I too thought the inverse of a move wasn't the inverse but it turns out that you aren't clicking on the face to turn it but the face and the individual cubie. When you click on the top cubie it moves and so the inverse moves too.

UBR is the inverse of URF'

Thanks Stefan, that did help! I see you've improved your move count even more Hope I can get to solve this puzzle soon.

I finally decided to start solving puzzles on gelatin brain a month ago and now I'm up to 110 puzzles solved. Thought I should post something now that I hit 100+ puzzles and comment on a few puzzles.
First of all, I'd thank gelatinbrain for making this amazing program. There's so many puzzles I've gotten to solve this way that can't exist in reality or are too expensive to buy off of Shapeways.

I'd also like to thank all the preview solvers for their tips on solving puzzles. Special thanks to Brandon for hanging out in IRC and helping me with puzzles.

So far, my favorite puzzle is 1.1.10 the master brilic. It has a fun reduction like you'd expect on a 5x5 or a gigaminx, but the centers are way more fun. And the backwards edge pairing is a nice change of pace.

The whole series of 4x4 and 5x5 circle puzzles were fun. It takes a while to identify the pieces and after that, they are relatively simple. I think it's really cool having 5x5 pieces on a 4x4 puzzle.

I think it's interesting how some of the puzzles are a lot easier than they first seem. Perfect examples are 3.13.1 and 3.10.1/2 (no letters). Initially they are quite intimidating at first, but once you get to know them, they are actually quite easy. I would highly recommend all 3 of these puzzles. Especially 3.13.1. Just happened to get a super lucky scramble on it today so I manage to reclaim the move count record from Agamemnon with an unassailable 3.

It's also interesting how there are some duplicate puzzles but they look different because they have strange cuts, circles, or special stickers. There's at least 3 super megaminxes out there. It took me a while to realize 1.2.19 was dino dodecahedron or that 1.1.11 wasn't starminx related.

Couple requests before I go.
First, could you display the name of the puzzle you're solving somewhere? Sometimes I forget which puzzle I'm looking at.
Second, could you make a version of 1.13.1 where instead of having 3 rotate and 1 translate, could you have 3 pieces translate and 1 rotate? It should be just as easy to solve but more confusing.

My internet died last night while I was solving puzzles. So here's a few certificates that didn't get emailed.
1.1.77
9e7cc64d10869e0dcde40a8eab16aa2c
14e4ba31841aa53482eda833d5584fb0
9d693bcc97762fc49b5d37ef9e4c3dc3
7689ec135ea1bc436e91dc237a85f40b
1.1.78
e6e7366ff8dc4f7af1e572d164b33579
f51b79b92773e2e972274966eace31e5
1ac034ee19d332b2586bb0a562c1c495
682fd09b6437c89e613dc27689ec135e

Welcome!

110 puzzles in a month? That's a truly amazing speed!

Before I started, I would have agreed with you, but there are a surprising number of easy and duplicate puzzles. There's nearly 20 circle cubes puzzles that if you can understand the principles of circles, you can easily do all of them. Nearly all of the puzzles also have a dual version or circle version too. I'm sure I can hit 150 without breaking a sweat. There's still a lot of tetrahedrons and vertex octahedrons I know I can do but haven't gotten to yet. Brandon's tutorials have also been helpful and I'll be starting on some deeper cut harder puzzles soon I hope.

Nevertheless, I'm really amazed like schuma how fast you proceed - congratulations also from me!!

Gelatinbrain, thanks for adding the new puzzles 3.9.5* series. I'm here to beg for clarifications again: is it true that only the stickers on the surface matter? Thanks.

I found a bug for the 3.9.5 series: once I shift + clicked, the whole window was frozen.

An unimportant thing is that although the new .jar file contains more puzzles, the size of the file is smaller than the previous version. I don't know why it happened.

Yes, only surface matters. The bug is fixed.
I don't know why the jar file is smaller. But sounds a good news.

I searched for two hours to find a pure 3-cyle for the center triangles of 3.4.1 but the best I could do is [7,1]. I've tried and tried to find a [1:[1:1],1] but I just can't find it. What am I missing? Is the routine not of that form?

It's so frustrating to try so hard an not succeed

I just solved 3.9.5. It looks simple but it's actually hard. It's even harder than the 3.9.1 series.

Although all pieces look the same, as in 3.9.1, they are divided into two groups by the available orientations.

But there's another trap. In my first attempt, I ran into the situation to twist a single piece by 120 degrees.

Although only the stickers on the surface matter, there's no other way around. In 3.9.1, the "core piece" can be used to do a counter-rotation. But in 3.9.5, the "core piece" is never moved and never seen.

Eventually I've got an inefficient method to resolve the issue. But my method is not directly applicable to 3.9.5b and c. And I don't fully understand the issue. It's about hidden orientation. But I don't know how to prevent it in advance yet.

The shortest I've been able to find is [5,1] pure. It's made up of 5 face turning moves and then a Skewb move to move the isolated x center. Here's the one I've been using:


R, U, R', U', R',
FDL',
R, U, R, U', R',
FDL,

Just so you know, I spent a long time finding this. But I do think this was the first pure algorithm I did find. I also felt that when I found it, I understood a lot of the 3.4.x's, and that this was essential knowledge to go on and solve more of them. This algo can be used to cycle pieces on a few other 3.4.x's too. For instants; it's pure for 3.4.3 and 3.4.10. And non-pure for a whole bunch of other puzzles.

Okay I don't feel so bad about not finding this now. I've looked at you routine over and over and I don't understand how it works. Your X portion doesn't isolate a piece. It "isolates" 3 pieces that get spun into each others' spot. That should make a 5-cycle or two 3-cycles. I explored many ways to use face moves to try to isolate a piece like you do but when I ended up with 3 being moved in the Y part I didn't even bother to finish the routine.

Something very special must be happening to cause what would be a 5-cycle to cancel a portion out and leave just a 3-cycle.

For example, [R, U', R', U], DBL', [U', R, U, R'], DBL also "isolates" 3 pieces in a vertex move but instead of ending up with a 3-cycle it generates a 5-cycle like I'd expect.

After all of the work I did last night I'm pretty sure it is impossible to isolate a single piece in only 5 moves. I never considered trying to make a pure 3-cycle out of something like this. How did you realize that some special condition is being met in your sequence to yield a 3-cycle instead of something longer? I just can't see it. How does it work?

Gelatinbrain has brought us another batch of puzzles! Also, now there is an animation speed slider. This is a feature I have wanted for a while for capturing video tutorials at a slower, easier to follow speed. I didn't have a heart to ask for it though. Thank you for reading my mind

Hi Brandon. That problem made me busy too for a while, I found an answer:


The A part of the sequence does a 4-cycle of the pieces 1,2,3,4 (see the picture).
Then the B part cycles 3,2,4 relative to 1.
Then comes A' and B'.
The effect is a 3-cycle.

Here is a table of what happens
1 2 3 4
A
4 1 2 3
B
4 2 3 1
A'
2 3 1 4
B'
2 4 3 1

Always something new..
Thank you, especially Katja for the move-sequence,
Stefan.

Edit: The same table as above again, a bit nicer:

Hi gelatinbrain. The new animation speed slider is cool. It's a good addition. Well done.
Thank you, Stefan.

Oh no! More 3.9.* puzzles? They'll take forever to understand and solve.

Found a small bug that if a puzzle is solved after completing a macro, it doesn't register it until you do a move and undo it.

The 3.13.1 series was a really fun puzzle for me so I wanted to share my method (at the risk losing records). Seeing the other solves (or lack there of), it seems most people aren't doing this like I am. I think anyone can get a sub-20 move count like this. Here's my basic order with more detailed hints revealed with highlighting.

1. Solve the white face. Solve each cubie with simple rotaions like (A A')
2. Solve the rotation of the cubies with the white face. Pick 1 cubie to be the standard. Click the white face of an adjacent cubie until it matches the standard.
3. Solve the yellow face. Like Step 1, but you have to do everything within 1 layer. Make sure you save 2 adjacent cubies to solve together at the end with something like (A A'). If you solve 3 before trying to get the 4th, you'll have to break 1 and fiddle with them both for a bit before you can fix them.
4. Solve the rotation of the cubies with the yellow face. See step 2. We're not trying to match it to the white layer, just the other cubies in the yellow.
5. Match the two layers. Do something like (UFR)*4. Note that I don't mean UFR4.

The b/c variants don't add too much. You just have to use 2x2 methods to permute the cubies and you can orient the cubes the same way. Step 5 has to be different which I don't have a great method for besides 2 3-cycles or just restarting.

GuiltyBystander: Thanks for sharing your 3.13.1 technique. It's good to have another person solving and keeping us on our toes. I also think it's good to share even at risk of losing records. I need to share my Dino Skewb (3.2.13) technique sometime. When I do that record will be easy to beat.

Schuma: At some point we discussed if Gelatinbrain can detect the Starminx solved into its inverse color scheme. I tried it today and it turns out you can't solve it into the inverse color scheme. You end up with two swapped Pyraminx Crystal edges. I wasn't expecting that.

Katja and Stefan: Thank you very much for the 3.4.1 routine and the analysis of it. I definitely would not have found it because I was looking for isolation.


Using a minor variant of Katja's routine and reduction, I was able to solve 3.4.1 in 100 moves for the record. I didn't try very hard. I wonder in Michael used a longer routine?

I also solved 3.4.3 with reduction to a 2x2x2 and crushed the record (344 moves). My record is easily beatable though so I think the previous record must not have been reduction.

I also solved 3.4.6 via reduction to a 3x3x3 and beat the record by a wide margin (464 moves). Again, this is not a particularly hard record to beat if you use reduction.

I really like the 3.4.X series, I should have tried these puzzles earlier.

After you said that, it becomes obvious that will happen. I should've seen it before.

(1) If the starting state and the objective state are left-right mirror images of each other, 4 edges are not moving and 26 edges are moving in the way of swapping 13 pairs. Since 13 is an odd number, this permutation is odd and thus impossible.

(2) If the relation from the starting state to the objective state is a left-right mirroring followed by a global rotation, the situation is the same because the global rotation is several 5-cycles and thus an even permutation. So the whole process is still odd.

I completely forgot about this! I didn't paste the algo into any puzzles before I posted it here yesterday. I would have worded it differently and also mentioned this if I had remembered it. I posted something here on the forum when I found it actually, but I'm not sure if anyone noticed it.

I wasn't sure whether it would work when I found it, but I had a feeling that it would so I tested it and it worked perfectly! This happened some time ago, and I wasn't sure how I'd analyze what actually happened and why it worked back then, but now that I'm a lot more experienced I would do it the same way as Stefan did and make a table. Thank you for your analysis Stefan! And no worries; that's what this thread if for

I tend to find algorithms of this type rather easily. I have a similar one (which does not isolated one single piece, but rather move them into each others spots and swaps them that way) for the Face turning octahedron (BRU, LUF', BRU', LUF, ULB', BRU, LUF', BRU', LUF, ULB, BRU, LUF', BRU', LUF, ULB', BRU, LUF', BRU', LUF, ULB,) and also for the Pentultimate (F, C', F', C, K', C', F, C, F', K, F, C', F', C, K', C', F, C, F', K,)

I also think a [5,1] is the shortest possible pure routine for the x centers on 3.4.1, but I have no idea how to prove it. At least, I can't see a way to affect only edges in one half of the puzzle and at the same time "isolate" an x center in less than 5 moves.

This is a bit different. It's a [[1,1],1]x2. The reason it works is that it does a 2-2 swap which is cyclic modulo 2 and a 3-cycle that is cyclic modulo 3. If you apply it twice the 2-2 swap cancels but you end up with an excess 3-cycle. Apply it 3 times and you have no 3-cycle but you get 2-2 swap.

This is also a 2-2 swap + 3-cyle. By applying it twice you cancel the 2-2 swap.


In this case we can use a proof by Julian. In brief: assume there is a shorter 3-cycle for the centers of 3.4.1. Then, Julian would have found it. Julian has not found a shorter cycle though which is a contradiction. Therefore there is no shorted 3-cycle. QED

Aw shucks! I don't know a shorter routine than [5,1] for 3.4.1. As a matter of fact, [5,1] routines came up so often in my solutions for 3.4.x that I would almost call that set "[5,1] city"! The basis of my algo for 3.4.1 is a bit different; it cycles 3 triangles in a face in 5 moves while messing up the other face:

L, F, DBL, F', L'

Commuting this with U or U' gives a pure 3-cycle, but not U2 (which gives a 2-2 swap instead). I seem to remember that I used a similar technique in most of 3.4.4-3.4.9.

Nice new solves of these puzzles, Brandon! At the time, some of us were racing to solve puzzles that nobody had ever solved before, in pioneering spirit. Our goal was to solve every puzzle by the end of 2008 and I think we succeeded (but there were "only" around 150 puzzles at the time). I tried to solve as efficiently as I could but I was quite new to Gelatinbrain and cycled everything back in those days.

I dig into the history of this thread and found that you were the one solved the last unsolved puzzle at that time. Great job! I'm again surprised by how fast Gelatinbrain created new puzzles recently. I collected some data of the total number of puzzles and made the following plot.

The x-axis is time and the y-axis is the total number of GB puzzles. The plot is based on these data:

Sep 26, 2007 96
Dec 29, 2008 ~150
Jan 26, 2010 221
Feb 20, 2010 246
Aug 13, 2010 284
Jan 09, 2011 378
Sep 13, 2011 503
Oct 06, 2011 537

I couldn't find more date/count, like, no point in 2009. If anyone knows more, I can add some points to the curve.

Hi Gelatinbrain,

I've solved 3.9.6c just now. But the solved state is not recognized. Please see attached an screenshot as a proof. The time there is 1:51:58. The move count is 11377. Note that it's 10000 more than 1377, which is in the screenshot. Most of the moves are macro moves. Would you kindly add it to the record page manually? Thanks.

The color scheme of 3.9.6c is identical to 3.9.2c. But by the time I solved 3.9.2c my solution was not recognized either. It seems like a bug. If I can solve 3.9.7c, maybe it will occur again and I may have to bug you for that again. Thanks in advance.

-- schuma

Hi Gelatinbrain,

Just now I've solved 3.9.7c. It was not recognized either. Here's the screenshot. The time is 1:37.07, the move count is 3909. I really appreciate it if you could add it manually to the record page. Thanks.

-- schuma

I added 3 simple puzzles, 1.1.81, 4.1.19 and 2.2.21.

1.1.81 and 4.1.19 are, in my view, dodecahedral and octahedral counterparts of 2x2x2.
Because all 3 puzzles share common properties:
· Deep cut (2-layer) puzzles divided into two equal parts.
· Consisting of only 1 set of pieces, each identical and oriented.

I added them because I think they are the simplest representations of twisty puzzles,
and a good start point to think about the mathematical definition of twisy puzzles.
And maybe helpful also for a more systematic approach to the solution.

Beside the evidence that they are all groups, what we can say about their algebraic structures and properties?

Hmm, are those simple? Without twisting them, they look like Pentultimate corners, Skewb Diamond Corners, and Pentultimate Centers (twist visible).

I have been pulled in too many different directions lately. I have been working on some mathematical ideas to solving, both in the form that the routines must take as well as finding short routines. GuiltyBystander and I have had some really great conversations about "complex" puzzles. I'm particularly interested in the complex face-turning dodecahedron but the program I'm planning will be able to handle any puzzle (logically, not graphically. I still don't understand how you do that!).

As long as you keep bringing out great puzzles to solve I won't have any time for programming and working on my ideas!


Edit: 4.1.19 doesn't have very many states (960 by my count) so by hitting scramble a bunch I've managed to get a 0-move solve. Via some more scrambling I managed to get a 1-move solve before the counter reached 1 second for a 0-second solve.

Thanks! I'd agree that 4.1.19 is very simple, but the pentultimate corners are pretty hard to cycle. A 0 move solve? I got a 1-move solve in 3 seconds.

I saw the new puzzles and read pentultimate in the post above so I wanted to revisit it.
So far my procedure was this:
4.1 commutator for center 3 cycle.
4.1.1 for corner placement (22) moves
4.1.1.3 for corner orientation. This is a 50 moves alg that is based on placing the corners than changing orientation of one of them then undoing the whole placement part (which itself consists of the center commutator)

So all of these just build up on each other. This just takes to long and is to hard to keep track of. But i sat down and came up with somethin better.

I found a 3.1 for centers and a 3.1.1 for corners. (8 and 18 moves)
These are not much better than the ones I had first but now comes the improvement:

I figured a way to orientate two corners without having to perform a full positioning "underneath" the orientation:

/*000000*/E,
/*000001*/B,
/*000002*/E',
/*000003*/D',
/*000004*/E,
/*000005*/B',
/*000006*/E',
/*000007*/D,
/*000008*/F,
/*000009*/E2,
/*000010*/F'2,
/*000011*/D',
/*000012*/E,
/*000013*/B,
/*000014*/E',
/*000015*/D,
/*000016*/E,
/*000017*/B',
/*000018*/E',
/*000019*/F2,
/*000020*/E'2,
/*000021*/F',

These are 22 moves for orientating two adjacent corners. In it is the 3.1 commutator for centers. But then I just orientate a corner with 3 moves and undo the whole thing and there is enough space solved on the puzzle so I dont have to do the positioning first.
So I have the same base for positioning and orientation except that in orientation I need three moves whereas for positioning I only need one move in the commutator.

But still at this point I would like to ask for the best algs that have been found for the puzzle. I couldn't find the right posts via search function. I guess there are better ways for placing corners than 18 move algs and also better ones for orientation of the corners.
If someone could post the best ways to solve corners on a pentultimate that have been found so far I would greatly apreciate it.

Me and a few others usually position and orient the corners simultaneously by using slightly more set up moves. It's a little more complex but very handy to know how to do if you are interested in getting good move counts. Brandon put in a massive amount of effort in designing a program to find short sequences to cycle corners and came up with some 10 move ones. I use one of them (well I did when I solved it last) A2, D', F, E2, D', E'2, D, F', A'2, D

In other news, the number of puzzles is now so dauntingly huge. As is the amount of discussion I have missed. I feel rather out of the gelatinbrain loop

I don't know if I'll ever be quite as present here as I once was. I have lost a lot of records I once had too! It's tempting to try and get a few of them back (especially gigaminx, pentultimate and starminx) but I haven't got the desire to solve enough to spend the effort. It's easier to live vicariously through the collective solvers and fewest move people's conversations and records

We have seven more puzzles. It's like the Cambrian explosion. So hard to catch up.

I would hate to see you stop solving But I know how you feel. I felt the same when I stopped solving for a few months and when I got back into it, there were over 100 new puzzles. I no longer see it at a reasonable goal to finish all of them, at least not for me. I just solve the ones I want and set goals along the way. For instants, my next goal is to solve 200. I stopped doing that. I felt it was too hard, and since I don't care about move-count, solving by permutation and then orientation is easier. My shortest pentultimate routine is [8,1], but I normally use my 20-move routine because I like it better.

I have to tell you:
3.9.3 solved!
8 sub-3x3x3.
Relative to the sub-3x3x3's the pieces are:
sub-3x3x3-Centers: visible:24 (X-face) / invisible:12
sub-3x3x3-Edges: visible:48 (+-face/ wing) / invisible:6
sub-3x3x3-Corners: visible:26 (corners/ edges/ centers) / invisible:1
sub-3x3x3-Cores: never visible (8)
It was 4 hours of pondering and fulfilment for me.
Thank you, Stefan.

schuma, my respect to you, that you solved all of gelatinbrains puzzles.

gelatinbrain, can you please make the moves-textarea always show the last moves (scroll down from alone)? thank you.

While I solved 3.9.1b, I got a problem with the last piece. I had all pieces looked solved except 1 center-piece with wrong orientation (90 deg twisted). 90 deg twisted means that the piece is in wrong position. The core piece was also wrong (edit: not suitable for the U-center), so I had to start new, this time knowing the right orientation of the puzzle, and solved it finally. I found out that there are 14 pieces of one orientation (for the 8 corners and the 6 face-centers) and 13 pieces of the other orientation (for the 12 edges and the core). If a piece is in the right position all arrows will look solved or 180 deg twisted, if in wrong postion, all arrows will have a twist of 90 deg, so checking the position is easy. Next time I will count the pieces before I start doing moves on it.

Stefan, when I solved 3.9.1b, I did count the pieces in the beginning to avoid the issue you just described. If you go along the 3.9.* series, there are more puzzles like this. I'd say the orientation issues in this series is more complicated than any other puzzles including high dimensional puzzles.

By the way, when I read your words "The core piece was also wrong", in the beginning I thought you meant "the core piece was wrong for its own location (core)", but that case you don't need to fix anything. Then I realized that you probably meant "the core piece was wrong for the U-center", in that case you do need to fix the global orientation. I think the latter way of understanding is what you meant, right?

Yes. I meant I could not use either the U-center piece or the core-piece for the U-center, as you said.
Regarding 3.9.x I thought about, why this 14-13 problem does'nt appear in 3.9.3, and the reason might be, that you don't see the orientation of the 5x5x5-face-centers.
For solving the 3.9.xc puzzels I will have to study the wraped pieces a bit. Crazy thing!
Thank you, Stefan.

Yes for the same reason this problem is not there for 3.9.1 (a), because the stickers on the face centers are not sensitive to orientation. For 3.9.3 you have even more freedom because all the 27 internal pieces are completely free. You don't need to worry about any of them.

I just solved 3.3.20 in 306 moves.
I wanted to get under 300 but I couldn't.
Still I'm 3rd in moves. I like it better than 3.3.8 (Curvy Copter II) because you can see the edge's orientation and can't get the parity on the center squares like on 3.3.8. I solved it 4 times and had that parity 3 times. Really anoying.

YEES. Pentultimate solved with only 268 moves. Still I am only 7th in the list.
But I used my 18 moves for corners and 22 moves for orientation because I can't understand the 10 moves sequences from Brandon. They are too darn genius.
Thank's to Elwyn for pointing the method with the setupmoves out. I would have never thought it to be practical but because of it I had to orientate only 4 corners in the end. All others were placed with orientation already correct.
Btw I could put in three corners of the white side all correct while doing the centers. I tried all 5 but it got to difficult.

here is a screen because I felt that the solve is so good by my standarts that it deserves one:



edit: sorry the numbers in the screen are so small.

I wish they were the product of genius! They were found by my program. I agree that most of them are quite hard to follow to see why they work.

There are quite a few Pentultimate-based puzzles now. Some of them are:

1.1.6
1.1.7
1.1.7b
1.1.27
1.1.35
1.1.35b
1.1.35c
1.1.51
1.1.80
1.1.81
2.2.5
2.2.6
2.2.21

Most of my computer-found routines have side-effects on the extra pieces of some of these puzzles.

Hey all, it's been a while since I posted a solution to anything but I think this is an interesting one. Earlier today Gelatinbrain gave us a bunch of new puzzles, most of them based around subsets of pieces to a Master Skewb.

One of them is 3.2.19 which turns without turning the corner much like TomZ's Compy Skewb:
If you have a short routine to twist two corners (such as [FRD, LDB', UBR, LDB, UBR', DFR', LUF, BRU', LUF', BRU]) it probably has this effect:
Both of those twisted corners are in the same orbit. If you solve the puzzle though you may end up in this situation:

No amount of setup moves is ever going to get you into a situation where you can solve those two corners in different orbits directly.

The trick is that if you re-orient the whole puzzle about one of the broken corners so that it is solved in this new orientation then that will transfer the twist to the diagonally opposite corner. That corner is in a different orbit. You can achieve this with a shift+click on a broken corner to fix it, putting the twist into the opposite corner in a different other orbit.


In other news, I solved my 256th puzzle today. Seems like a good milestone

Julian, if you're up for a challenge, I threw down a pretty good solve on 3.6.1 (Dino + Helicopter Cube). 248 versus your 316 moves. 220 moves should be possible by being more careful while applying my technique.

Definitely, congratulations!

I've been thinking about going back to using the algorithm bar again. That way I'd be able to solve way more puzzles and with a lot less effort too. That way I'd actually be able to solve more often, as I don't have much spare time due to uni. And with the amount of puzzles on the site, solving as many as possible without the macro function seems almost impossible.

I tried to solve 3.9.5 and I got the same problem. I guess it is the cores orientation, wich is not visible from outside, wich matters. I work on a way, to detect the cores orientation in checking the orientation of all outside pieces. I guess on 3.9.5b this problem will not appear, but on 3.9.5c it will.

Yes I think you are right. On 3.9.5c it comes back with a more stringent constraint because all pieces are distinct. This type of problem also comes on 3.9.6c and 3.9.11. I don't know a good way to prevent it in advance and I really hate it.

UFF. I just finished solving the master pentultimate the second time.
I was going for as few moves as I could and ended up with 848. That's much better than the 3055 moves in the first solve but I hoped to even be able to come close to Agamenon or even beat him. He has 735 so that was quite a fail in solve and self-assessment
But still not bad I think.
I use way to many setup moves for the trapezia (Starminx-face-triangles). I suppose you guys that have much lower move counts use different algos for those? Because I only used the same [3.1] the whole time and tried to get three pieces at a time as often as possible.

I tried to solve 3.9.5c, had to start 4 times (thats bad) and finally solved it.
Here are two of the situations:
I worked on a better way, using 3.9.5, which has the same issue.
You have a chance of 1 from 3 not to get a single twisted piece at the end.
There must be a way to measure the cubies-orientation-sum, to turn the puzzle right, before you start solving.
I have tried that in the following way.
Each cubie has an up and down face according to the puzzles up and down colors. If you compare a cubie with the puzzles up and/or down colors, it may have a twist of 0, 1 or 2. You can use only 4 of the 8 cubie-corners to get a consistent analysis. In the picture below, where the lines cross the cubie corners are the corners I would use.

Lets see, what happens to the cubie-orientations-sum, when we turn a whole solved puzzle round the URF corner by 120 deg.
before the turn all cubies had 0.
the twist of the cubies after the turn is as follows:
corner-cubies: 1,1,1,1, 1,1,1,1
edge-cubies: 2,2,2,2, 2,2,2,2, 2,2,2,2
face-cubies: 1,1,1, 1,1,1
The sum of the corner-orientations is 8 modulo 3, which gives 2.
The sum of the edge-orientations and the face-orientations modulo 3 is both 0.
So the complete sum after the turn is 2.
When you have a puzzle like this:
where the URF corner cubie is clockwise twisted, you have a cubie-orientations-sum of 1 and you need to turn the whole puzzle clockwise round the URF corner, which adds 2 to the 1 to solve the puzzle. Then you have to keep the color scheme from before the turn i.e. solve orange to the up face, purple to the right face and so on.

In hope you figure it out, Stefan.

Great analysis, Stefan!

So your method is like "try and then fix". With probability 2/3, one needs to solve the puzzle essentially twice. Is there a way to find the correct orientation in the very beginning before trying to solve? I believe it's possible but it seems to be too complicated for me. Consider it's a saving of hundreds of moves, I think it'll be worth doing if we know how to do it.

Yes, you can derive the cubie-orientations-sum before you do any moves and then fix the puzzles global orientation. That works, I have done it 2 times with 3.9.5 today. With 3.9.5c it seems to be harder to detect cubie-orientations.
That approach might seem complicated, maybe it can be simplified, but it's the best one I know, until now.

Thank you, Stefan.

Let me learn how you did it on 3.9.5. On 3.9.5 there are two kinds of pieces: the pieces that should go to edges or others. I can think of two strategies.

One strategy is to use 3-cycles to get the pieces in the correct positions, and then count the orientation-sum, and then fix the global orientation, then solve the piece-wise orientation. It seems like you are not doing this.

Another strategy is to count the orientation-sum without doing any move. If a piece is in a correct position, you can assign {0,1,2} to it by looking at the position of the yellow sticker. If a piece is in a wrong position, how do you assign the number? One needs to first move it using a 3-cycle into the correct position and then rotate it. But during the 3-cycle, the orientation of three pieces are changing. Do you have to keep track of it?