Thanks, I guess I wasn't subtle enough The idea behind inner cube is that the edge pieces can rotate inward towards the center of the cube, revealing stickers that were previously "inside" the cube. This rotation is linked to normal face rotations in the precise manner explained in my original post and the accompanying diagrams. Coming up with a physical mechanism seems quite challenging, which is why I was hoping/wondering if your app could do this. Also, somewhat more in line with this thread, I am curious about the solution methods and how different they would be for the two variations I described (which I suspect vary considerably in difficulty, but I'm not sure).

As bmenrigh points out, there is some slight similarity your 3.9.1.

As a general suggestion, I would love to see a scripting language for your app that would allow end users to implement their own puzzles.

So far, support of castom puzzles is not my priority. I'm sorry.
But such a tool already exists. For example :
http://www.ultimatemagiccube.com/
With this program you can design your own playable twisty puzzles.
I don't know if it supports the type of puzzles you describe.

If I understand well, there's a very interesting point in your puzzle :
If bottom edges turn to the same direction regardless of the turning direction of associated face, it's a very special puzzle in which turning direction has the special signification.
Turning left is not the inverse element of turning right.
The inverse element of "turn to left by 90º" is "turn to left by 270º and not "turn to right by 90º".
I don't know yet such a puzzle.

I'm afraid entering into details of solution method becomes too off topic.
Anyway I think your idea is very interesting, but your original presentation too sketchy.
Maybe with more details it could have got more positive reactions...

Thanks! 3.6.4 is a nice puzzle to have, but it wasn't the one I was thinking of. Can you also add an all-deepcut 3.6.5 = Skewb 3.2.1 + Little Chop 3.3.7 sometime?

I spent much of this evening solving 3.3.14 (great puzzle); tomorrow I will try 3.6.4.

Thanks a lot for the Dino Skewb, Gelatinbrain I've been hoping you would add one. It's a lovely puzzle.

Regarding the Pentultimate and the Master Pentultimate:

I just found a 16 move routine for the corners:

B', F', B, H, B', F, B, H',
B, C, B', I', B, C', B', I,

Which is just a simple 3-cycle of corners on for instants the Megaminx and the inverse of it. I also solved the Master Pentultimate/1.1.6, but this cycle's not pure for 1.1.6 by itself. But it's easy to make it pure, by adding some slice moves:

B&2,
B', F', B, H, B', F, B, H',
B&2,
B, C, B', I', B, C', B', I,
B'2&2,

The Master Pentultimate/1.1.6 is a frightening puzzle by appearance but it's not so bad once you get to know it

EDIT: I just solved the circle version of the Pentultimate (1.1.35), and used over 10 000 moves Horrible, horrible, horrible! Julian and schuma, since you're the two only solvers on this, I could use some tips, hints, pointers etc.

Katten you're on a tear! Congrats on your solves.

Julian has posted previously that he thinks the circle-bitten corner pieces on 1.1.35 require a (10,1) commutator. If that's true it's one of the longest minimum ones known. I have been meaning modify my Pentultimate routine finder to check but I need to finish some of my other twisty responsibilities first.

My method of solving 1.1.35 is as follows: (1) Ignore the circular segments (the pieces between arcs and chords), and solve the rest like a pentultimate. (2) Solve the circular segments using a clean 3-cycle algorithm.

In order to construct a clean 3-cycle of the circular segments, first notice the effect of [A,L']. [A,L'] rotates the whole solid except the pieces within the front circle and the back circle. Therefore [A,L'] followed by a whole-solid rotation is the rotation of the pieces within the front circle and the back circle. Then, if you have a pentultimate algorithm that affects one corner in the front face and no corner in the back face, you can construct a commutator using it and [A,L', whole-solid rotation].

In my method, I don't need clean 3-cycle algorithms for the circle-bitten corners, which are considered by Julian. Maybe his method gives a shorter solve.

I notice that GB has added 3.6.5 as you described, and also 1.3.12 and 1.5.3. It's time to work.

Good stuff, Katja! With 1.1.6 & 1.1.7, if you try Sune (7 moves) or a Rubik's Cube algo for flipping two edges in the final layer (6 moves), they will swap just one corner in a layer with no side effects.

I tried the method schuma describes before I solved 1.1.35 but I couldn't work out a short algo that way. Here are hints to make a (10,1) pure algo for the circle pieces:

First make a (3,1) algo where the 3 moves use two non-adjacent faces, pushing one center and two corners into another half, and that half is twisted on the 4th and 8th moves. After the 8 moves, look carefully at another half, which has remained the same apart from one corner and two circle pieces. With an extra move, the corner and one of the circle pieces is moved out of that half, leaving just a swapped circle piece in the half: [inverse of extra move] + (3,1) + [extra move] = 10 moves to isolate a single swapped circle piece.

I had the advantage of moving to 1.1.35 right after trying lots of other 1.1.x circle puzzles and exchanging ideas in this thread with Brandon and Elwyn. 1.1.35 is one of the hardest puzzles and it's a great achievement for you to jump in and solve it like this. Guessing here, did you repeat a commutator 3 or 5 times to cancel out side-effects, and then commutate that to cycle the circle pieces?

Thanks again GB! I'll try 3.6.5 this weekend.

Edit: I jumped ahead and solved it this evening; solution outline below on this page.

Thanks for sharing your steps. I used the same two basic steps as you, but before I comment on your clean 3-cycle construction, I'll have to do a re-solve. But to avoid confusion, by clean do you mean pure? That's exactly what I did, hence the horrible move count. I used my 20 move routine, and then I turned the layer holding one of the corners, leaving the circle piece untouched by it, then I preformed it again and then I reversed these steps. The move count of this, as you can imagine, is quite high: >50 moves. It works, but I had no other idea on how to cycle the circle pieces but I still really wanted to finish the solve. Thanks, I'll try this out later as well I tried really hard to come up with a shorter algorithm yesterday, but after 30 minutes of hard work, I still had nothing. On that basis I decided to still solve it when I realized I could do as I described above. This is a very hard puzzle, but I like it a lot.

Gelatinbrain, thanks for even more new puzzles! I love the dodecahedron. They're next on my to-solve list.

Yes, I meant pure 3-cycle algorithms, which are the ones that only affects those three pieces but not anything else. Sorry for any confusion.

3.6.5 (Skewb + Little Chop)

Solution Outline

Step 1 - Make some intuitive moves to solve as many square pieces as possible.

Step 2 - Complete the square pieces with non-pure (6,1) commutators. The 6 moves are 1 + (1,1) + 1: a setup move, then alternating corner and edge turns as far apart as possible, then an undo of the setup move.

Step 3 - Use Skewb moves to permute and twist Skewb corners to quickly solve as many triangle pieces as possible.

Step 4 - Cycle the triangle pieces pure with (8,1) commutators. The pieces come in two distinct sets/subgroups/orbitals/orbits. When you have an algo to cycle pieces of one set, the mirror image of the algo will cycle pieces of the other set. The 8 moves are a (3,1) commutator where the 3 moves are again alternating corner and edge turns as far apart as possible.

Highly recommended -- it only has 72 pieces, so it doesn't take a very long time to solve. Setups are tricky but short -- perhaps 80% of the time you won't need to use more than 3 moves to set up cycles to solve 2 pieces at a time.

Today I saw this picture of a shallow-cut edge-turning octahedron



in this thread:

viewtopic.php?f=4&t=19543

I am surprised when I could not find it in GB's page. Gelatin Brain, is it convenient to add such a puzzle? Thanks a lot.

I think a shallow-cut edge-turning octahedron would be a great addition

I'm in need of some help. I have completely failed at figuring out 3.1.15. How should I approach this puzzle? I feel I've tried numerous things but non have succeeded, obviously.

Also, I'm now 8 puzzles away from my 100th puzzle. Since this is very special to me, I'd like my 100th to be a real challenge. I have one candidate already, the Big Chop/1.4.3. I was wondering if anyone had other suggestions?

Edit: Sorry, I misread the puzzle number! (Thanks for the heads up, schuma and Brandon.) Adding a title/header to clarify what follows...

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

3.3.15 Solution Outline

Piece types 1, 2, 6 & 7 solve exactly like 3.3.5 because they are outside the circles, but the others are trickier to figure out and have really difficult setups. After solving the corners and centers...

Type 3 pieces cycle with ((AB)*3, C) commutators, where A and B are adjacent edges.

Type 4 pieces cycle with (1,1).

Types 5 & 6 cycle with (1 + (1,1) + 1, 1) = (6,1), where the edges of the (1,1) are far apart.

Type 7 pieces cycles with ((3,1), 1) = (8,1), where 3 = two edges far apart back and forth.

Type 8 pieces cycle with ((3,1), 1) = (8,1), where 3 = (move slice move). Here is the kind of position that you need to aim for after 8 moves, so you can then slice a single piece away with the green/white or orange/blue edge:

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

Or how about a face turning icosahedron like 2.1.1, which for many of us was a big solving milestone? It is less difficult than the Big Chop but I like that it has a variety of piece types instead of 120 pieces all the same shape.

Julian, thanks for sharing the method of 3.3.15. But I think Katten was asking about 3.1.15 rather than 3.3.15...

For 3.1.15, I found the type of moves like R&7 very useful to construct algorithms, because it rotates everying except the core, which means essentially rotating only the core.

Also, I would like to GB for adding 4.3.6, the shallow-cut edge-turning octahedron. It is fun to solve it.

You should take Julian's advice for 3.3.15 but if you're asking about 3.1.15, the thing is deceptivly evil, isn't it .

In short, 3.1.15 is a 5x5x5 where you can't turn the side slices (but you can turn the center slice). See this post.

For your 100th I agree with Julian that a puzzle like 2.1.1 would be a good choice. I was thrilled when I figured it out. If you can solve the Big Chop that would be a huge achievement.

I was asking about 3.1.15 , but I was more than happy to read your 3.3.15 solution outline, Julian Though I think I might solve 3.3.5 before attempting it. It's somewhat funny that you suggested this one, as I came up with all the algorithms for it last week. But I agree; this would definitely be worthy of my 100th puzzle. By first inspection, I reckon it can be solved similar to a FTO. The exception is the butterfly-looking edge pieces. So far I've only got a 62 algorithm to 3-cycle them with, but I'll hopefully be able to shorten it down some. I see your solve on the score rankings page, but when I try to open it through the FILE button, this is what I see: No 4.3.6. A bug, perhaps? Yes, it absolutely is! Thanks for linking to your post about it. I think I understand it better now, but I'm still not sure I know how to solve it.
Regarding the Big Chop: I don't know how to solve it... yet. So far I've only been able to find a 2-2 swap (at least I think that's what it's called), but I feel I'm on to something.

EDIT: I tried 3.1.15 again, thinking I'd get it solved this time, since I read Brandon's post. But no, I'm still getting nowhere

3.1.15 Hints

The puzzle has 4 piece types: let's call them A, B, C & D. My method is to solve type A intuitively partway then with (1,1) non-pure commutators; then type B non-pure (1,1); then types C and D in either order pure (4,1) and (3,1). Types A & B have something a bit special about them. Good luck!

3.3.10 & 3.3.11 (Circle Little Chops)

Figuring out 3.3.15 (circle 3.3.5) gave me an idea that I hadn't tried with its deeper cut brothers, 3.3.10 and 3.3.11. Both the "bitten" little chop pieces and the leaf-shaped circle pieces of these can be solved with pure (6,1) algos. The 6 moves are of the form:

(2 setup moves)
(slice move simulated by making 2 opposite moves followed by a puzzle rotation)
(2 undo moves)

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

Puzzle request for Gelatinbrain:

Please can you add another circle Little Chop, with small circles? If the circles added to the Little Chop are cut with the same depth as 3.3.9, we get a challenging puzzle with 2 piece types that is less scary than 3.3.10 and 3.3.11 and can act as a warmup to them. Thanks!

Gelatinbrain, thank you so much for the new circle little chop; it was a lot of fun to solve! Though it was much harder than I first thought. My method may be the fault here.

1.) Solved the normal little chop, ignoring the circle pieces -- I actually forgot how hard the normal one is.
2.) Then I solved as many of the circle pieces as possible using intuition.
3.) Then I resorted to using a long, pure 3-cycle to solve the remaining ones.

I felt really proud after finishing this solve, but it was kinda sad to see that Julian's move count was around 200. Mine was around 2000 I spent almost 800 moves doing the normal little chop, as I had completely forgotten all my set-up tricks from before.

I just want to say awesome job you guys. I can't believe this thread is still alive and kicking. =]

It's always nice to get a visit from our favorite thread's founder! Best wishes.

Yes, thank you, Gelatinbrain! Isn't 3.3.17 a cute puzzle?
It is difficult to solve though. It took me nearly 2 hours because I found the setups so tricky. My solving order is the same as yours. I cycle the circle pieces with pure (6,1) algos. If you turn two opposite edges and then rotate the puzzle 180 degrees on the same axis, you have affected 4 circle pieces. Now find 2 setups moves that push these pieces around to leave 3 in one half and 1 in the other, and make a commutator. The same routine solves the "bitten" pieces of 3.3.10 and 3.3.11.

So i actually solved 1.1.17 using my ridiculously complex reduction method. I don't think i've ever put that much effort into solving a gelatinbrain puzzle before but it paid off!

It took me 720 moves and over 6 hours (though i did have breaks) and i did have to write down all the combinations of megaminx edges i had to make but it's done! Oh and of course, yes i did get multiple types of parity just my luck.
So Julian if you do ever re-visit 1.1.17 you now have something to aim for but be warned as predicted i now have rather sore eyes and a sore brain

Just a small breakdown of the moves:

134 to build the basic megaminx corners out of the 2 colour pieces and then fix parity which appeared as just two 2 colour pieces needing to be swapped but actually was 2 pieces and 2 entire corners needed swapping.

At 341 i had added the large triangles to the corners and solved the pentagonal centres

At 407 i had built all necessary megaminx edges and fixed the easy parity

at 562 it was completely reduced (as in i had added the small triangles to the corners) and the last 158 moves was the, very hard to recognise what the hell i was doing, megaminx solve.

Always nice to beat a record by more than half hahaha

720 moves?! That is amazing, good job! By the way, I reckon you could improve your 1.1.18 solve a lot. You got a sub-1000 on 1.1.20, which has more pieces and if you take into account what you just accomplished, you'd be able to shave off quite a bit.

I spent my evening solving 1.1.13: Time's a bit slow, because I decided to take a break and watch a TV show Anyways, I really, really liked this puzzle. The way I solved it, I got to solve a combination of a lot of puzzles:

1.) Solve the corners and the edge pieces --> 1.1.3 --> which again is 1.1.12 + edges.
2.) Solve the cube-shaped pieces and the small wide triangles --> the diamond and triangle shaped pieces of 1.1.10.
3.) Solve the pentagonal center pieces --> 1.1.4/1.1.5/1.1.7 etc.
4.) Solve the thin triangle pieces --> 1.1.4/1.1.5 etc.

I'd also like to mention another puzzle that I really like, in fact I think it may be my new favorite: 1.5.3. It's a hybrid of 1.1.5 and 1.4.2. Finding commutators for it is very easy and intuitive and there should be more than 3 solvers of it

I just want to remind everyone that GB has added a new puzzle that is very neat: Little Chop + Dino Cube. Its look is identical to a Little Chop or a Dino Cube. It can be found in the File menu -> cube -> mixed -> the empty space just next to 3.6.5 (as shown in the following screenshot). Currently there is no number assigned to it. But I would assume it would be numbered as 3.6.6.



Although it has the Little Chop moves, unlike the Little Chop, it is pretty easy and intuitive to solve.

I decided to solve 4.3.6 again, and when I finished it, the timer didn't stop:



Also, the Little Chop/Dino cube Hybrid is not appearing in the menu for me yet. It should appear over time though.

-Mark-

Thanks, 1.1.17 is the method and record i'm most proud of. Followed closely by 1.3.2 but i had to ask Julian for an alg for that one.Yeah i know, if you read my 1.1.18 outline wherever it is i say it could be done a lot better but because 1.1.14 (one of the next puzzles i hope to do) can be solved like 1.1.18 with just one extra step i don't want to solve two such similar puzzles close together. If someone beats my record though that's a different story But i do mean to better that move count eventually.

Yes, certainly easier, but I'm not sure I'll be able to solve it in 62 moves like you did. I did solve it easily, though. But I needed more moves. This happened to me a few weeks back. But I was able to get the applet to realize that the puzzle was solved by doing a random move and then undoing it. Did you try that?

Gelatinbrain, I have some puzzle suggestions that I think will make great additions to the 1.5.x series:

- A master version of 1.5.3 -- which would be 1.1.20 that could turn on both the faces and the edges.
- 1.4.1 + 1.1.8

New circle puzzles: 3.5.3, 4.1.12, 4.1.13.

I've never seen such a weird circle puzzle like 4.1.13... Take some time to convince myself that they are indeed circles.

I drag the puzzle to a "seeing is believing" angle, like so:Nice puzzle!

Gelatinbrain my suggestion for a further puzzle is a quite obvious one- at least for me.
3.1.3 (4x4x4) combined with
3.2.1 (skewb) with
3.2.4 (dino) with
3.3.1 (helicopter) and with
3.3.7 (little chop)

Four layers in faces, edges and vertices.

You have some puzzles that are close, but not quite what I mean: 3.7.2 , 3.7.5 ...

Or did I miss something?

Here is a 1.1.28 solution outline wich I have created today:

I faces
II corners
III edge-face (small triangles) (3,1) (( I&2 [L'&2] I'&2), A'2 )
IV circle-edge (3,3) ( (I&2 [L2] I'&2), (F'2 [A'2&2] F2) )
V circle-corner (wedges)(1,3) ( K'2&2, F [B'] F' )
VI corner-face (bitten trianlges) (5,1) ((K'&2, F [B'] F', K&2), any E)
I have not yet solved it, but I will tomorrow. This was previously only solved by one person.

Hi Julian, did you use shorter algorithms for 1.1.25 ?

My outline for 1.1.25 is
I corner
II edge
III face
IV circle edge with (3,1) ((E2 [ C&2 ] E'2), C'2)
V circle corner (small triangle) with (6,1) ((A [ C,F,C',F' ] A' ), K2)



I love 1.1.29. It's neat.

Is there already a physical version of it? It's like a Megaminx but with evil hidden edges, wich appear as circle pieces. This would be a nice physical puzzle.

Stefan

I used the same order and length of algos as you. That (6,1) algo is useful for lots of puzzles!

Hi Stefan,

I have the exact same outline as you for 1.1.25, though I haven't solved it just yet. My algorithms are longer than yours; for the circle pieces I use a non-pure 18 move 3-cycle. For the thin triangles I use a pure 26 move 3-cycle. But I really like your (6,1) better. If I wasn't so set on using my own, I'd probably "borrow" it I really don't understand puzzles with "invisible" pieces. They're visually confusing and painful to solve, in my opinion.

I find them to be some of the most fun puzzles. The circle 2x2x2 (3.1.8) is very fun but for some reason took you a lot longer than i thought it would. The best way i think you'll be able to understand it (and in turn others with similar hidden edges) is to compare it to the normal circle 3x3x3 (3.1.7) all the circle 2x2x2 pieces are there (in the corners)and it shows nicely how each pair of circle pieces are connected through the puzzle to an edge. For example the red and yellow circle 3x3 edge will always have a green circle piece to the right and a blue to the left and those green and blue pieces never move relative to each other so for a circle 2x2x2 you look for the green and blue pieces connected and know the correspond to the red yellow edge.

Once you know how they work i find them rather fun, i especially like 1.1.23

Elwyn, thank you for your insight! I understand how to solve such puzzles now, and I'm not so slow to solve 3.1.8 anymore; just did it in 3 minutes I'm slightly upset with myself for not figuring this out by myself, but now I'll hopefully be able to enjoy these puzzles.

Also I think it's rather funny that I was able to figure out puzzles like the circle Pentultimate by myself but not a case of hidden edges

I do not know, if this has been said before: I had technical problems earlier, but with my current computer environment (W7 64 bit, Java 1.6._022, decent security settings) I can run the Gelatinbrain applets without problems (I'll get a warning, though).
bmenrigh hat tried to help me and all he could find out then, was that without security check it would run.
I do not know if Gelatinbrain has done something or if the newer Java release has helped (my problems had happened with 6.21).

would cuboids be possible? they could be made non proportional as a way out

Gelatinbrain's code relies on puzzles symmetries which mostly limits to platonic solids. The Spheres are the only exception with their jumbling moves but I think those took a whole bunch of special case code and graphically they are still symmetrical.

Maybe I'm in the minority but I don't really like cuboids, bandage cubes, the crazy plus, siamese cubes, and other puzzles that have blocking/limited/non-symmetrical moves. I don't like them for the same reason they are hard to program and hard to solve, a sequence that can be applied to one part of the cube might not be able to be applied if the puzzle changes orientation.

My 1.1.28 method worked well: You see, I solved it as I have announced.

Hi Elwyn, I'm impressed by your 1.1.17 solve move count of 720 . This is magic. I found, this was a beast when I solved it. The layout of this puzzle is so confusing, when it is scrambled. I admire your solving method.

1.1.17 is the only puzzle that gave me a headache from solving. It is so visually complex when scrambled that my eyes were seeing a strobing disorienting effect after a few hours of staring at the puzzle.

720 moves is amazing.

I don't like bandage cube and crazy plus'es either. But I think cuboids are fine as long as they don't change shape. The regular siamese are OK, too. Although cuboids and siamese cubes are not as symmetric as the original Rubik's cube, the permutations are subgroups, generated by fewer generators. For this reason, I still like them.

To clarify what I said, you can think of the generating set {F,B,R,L,U,D}. It generates the group of the original Rubik's cube. A limited generating set {F2, B2, R2, L2, U, D} generates the group of a Rubik's cube with limitation, which is essentially a cuboid-type puzzle. Another generating set {F,U,R} generates a certain type of siamese cube. They are still groups! It lacks some symmetry but not that bad.

But those bandage cubes, as I understand, are not groups. And I just don't like them.

In 1.1.* category, Gelatinbrain has some non-platonic solids that are truncated dodecahedra. I wonder if it is convenient for him to add more truncated solids, like, the other Archimedean solids. Recently I've seen many cuboctahedron-shaped puzzle made in reality.

Here is my outline for 1.1.27.
First solve 1.1.6 pieces, then the thin circle corners.
I edge
II face (3,1): ((I[L'].), A)
III corner-face (3,1): ((E2[C&2].), C')
it does:
IV corner (6,1): ((B[ (A,F) ].), L) thanks to Julian
it does
V circle-corner (8,1)=((3,1),1): (((E2[C'&2].), C'), L)
it does
And here is my result: 2nd in move-count and 2nd in time

congrats, and such a good time!

100th puzzle! More time consuming that I thought. Thanks. I worked out a way of easily recognize the pieces quickly. Also might have something to do with the fact that recently I've enjoyed physical puzzle solving, so I easily recognize colors as well

I'm not able to reach your 03:46 on 3.1.8. Also congrats for reaching your 100th gelatinbrain puzzle.

Hello, today I have reached my 150th puzzle.
I solved 1.1.30 and here is a short outline:
I corner face, reduce to the corners with (1,3) shortened to 5 moves: ((K2&2, (F'[C']. ))
II reduced corners (I and II is as 1.1.39)
III circle corners with a (3,3): (( F'[C]. ), ( E2[K2&2]. ))
Here my result, it wasn't really hard :