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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 7:21 pm 
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There are so many possibilities here (I got to thinking what I might do with my leftover and half made pieces):

The opportunity to bandage a 2 face so that it cannot move (unless all circle pieces surround one of these type of faces it will twist) as I suggested above^^. Maybe we could call the `locked 2 faces` 3 faces? This would give 0, 1, 2 & 3 face types. It would occur when you use `2-face edge & corner pieces` and a `0-face centre piece`.

The opportunity to combine this with traditional bandaging on a Crazy 333: Like in the CT bandaged 333 thread, but we could bandage anything together, CCs >< Inner Edges, Unbandaged Corners >< Unbandaged Edges, Bandaged Edges >< Bandaged Corners, Half Bandaged Edges >< Partly Bandaged Corners, Clocked Centres >< Inner Edges, Inner + Outer Edges, faces with combinations of bandaging. All of the possibilities for combinations of 0, 1, 2 & 3 faces with traditional bandaging are almost limitless. So we would have a bandaged Circle Cube, with bandaged 2 faces, bandaged 3 faces, and then bandaged traditionally :) .

I’m sure we’ll get some good puzzles out of those!
Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sat Mar 23, 2013 11:53 pm 
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I’m sure we’ll get some good puzzles out of those!

Well my head is spinning and I feel like I've kickstarted a runaway train. Now, who will list all the possible puzzles able to be made from what Burgo suggested? It won't be me! :lol:

Also, now that there are many more possibilities, we need a better naming system for each puzzle, but also for the whole set. I implemented the 1st prototype, Burgo came along and improved it. We're both Australian. I vote for "The Aussie Cube"! :P

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:42 am 
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I finished making my Crazy 2 Face set, and I made a few slightly more traditionally bandaged pieces as well which I'll show:
Attachment:
Small Bandage Set.jpg
Small Bandage Set.jpg [ 756.06 KiB | Viewed 7660 times ]

I think I might name the 4th type of Crazy bandaging B4? So we have O, 1, 2, 3 & B4.
Attachment:
Crazy B4 Cube.jpg
Crazy B4 Cube.jpg [ 929.53 KiB | Viewed 7660 times ]

The featured puzzle is only for an example of the kinds of bandaging that are possible. I don't care too much for presenting, I just want to share my ideas, obviously Rline's Crazy 2-Face inspired it, but for the sake of it.. I'll call it the `Crazy B4 Cube`.

EDIT: I just read Rline's post about naming things.. I have no idea how to go about naming everything. The Crazy 2-Face lends itself to a table, but further bandaging probably needs photographic presentation like in the CT bandaged 333 thread (along with face numbering like: [Y0, R1, G3, O2, B0, W0]).

EDIT 2: I just managed to thoroughly scramble the example cube ^^. At first I didn't think it was fully scramblable. It would be a very tough puzzle if anyone wishes to attempt it (I think it might be interesting to put it together in the scrambled situation to see what you think of it too?):
Attachment:
Fully scrambled B4 example cube.jpg
Fully scrambled B4 example cube.jpg [ 688.3 KiB | Viewed 7321 times ]
The Centres pattern is [Y0(0), G0(0), R0(0), W1(+), O2(+), B3(0)].

Cheers,
Burgo.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


Last edited by Burgo on Wed Mar 27, 2013 5:38 am, edited 2 times in total.

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:45 am 
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Trust you Burgo! Take an insanely difficult set of puzzles... and make them harder :D

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:56 am 
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Yeah, I'd say the example has too many incidents of bandaging, it's only an example :) . I think the better ones will have only 1 or 2 B4 bandagings. Maybe I'm wrong?

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 6:48 am 
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Well I'm sure there are a whole lot of possibilities, ranging from the easier side of things to the harder, much like the bandaged 3x3 thread we had. I just meant that these crazy puzzles with 2 type faces are already very difficult I'm sure, and your first thought before solving them seems to be 'hmm...how can I make these even more difficult?' :lol:

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 Post subject: Re: Crazy 2-Face
PostPosted: Sun Mar 24, 2013 5:57 pm 
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martywolfman wrote:
Well I'm sure there are a whole lot of possibilities, ranging from the easier side of things to the harder, much like the bandaged 3x3 thread we had. I just meant that these crazy puzzles with 2 type faces are already very difficult I'm sure, and your first thought before solving them seems to be 'hmm...how can I make these even more difficult?' :lol:

Marty, I can guarantee you that (from PMs) Burgo's 1st thought is definitely "How can I make this harder?" :lol:

martywolfman wrote:
I just meant that these crazy puzzles with 2 type faces are already very difficult I'm sure

I concur. I've been playing with a few variants. Essentially, the puzzles are the planet puzzles with some extra 2-faces. So for example, puzzle O is a uranus cube with two 2-faces. So I made it up and started by trying to make the red-white complete edge, as I would for the standard uranus. This is the 1st step in a reduction solve, and on uranus it's a matter of seconds. So far, I haven't been able to do it. Why? because the two 2-faces mean I just can't turn my required faces without a million 2-face pieces stopping me from doing it. It's disheartening :lol: I mean, either I'll have to figure out a way of putting all those pieces right out of the way and keeping them out of the way, or else come up with some new way of solving this puzzle. I think this may be where a lot o the challenges lie. Initially I thought the 2-face pieces might just make things more tedious, but for me at least, this is an example of it changing things entirely.

I still think A will be the hardest of the lot.

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 Post subject: Re: Crazy 2-Face
PostPosted: Mon Mar 25, 2013 7:00 pm 
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Is the six 2-Face (i.e. a 3x3 cube) a trivial member of the Aussie Planets?

Will HKNowStore send them unstickered and if not, who will?

This is a great idea that keeps getting better every time I read this thread. 8-)

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 Post subject: Re: Crazy 2-Face
PostPosted: Mon Mar 25, 2013 7:10 pm 
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Pete the Geek wrote:
Is the six 2-Face (i.e. a 3x3 cube) a trivial member of the Aussie Planets?

Will HKNowStore send them unstickered and if not, who will?

This is a great idea that keeps getting better every time I read this thread. 8-)

Yes the six 2-face is a trivial member. For that matter, so is the five 2-face. Even if the 6th face on that one is a "0" face, it can't be scrambled apart from a single turn. So really, the challenges lie in the one, two, three and four 2-faces, as well as all the other options Burgo has explained.

HKnowstore sent the puzzles to me unstickered (without me asking) so I suspect they'd do that for anyone else.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Mar 27, 2013 5:46 am 
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For those interested, I just edited my post above^^ with pictures of the example Crazy B4 Cube fully scrambled. I also put the Centres pattern in the post so it's possible to replicate the puzzle. The interesting thing is that I only made it to show off the pieces, but it turns out to be a really diffficult and fully scramblable puzzle. Can anyone pick the 2 pieces that actually can't be scrambled?

Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Tue Apr 02, 2013 12:18 pm 
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rline wrote:
bmenrigh wrote:
There are 25 configurations if you count mirror states as different. Since mirrored configurations solve the same way, there are only 24 essentially unique versions.

Well that's no good. We'll need to throw out a couple of the letters of the alphabet. :shock:


May I suggest Crimean Tatar, Leonese, Maltese, Pan-Nigerian, Swahili, Uzbek or Volapük alphabet? They are all Latin based and have exactly 24 letters each.

When you make and solve the different combinations, would you mind listing them in order of difficulty? I'd like to make one (and it would be possible to make one of your crazy 2-faces using only a single crazy planet, right?) but I probably want one of the easiest.

And I was thinking, wouldn't it be even more challenging if you spread out the cut pieces so that no side has a complete circle in the solved state? Though I suppose this would take away the pleasure of having a complete set, with manageable size, of possible puzzles.


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 Post subject: Re: Crazy 2-Face
PostPosted: Tue Apr 02, 2013 8:15 pm 
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Quote:
When you make and solve the different combinations

Well, for me at least, I probably won't be doing this. Something else (non TP-related) has come up which will mean I won't really be able to contribute to this all that much from here on in.

Quote:
would you mind listing them in order of difficulty?

I think essentially it depends on the base planet and the method you use. Eg. using reduction, I found the order of difficulty to be something like jupter, uranus, mercury, earth, venus, neptune, mars, saturn. Putting an extra 2-face or two on the puzzles generally means it'll increase the difficulty. I've solved a few of the easier ones and found this. I stll think 000002 will be the hardest, and this was the one that originally inspired the idea of it, following the 0002 uranus tetrahedron.

Quote:
and it would be possible to make one of your crazy 2-faces using only a single crazy planet, right?) but I probably want one of the easiest

then I'd make F. I think that one is the easiest.

Quote:
And I was thinking, wouldn't it be even more challenging if you spread out the cut pieces so that no side has a complete circle in the solved state?

Definitely. I think that was what Burgo was doing above.

Quote:
Though I suppose this would take away the pleasure of having a complete set, with manageable size, of possible puzzles.

Have a good look through Burgo's posts in this thread. He has given instructions of how to make every combination you could want using just 2 puzzles.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 03, 2013 6:58 am 
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I tried Jupiter, with one added 2 face adjacent to the 0 face, so 021111 I guess. I'm still waiting for the sandpaper I ordered to arrive, so I just put it together with a black face so I havent tried much of this yet, but that puzzle was extremely easy, once you can solve the crazy Jupiter, it didn't add a great deal to the solve really, other than keeping the 2 pieces away from the 0 face.

rline wrote:
I stll think 000002 will be the hardest, and this was the one that originally inspired the idea of it, following the 0002 uranus tetrahedron.



Whilst I bow to your far superior twisty puzzle knowledge and solving ability, and I haven't tried this yet, I'm not convinced that this is entirely correct. I think that the difficulty (although I haven't tried it that much) of this and the other crazy tetrahedrons is based on the fact that there is very little you can do in terms of turning that doesn't put a 2 piece on a zero face, making it impossible to turn. With a 000002 cube you've more space to put the 2 pieces to keep them out of the way, and it's not so difficult to keep the 2 pieces on one face out of the way I think, say at the back of the puzzle while you solve the rest I would expect something like 000022 or 000222 (If you are prepared to go to 3 type 2 faces) to be a lot harder, simply because there are more 2 pieces floating around that would get in the way.

What do you think?

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 03, 2013 8:02 am 
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Then again, 000222 has three faces that will always turn.

Are there any 3x3s whose pieces would fit together with the circle cubes? If so, that would be awesome.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 03, 2013 3:17 pm 
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martywolfman wrote:
I tried Jupiter, with one added 2 face adjacent to the 0 face, so 021111 I guess. I'm still waiting for the sandpaper I ordered to arrive, so I just put it together with a black face so I havent tried much of this yet, but that puzzle was extremely easy, once you can solve the crazy Jupiter, it didn't add a great deal to the solve really, other than keeping the 2 pieces away from the 0 face.

rline wrote:
I stll think 000002 will be the hardest, and this was the one that originally inspired the idea of it, following the 0002 uranus tetrahedron.



Whilst I bow to your far superior twisty puzzle knowledge and solving ability, and I haven't tried this yet, I'm not convinced that this is entirely correct. I think that the difficulty (although I haven't tried it that much) of this and the other crazy tetrahedrons is based on the fact that there is very little you can do in terms of turning that doesn't put a 2 piece on a zero face, making it impossible to turn. With a 000002 cube you've more space to put the 2 pieces to keep them out of the way, and it's not so difficult to keep the 2 pieces on one face out of the way I think, say at the back of the puzzle while you solve the rest I would expect something like 000022 or 000222 (If you are prepared to go to 3 type 2 faces) to be a lot harder, simply because there are more 2 pieces floating around that would get in the way.

What do you think?

What do I think? I welcome the opinion. I asked more than once above in the thread for people's opinions on difficulty but don't think anyone took that up. Thanks for contributing! :) On reading what you wrote, I'd say I probably agree with you.

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 04, 2013 9:43 am 
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Yeah, I'm not the best at judging the difficulty of these things before I start playing with them :D

I was waiting until I got them made before I did any real comments. I now have a couple of proper faces done, sanded and stickered now. I plan to do a couple more. I have 3 of these puzzles, so I can make several different variations at the same time.

So far as I mentioned above I've made the Jupiter with one added 2 face adjacent to the white 0 face, which was a relatively trivial solve, if you can solve Jupiter, you can solve that. I plan to try it with 2 type 2 faces later. Whilst making a Mercury in the same format - a type 2 Face adjacent to the white 1 face. I haven't tried it yet, but I will later today. However, having to swap the centre over from a 1 face, so that the 2 face would turn, also made me come accross another possibility, I guess I'd call it a type 3 face. The 0 centre, with type 2 pieces surrounding it, of course make a face that cannot turn, so it's almost like of of those constrained cubes, a completely blocked face (unless you populate it with circle pieces of course) I think that will add an interesting variation to the puzzles too, having faces that are unable to turn.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 10, 2013 4:26 pm 
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Well, I've been playing around with a few of these this week, they are definitely fun! I've mostly been doing variations on the jupiter version so far. With just one type 2 face, its trivially different to the regular Jupiter, with 2 type 2 faces its still not much different. However adding a type 3 face as I mentioned in my last post definitely spices things up a bit.

With one type 2 face and one type 3 face, adjacent to each other, and both adjacent to the white, 0 face, it definitely adds some difficulty. It's not horrendously difficult, I solved it, which says a lot :lol:

I'm currently working on this one, which is giving me problems:
Attachment:
type2.jpg
type2.jpg [ 12.5 KiB | Viewed 6648 times ]


The yellow face is the type 3 face, so no circle, but a fixed centre. I'm struggling with this one. I've got all the edges and corners reduced, but that took me a while. I can't get it solved at the moment without messing the paired pieces up though. A WIP this one :)

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Apr 10, 2013 5:10 pm 
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bmenrigh wrote:
rline wrote:
Every fibre of my being hopes you can prove to me (and others) that there are somewhere closer to 57 puzzles to make, but I think 26 might be the limit.

Alright I hacked up some code to check this. The constraint is that the puzzle must have at least one 0-face and one or two 2-faces.

There are 25 configurations if you count mirror states as different. Since mirrored configurations solve the same way, there are only 24 essentially unique versions.
Adding a 4th face type using martywolfman's "type 3" non-turning faces like so:

Image

Yields more interesting results. There are 220 possible configurations using 4 different face types. Here is a breakdown for each type:
Code:
# type-0   # type-1   # type-2   # type-3   ->    Count
0006 -> 1
0015 -> 1
0024 -> 2
0033 -> 2
0042 -> 2
0051 -> 1
0060 -> 1
0105 -> 1
0114 -> 2
0123 -> 3
0132 -> 3
0141 -> 2
0150 -> 1
0204 -> 2
0213 -> 3
0222 -> 5
0231 -> 3
0240 -> 2
0303 -> 2
0312 -> 3
0321 -> 3
0330 -> 2
0402 -> 2
0411 -> 2
0420 -> 2
0501 -> 1
0510 -> 1
0600 -> 1
1005 -> 1
1014 -> 2
1023 -> 3
1032 -> 3
1041 -> 2
1050 -> 1
1104 -> 2
1113 -> 4
1122 -> 6
1131 -> 4
1140 -> 2
1203 -> 3
1212 -> 6
1221 -> 6
1230 -> 3
1302 -> 3
1311 -> 4
1320 -> 3
1401 -> 2
1410 -> 2
1500 -> 1
2004 -> 2
2013 -> 3
2022 -> 5
2031 -> 3
2040 -> 2
2103 -> 3
2112 -> 6
2121 -> 6
2130 -> 3
2202 -> 5
2211 -> 6
2220 -> 5
2301 -> 3
2310 -> 3
2400 -> 2
3003 -> 2
3012 -> 3
3021 -> 3
3030 -> 2
3102 -> 3
3111 -> 4
3120 -> 3
3201 -> 3
3210 -> 3
3300 -> 2
4002 -> 2
4011 -> 2
4020 -> 2
4101 -> 2
4110 -> 2
4200 -> 2
5001 -> 1
5010 -> 1
5100 -> 1
6000 -> 1


Where "2310 -> 3" means that there are three configurations with two 0-type faces, three 1-type, one 2-type, and zero 3-type faces.

rline's 24 configurations are the sum of:
Code:
1320 -> 3
1410 -> 2
2220 -> 5
2310 -> 3
3120 -> 3
3210 -> 3
4020 -> 2
4110 -> 2
5010 -> 1


It seems like the next most interesting criteria would be at least one 0-type, exactly one 3-type, and one or two 2-type faces. This is basically rline's criteria but adding a 3-type face. There are 31 unique configurations:
Code:
1221 -> 6
1311 -> 4
2121 -> 6
2211 -> 6
3021 -> 3
3111 -> 4
4011 -> 2

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 11, 2013 1:02 am 
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It'd be nice if we read the thread guys. I was talking about the 3 face (and I even called it that too) and a number of other things quite early on. Not that I want to brag, or lay claim to things, it's just nice to feel that what you contribute actually gets read :) .

Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 11, 2013 5:15 am 
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Argh, sorry burgo, I probably did read it, I'm sure I read the whole thread at some point but forgot about it before posting. That's maybe even where I subconciously got the idea

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 Post subject: Re: Crazy 2-Face
PostPosted: Thu Apr 11, 2013 6:30 am 
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No problem Marty, it’s just one of the things that happens in threads. Funny how we both independently thought to call it the 3 face.

And thanks to Brandon for the legwork on the analysis.. I think you’re right: `exactly one 3-face` is the most interesting, because if you have 2 3-faces: If the 3-faces are adjacent, then there is an unmovable edge wedged between them, and also (therefore) you can never make a turnable 0-face out of either of them during the scramble/solve. If the 3-faces are opposite then it negates this, but there are limited cases of this, however, they could be interesting because they fit the Saturn format.

Personally, I’ve had my puzzle set up as my `crazy B4 example cube` and been pondering solving that, but it’s fantastically difficult, and I think I might photograph it in its current state and come back to it another day because there are too many 2-face puzzles to have fun with first.

Cheers,
Burgo.

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 Post subject: Re: Crazy 2-Face
PostPosted: Wed Sep 18, 2013 1:12 pm 
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After counting by Polya Enumerations in combinitorics.

If 3 types are allowed for each face, then there are 57 cases.
The generating function is:
Code:
a^6+a^5*b+a^5*c+2*a^4*b^2+2*a^4*b*c+2*a^4*c^2+2*a^3*b^3+3*a^3*b^2*c+3*a^3*b*c^2+2*a^3*c^3+2*a^2*b^4+
3*a^2*b^3*c+6*a^2*b^2*c^2+3*a^2*b*c^3+2*a^2*c^4+a*b^5+2*a*b^4*c+3*a*b^3*c^2+3*a*b^2*c^3+2*a*b*c^4+a*c^5+
b^6+b^5*c+2*b^4*c^2+2*b^3*c^3+2*b^2*c^4+b*c^5+c^6


'a' means Type-0
'b' means Type-1
'c' means normal face.
The term '3*a^3*b^2*c' means there are 3 cases for 3 a's, 2 b's and 1 c's.

Suppose there must be at least 1 a's and 1 c's, then there are 38 cases.
The generating function is:
Code:
a^5*c+2*a^4*b*c+2*a^4*c^2+3*a^3*b^2*c+3*a^3*b*c^2+2*a^3*c^3+3*a^2*b^3*c+6*a^2*b^2*c^2+3*a^2*b*c^3+2*a^2*c^4+
2*a*b^4*c+3*a*b^3*c^2+3*a*b^2*c^3+2*a*b*c^4+a*c^5


But, actually, I didn't minus the trivial cases. For example, 'a*c^5'.


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