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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun May 24, 2009 4:12 am 
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I got another 3 solves on the board. But the main purpose of this post is just as a note to myself.

1.1.13
1.1.14
1.1.17

1.2.3-1.2.11

1.3.1
1.3.2
1.3.3

1.4.3
1.4.5*
1.4.6


2.1.4
2.1.5
2.1.6

2.2.7

2.3.1
2.3.2

2.4.1


3.2.3*
3.2.5

3.3.2-3.3.6

3.4.3
3.4.4
3.4.6
3.4.7
3.4.9
3.4.10

3.5.1

3.6.2-3.6.5

3.7.3*
3.7.4*


4.3.x (* on 4.3.3)

4.4.1

4.5.x

4.6.x

4.7.x


5.3.2


6.x.x

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Last edited by Danny Devitt on Tue Jun 30, 2009 1:34 am, edited 20 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun May 24, 2009 3:05 pm 
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1.1.7/Pentultimate -- Fast Solution (200 moves average)

Stage 1 -- Solve 5 corners around a face:
Image

Stage 2 -- Solve the next 5 adjacent faces:
Image

Stage 3 -- Permute the last 6 faces:
Image

Then solve the last 15 corners, simultaneously permuting and orienting them, mostly a pair at a time.

Stages 1 and 2 are fairly easy. With U as the first face solved, if a corner in stage 1 needs reorienting before rolling into position, we borrow unsolved corners as necessary to bring the corner down to the D half and spin it around. The same technique can be used to orient the centers correctly with stage 2, if solving 1.1.7b/Super-Pentultimate.

For stage 3 we can use Sune-like algos where we borrow a center or two from the solved half and throw it/them back on again:
Image

Stage 4 relies on a short way of isolating a swapped corner in half of the puzzle. The Rubik's Sune algo R U R' U R U2' R' does this in 7 moves, which is pretty good, but the corners are not so well placed to set up and undo to give all orientation possibilities. The 3-gen algo B UR UL UR' UL' B' does it in 6 moves and the corners are nicely placed. Setup and undo sequences are shown in parentheses. The algos solve the corners shown in the corresponding screenshots. I've also embedded little diagrams in case they are helpful. A = anticlockwise twist, C = clockwise twist, -- = orientation unchanged. All 9 possible clockwise corner cycles are shown; for an anticlockwise cycle just use the inverse of the appropriate algo. Pm means "mirror image of P". The length of each algo is shown circled in blue. Face rotations are shown at the beginning of some algos in lower case.

I don't think that more than 3 setups are ever needed to position corners adjacent to each other to be cycled. Always look for a corner adjacent or almost adjacent to where it needs to be, and work from there. If a single corner is already in place but misoriented, move it away at the same time as solving 1 corner instead of 2. As there are 15 corners to be solved, doing this once doesn't impede solving the corners with 7 cycles. If 2 corners are already in place but misoriented, leave them to the end. If opposite twists are needed, (L' R)*8 (L R')*8 twists F/DR/DL clockwise and U/UR/UL anticlockwise. If same twists are needed, there will be a 3rd corner left at the end to be twisted the same way, so once they are set up, twist them while cycling them out of position then cycle them back plain, or vice-versa.

P = B UR UL UR' UL' B'
P' = B UL UR UL' UR' B'
Pm = B' UL' UR' UL UR B
Pm' = B' UR' UL' UR UL B


Image

Edits: Rotated the algos for stage 3 to make it clearer how to combine double swaps, including left/right mirroring. Also rotated the algos for stage 4 to make them more suitable for speedsolving.


Last edited by Julian on Fri May 29, 2009 5:31 pm, edited 4 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun May 24, 2009 4:05 pm 
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I use the exact same steps. The difference is that I use far less and less optimal algs. You're method obviously gives a lower move count, but I'll stick with my method for speed since I think it requires less set-up moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun May 24, 2009 7:30 pm 
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Danny Devitt wrote:
I use the exact same steps. The difference is that I use far less and less optimal algs. You're method obviously gives a lower move count, but I'll stick with my method for speed since I think it requires less set-up moves.
It seems to take an average of between 1.5 and 2 setup moves to get corners adjacent to each other for cycling. And although I posted my new method mainly for least moves interest, it is proving to be relatively fast for me. I submitted a 12:32 tonight, which includes continually referring to my notes because I don't have any of the algos memorized (except for R L' R' L and D DL DR DL' DR' D' of course!).

I'll post my "1.1.7b (300 moves average)" expansion pack tomorrow -- 8 more algs to twist the centers.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun May 24, 2009 7:36 pm 
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Well I submitted an 11:50 (or something close) earlier tonight so my method is still faster, for the moment. I'll have to submit a faster super solve as well, as you are already dangerously close to overtaking me.

EDIT: I just got a 8:45 on the regular pentultimate. I'll stick with that for now and move on to the super.

EDIT-2: 15:09 and 549 moves on the super. I'm pretty sure I can improve that further.

EDIT-3: Sorry for all the edits, but I just keep improving. 9:24 and 462 moves on the super. I'll stop editing now, and you can just see for yourself when the board updates.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon May 25, 2009 9:38 am 
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Danny Devitt wrote:
Well I submitted an 11:50 (or something close) earlier tonight so my method is still faster, for the moment.
Said Danny Hare to Julian Tortoise! I said "relatively fast for me" as I'm not a speedsolver. There are speedy people who solve the 3x3x3 faster with Don Taylor's method than others solve it with full Fridrich, but that says nothing about the speedsolving possiblities of the methods. The real question is, regardless of the respective speedsolving skills of the people talking, does the proposed method have the potential to be a very fast method, in the right hands?

The logic behind my new method is as follows:
1) The hardest things about the Pentultimate are: a) it's "deep-cuttedness"; b) quickly recognizing where pieces need to go (12 color dodecahdron = tricky); c) quick recognition of corners.
2) Assuming someone becomes skilled at quickly seeing which corner needs to go where, including its correct orientation, A=>B, why not extend this to see where the piece currently at position B needs to go, then solve the corners mostly a pair at a time?
3) The corner cycling algos are 19.33 moves long on average, of which 12 moves are simply the "core" algo D DL DR DL' DR' D' or its inverse, mirror, or inverted mirror. So the algos are far easier to remember than Fridrich last layer algos, as only 34% of the moves change from case to case, and of those, all except 2 of the distinct moves are always at the beginning and end. An average of 2 setup moves* to put the corners adjacent to each other, then 1.22 face rotations, 2.67 moves ahead of the "core" sequence (remembering which degree of UR/UL turn is used), then undo them after the core sequence.

I conjecture that a skilled speedsolver would be able to make Pentultimate solves under 4 minutes using my method, with a reasonable amount of practice. Maybe even sub-3:00 sometimes. I'd expect maybe 40% of the solving time to be spent looking/thinking/planning.

Your method is obviously fast too, and your times are impressive. 6:33 :!: Please can you give details? Do you position and orient corners one at at time until you get to the last 3? I wish there was more discussion of solution details in this thread, given its title. :|

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

* The average is shaping up closer to 2 than 1.5.


Last edited by Julian on Tue May 26, 2009 7:20 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon May 25, 2009 1:46 pm 
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My method is basically an optimized version of Noah's method. (Note: all pictures can be clicked for full size versions).

Notation:



Step 1: Solve the 5 corners around one center. This is done intuitively, and is very easy to do.



Step 2: Solve the other 5 centers around the face. Again, this is intuitive, easy, and fast.



Step 3: Solve the rest of the centers. This is done with Noah's algorithm [R+ L- R- L+] plus single set-up moves where needed. You can of course commute this with a single move in order to do a 3-cycle as well.



Step 4: Solve corners. Orientation and permutation are done at the same time, when possible. The main (base) alg that is used is Noah's: (R++ L-- R-- L++)x3 which does the following:


As Noah points out, this can be used for a 3-cycle or 5-cycle or any other cycle with even permutation. For instance, a 3-cycle: (R++ L-- R-- L++)x3 U+ (R++ L-- R-- L++)x3 U+ (R++ L-- R-- L++)x3 U-- (R++ L-- R-- L++)x3.

What is new in my method is that it doesn't require the final step (orientation) because it orients the corners as you permute them. How? You commute the base alg with with either [FR- FL-] or [FL+ FR+] as needed. Using only this and set-up moves (you can use U, FL, FR, and B moves without disturbing the two corners in back) you can solve all of the corners.

However, you will probably come to a situation in which the corners you are dealing with are permuted but not oriented correctly. You simply do something such as: (FR- FL-) [(R++ L-- R-- L++)x3] (FL+ FR+) [(R++ L-- R-- L++)x3] which does the following:


However, this is most likely not very useful since it orients two corners that are far away. However, using the same idea, you could use: (FR- FL-) [(R++ L-- R-- L++)x3] (FL+ FR+) [(R++ L-- R-- L++)x3] U- (FL+ FR+) [(R++ L-- R-- L++)x3] (FR- FL-) [(R++ L-- R-- L++)x3] U+ which does the following:


Other than what I've shown, solving is intuitive. I just combine the base alg, [FR- FL-] and [FL+ FR+], and set-up moves. Sometimes this winds up being very complicated, but it works. I think an example solve might be useful, but I can't find any good, free, screen recording software for mac. Do you know of any?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon May 25, 2009 3:07 pm 
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Danny -- Many thanks for your post, it's interesting and I shall definitely try some Pentultimate solves that way. I have a couple of suggestions for twisting two corners at the end: when going for speed rather than movecount, the spread-apart position can be done very quickly with 32 clicks: (R L')*8 (R' L)*8. And to twist the corners shown in your last screenshot, you can use 2 setup moves: the medium blue face counter-clockwise 1/5 followed by B moves the White/Purple/D.Green corner to the top.
Danny Devitt wrote:
I think an example solve might be useful, but I can't find any good, free, screen recording software for mac. Do you know of any?
I'm not a Mac user but Copernicus is freeware that seems to be reasonably well thought of and can be downloaded from here: http://www.pure-mac.com/screen.html


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon May 25, 2009 3:54 pm 
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Wow! That algorithm is very fast and almost twice as efficient! With that I think I'll be able to beat fusion's time. Thanks!

As for Copernicus, it looks like it will work fine. I'll make a video later today.

EDIT: Check the scoreboard :D :wink: (when it updates)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue May 26, 2009 7:16 am 
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Just solved 3.4.8, tricky. :shock:

I think I could cut about 300 moves, but I really can't be bothered to solve that one again.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri May 29, 2009 6:44 am 
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Also, oddly enough solving the 1 corner twisted problem on 3.4.8 has given me new insight on how to solve the 1 corner twisted problem on the icosa-pentultimate.

edit ---

solved 3.4.1, then 3.4.10. :D
I'm still too scared to touch the 3 remaining FTOs I haven't solved.

double edit ---

solved the professor / elite skewb, now solving all the patterned dogic variations.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jun 01, 2009 3:06 pm 
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1.1.7b / Super-Pentultimate

Solve like a Pentultimate (see solution here, where all the algos are compatible with the Super-Pentultimate), but with two differences:

1) In stage 2, orient each center correctly as you place it. With the first 4 centers of this stage, it is easy to borrow an unsolved face adjacent to the starting face (U) to move the center to be solved down to D and spin it around to its correct orientation. With the 5th/last center of stage 2, you may need to place it misoriented by 72 degrees, then immediately move it away and re-solve it correctly.

2) Between stages 3 and 4, twist the last 6 centers into their correct orientation. First take a quick orientation survey, adding up 1/5-turns needed to twist all the centers correctly (I count clockwise as positive, counterclockwise as negative). If you don't end up with a multiple of 5 (including 0), use one of the first two algos below or its inverse to correct the situation. (If you don't do this and twist the centers using commutators, you'll end up with a single twisted center.) Then use a combination of the other 7 algos until the centers are perfectly solved. Then do stage 4 just like the Pentultimate.

+ = twists face clockwise 72 degrees, or 1/5
++ = twists face clockwise 144 degrees, or 2/5
- = twists face counterclockwise 72 degrees, or 1/5
-- = twists face counterclockwise 144 degrees, or 2/5
Image


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jun 01, 2009 3:21 pm 
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2.2.6 / Icosa-Pentultimate

Solves like 1.1.7b / Super-Pentultimate (see previous post) but with orientationless corners. If you are interested in minimizing your movecount, you can find different (6,1) and (7,1) commutators to cycle the centers if you like.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jun 01, 2009 4:10 pm 
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2.4.1

This one is the dual of 1.3.2. It's currently mislabeled in the list; it's actually 2.1.5 + 2.2.6, combining deep face cuts with deep vertex cuts.

First I solved the 2.2.6 / Icosa-Pentultimate pieces (see previous post):

Image

The above stage is slightly faster than solving a 2.2.6, as we can use face setups along with vertex setups when cycling the centers.

Then I cycled the two-colored "arrow" edges non-pure with an (8,1) commutator:

Image

Then I finished by cycling the wings/tippies pure with a (14,1) commutator.

For hints on finding suitable commutators, and example algos, see my previous outline for the dual puzzle 1.3.2 here.

I took 236 moves on the 2.2.6 pieces, 780 moves on the arrows, and 833 moves on the wings, for a total of 1849 moves.


Last edited by Julian on Mon Jun 01, 2009 4:50 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jun 01, 2009 4:45 pm 
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Just 4.3.5 remains unsolved by anyone. Is there an adventurous puzzling soul who will complete GB for us this summer? (I'm in no rush to try to solve it, as I find the interface for 4.3.5 really confusing the way it is at the moment.)

Thanks again to gelatinbrain for creating twisty puzzle cyberheaven and to Noah for popularizing his site. :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Jun 01, 2009 7:08 pm 
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My 1.1.7b method:

Solve the first 6 centers with correct orientation. You do this just by using simple 4 move commutators, in a similar fashion to first layer corners of a 3x3 in a beginners method.

Then you do the count of turns as Julian said. If it's a multiple of 5, great. If not, turn the top face the number of turns you need. For instance, if you get -2, turn the top face two moves counter-clockwise.

Next, solve all of the centers, orienting along the way when possible.

Then perform the alg I gave before (R+ L- R- L+) however many times you need to solve the center in back. Commutate what you've done with a single turn to swap that center with another one.

After that, solve the corners normally. Nothing messes with the center orientation.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Jun 06, 2009 6:20 pm 
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2.1.1 in <1500 moves

Big edges -- intuition; at the end, flip 1 or 2 pairs with a commutator if necessary.
Corners -- permute with (1,1) commutators, then orient in pairs with (3,1) commutators.
Tippies/centers -- cycle non-pure with (6,1) commutators.

Image Image Image

Finally, cycle the small edges pure with (6,1) commutators. Tonight I solved using this method in 161 + 120 + 481 + 636 = 1398 moves. I took 3 hours 17 minutes without trying to solve quickly, so I'm sure speedy solvers will have no problem solving it in under 2 hours.

2.1.2 -- solves the same as 2.1.1, then cycle the centers pure with (3,1) commutators at the end.
2.1.3 -- solves the same as 2.1.2 but without any big edges at the beginning.


Last edited by Julian on Sat Jun 06, 2009 8:12 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Jun 06, 2009 6:52 pm 
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Thank you, Julian. I now know how to solve 2.1.1, 2.1.2, and 2.1.3 although it will definitely take me a while.

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 Post subject: Four new puzzles added!
PostPosted: Sat Jun 06, 2009 8:31 pm 
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Since the last update, 4 new puzzles have been added to Gelatinbrain! They are all dodeca edge turners joining 1.4.x.

I believe there is one more interesting and feasible dodeca edge turner possible, and it's the puzzle you'd get if you made 1.4.6 with still deeper cuts, so that when turning around the White/Purple edge, the cut intersects the midway point of the following edges: Blue/Brown, L.Blue/D.Green, Blue/Orange, and D.Green/Red. By my count that puzzle would have 332 pieces.

Thanks for the new puzzles GB! :D

[Edit 1: Clicked the wrong button by mistake, thinking I was quoting myself rather than editing, so accidentally erased my original post!]
[Edit 2: Quickly restored the gist of my original post.]


Last edited by Julian on Thu Jun 11, 2009 9:06 pm, edited 3 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Jun 06, 2009 9:13 pm 
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:shock: Oh wow, new puzzles! Thanks Gelatinbrain!!! :D

EDIT: Already solved 1.4.1 since it's basically a dodecahedral helicopter cube. I always wondered why this puzzle didn't exist. Very fun!

And now that I think about it, do you think GB will be making the dual puzzles as well?

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Last edited by Danny Devitt on Sat Jun 06, 2009 9:40 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Jun 06, 2009 9:28 pm 
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Did a gigaminx for the first time, it took me 45 minutes. I also solved a helicopter cube in under 70 moves and the super-x in just under 80! I'm still having trouble submitting though, I've read through a little bit, but whatever, it isn't like I'm setting records.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 07, 2009 4:34 am 
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Hehe, just solved 1.4.1, very easy. Too bad I'm still god awful at deeper cut edge puzzles (although I'm getting very close with 3.3.2!)

edit -----------

Thanks GB!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 07, 2009 5:51 am 
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Danny Devitt wrote:
And now that I think about it, do you think GB will be making the dual puzzles as well?
Good question. We now have 187 visible puzzles out of a total of 189 stated at the bottom of the rankings page, so maybe the last 2 will be icosa edge turners? AndrewG gave UMC screenshots for some possible icosa edge turners here. I think that:

E23 (top left) = shallow cut helicopter, doesn't exist in 1.4.x
E34 (top center) = 1.4.1
E44 (top right) = 1.4.4
E50 (lower left) = 1.4.5
E69 (lower center) = 1.4.2
E80 approx (not shown) = 1.4.6
E90 (lower right) = deeper cut than 1.4.6, where the cuts intersect midpoints of edges, doesn't exist in 1.4.x

If GB is going to add 2 icosa edge turners, I'm guessing they'll be the duals of 1.4.1 and 1.4.5, for psychological reasons. :) I've noticed that GB has a fondness for equivalent puzzles across the board, so {1.4.1, dual of 1.4.1, 3.3.1, 4.3.1, 5.2.2} would make a nice set; and he is also fond of puzzles with faces that look the same, and the dual of 1.4.5 would have faces exactly like 4.3.2.


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 Post subject: Re: Four new puzzles added!
PostPosted: Sun Jun 07, 2009 8:34 am 
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Julian wrote:
That deeper cut one, 1.4.6, amazes me because if I'm counting right it has 470 pieces!
1.4.6 - Solution Outline (no algos)

1.4.6 turns out not to be super-hard, though solving the corners is a bit confusing and it will take lots of time to set up and solve all the little pieces. As it could be a long time before I get around to solving this one (again, that's 470 pieces!), I'm posting an outline in advance. No actual algos, just a possible solving order/method:

Image

1 Edge-aligned kites - Directly solve as many as possible, then cycle the remainder with (3,1) commutators
2 Corner-aligned kites - Cycle with (1,1) commutators
3 Corners - Solve mostly in pairs using base (3,1) commutators, with extra setups to adjust orientation
4 Edges - Cycle with (1,1) commutators
5 Edge-adjacent tippies - Cycle with (6,1) commutators
6 Other Fat tippies - Cycle with (4,1) commutators
7 Thin tippies - Cycle pure with (6,1) commutators

[Edits: V1 solution order was 3 2 1 4 5 6 7; V2 order was 3 1 2 4 5 6 7. A sub-4000 move might be possible with V3 above; we'll see.]


Last edited by Julian on Thu Jun 25, 2009 4:30 pm, edited 2 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 07, 2009 11:07 am 
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I swear, if you scramble that puzzle it looks more confusing than a petaminx. :lol:

Off-topic, does anybody know why GB removed this puzzle from his site?
Attachment:
hexa_v2.gif
hexa_v2.gif [ 2.62 KiB | Viewed 4625 times ]

It's a higher order 3.2.5 (I think).

Edit ------------

Julian, the two hidden puzzles are just different colour variations of 6.1.1.
You can find them while in the applet, just go File > New > Spheres > 6.1.4/6.1.5


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 07, 2009 12:59 pm 
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Percy wrote:
Off-topic, does anybody know why GB removed this puzzle from his site?
[image]
It's a higher order 3.2.5 (I think).
As hexa_v2.gif is now the image for 3.2.3, my guess is that GB had the wrong image up for a while and then fixed it. The puzzle shown in your post is available in the Windows standalone version: File > New > Cubes > V3. But I've never noticed "3.2.5's Revenge" as an option among the web applets. All the pieces of 3.2.5 are there but the evil big brother also has corners (which are permanently attached to the squares adjacent to them), centers, and the squares adjacent to the centers. The centers and adjacent squares can be cycled at the end, but I can't see how to solve the corners without messing up the edges, or vice versa. That part looks really really hard.
Percy wrote:
Julian, the two hidden puzzles are just different colour variations of 6.1.1.
You can find them while in the applet, just go File > New > Spheres > 6.1.4/6.1.5
Thanks -- funnily enough, I never thought to click File in the web version, at least not for the longest time!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jun 09, 2009 1:08 am 
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I solved 1.2.2 for the first time today. The time and move count were both pretty bad. The first time I solved it, I thought this puzzle was pretty straightforward. On my next attempt though, I ran into a situation where I had one corner misoriented. I know that other people in this thread have had this same problem so it isn't just glitching on me, but I can not seem to come up with a solution. Does anyone have a simple one?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jun 09, 2009 2:20 am 
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Dang, Julian, you solved 1.4.4 first! I came up with a solution earlier tonight but didn't have time to solve yet. Here's my method, what's yours?

1. corners- intuitive
2. large triangle centers- 8 move 3-cycle, non-pure
3. kite centers- (1,1) commutator 3-cycle, non-pure
4. small triangle centers- (4,1) commutator 3-cycle, non-pure
5. edges- (4,4) commutator 3-cycle, pure



SteveRider wrote:
I solved 1.2.2 for the first time today. The time and move count were both pretty bad. The first time I solved it, I thought this puzzle was pretty straightforward. On my next attempt though, I ran into a situation where I had one corner misoriented. I know that other people in this thread have had this same problem so it isn't just glitching on me, but I can not seem to come up with a solution. Does anyone have a simple one?

You have to turn the corner and then resolve.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jun 09, 2009 1:22 pm 
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Danny Devitt wrote:
Dang, Julian, you solved 1.4.4 first! I came up with a solution earlier tonight but didn't have time to solve yet. Here's my method, what's yours?

1. corners- intuitive
2. large triangle centers- 8 move 3-cycle, non-pure
3. kite centers- (1,1) commutator 3-cycle, non-pure
4. small triangle centers- (4,1) commutator 3-cycle, non-pure
5. edges- (4,4) commutator 3-cycle, pure
Dang, Danny, your solution is much better than mine! :lol: With your approach I would probably have taken 500+ fewer moves and got to bed a lot earlier. My stages 1 and 2 were the same as yours (solving an edgeless 1.4.1) but then I did edges (1,1), kites (6,1) and small triangles (6,1). I completely forgot an important principle of efficient solving: "the needs of the many outweigh the needs of the few." With 120 small triangles and only 30 edges, I should have tried to look for quick ways to the triangles non-pure, and left the edges to the end, as you did. (The same numbers cropped up with 2.1.4 and I was smart that time and left the edges to the end.)

I'm going to try your method this weekend, with a few small refinements:

1) Michael's really low move count for 1.4.1 makes me wonder if he somehow scoops up the right triangles at the same time as he places the corners as often as possible, before cycling the stragglers at the end. This trick would work at the beginning of 1.4.4 too.

2) 3 small triangles can be cycled non-pure (edges move too) in 8 moves with an algo like (ABA C)*2.

3) 3 edges can be cycled pure in 12 moves with an algo like (ABCBA D)*2.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Jun 09, 2009 6:13 pm 
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1) Yes, I wondered this too. I also thought he might have used a corners-last method.

2) Found the alg, I'll be using it.

3) I can't seem to find it. But considering it's only an extra 4 moves and I'm not really going for moves, I might just stick with mine.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jun 10, 2009 2:03 pm 
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1.4.4 Orbital Alert

The large triangles solved in Danny's stage 2 lie in 6 orbitals of 10 pieces, so if you don't check ahead there's a 5/6 chance of starting out by solving the corners into impossible positions. If you follow an orbital of pieces snaking around a Pentultimate cut and find that white and yellow are missing, that Pentultimate cut lies midway between the white and yellow faces. Once you've examined two orbitals you'll know how to solve the corners into valid positions. (The same orbitals exist with 1.4.1, but because 1.4.1 has fixed centers, there's no need to notice them.)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jun 10, 2009 2:31 pm 
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Another new puzzle added!

2.3.2 = icosa edge turner
Attachment:
File comment: GB 2.3.2
icosa_e1.gif
icosa_e1.gif [ 3.61 KiB | Viewed 4355 times ]
Thank you again GB! :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jun 10, 2009 5:50 pm 
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Julian wrote:
1.4.4 Orbital Alert

The large triangles solved in Danny's stage 2 lie in 6 orbitals of 10 pieces, so if you don't check ahead there's a 5/6 chance of starting out by solving the corners into impossible positions. If you follow an orbital of pieces snaking around a Pentultimate cut and find that white and yellow are missing, that Pentultimate cut lies midway between the white and yellow faces. Once you've examined two orbitals you'll know how to solve the corners into valid positions. (The same orbitals exist with 1.4.1, but because 1.4.1 has fixed centers, there's no need to notice them.)


I noticed the problem but couldn't figure out the solution. That makes sense. Thanks.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jun 10, 2009 8:09 pm 
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Julian wrote:
1) Michael's really low move count for 1.4.1 makes me wonder if he somehow scoops up the right triangles at the same time as he places the corners as often as possible, before cycling the stragglers at the end. This trick would work at the beginning of 1.4.4 too.


I do - in 1.4.1 (and the Helicopter Cube) I place all but the last layer corners F2L style. I put the triangle on the "D" layer in first, and then once I have the corner correctly positioned I will add on the other two adjoining triangles before inserting it. I think this is a bit hard to recognize on 1.4.4 but it would definitely be an option.


Anyway, I did 1.4.4 today! :D My method was:
1) Figure out where the heck to put the first two faces :P I chose white and teal for the first two, and since the corner centers are in 6 orbitals (as you guys have mentioned) I used them to figure out where to go. Hint: The only centers that a given corner center can't be on is the one it "points" to (and the opposite one), so you can figure out where a given color goes by process of elimination. There are two solutions, though, and I think one is the wrong chirality (the corners don't fit).
2) Solve the corners 1.4.1 style.
3) Solve the corner centers 1.4.1 style. I probably could've saved some moves by placing them with the corners but I didn't want to put too much thought into it at this point because of the last step.
4) Solve the edge centers ('kites'). I used nonpure 4-move commutators.
5) Solve the edges. I again used nonpure 4-move commutators. I actually solved permutation and then orientation (there's an 8- or 10-move 2-flipper) because I'm lazy; could've saved moves here of course.
6) Solve the edge wings (those little triangular bits) pure. This step took me probably half of my time spent and about half of my moves too, because there are 120 little fiddly pieces (in 2 orbits - orbits on a dodecahedral or icosahedral puzzle can't have more than 60 pieces). My commutators were mostly at least [3,3], I think I used some [3,4] and [4,4] and even [3,5]... just ugly stuff. In general it's a commutator of a move that leaves one edge group (edge + 2 wings) unchanged except for one wing, and an edge group 3-cycle. I think I used way too many setup moves too (like 8-10 for the trickier cycles).
Anyway, 2:00:29 and 2096 moves (in one sitting). I've never spent over two hours on a gelatinbrain puzzle before... so ouch. Go ahead and beat my movecount and time if you want - I don't think I'll be solving this one again :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Jun 10, 2009 8:32 pm 
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I think you'll beat my move count, but I may beat you for time. In any case, I doubt I'll get a solve up until the weekend.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 11, 2009 3:16 pm 
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I tried my luck today on the sheperd's and maze 3x3s, and after a couple of hours on both of them I have concluded they are impossible. I have to ask, if either of the two ever read this, how the hell did Ethan get 39 moves and 2:18 on the sheperd's cube and even crazier, how did Doug get 24 moves on the maze 3x3? I can't even do either of those two move counts on a normal 3x3!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 11, 2009 7:15 pm 
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I would assume Doug figured out the equivalent position on a regular cube and then did a FM solve on that. As for Ethan, I guess he's just quick.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 11, 2009 7:50 pm 
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qqwref wrote:
In 1.4.1 (and the Helicopter Cube) I place all but the last layer corners F2L style. I put the triangle on the "D" layer in first, and then once I have the corner correctly positioned I will add on the other two adjoining triangles before inserting it. I think this is a bit hard to recognize on 1.4.4 but it would definitely be an option.
Thanks, I shall try this.
qqwref wrote:
Anyway, I did 1.4.4 today! :D My method was:
1) Figure out where the heck to put the first two faces :P I chose white and teal for the first two, and since the corner centers are in 6 orbitals (as you guys have mentioned) I used them to figure out where to go. Hint: The only centers that a given corner center can't be on is the one it "points" to (and the opposite one), so you can figure out where a given color goes by process of elimination. There are two solutions, though, and I think one is the wrong chirality (the corners don't fit).
Hmm, you're right, and with my way of checking 2 orbitals there's still a 50/50 chance of trying to solve into the inverted color scheme, and the corners won't fit. But if you examine 3 orbitals you can be sure. For example, let's say after checking 2 orbitals you know white/yellow and teal/orange but you can't be sure which way round they are. Line up a candidate white face as U with candidate teal as F, then look through the orbital of triangles running through U, F and L but not R, and see if there is a brown triangle among them. If you don't find a brown, that proves the white/teal/brown corner doesn't belong at U/F/L and you're actually looking at yellow as U and orange as F.
qqwref wrote:
I think I used way too many setup moves too (like 8-10 for the trickier cycles).
I think the puzzle is just evil that way, with some longer setup sequences unavoidable.
qqwref wrote:
Anyway, 2:00:29 and 2096 moves (in one sitting). I've never spent over two hours on a gelatinbrain puzzle before... so ouch. Go ahead and beat my movecount and time if you want - I don't think I'll be solving this one again :)
Danny Devitt wrote:
I think you'll beat my move count, but I may beat you for time.
Other way round for me! I'll never solve a puzzle like that in under 3 hours but I'm setting myself a target of 1700 moves for my second solve.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 11, 2009 9:01 pm 
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Julian wrote:
I believe there is one more interesting and feasible dodeca edge turner possible, and it's the puzzle you'd get if you made 1.4.6 with still deeper cuts, so that when turning around the White/Purple edge, the cut intersects the midway point of the following edges: Blue/Brown, L.Blue/D.Green, Blue/Orange, and D.Green/Red. By my count that puzzle would have 332 pieces.
I've made a more detailed diagram since then, and I've realized that it isn't feasible after all. That puzzle would have 692 pieces, of which 120 are tiny, so we now have all the "sensible" single cut dodeca edge turners in Gelatinbrain.

But there is a double cut dodeca edge turner that I think would be fun -- a kind of 1.4.2 + 1.4.3, where regular clicks are 1.4.2 turns and shift-clicks are the slices between the 1.4.2 and 1.4.3 turns. 10 big triangles, 10 medium triangles, and 10 small triangles on each face, with all the triangles split between left-handed and right-handed orbitals.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Jun 11, 2009 11:14 pm 
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Danny Devitt wrote:
I would assume Doug figured out the equivalent position on a regular cube and then did a FM solve on that. As for Ethan, I guess he's just quick.


Still, 24 moves is absurd!

I tried my luck with 1.4.1, and I have to say that this is a very enjoyable puzzle! I my first try was 402 moves, and my second try was 387 after reading qqwref's post.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jun 12, 2009 12:01 am 
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I took the time to solve 1.4.4 tonight. 3:35:49 and 2970. This wasn't straight through or anything and I was also still playing with my algs as I went along. I'll probably solve again some time, possibly this weekend. I wouldn't expect the move count to get that much better, but the time should significantly decrease. I'm hoping my new time will be comparable to Michael's.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Jun 13, 2009 4:18 pm 
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Solving 1.4.1 "F2L style" (as described by Michael above) is really fun. :)

Solving the corners and big triangles of 1.4.4 the same way was okay. I focused my eyes on the shapes of Pyraminx Crystal corners and assembled those corners. With the 1.4.1 pieces solved in 302 moves, I continued with the same solution order as Danny's outline, taking 1870 moves overall. Assuming I saved around 100 moves with F2L for the 1.4.1 pieces and another 150 moves by solving the small triangles non-pure with shorter algos and leaving the edges to the end, my solve was otherwise in the same ballpark as Michael's. But it took me 6+ solving hours plus extended breaks to prevent exhaustion. You guys are fast!

1.4.5 should be easier, as there aren't any pesky orbitals to worry about, and 4 out of 6 piece types solve exactly the same as 1.4.4.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Jun 13, 2009 7:19 pm 
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I hadn't even looked at 1.4.5 before you mentioned it. My method would be:

1. corners
2. diamond centers
3. big triangle centers
4. pentagonal centers
5. small triangle centers
6. edges

I already have all the algs I need too so it's just a matter of having the time to solve it.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 14, 2009 3:00 pm 
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Before I start on 1.4.5, I have a question: is there still a problem of putting the corners in the wrong place? I don't want to put hours into this puzzle only to find out I did the first step wrong.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 14, 2009 8:52 pm 
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Danny Devitt wrote:
Before I start on 1.4.5, I have a question: is there still a problem of putting the corners in the wrong place? I don't want to put hours into this puzzle only to find out I did the first step wrong.
You're safe. Every move of 1.4.5 changes the sign of corner perm, center perm, and edge orientation. So when you've solved the corners, by definition they are in an even perm and all the other pieces are too. And apart from the obvious left-handed, right-handed split between the large triangles, there are no orbitals to worry about.

I solved 1.4.5 today in several mini-sessions. My order was almost the same as your suggested method, except I left the big triangles to second-last, just before finishing with the edges. If you solve the small triangles with a commutator like (ABA, CDC) or (ABCBA, D), notice that if you allow big triangles and edges to be moved around you have a choice of 4 different moves for D. Including mirror images for non-symmetrical positions, that gives 7 possible places to set up the 3rd small triangle for each cycle, which makes setting up easier, faster, and probably saves around 100 moves too.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jun 14, 2009 9:10 pm 
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Alright, good to know. I still have school all this week and I have projects I need to work on and finals to study for so I probably won't be solving this for another week or so. But then it's summer so I'll have plenty of time to work on puzzling.

This morning I solved my 120th puzzle to tie Campbell so I'm happy about that. But then Doug has another 26 puzzles on me! That's ridiculous! And that's without some of the newer puzzles! Point is, I still have a way to go!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jun 19, 2009 9:44 am 
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Problem on the icosa-pentultimate

I went with Julians method for the super-pentultimate, but the triangle centers (pentultimate corners) just with one alg. First, I put all of the pentagonal pieces in place, then I was turning them around, and had almost all of them, exept for one pentagonal piece that needed a + twist, But, I couldn´t come up with a combination of the algs Julian posted.

Any suggestions?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jun 19, 2009 1:54 pm 
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Hi Sjoerd,

The inverse of the first algo pictured in my outline for 1.1.7b will resolve the situation. You'll end up with an balance of + and - twists, 3 of each. Or you can twist the problem corner 72 degrees clockwise and solve the 5 neighboring corners again with commutators. It's a good idea to count up the + and - right after you've permuted the last 6 corners, that way you won't arrive at the annoying situation of a single twisted corner.

By the way, it's bugging me that I can't find Doug's 24 move fix for a single twisted corner of 2.2.3-2.2.5 (here). Doug, if you're reading this, can you throw me a bone and let me know if it's 8 moves repeated 3 times, perhaps (3,1)*3? 3-gen, 4-gen, or 5-or-more-gen? I'm guessing it's cycling 3 blocks of pieces with a side effect of twisting a corner 2/5, so when repeated 3 times all the blocks are back but with a corner twisted 6/5 = 1/5. Every few weeks I immerse myself in 2.2.3 and spend an hour or so experimenting, but I can't twist a single corner without moving other corners or edges. :?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jun 19, 2009 3:47 pm 
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Hello
I'm wondering if anyone has a quick fix to this very annoying helicopter cube problem
Image


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jun 19, 2009 4:29 pm 
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Ah! Of course! Thanks Julian.

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