this because they affected the fewest pieces possible for an alg in one axis. After I started considering use of the temporaryswapprinciple it didn't take too long to find an XY pair that overlapped by only 1 piece in addition to the temporarily swapped pieces. This left me with a [6,6]... however, because each of those 6's does the same thing forwards as they do backwards, some rearranging allowed for 2 move cancellations resulting in the [5,5]. At first sight, the algorithm Julian found which Brandon's program found the shortened version of seems quite different from mine, but actually they are related. Julian/Brandon's alg can be easily converted to a [5,5] with X in one 3fold axis, and a Y in one 5fold axis: [BC,EF,EK,AB,EK,AB,EK,EF,BC, AF, BC,EF,EK,AB,EK,AB,EK,EF,BC, AF] (original alg) = [EK,AB,EK,AB,EK, EF,BC,AF,BC,EF, EK,AB,EK,AB,EK, EF,BC,AF,BC,EF] (moved the first 2 moves to the end) For my solve, I started by solving as much as I could intuitively, and then simply pure 3cycled the rest. The only other tool in my "bag" for this puzzle was a slew of [8,1] double 3cycles (1 cycle per orbit), however I decided this would actually mess up more than it would save, because I was starting with many pieces solved already (so I didn't use it at all). This is how far intuition got me, 2.8 faces solved and a 4th face half solved (pink) in 74 moves: Attachment:
1.4.3intuitivepart.PNG [ 45.12 KiB  Viewed 5430 times ]
An indirect bonus of intuitively solving a few faces first is that the rest of the faces are more likely to have multiples of a color (which means more pieces that can be defined as already solved). This is further helped by the fact that you get to define your own colorscheme. In this state, I counted that only 66 pieces needed to be cycled. After another 718 moves of setups/commutators, I finished the puzzle with a total of 792 moves. Now after having solved this, I should mention that I think there are potentially some clever ways to make use of shorter, nonpure algs. For one, Brandon has mentioned to me there is a [7,1] paired double3cycle, which I think would have been very easy to take advantage of. I also know Brandon is working on some completely different clever method of his own, so I look forwards to seeing just how low a move count is feasible on this puzzle.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Apr 26, 2012 5:49 pm 

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

DKwan wrote: For my 200th puzzle I wanted to do something special, so I decided to do Big Chop (1.4.3) as a nice landmark puzzle. Congratulations, both on the 200 puzzles and a great solve! DKwan wrote: An indirect bonus of intuitively solving a few faces first is that the rest of the faces are more likely to have multiples of a color (which means more pieces that can be defined as already solved). This is further helped by the fact that you get to define your own colorscheme. The first time I realized this about these kinds of puzzles was when I read your posts about 3.3.7. It just never occurred to me that the program would accept a different color scheme as a solved state. It's a really useful insight/discovery. DKwan wrote: I should mention that I think there are potentially some clever ways to make use of shorter, nonpure algs. For one, Brandon has mentioned to me there is a [7,1] paired double3cycle, which I think would have been very easy to take advantage of. If the algorithm cycles 3 lefthanded pieces where it doesn't matter that 3 adjacent righthanded pieces get cycled too when none of those righthanded pieces are solved, I'm sure that could be used a few times and save some moves. DKwan wrote: I also know Brandon is working on some completely different clever method of his own, so I look forwards to seeing just how low a move count is feasible on this puzzle. I wish him luck! Your 792 moves is pretty amazing.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Apr 26, 2012 6:21 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

Julian wrote: Congratulations, both on the 200 puzzles and a great solve! Thanks! Julian wrote: If the algorithm cycles 3 lefthanded pieces where it doesn't matter that 3 adjacent righthanded pieces get cycled too when none of those righthanded pieces are solved, I'm sure that could be used a few times and save some moves. Yes, this is one direct reason why, but the other reason is because I would be able to use extra setup moves to pair pieces for cycling, thus allowing me to solve a minimum of 4 pieces per cycle (with a lot of effort). And of course, sometimes 2 pieces of the same color are adjacent and on the wrong face, so in some cases the setting up wouldn't even be that bad. The nonpaired double 3cycles I had found were too spread out that setting up for them in this way would be impossibly hard. Julian wrote: The first time I realized this about these kinds of puzzles was when I read your posts about 3.3.7. It just never occurred to me that the program would accept a different color scheme as a solved state. It's a really useful insight/discovery. I had also not been aware of this for a long time. I never "risked it" to check until 3.3.7 I think (because it happens "accidentally" using my method). Puzzles like the dino cube can also be solved to their mirrorimage color scheme. Also, for icosahedral puzzles, the program still requires opposite faces to be the same color. I discovered this on 2.2.8 (10color dogic), where I reduced the faces to all being solid in 120 moves, and then had to use 13 "doublemoves" to shuffle the faces around afterwards.


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Apr 30, 2012 10:32 am 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

After taking on Big Chop, I decided to finish the 23 layer, straightcut 1.4.x's (ignoring stickermods for now). This meant finally taking on 1.4.6, an absolute beast of a puzzle. I don't think finding algs is too hard for this puzzle, but the sheer quantity of pieces in this puzzle, having 2 different pairs of chiral piecesets, makes for a very intimidating solve. I think the flexibility of this puzzle allows for a variety of good solution methods. I came up with 2 solve strategies. Here is the second one, which I used in my actual solve. I think my first method might have been a little more moveefficient, but this one is significantly easier to apply. 1.4.6: 2804 moves 1. Reduce Centers (10 kites per face): Reduce 10 full faces with intuition. This sounds hard, but realize that a single turn only really affects 2 faces, cutting them in half (it also swaps 2 full faces but that doesn't matter). For each face, you assemble two "halves" one piece at a time, and then join them into a full face. When it starts getting difficult after the first half or so faces, you can make up conjugates onthefly where the Y part is a single turn, and the X part is setups that move a face around to be positioned for being cut in half (without affecting the 2 faces which are also swapped by Y). Here is an example conjugate that uses 2 setups [LG,LJ,EF,LJ,LG]. For the last 2 faces, reduce the edgekites in this way, and then solve the cornerkites with [1,1]. Attachment:
1.4.61CentersReduced.PNG [ 42.5 KiB  Viewed 5366 times ]
2. Permute the Reduced Centers: Use this 6move 22 swap (it would be a [1,1] if slice moves were supported) > [AB,FJ,GC,LK,GC,FJ] Note that you might find this alg useful for step 1 as well, as you can use it similarly to my littlechop method. Attachment:
1.4.62CentersDone.PNG [ 42.24 KiB  Viewed 5366 times ]
3. Corners: [3,1] 3cycle > [FJ,DE,BC,DE,FJ,DE,BC,DE] Attachment:
1.4.63CornersDone.PNG [ 41.94 KiB  Viewed 5366 times ]
4. Pair Chirals: Pair them into bigger triangles, using [1,1]s to setup 4 unmatched pairs and a single turn to do a 22 swap with pairings. This is basically an intuitive/organic application of this [4,1] 3cycle > [GC,AF,GC,AF,DE,AF,GC,AF,GC,DE] Attachment:
1.4.64ChiralsPaired.PNG [ 42.01 KiB  Viewed 5366 times ]
5. Permute the Reduced Chirals: [4,1] 3cycle > [GC,AF,GC,AF,AE,AF,GC,AF,GC,AE] You can theoretically solve at least half of them with [1,1]s, which I was hoping to do, but I was finding those frustrating to deal with (because of having to be careful with the setups to not break up pairs that are being cycled) so I just used the [4,1] for basically the whole step. Attachment:
1.4.65ChiralsDone.PNG [ 40.43 KiB  Viewed 5366 times ]
6. Edges: [4,4] 3cycle w/ one move cancellation (14 moves) > [GC,AF,GC,AF,LI,AF,LI,GC,AF,GC,AF,LI,AF,LI] Attachment:
1.4.66EdgesDone.PNG [ 39.69 KiB  Viewed 5366 times ]
7. CornerCenters: [4,3] 3cycle > [GC,AF,GC,AF,LH,DG,LH,AF,GC,AF,GC,LH,DG,LH] Attachment:
1.4.67Solved.PNG [ 38.7 KiB  Viewed 5366 times ]
Parity Notes: Because of the way the centers are reduced and then cycled afterwards, you have to be careful not to solve them into an odd permutation. Additionally, as previously mentioned about this puzzle, since slice moves aren't supported, you need to finish the center reduction step with an even number of total moves to avoid the cornerswap parity.


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Apr 30, 2012 5:24 pm 

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

DKwan wrote: 1.4.6: 2804 moves Nice! It's interesting to see the movesaving ideas your method has compared to the one I used: solving centers then permuting them; pairing the little triangles then solving them; and leaving the edges until later. P.S. I just looked through the leaderboard page and gasped at your 413 moves for 2.2.4. I need to go back to that one some time to try to figure out how you did that!


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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri May 04, 2012 5:21 pm 

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

Michael Gottlieb published a video of him solving Pentultimate using his own simulator. It only took him 1 min 49 sec. (5.68 moves per sec) That's so so fast! http://www.youtube.com/watch?v=jdGgSev_ ... ture=guuTo achieve a faster speed, he chose to use algos with more moves with easier recognition. So in this video his move count is 620, which is significantly larger than his fewest move count on GB, 256.
_________________ Check out some virtual puzzles I created at http://nan.ma


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri May 04, 2012 5:47 pm 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

schuma wrote: To achieve a faster speed, he chose to use algos with more moves with easier recognition. So in this video his move count is 620, which is significantly larger than his fewest move count on GB, 256. Michael's speed is truly amazing, and that video is jawdroppingly impressive. I don't think that speed should be completely unexpected though, considering his equally impressive GB time records (most of which have survived the "test of time"). I think in general, solving for speed versus fewest moves are two completely different tasks which require completely different strategies/skills. That is to say, for many puzzles, if I were to try solving for speed, I would certainly employ a different set of algorithms and/or a different solve order than I do for fewest moves on the same puzzle. While talking about this, I think I should mention that I also believe YOUR task of solving all GB puzzles is another goal that benefits from a different set of strategies/skills. Your approach to solving GB puzzles is very much tailored towards spending the least amount of realtime solving a new puzzle as possible. Not only does your approach generally do "poorly" for fewest moves, but fewest moves approaches also do "poorly" for solving as many unique puzzles as possible in a limited amount of freetime. It's a matter of specialization. =)


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DKwan

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Jun 08, 2012 10:55 am 

Joined: Fri Feb 18, 2011 5:49 pm Location: New Jersey

I had noticed that Julian had recently resolved 1.3.2, so I decided to finally solve it. I had already worked out the 2 algs necessary (one of which is 1move shorter than the alg previously posted by Julian) about a month ago but never got around to the actual solve. I found this solve to be a lot of fun actually because there is no tedious commutators step. 1.3.2: 549 moves 1. Intuitively reduce 6 full faces. This was not as hard as I thought it might be. Use faceturns freely to setup for cornerturns. The first 4 faces took me about 25 turns each, and the 5th and 6th faces took about 35 turns each. Attachment:
1.3.26faces.PNG [ 51.79 KiB  Viewed 4926 times ]
2. Check cornertwist parity. If it needs an extra cornertwist, align the 6 unsolved centers around a cornerequator and make the extra turn. 3. Reduce at least 3 more full faces with a [1:4], then with this same conjugate, finish all the +centers (star tips) of the last 3 faces: [AEF',F',C',F,C,AEF] It's hard to tell which pieces are being cycled, since the centers get moved around, so here's a reference. Attachment:
1.3.2reference1.PNG [ 24.67 KiB  Viewed 4926 times ]
4. Finish the reduction with a [5:4] to cycle the remaining Xcenters (wide triangles): [ADE',D'2,DGK',D2,ADE,F',C,F,C',ADE',D'2,DGK,D2,ADE] In my actual solve, I only needed to use this alg 3 times, since I had already solved the rest of them in step 3. Attachment:
1.3.2reference2.PNG [ 24.42 KiB  Viewed 4926 times ]
5. Solve the reduced pentultimate!


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Julian

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Sun Jun 10, 2012 2:01 pm 

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

DKwan wrote: 1.3.2: 549 moves Nice! I'm impressed with how efficiently you managed to build the 5th and 6th faces. I just can't do it. I tried 1.3.2 again last night and I had no problem with the first 4 faces but I got stuck building the 5th and 6th. I could do it, but so inefficiently that I figured I was probably taking longer than I would using [1:4] algos so I clicked Undo back to the 4 faces and moved onto to the next stage. This time I tried to plan very carefully when pairing thin and wide triangles and I did much better than previous attempts: after 341 moves I had 11 wide triangles left, which took 5 cycles to solve, giving a reduced Pentultimate at 431 moves, solved at 594 moves. I'm happy I managed to finish under 600 moves. I agree that this is a very fun puzzle to solve. In step 2 of your solution guide above, I use Stefan's method of figuring out the corner parity here.


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Danny Devitt

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Jul 19, 2012 5:48 am 

Joined: Tue Mar 25, 2008 2:51 am Location: Malibu, California

Hey guys! It would seem no matter how long I stay away, I always wind up coming back to these.
In any case, I'm mainly posting because a solve of mine didn't get registered. Normally this wouldn't be a problem, because I took a screen shot, and hence figured I could just email the certificate if needed. Well, it turns out that the certificate is actually slightly scrolled if you don't change your name (and why would you?) and so I'm missing the top line. Hopefully this is good enough?
Attachments: 
Screen shot 20120716 at 4.24.31 PM.png [ 164.88 KiB  Viewed 4133 times ]

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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Jul 19, 2012 4:57 pm 

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

Danny: That's a really fast time for such a low movecount. Great job.
Gelatinbrain: thank you for the new puzzles: +5.5.1 +5.5.1b +5.5.1c +5.5.1d +5.5.1e +5.5.1f +5.5.1g +5.5.1h Without shading I find it somewhat hard to understand what I'm looking at. I have to drag around the view to understand their shape. I'm not sure if there is much that can be done about this though.
Along the lines of a 60 turning tetrahedron, I've been trying to use 6.3.1 to help me understand the jumbling (and therefore, unjumbling) of the Split Jing's Pyraminx. Perhaps you could make a 6.3.2 that's deeper than 6.3.1 and corresponds to the Split Jing's Pyraminx?
Also, have you made a table of the Complex Dodecahedron piece types that appear in your various 1.1.X and 2.2.X puzzles? I have an incomplete table but I figured you might have a full table of all 82 piece types and which ones are appear in which puzzles? One piece type I think is missing is the 4grip piece you get with a sliceonlyMegaminx. I'm sure there are a lot more.
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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Thu Jul 19, 2012 5:08 pm 

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

bmenrigh wrote: Gelatinbrain: thank you for the new puzzles: +5.5.1 +5.5.1b +5.5.1c +5.5.1d +5.5.1e +5.5.1f +5.5.1g +5.5.1h
I haven't been solving GB puzzles, and I'm very excited to see new puzzles. I noticed that the notation is buggy. When I keep clicking the "B" side, it shows: B, B', B, B, B. Shouldn't it be something like B, B2, B3 etc? Also, when the puzzle is reoriented, the move list is not updated. 5.8.* also have this problem. On 5.5.1*, clicking the truncated vertex doesn't turn the part that is close to the vertex, but the face opposite to it. I understand that's probably because the part close to the vertex can only be turned by 120 degrees rather than 60 degrees. But since this part is smaller, it would be very convenient if there's a way to turn it, maybe by shift+click or something like that. It will make solving much easier. Thanks!
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Danny Devitt

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Fri Jul 20, 2012 9:58 am 

Joined: Tue Mar 25, 2008 2:51 am Location: Malibu, California

bmenrigh wrote: Danny: That's a really fast time for such a low movecount. Great job. Heh, thanks. The two are not unrelated though. The main reason I was able to get such a low time was that I didn't have to use as many setup moves as usual. This led to both a much more fluid solve and a lower move count.
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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Jul 23, 2012 2:08 pm 

Joined: Sun Aug 29, 2010 1:56 pm

It is long ago since my last post (at least 3 months), I also have'nt solved GB puzzles since that time. I also noticed that others have posted nothing more. Perhaps it was a bit to gain distance. I was often in the forum to read other's posts. The last thing I planed to post here was a classification table for gelatinbrain's 3.3.n series (edgeturning cubes), wich I created about 3 months ago when I myself dealt with the edgeturning cubes (3.3.n), to illustrate similarities between the puzzles, to help 'solvingwise' this series. I always pushed that before me, not sure when to post it. The table was planned to facilitate the work with the puzzles. A different question is whether it really does  maybe you can tell me that. Some problems have occurred when I created the table. But first to the rules of the classification: a piece is classified through the set of moves, that moves it (movesetclassification) it is assigned to a piecetype, which includes all pieces of same type a puzzle is classified by the contained piecetypes puzzles are associated with particular slicetypes (listed on an extra sheet) piecetypes have: a name, such as "edge" moveset: list of moves that move the piece of this piecetype number of pieces included in the piecetype possible orbit's (subgroups) orientation options permutationparity options The difficulty with the name is, if other puzzles again have a piecetype with the name 'Edge', which however has not the same moveset. then, roman numerals were used to distinguish the piecetypes, for instance "Edge II", "Edge III" ect. Another difficulty is when puzzles have several slices per axle (slicetype). Then, the '&' character was used. An extra sheet was created to list the slicetypes. Also I have not managed to complete the table, it contains some gaps, but on the whole deal it is complete. It's also to be expected that it contains errors or/and complicated approaches. So if you may not understand some parts of it, it is maybe an error by me. I would like to thank especially gelatinbrain for the puzzle sims., GuiltyBystander and Brandon for the hints in the "How to visualize pieces of a complex puzzle"  thread ( here). Attachment:
File comment: contains the original openoffice document and a pdfprintout
3.3.n classification.zip [90.04 KiB]
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Attachment:
File comment: the whole table
3.3.n.classification.PNG [ 147.74 KiB  Viewed 3890 times ]
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3.3.n.slicetypes.PNG [ 59.55 KiB  Viewed 3890 times ]


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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Mon Jul 23, 2012 5:09 pm 

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

schuma wrote: it would be very convenient if there's a way to turn it, maybe by shift+click or something like that. It will make solving much easier.
I did it, but looks too late since you already solved all. Wasn't this hard for a puzzle only with 28 pieces? I thought so without really trying myself. But your move counts(600~4000) looks to confirm my guess. bmenrigh wrote: Along the lines of a 60 turning tetrahedron, I've been trying to use 6.3.1 to help me understand the jumbling (and therefore, unjumbling) of the Split Jing's Pyraminx. Perhaps you could make a 6.3.2 that's deeper than 6.3.1 and corresponds to the Split Jing's Pyraminx?
Shapeshifting puzzles are hard to realize without shading and perspective. A spherical version can be possible. Do you have a concrete image of how a spherical version looks like? bmenrigh wrote: Also, have you made a table of the Complex Dodecahedron piece types that appear in your various 1.1.X and 2.2.X puzzles? I have an incomplete table but I figured you might have a full table of all 82 piece types and which ones are appear in which puzzles? One piece type I think is missing is the 4grip piece you get with a sliceonlyMegaminx. I'm sure there are a lot more. No, not yet. The only table I made it that of 2~3 layer faceturning dodecahedron, here. http://users.skynet.be/gelatinbrain/App ... calist.htmBy the way Brandon, this weekend, I ported the C++ version of my program to Linux using QT libraries. I couldn't port all puzzles, and for a while I will not have time to complete. But it works anyway. If you want to test, PM me, I will upload it somewhere. And if you like to continue, I will send you the complete source.
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Andreas Nortmann

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 12:38 pm 

Joined: Mon Aug 02, 2004 7:03 am Location: Koblenz, Germany

Stefan Schwalbe wrote: The last thing I planed to post here was a classification table for gelatinbrain's 3.3.n series (edgeturning cubes), wich I created about 3 months ago when I myself dealt with the edgeturning cubes (3.3.n), to illustrate similarities between the puzzles, to help 'solvingwise' this series. Great work. This reminds of the project I wanted to push with your help before I was assigned as moderator the museum. You might remember it too. I used a very similar approach but with these differences:  Different names for the pieces: E.G. "+Face" is replaced by "TFace" or just "T"
 I use the number of moves pieces to differentiate between pieces of equal type: "Edge" becomes "E1" and "Edge II" becomes "E5". Sadly this system can't remove all ambiguities.
 I ignored orientations and number of pieces because these can be derived directly from the piece type.
 I ignored the orbits. In most (but not all as you recognized) cases this number is 1 or 2 (for an EdgeSide)
 I have no associated slice type but a number for order. I still hope that order is sufficient no matter how complicated layers might be connected.


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 12:50 pm 

Joined: Sun Aug 29, 2010 1:56 pm

Hi gelatinbrain, This is a nice simple table,
I have a question regarding your table, what exactly are the binary numbers in the 2nd and 3rd header rows standing for? should the binary numbers in the 2nd and 3rd header rows not have 12 characters to reflect all 12 axes, or have I something not quite understood. The 1. header row is containing a name, composed of a letter and a number. C for Core, F for Face, V for Vertex, E for Edge, I and G for the rest.
Is the 2nd header row for the normal moves, and the 3 header row for the shift+click moves?
The V1000 column contains 10010000 01001000 This column represents the Megaminx corners. Since there are 3 normal moves that move one megaminx corner, i miss one '1'.
Thanks, Stefan.


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 2:18 pm 

Joined: Sun Aug 29, 2010 1:56 pm

Hi Andreas, thank you for your praise, of course I can remember on your project, in which I wanted to help you. (When I think about, I feel myself a bit useless. ) We were never done, but it has certainly hurt none of us. Now to your 5 points: 1. (other name): yes why not 2. (other numbers behind the name): yes why not 3. number and orientation options: I have sometimes found deviations , e.g. in + FaceIV and CornersideII 4. additional information about the orbits can be helpfull in the development of solutions. It should be possible to hide any additional informations to get a similar simple table such as that of gelatinbrain. 5. I should change my slice type names here perhaps. The number should reflect the number of the logical slices. For example 'Typ 5c' would then be a 'Typ 3.' But you would call it an 'order 5'? kind greetings, Stefan.
Last edited by Stefn on Tue Jul 24, 2012 3:28 pm, edited 1 time in total.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 2:32 pm 

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

Stefan Schwalbe wrote: 3. number and orientation options: I have sometimes found deviations , e.g. in + FaceIV and CornersideII[...] I think there needs to be a distinction between the number of orientations versus the number of reachable orientations. The + FaceIV piece in 3.3.13 have two orientations but the orientation of the piece is tied to the position it is in (much like Dino cube edges). The Complex 3x3x3 also has pieces that can't reach all orientations (the UD pieces have 8 orientations but only 4 are reachable). Also, the UD pieces can't be permuted. The position they are in (relative to each other or relative to the core) is fixed.
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schuma

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 2:59 pm 

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

gelatinbrain wrote: I did it, but looks too late since you already solved all. Wasn't this hard for a puzzle only with 28 pieces? I thought so without really trying myself. But your move counts(600~4000) looks to confirm my guess. Thanks any way. They are pretty hard, not because it's hard to construct 3cycles, but because there are two parity issues. The pieces can have an odd permutation, and a single piece can be rotated by itself. The two parities come together on the last color variation (5.5.1h). In other color variations, I don't have to worry about both issues because either there are identical pieces, or there are pieces with plain colors. So in 5.5.1h, I abandoned a lot of work because of the odd permutation issue. There's still a bug regarding the macro though. If you enter A in the text input box, the outcome in the text output is A'. If you enter A', the outcome is A''. If you enter A'', nothing is moved ... And the new corner turning moves are also buggy. When entering DAB, the outcome is DAB', entering DAB again, it's still DAB'. If enter DAB', the outcome is DAB''.
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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 3:01 pm 

Joined: Sun Aug 29, 2010 1:56 pm

regarding Brandon's last post: The corners of the skewb diamond is another example of that issue, I can remember. One would expect 4 orientations, but there are only 2. With the deviations in + FaceIV I meant the number of parts wich is actually 12 instead of 24 (for +faces). But in principle, +FaceIV is no real +face but a double +face or something similar. The number of parts, should arise from the symmetries. The additional information should cause no confusion. Technically you need no additional information, it should however be available. Incidentally, + FaceIV is indeed a pretty confusing piecetype.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 3:18 pm 

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

Stefan Schwalbe wrote: regarding Brandon's last post: The corners of the skewb diamond is another example of that issue, I can remember. One would expect 4 orientations, but there are only 2. With the deviations in + FaceIV I meant the number of parts wich is actually 12 instead of 24 (for +faces). But in principle, +FaceIV is no real +face but a double +face or something similar. The number of parts, should arise from the symmetries. The additional information should cause no confusion. Technically you need no additional information, it should however be available. Incidentally, + FaceIV is indeed a pretty confusing piecetype. The terminology I've used for turnable parts (whether they be edges, corners, faces, or something else) is "grip". I like "grip" because it's generic and doesn't get bogged down by the inconsequential outer geometry of the puzzle. For 2grip pieces like these +FaceIV pieces, I usually think of 2grip pieces as some form of edge. I think the confusion arises in how the +FaceIV pieces behave not because they are a confusing piece but because of the way they show up on Gelatinbrain's puzzles. Yes they appear on the faces on 3.1.13 but that's like calling the Megaminx Edges on 1.1.29 "face pieces". EDIT: and because I think of them as edges, having 12 of them isn't much of a problem.
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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 3:41 pm 

Joined: Sun Aug 29, 2010 1:56 pm

Attachment:
+FaceIV.PNG [ 22.43 KiB  Viewed 3765 times ]
Could you assign them to any edge? They halve a face (crossways) from an edge to the opposite edge, maybe call them "facedivider" bmenrigh wrote: The terminology I've used for turnable parts (whether they be edges, corners, faces, or something else) is "grip". I like "grip" because it's generic and doesn't get bogged down by the inconsequential outer geometry of the puzzle.
I like that. I agree to it. That should appear first.


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Brandon Enright

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 4:16 pm 

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

Stefan Schwalbe wrote: Could you assign them to any edge? I'm not sure exactly what you mean. I'd say the pieces are edge pieces even if they don't appear on the edge of the puzzle. This is a really handwavy description though since there is nothing special list of properties that edge pieces have. It's just that so many edge pieces are 2grip pieces and it's easy to think about them that way. Calling them "edge pieces" is really about a frame of mind and not a fundamental property of the pieces. But, there is some external geometry for the puzzle where they actually would be piece on the edge of the puzzle. Take 4.3.1 for example. If you add the same circle cuts as 4.3.8 then you get something that looks like: Attachment:
circle_4.3.1_mockup.png [ 10.36 KiB  Viewed 3751 times ]
The two edgewings I have labeled A and B are now one piece  the same + FaceIV piece in 3.3.13
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gelatinbrain

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Tue Jul 24, 2012 5:31 pm 

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

Stefan Schwalbe wrote: what exactly are the binary numbers in the 2nd and 3rd header rows standing for?
Each binary digit represents 8 concentric orbits within a piece set around a face. The '1' twists and the '0' doesn't. The 3rd row means an alternative combination of orbits(if exists) that can be considered logically same as the 2nd. I think my approach is essentially same as yours and that of Andreas. schuma wrote: There's still a bug regarding the macro though. If you enter A in the text input box, the outcome in the text output is A'. If you enter A', the outcome is A''. If you enter A'', nothing is moved ... And the new corner turning moves are also buggy. When entering DAB, the outcome is DAB', entering DAB again, it's still DAB'. If enter DAB', the outcome is DAB''.
Fixed.
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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Wed Jul 25, 2012 5:29 am 

Joined: Sun Aug 29, 2010 1:56 pm

bmenrigh wrote: For 2grip pieces like these +FaceIV pieces, I usually think of 2grip pieces as some form of edge. I agree, it's the edge between two edges on the edgeturning cube. It's a two grip piece and '{URUL}piece' would be the first name for it. bmenrigh wrote: I'm not sure exactly what you mean. I'd say the pieces are edge pieces even if they don't appear on the edge of the puzzle. If I say "edge", i would immediately think, it is one of the normal cube  edges, i found that a bit missleading For the piecetypecategory (face,edge,corner,ect.) I would say, we have to create a new category, because they only appear in the edgeturning cube system, but I have no good name for it. Maybe you'll find one.


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Stefn

Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread Posted: Wed Jul 25, 2012 6:17 am 

Joined: Sun Aug 29, 2010 1:56 pm

gelatinbrain wrote: Stefan Schwalbe wrote: what exactly are the binary numbers in the 2nd and 3rd header rows standing for?
Each binary digit represents 8 concentric orbits within a piece set around a face. The '1' twists and the '0' doesn't. The 3rd row means an alternative combination of orbits(if exists) that can be considered logically same as the 2nd. I think my approach is essentially same as yours and that of Andreas. I am amazed by your approach. I expected something like: use the letters of the gelatinbraindodecahedronnotation: ABCDEFGHIJKL create a binary representation (twists or twists not): 000000000000 The piecetype of the megaminxcorners could be called simply: {A,B,C}piece or 111000000000


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