Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum

It is currently Fri Jul 11, 2014 8:46 am

All times are UTC - 5 hours



Post new topic Reply to topic  [ 3096 posts ]  Go to page Previous  1 ... 58, 59, 60, 61, 62  Next
Author Message
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 05, 2012 2:21 pm 
Offline
User avatar

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 8-) . 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.


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

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 Stef-n on Fri Jan 31, 2014 1:45 pm, edited 2 times in total.

Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 05, 2012 3:55 pm 
Offline
User avatar

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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 05, 2012 9:18 pm 
Offline
User avatar

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
Julian wrote:
When most of us solved 3.3.2-6, those puzzles didn't have shift-click, 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 outline-notes 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 3-cycle 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 3-cycle for this). You can also use simple 3-move truncated [1,1] commutators for this.
3. Solve the reduced 2x2

Note: My first strategy for this was a reduction to dino-cube, 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 X-centers to corners (same as previous, except using slice moves to pair)
3. Solve the not-quite-reduced 2x2
4. Pair edges: Use a [3,1] 3-cycle 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 dino-edges, these have set orientations that cannot be changed with master-skewb 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] 3-cycle

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 7-move, truncated [3,1], then finish the reduction by solving the X-centers with another 7-move, 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 diamond-shaped 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] 3-cycle
3. Solve edge/corner pieces via [3,1] pure 3-cycle

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 X-centers: 3x3 turns to setup, corner turns to pair
2. Fix center permutation via [1,1] 2-2 swap
3. Pair chirals to edges via 7-move truncated [3,1] 3-cycle: [URF',U'&2,URF,D',URF',U&2,URF,D]
4. Pair +Centers to edges via 9-move truncated [4,1] double 3-cycle: [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 X-centers: 3x3 turns to setup, corner turns to pair
3. Pair chirals to edges via 7-move truncated [3,1] 3-cycle (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 edge-orientation 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 rex-cube tips via [3,1]

Yikes, sorry for this post being so long =O


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Mar 08, 2012 3:22 pm 
Offline
User avatar

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 little-chop-like puzzles from 3.3.26-30 to be very entertaining. Puzzles 26 and 29 were relatively easy, as the slice move makes it "simple" to construct a [3,1] 3-cycle 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 double-digits for 3.3.27), I was sure I was missing something... Turns out it may not have been so obvious after-all though...

Here's my story for this strange puzzle, 3.3.27:

There are various ways to do a 2-2 swap on this puzzle, for example: [RU,FL,RU,FL,RU,FL]

I couldn't find a nice short 3-cycle (there might be one, I just didn't find it), so I decided to see if I could solve it with just the 2-2 swap anyway. However, part way through a solve I found my 2-2 swap very difficult (almost impossible) to setup for. At that point, I gave in and nested my 2-2 swap into a [6,1] 3-cycle 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 3-cycle "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 3-cycle. At first I thought it was just an unfortunate coincidence of how my 3-cycle interacts with the geometry of the puzzle, but it turns out I had stumbled upon what I now believe to be move-able 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 2-2 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 cube-faces, 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 2-2 swaps and/or 3-cycles, 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 6-move 2-2 swap and the [6,1] 3-cycle 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...
3.3.27-orbitmap.PNG
3.3.27-orbitmap.PNG [ 6.63 KiB | Viewed 6314 times ]
File comment: The 4 pieces that have been moved comprise one "orbit".
3.3.27-orbit.PNG
3.3.27-orbit.PNG [ 6.58 KiB | Viewed 6318 times ]
Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Mar 09, 2012 12:58 am 
Offline
User avatar

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 :(


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

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 2-2-swap, 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 piece-positions, 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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Mar 10, 2012 2:55 pm 
Offline
User avatar

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 semi-retirement 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 2-2 swaps or 3-cycles 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 2-2 swaps or 3-cycles 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 re-orientation of the puzzle as if no swaps had happened, while a third swap including an already-swapped 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 2-2 swaps and 3-cycles 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 3-cycle 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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Mar 13, 2012 10:34 pm 
Offline
User avatar

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


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 19, 2012 6:22 pm 
Offline
User avatar

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 5-move 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 8-9 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
Little Chop paired pieces.jpg [ 25.01 KiB | Viewed 6049 times ]
What would you do next, please? I am looking forward to re-solving 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!


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Mar 19, 2012 7:45 pm 
Offline
User avatar

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
Ok, so the tricky part I think lies in the fact that the 5-move 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 3-move conjugate [RF,FL,RF] (which swaps 2 opposite faces), although all cases can be resolved with the 5-move 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 face-swap. [(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
3.3.7-parallelogram.PNG
3.3.7-parallelogram.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
3.3.7-matchedtriangle.PNG
3.3.7-matchedtriangle.PNG [ 8.46 KiB | Viewed 5994 times ]


Un-matched 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
3.3.7-unmatchedtriangle.PNG
3.3.7-unmatchedtriangle.PNG [ 8.35 KiB | Viewed 5994 times ]


When applying these algs, I always use the face-swapping algorithm from the same orientation (for me, with the U and F faces being the ones getting swapped), so I reorient the puzzle mid-sequence. This helps me understand/remember the combinations better. My actual application of the un-matched 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 move-count, 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 face-swaps 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 move-count 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 1-19: Intuitively solving a full face
Moves 20-22: Solve the centers
Moves 23-120: Solve the remaining edges with 8 3-cycles with a total of 17 setup moves
I would say that with some luck, sub-100 is certainly within reach.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Mar 20, 2012 6:41 pm 
Offline
User avatar

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! :)


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Mar 20, 2012 7:01 pm 
Offline
User avatar

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


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Mar 20, 2012 10:00 pm 
Offline
User avatar

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!


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Mar 28, 2012 12:01 pm 
Offline
User avatar

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
GB, there is a bug with the solve-recognition for 1.1.35b. It prematurely recognized the puzzle as solved before I fixed the center orientations.

Attachment:
1.1.35b-solverecognitionbug.PNG
1.1.35b-solverecognitionbug.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:
1.1.35b-solved657.PNG
1.1.35b-solved657.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 move-count 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 slice-moves 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 8-move double-5-cycle conjugates), then orient the centers at the end. Half of the centers can be fixed with simulated slice-moves, and the other half I fixed using a 24-move algorithm (can be truncated to 21 moves with move cancellations) that twists 2 non-opposite 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 circle-pieces on 2 of the faces.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Mar 29, 2012 2:02 am 
Offline
User avatar

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
Image 000.png [ 7.85 KiB | Viewed 5817 times ]


It's an "edge-turning" (actually "sliding" not "turning") tetrahedron. There are six axes, just like the face-turning 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


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Mar 29, 2012 2:11 pm 
Offline
User avatar

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
Icosa-ddodecahedrons -> 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 well-known 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. 8-)

_________________
Virtual Magic Polyhedra
Applet(Online)
Executable Jar Installer
Win32 Executable(Download)
troubleshooting


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

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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Apr 04, 2012 12:13 am 
Offline
User avatar

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 2-3 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 long-term goal of mine, and I'm proud to say I currently have the fewest-moves records on all 61 of them.

A lot of the puzzles 1.1.50+ are visually very intimidating. Many of them involve circles and slice-only turns, which results in many non-intuitive piece-types. The result of these many circle/slice-only puzzles are a combination of difficult-to-solve pieces, and pieces made up of non-adjacent stickers/surfaces that makes this series rich with variety and difficulty, both theoretically and visually.

Just as examples... The circle-starminx-tip 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 visual-difficulty side, the stickers on 1.1.83 that are at the union of the center-circles and the outer-circles 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 2-3 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 2nd-to-last, 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 60-piece 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 7-moves 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 sub-1k possible (my solve took 1053).

Centers: Intuition, [1,1] 2-2 swap, [3,1] 3-cycle, yada yada... same as 1.1.5 centers

Xcenters: Circle-pentultimate pieces. I used the same double 5-cycle 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 1-hemisphere 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 4-piece macro-edge 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 11-move alg --> [E',C,E,J',E'&2,J'&2,E&2,C,F',C',F]. The last 3 macro-edges 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)

Macro-edges: Solve about 10 of them with intuition (slice moves) and [1,1] --> [F'&2,B&2,F&2,B'&2], and 3-cycle 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 macro-edge 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 2-3 layer 1.1.x puzzle... it was also very clearly my highest move-count 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 2-sticker pyra-crystal edge and two 1-sticker pieces that are each 1-grip shy of being a pyra-crystal edge. Pairing is done with a regular turn, and setups for the pairing are done by shuffling around these macro-pieces with standard pyra-crystal [1,1]s.

PC-edge groups: Because of the way they are reduced, solving these must be done solely with [1,1] commutators and with careful setups so-as not to break up the pairings.

Corners: [4,1] --> [C',F,C,F',E',F,C',F',C,E]

Reduce/Pair the star-points: Pairing is done with a regular turn (which must be eventually turned back). Tip groups are moved onto the "pairing-face" 2-at-a-time with [3,1] --> [F',C,F,J,F',C',F,J'] and when it gets harder, 1-at-a-time 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 already-paired tips, which I believe I did a few times in my actual solve unintentionally (this happens if you break a tip-pair in the setup moves, and it gets cycled in the placement-commutator).

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 3-cycle for about half of the tips before completing the centers with it (the difference is even greater in this case because the star-tip commutator is longer than on 1.1.5).

Star-tip pairs: [4,3] --> [C',F,C,F',L,G,L',F,C',F',C,L,G',L']

Circle-corners: [6,1] --> [B,A,F,A',F',B',L',B,F,A,F',A',B',L]

Note: The reduction method to form pyra-crystal edge-groups is applicable to ~10 puzzles in the series. It is applicable for not only true PC-edges, but also 2-grip pieces that are functionally similar.


EDIT: I just realized that for 1.1.72, I can use this even shorter 9-move 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 11-move 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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Apr 05, 2012 10:05 am 
Offline
User avatar

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   2010-06-14   moves
Billy .C               3.2.4   2010-06-18   moves,time
billy.c                3.2.4   2010-07-12   moves
billy 98               3.2.4   2010-07-22   moves
billy98                3.2.4   2010-07-22   moves
billy 1998             3.2.4   2010-07-24   moves
billy1998              3.2.4   2010-07-24   moves,time
billy.c1998            3.2.4   2010-07-27   moves
billy .c 1998          3.2.4   2010-07-29   time
billy.c 1998           3.2.4   2010-07-29   time,moves
billy . 1998           3.2.4   2010-08-22   time,moves
billy . 1998 . c       3.2.4   2010-08-22   moves
billy . 1998 . c 9 8   3.2.4   2010-08-23   time
billy . 1998 . c 98    3.2.4   2010-08-23   time,moves
billy Clemens 1998     3.2.4   2010-08-31   moves,time

_________________
Real name: Landon Kryger


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Apr 09, 2012 4:28 pm 
Offline
User avatar

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 re-pairs the FL, RU, and BD 3.3.7 pieces. My original description of longer 15- and 17-move 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 re-solve 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 sub-400 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.

Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Apr 13, 2012 1:43 am 
Offline
User avatar

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 clever-er.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Apr 14, 2012 9:18 am 
Offline
User avatar

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 clever-er.
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 11-move sequence to re-pair 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 17-move 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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Apr 26, 2012 2:28 pm 
Offline
User avatar

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 3-cycle 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 easy-to-remember 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 face-centered axis, 6 slices around a corner-centered axis, and 4 slices around an edge-centered 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. 6-move 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 (face-centered for the former, corner-centered 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 temporary-swap-principle it didn't take too long to find an X-Y 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 3-fold axis, and a Y in one 5-fold 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 3-cycled the rest. The only other tool in my "bag" for this puzzle was a slew of [8,1] double 3-cycles (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:
1.4.3-intuitivepart.PNG
1.4.3-intuitivepart.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 color-scheme. 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, non-pure algs. For one, Brandon has mentioned to me there is a [7,1] paired double-3-cycle, 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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Apr 26, 2012 5:49 pm 
Offline
User avatar

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 color-scheme.
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, non-pure algs. For one, Brandon has mentioned to me there is a [7,1] paired double-3-cycle, which I think would have been very easy to take advantage of.
If the algorithm cycles 3 left-handed pieces where it doesn't matter that 3 adjacent right-handed pieces get cycled too when none of those right-handed 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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Apr 26, 2012 6:21 pm 
Offline
User avatar

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 left-handed pieces where it doesn't matter that 3 adjacent right-handed pieces get cycled too when none of those right-handed 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 non-paired double 3-cycles 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 mirror-image color scheme. Also, for icosahedral puzzles, the program still requires opposite faces to be the same color. I discovered this on 2.2.8 (10-color dogic), where I reduced the faces to all being solid in 120 moves, and then had to use 13 "double-moves" to shuffle the faces around afterwards.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Apr 30, 2012 10:32 am 
Offline
User avatar

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
After taking on Big Chop, I decided to finish the 2-3 layer, straight-cut 1.4.x's (ignoring sticker-mods 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 piece-sets, 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 move-efficient, 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 on-the-fly 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 edge-kites in this way, and then solve the corner-kites with [1,1].
Attachment:
1.4.6-1-CentersReduced.PNG
1.4.6-1-CentersReduced.PNG [ 42.5 KiB | Viewed 5366 times ]


2. Permute the Reduced Centers: Use this 6-move 2-2 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 little-chop method.
Attachment:
1.4.6-2-CentersDone.PNG
1.4.6-2-CentersDone.PNG [ 42.24 KiB | Viewed 5366 times ]


3. Corners: [3,1] 3-cycle --> [FJ,DE,BC,DE,FJ,DE,BC,DE]
Attachment:
1.4.6-3-CornersDone.PNG
1.4.6-3-CornersDone.PNG [ 41.94 KiB | Viewed 5366 times ]


4. Pair Chirals: Pair them into bigger triangles, using [1,1]s to setup 4 un-matched pairs and a single turn to do a 2-2 swap with pairings. This is basically an intuitive/organic application of this [4,1] 3-cycle --> [GC,AF,GC,AF,DE,AF,GC,AF,GC,DE]
Attachment:
1.4.6-4-ChiralsPaired.PNG
1.4.6-4-ChiralsPaired.PNG [ 42.01 KiB | Viewed 5366 times ]


5. Permute the Reduced Chirals: [4,1] 3-cycle --> [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:
1.4.6-5-ChiralsDone.PNG
1.4.6-5-ChiralsDone.PNG [ 40.43 KiB | Viewed 5366 times ]


6. Edges: [4,4] 3-cycle w/ one move cancellation (14 moves) --> [GC,AF,GC,AF,LI,AF,LI,GC,AF,GC,AF,LI,AF,LI]
Attachment:
1.4.6-6-EdgesDone.PNG
1.4.6-6-EdgesDone.PNG [ 39.69 KiB | Viewed 5366 times ]


7. Corner-Centers: [4,3] 3-cycle --> [GC,AF,GC,AF,LH,DG,LH,AF,GC,AF,GC,LH,DG,LH]
Attachment:
1.4.6-7-Solved.PNG
1.4.6-7-Solved.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 corner-swap parity.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Apr 30, 2012 5:24 pm 
Offline
User avatar

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 move-saving 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. :shock: I need to go back to that one some time to try to figure out how you did that!


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri May 04, 2012 5:21 pm 
Offline
User avatar

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=g-u-u

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.

_________________
Check out some virtual puzzles I created at http://nan.ma


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri May 04, 2012 5:47 pm 
Offline
User avatar

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 jaw-droppingly 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 real-time 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 free-time. It's a matter of specialization. =)


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jun 08, 2012 10:55 am 
Offline
User avatar

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
I had noticed that Julian had recently re-solved 1.3.2, so I decided to finally solve it. I had already worked out the 2 algs necessary (one of which is 1-move 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 face-turns freely to setup for corner-turns. The first 4 faces took me about 25 turns each, and the 5th and 6th faces took about 35 turns each.
Attachment:
1.3.2-6faces.PNG
1.3.2-6faces.PNG [ 51.79 KiB | Viewed 4926 times ]


2. Check corner-twist parity. If it needs an extra corner-twist, align the 6 unsolved centers around a corner-equator 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:
1.3.2-reference1.PNG
1.3.2-reference1.PNG [ 24.67 KiB | Viewed 4926 times ]


4. Finish the reduction with a [5:4] to cycle the remaining X-centers (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:
1.3.2-reference2.PNG
1.3.2-reference2.PNG [ 24.42 KiB | Viewed 4926 times ]


5. Solve the reduced pentultimate!


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 10, 2012 2:01 pm 
Offline
User avatar

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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 19, 2012 5:48 am 
Offline
User avatar

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 2012-07-16 at 4.24.31 PM.png
Screen shot 2012-07-16 at 4.24.31 PM.png [ 164.88 KiB | Viewed 4133 times ]

_________________
I am taking a break from the forum. You can reach me by PM if needed.
Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 19, 2012 4:57 pm 
Offline
User avatar

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Danny: That's a really fast time for such a low move-count. 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 4-grip piece you get with a slice-only-Megaminx. I'm sure there are a lot more.

_________________
Prior to using my real name I posted under the account named bmenrigh.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jul 19, 2012 5:08 pm 
Offline
User avatar

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!

_________________
Check out some virtual puzzles I created at http://nan.ma


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jul 20, 2012 9:58 am 
Offline
User avatar

Joined: Tue Mar 25, 2008 2:51 am
Location: Malibu, California
bmenrigh wrote:
Danny: That's a really fast time for such a low move-count. 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.

_________________
I am taking a break from the forum. You can reach me by PM if needed.


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

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 edge-turning cubes (3.3.n), to illustrate similarities between the puzzles, to help 'solving-wise' 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 (moveset-classification)
-it is assigned to a piece-type, which includes all pieces of same type
-a puzzle is classified by the contained piece-types
-puzzles are associated with particular slice-types (listed on an extra sheet)
piece-types have:
-a name, such as "edge"
-moveset: list of moves that move the piece of this piece-type
-number of pieces included in the piece-type
-possible orbit's (subgroups)
-orientation options
-permutation-parity options
The difficulty with the name is, if other puzzles again have a piece-type with the name 'Edge', which however has not the same moveset. then, roman numerals were used to distinguish the piece-types, for instance "Edge II", "Edge III" ect.
Another difficulty is when puzzles have several slices per axle (slice-type). Then, the '&' character was used. An extra sheet was created to list the slice-types.
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 open-office document and a pdf-printout
3.3.n classification.zip [90.04 KiB]
Downloaded 65 times
Attachment:
File comment: the whole table
3.3.n.classification.PNG
3.3.n.classification.PNG [ 147.74 KiB | Viewed 3890 times ]
Attachment:
File comment: slice-types
3.3.n.slice-types.PNG
3.3.n.slice-types.PNG [ 59.55 KiB | Viewed 3890 times ]


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jul 23, 2012 5:09 pm 
Offline
User avatar

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?

Shape-shifting 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 4-grip piece you get with a slice-only-Megaminx. I'm sure there are a lot more.

No, not yet. The only table I made it that of 2~3 layer face-turning dodecahedron, here.
http://users.skynet.be/gelatinbrain/App ... calist.htm


By 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.

_________________
Virtual Magic Polyhedra
Applet(Online)
Executable Jar Installer
Win32 Executable(Download)
troubleshooting


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jul 24, 2012 12:38 pm 
Offline
User avatar

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 edge-turning cubes (3.3.n), to illustrate similarities between the puzzles, to help 'solving-wise' 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 "T-Face" 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.


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

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.


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

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. :oops: ) 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 Stef-n on Tue Jul 24, 2012 3:28 pm, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jul 24, 2012 2:32 pm 
Offline
User avatar

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.

_________________
Prior to using my real name I posted under the account named bmenrigh.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jul 24, 2012 2:59 pm 
Offline
User avatar

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 3-cycles, 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''.

_________________
Check out some virtual puzzles I created at http://nan.ma


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

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 piece-type.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jul 24, 2012 3:18 pm 
Offline
User avatar

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 piece-type.
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 2-grip pieces like these +FaceIV pieces, I usually think of 2-grip 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.

_________________
Prior to using my real name I posted under the account named bmenrigh.


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

Joined: Sun Aug 29, 2010 1:56 pm
Attachment:
+FaceIV.PNG
+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 "face-divider" :?
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.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jul 24, 2012 4:16 pm 
Offline
User avatar

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 hand-wavy description though since there is nothing special list of properties that edge pieces have. It's just that so many edge pieces are 2-grip 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
circle_4.3.1_mockup.png [ 10.36 KiB | Viewed 3751 times ]

The two edge-wings I have labeled A and B are now one piece -- the same + FaceIV piece in 3.3.13

_________________
Prior to using my real name I posted under the account named bmenrigh.


Top
 Profile  
 
 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jul 24, 2012 5:31 pm 
Offline
User avatar

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. :)

_________________
Virtual Magic Polyhedra
Applet(Online)
Executable Jar Installer
Win32 Executable(Download)
troubleshooting


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

Joined: Sun Aug 29, 2010 1:56 pm
bmenrigh wrote:
For 2-grip pieces like these +FaceIV pieces, I usually think of 2-grip 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 '{UR-UL}-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 piece-type-category (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.


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

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 gelatinbrain-dodecahedron-notation:

ABCDEFGHIJKL

create a binary representation (twists or twists not):

000000000000

The piece-type of the megaminx-corners could be called simply:
{A,B,C}-piece or
111000000000

:?


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3096 posts ]  Go to page Previous  1 ... 58, 59, 60, 61, 62  Next

All times are UTC - 5 hours


Who is online

Users browsing this forum: No registered users and 2 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group