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 Post subject: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 5:50 am

Joined: Fri Apr 25, 2014 2:04 am
Hi,

I like to solve puzzles on my own. Unfortunately, sometimes it is neccessary for me to look for a tutorial. Before doing so, let me ask you following questions. If I can solve these puzzles, should I be able to solve

1.) crazy 4x4x4, type II? (I am prrety stuck on little triangles - at the moment I can not even solve them independently on other pieces)

2.) AI 4x4x4 cube? (I am prrety stuck on fourth 2x2x2 cube - I played with it like 20 minutes though, so I can make some progress in the future maybe)

Note: I am not looking for a tutorial yet, rather yes/no sort of answer.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 7:56 am

Joined: Wed Jan 01, 2014 11:06 am
I think that once you realize how exactly the little triangles work, you should be able to solve the circle 4x4 II. I personally don't have experience with the AI cube, so I'm not sure about that one.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 8:36 am

Joined: Mon Mar 30, 2009 5:13 pm
Depends how you solved the original puzzles...

If you figured out the solution on your own then I would say yes, but if you relied on algorithms published by someone else you might find these other puzzles difficult unless you find published algorithms for those too.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 11:46 am

Joined: Tue Sep 11, 2012 1:51 pm
Location: Bedford, England
The crazy 4x4 - I think it must ve version III if you have little triangles. Trying not to give any spoilers here, but if you understand them, they are easy. With the puzzles you own you can definitely solve this, however it takes a little thought to realise just what those triangles are. Once you figure that out, you should hopefully be able to figure it out. spend a little time trying to fiond out exactly what you have to do to move them around, and you might get somewhere.

I'm trying hard not to give you concrete suggestions here

The bandaged AI is a harder prospect, and that also takes a realisation step. the last 2x2 block is definitely difficult, but using what you haev done to solve the other 3, should allow you to solve the final one, with one slight alteration, However I don't know of any other puzzle, that will definitely give you the knowledge to solve the last part of this one.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 11:59 am

Joined: Mon Mar 30, 2009 5:13 pm
And besides, what's the point of getting a puzzle you know you can solve?

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 5:03 pm

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
KelvinS wrote:
And besides, what's the point of getting a puzzle you know you can solve?
I agree! That's like getting a beer that you know you like and can finish

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 5:24 pm

Joined: Mon Mar 30, 2009 5:13 pm
Gus wrote:
KelvinS wrote:
And besides, what's the point of getting a puzzle you know you can solve?
I agree! That's like getting a beer that you know you like and can finish
Well that would rule out Nukey Broon!

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 5:27 pm

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
KelvinS wrote:
Gus wrote:
KelvinS wrote:
And besides, what's the point of getting a puzzle you know you can solve?
I agree! That's like getting a beer that you know you like and can finish
Well that would rule out Nukey Broon!
100% true.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jun 25, 2014 5:49 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Hi bcube, going by your title, if you can solve X can you solve Y, I'd say it depends on how you approach X. I gather you tend to think of each puzzle as a completely different solving challenge and you have to tailor a specific solution to each. In that case solving new puzzles will continue to be hard. If instead you break puzzles down into little solving steps and you approach each step very analytically you will build up a repertoire of tools and knowledge that you will be able to apply to solve a great number of puzzles.

Have you studied the structure of memorized sequences to recognize general commutator and conjugate constructions? Have you started to recognize how even very different puzzles seem to share a lot of similarities in the move sequences you use to cycle pieces?

There is some neat trickiness to understanding what the pieces on a Crazy 4x4x4 II / III are but the actual move sequences needed to solve them are very similar to move sequences you already know so you should be able to put together the pieces into a solution.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jun 26, 2014 1:57 am

Joined: Fri Apr 25, 2014 2:04 am
martywolfman wrote:
The crazy 4x4 - I think it must ve version III if you have little triangles.

I am sorry for not making myself clear. I meant elongated triangles (but still the smallest pieces on the puzzle), there is 8 of them on one side. I believe it is crazy 4x4x4, type II.

martywolfman wrote:
I'm trying hard not to give you concrete suggestions here

And I appretiate that very much!

KelvinS wrote:
And besides, what's the point of getting a puzzle you know you can solve?

The point is to solve the puzzle without getting instructions. Plus, believe it or not, martywolfman´s and rayray_2561´s opinions had great psychological effect on me. Now I´m super-decided to solve crazy 4x4x4 II.

Gus wrote:
That's like getting a beer that you know you like and can finish

I have a similar, yet different opinion: That's like getting a beer that you know you like and can NOT finish (yet).

Brandon Enright wrote:
it depends on how you approach X
KelvinS wrote:
Depends how you solved the original puzzles...

Sounds about right. I have written an article how I try to solve the puzzle. Incidentaly, it is written in some kind of dead language Allow me to translate it (in short). Of course, you can skip this part... In italic will be translated chapters.

*****************************************************************************************
Solve before scrambling - before scrambling a new puzzle, take a good long look at it. Sometimes it is good to document it (take a picture, make a video of it), while it is still solved. Simulators can be almost ïrreplacable if you want to try something on your puzzle but you don´t want to scramble it more than it is now.

Less is more - solve rather one piece at a time than more pieces at the time. Solve rather one type of pieces at a time than more types of pieces at a time.

CCC - Commutators + Conjugates Combination. It is powerfull tool for solving the puzzles.

Take some notes while solving - Indeed take some notes while solving before you forget the solution.

First thing to do is a break - Take five after approximately half an hour of finding out your solution (time can vary in dependance of how much a cuber is experienced). Take some physical activity to "ventilate" your brain.

Nothing like a known solution - Don´t think of two similar puzzles as two different challanges. Use knowledge from before to solve your current puzzles. Maximally use similarities of the puzzles. (Rubik´s cube and Fisher cube, Square-1 and Square-2, Skewb and Skewb Diamond are indeed the same things).

(Do not) cheat! - Cheating is to peel off stickers and change two pieces manually. It is not chaeting to take one piece out and put it in back(typical state of your puzzle when you borrrow it to your 4 years old brother and he give it to you back) - i.e. trying to solve unsolvable puzzle is not cheating.

Google is your friend - (self-explanatory, I don´t wanna use this option in case of crazy 4x4x4 II yet )
*****************************************************************************************

Brandon Enright wrote:
There is some neat trickiness to understanding what the pieces on a Crazy 4x4x4 II / III are but the actual move sequences needed to solve them are very similar to move sequences you already know so you should be able to put together the pieces into a solution.

I have already some ideas what the little triangles are (they kind of support my theory that I failed to 3-cycle only 3 of them so), I will continue to explore them

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jun 26, 2014 2:18 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
bcube wrote:
I failed to 3-cycle only 3 of them

Sounds like you already have a really big hint to them

If you perform a "grip analysis" for the pieces you will learn exactly what they are. Andreas's term for grip analysis is "twistability analysis" or "analysis of twistability". You can use the search on this site to read a bit about what I mean by this. You may also find this post enlightening.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jun 26, 2014 2:27 am

Joined: Fri Apr 25, 2014 2:04 am
Brandon Enright wrote:
You may also find this post enlightening.

Thank you but no thank you It´s not a time for reading it yet. When I solve crazy 4x4x4 II, I will, of course, read it.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jun 26, 2014 2:56 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
bcube wrote:
Brandon Enright wrote:
You may also find this post enlightening.

Thank you but no thank you It´s not a time for reading it yet. When I solve crazy 4x4x4 II, I will, of course, read it.

That post has nothing at all to do with the Crazy 4x4x4 II but it does have to do with a general method of identifying piece types based on what grips turn them. I think it's pretty safely on the non-spoiler side of things .

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jul 02, 2014 2:58 am

Joined: Fri Apr 25, 2014 2:04 am
Well, it seems you guys overestimated me.

rayray_2561 wrote:
once you realize how exactly the little triangles work

I know it and don´t know it at the same time. I mean I can see it but I can not "put it in order".

Brandon Enright wrote:
the actual move sequences needed to solve them are very similar to move sequences you already know

Oh really? I would swear I never met similar pieces like those before. Closest ones that come in mind is an edge on gear cube extreme, because it has very strange behavior as well. So far I have been able to solve everything but 4 circles. In theory I can imagine I could solve the puzzle using 3-cycles of center pieces known from 4x4x4 cube (effect on crazy 4x4x4 cube is 2 3-cycles of those elongated triangles), but it would require brutal setup moves (that is the reason I only ended up with 2 circles solved - I solved circles last, just like in case of center pieces for 4x4x4).

So in conclusion, in theory, I think I could solve those little elongated triangles. In reality, on contrary, I haven´t solved them yet. Is there a "little hint" how to solve them which is not completely obvious at the same time?

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Wed Jul 02, 2014 3:17 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
I guess that the nature of the little triangles are not completely clear yet.
Let me ask this question: Are you aware that the number of pieces is not identical to the number of stickers on this piece type?
Hint: If you are counting 48 pieces, please, think harder.

I have written a long topic about this puzzle years ago. Obviously, you are not asking for a solution, so, I'm not posting a link.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 6:08 am

Joined: Fri Apr 25, 2014 2:04 am
Are you aware that the number of pieces is not identical to the number of stickers on this piece type?

I wasn´t untill you asked. Finally, now I am slowly moving forward again.

If you are counting 48 pieces, please, think harder.

I was thinking as hard as I could but it paid off . Currently I can solve only 8 two-colored triangles but hopefully I will figure out the rest too. Thank you for helping me by "not helping me"

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 6:32 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
I'm glad that I did not help you too much

OK, let us check: How many pieces of this type are you counting now?

How do you solve the ordinary 4x4x4? (Reduction to a 3x3x3 or something else?)

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 6:47 am

Joined: Fri Apr 25, 2014 2:04 am
OK, let us check: How many pieces of this type do you count?

I count 24 pieces. Some of them are identical at first sight but they can be distinguished by orbits where they belong to (similarly to the edges in case of normal 4x4x4 cube).

How do you solve the ordinary 4x4x4?

I used to solve it by reduction years ago. Now I am symhatizer of Cage method (so that I would be able to "avoid" parities. Cage method works pretty well for crazy 4x4x4 type I, for example).

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 7:10 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
bcube wrote:
...
I count 24 pieces. Some of them are identical at first sight but they can be distinguished by orbits where they belong to (similarly to the edges in case of normal 4x4x4 cube).....
OK, just I would say that they are in one orbit.
You are right, though, that there are pairs with identical sticker colours. I would call them "mirror-inverted".
Can you see them now on an ordinary 4x4x4 Super Cube?
(On an ordinary 4x4x4 they would have two stickers with identical colour each. This would look not really nice but would be easier to solve.)

Have you ever solved a 4x4x4 Super Cube? (I have made oneself by putting little numbers on the 4x4x4 centres some thirty years ago.) Probably it will help if you try that first.

BTW, I do not know the Cage method. Do you have a link? (I didn't try Google yet.)
If you use reduction and have solved the inner 2x2x2 first, you would not see the parity "one 3x3x3 edge flipped".
You can get the situation where you need to swap two 3x3x3 edges (a 2-2 swap of 4x4x4 edges indeed). The second case is not a "parity" because it needs two (= even number) swaps of 4x4x4 edges.
This is the same as on the 4x4x4 Super Cube.
I posted yesterday a move sequence for this that does not corrupt 4x4x4 Super cube centres:
viewtopic.php?f=8&t=27448&p=321123#p321123

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 7:45 am

Joined: Fri Apr 25, 2014 2:04 am
OK, just I would say that they are in one orbit.

I agree. I realized it just after I posted it. Anyway, they can be distinguished by places where they belong to (if it´s not better then I give up to describe it in English )

You are right, though, that there are pairs with identical sticker colours. I would call them "mirror-inverted".

Maybe this notation is explained in post Brandon suggested to me to look at (since I haven´t solved crazy 4x4x4 type II yet, I didn´t read it yet). But mirror-inverted pieces are easily understandable anyway.

Can see them now on an ordinary 4x4x4 Super Cube?

I haven´t thought of 4x4x4 super cube. And no, I can not see them right now on 4x4x4 super cube.

Have you ever solved a 4x4x4 Super Cube?

No, never tried (never have been in touch with 4x4x4 super cube).

BTW, I do not know the Cage method. Do you have a link?

Well, I do have a link but that tutorial is only written in Czech (on the other hand, it uses step-by-step applets). But google / youtube is probably better choice for you.

If you use reduction and have solved the inner 2x2x2 first, you would not see the parity "one 3x3x3 edge flipped".
You can get the situation where you need to swap two 3x3x3 edges (a 2-2 swap of 4x4x4 edges indeed). The second case is not a "parity" because it needs two (= even number) swaps of 4x4x4 edges.
This is the same as on the 4x4x4 Super Cube.
I posted yesterday a move sequence for this that does not corrupt 4x4x4 Super cube centres:
viewtopic.php?f=8&t=27448&p=321123#p321123

Alright, I read first sentense of this paragraph and decided to not read more (even though I agree). Time to explore it by myself

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 9:25 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
OK, I'm convinced that the nature of these 24 pieces (with two elongated triangular stickers on each of them) is still not completely understood.
Hint: I ensure you that counterparts (obviously in different shape) exist on a 4x4x4.
They can be even desribed better on a 4x4x4 Super cube:
maps how to ?

Some pieces on the left one are not visible on the right one, but the pieces in question are!

One thing more: Even when it is completely clear what they are, it is still visually challenging to place them correctly
Brandon Enright in a topic about "The most entertaining twisty puzzles" four years ago wrote:
Those xxx pieces (I like to think of them as "holographic" pieces) are a real brain twister.
I changed the original name used by Brandon to xxx pieces.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 11:21 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Brandon Enright in a topic about "The most entertaining twisty puzzles" four years ago wrote:
Those xxx pieces (I like to think of them as "holographic" pieces) are a real brain twister.
I changed the original name used by Brandon to xxx pieces.

Whoa 4 years ago? Time flies. I really love this forum and all of the smart, nice people on it It was actually Carl's very long musings on what the Crazy 4x4x4 II puzzle was that prompted me to create an account in the first place.

Konrad, for hints, you've taken a much more direct approach by suggesting the puzzle be compared to a Super 4x4x4 for insight. I was really hoping my mention of grip analysis and the links I provided would serve as guides to help bcube arrive at the technique used to find the answer, rather than the answer directly.

bcube, take Gelatinbrain's 3.2.23 puzzle which is a strange Circle-Skewb that turns like:
Attachment:

circle_skewb_3.2.23_turn1.png [ 16.42 KiB | Viewed 368 times ]

Attachment:

circle_skewb_3.2.23_turn2.png [ 16.78 KiB | Viewed 368 times ]

This puzzle has pieces that are 100% equivalent to Dino Cube edges. If you read about grip analysis and can figure out why this puzzle has Dino edges, you'll be able to apply the same technique to figure out what the wedge pieces are on the Crazy 4x4x4 II.

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Thu Jul 03, 2014 11:53 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Brandon, this sounds similar to me, as if somebody says: "Oh, you do not understand Quantum theory, just have a look at M-theory."

BTW, have you seen bcube's post before I stepped in?
bcube wrote:
Well, it seems you guys overestimated me.

rayray_2561 wrote:
once you realize how exactly the little triangles work

I know it and don´t know it at the same time. I mean I can see it but I can not "put it in order".

Brandon Enright wrote:
the actual move sequences needed to solve them are very similar to move sequences you already know

Oh really? I would swear I never met similar pieces like those before.
.....
I have made the experience four years ago that I tried to explain in PMs the nature of "those pieces" by calling them out very explicitly and the receiver did not follow me.
BTW, you are probably overestimating me as well. So far, I do not understand 3.2.23

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Sat Jul 05, 2014 7:58 am

Joined: Fri Apr 25, 2014 2:04 am
Are you aware that the number of pieces is not identical to the number of stickers on this piece type?
Hint: If you are counting 48 pieces, please, think harder.

<offtopic>Sir, you nailed it! I must be using worst method ever (in terms of solving time), but it works. I can solve crazy 4x4x4 type II now (by Cage method with setup moves). Even though I wanted to try pyramorphix next, I guess 4x4x4 supercube will be next (some bird on the roof told me Boris is thinking about adding it into pCubes). Also, time for reading what´s "grip analysis" is as well as the rest of your and Brandon´s posts I skipped on purpose.</offtopic>

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Sat Jul 05, 2014 11:39 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
bcube wrote:
I can solve crazy 4x4x4 type II now (by Cage method with setup moves).
Great! Did you figure out what those pieces are or did you just come up with a method of cycling them?

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Sun Jul 06, 2014 2:41 am

Joined: Fri Apr 25, 2014 2:04 am
You can get the situation where you need to swap two 3x3x3 edges (a 2-2 swap of 4x4x4 edges indeed). The case is not a "parity" because it needs two (= even number) swaps of 4x4x4 edges.

Personally I agree. Mathematically speaking, you are right. Still, some speedcubers (they use reduction) would disagree.

OK, I'm convinced that the nature of these 24 pieces (with two elongated triangular stickers on each of them) is still not completely understood.

From your point of view it isn´t. You say "The logical pair white/red to which the arrows are pointing is virtually connected to the location under the green centre (and we know this not a centre at all but 1/3 part of a corner of the inner 2x2x2)". I don´t get an idea of virtual centers at all. What´s so virtual about them? I imagine two inner edges as one piece, whose orientation is determined by its permutation (and vice versa). I don´t see what holographic virtual face centers are.

Brandon Enright wrote:
If you read about grip analysis ... you'll be able to apply the same technique to figure out what the wedge pieces are on the Crazy 4x4x4 II.

It is way too much beyond my capabilities of understanding. I was browsing this and this thread but I didn´t understood much. Imaginary pieces here, zero volume over there and you call this a solved cube? What on Earth? Quite frankly, only undertsandable things about "grip analysis" was expressed by Carl to me - this and this. So, would it be possible to explain what exactly did you mean by grip analysis on specific/particular crazy 4x4x4 II?

Brandon Enright wrote:
Did you figure out what those pieces are or did you just come up with a method of cycling them?

From the beginning I was thinking about them as centers (based on knowledge from normal 4x4x4 and crazy 4x4x4 I). Before Konrad stepped in, I thought 1 center is formed by two triangles (so far so true). That´s why I wrote "they kind of support my theory that I failed to 3-cycle only 3 of them" because you just can´t cycle 1.5 centers. Initially I thought two neighbouring triangles in a circle form that center (which is the reason I was stuck for a long time). When Konrad gave me that hint and I realized 1 center is formed by other two triangles. Then it was obvious to me what needs to be done. Since Cage method requires to cycle centers at the of the solve, I am kind of pushed to cycle them . So yes, I figured out (from my point of view, which is different from Konrad´s and your) what those pieces are but also yes, I came up with method of cycling them.

P.S. I am looking forward to getting your "little help" (which is in fact BIG help) in the future. I prepare to solve 4x4x4 supercube, pyramorphix, AI 4x4x4 cube, ultimate skewb and gear pyraminx. If I get stuck, you will be first who will know it

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Sun Jul 06, 2014 12:52 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Before I begin my reply, let me say that I do understand nothing about "complex puzzles" or "pieces without volume" and so on myself.
I'm just a guy who likes solving physical puzzles. I use sometimes puzzle simulators as an aid, but I'm not so much in group theory and specialties like "grip analysis".
Still, I owe Carl Hoff a lot of insight regarding Circle puzzles. I'm talking about his POV-ray illustrations and other graphics, not about his theoretical contributions in several threads. They are above my horizon.
bcube wrote:
...
From your point of view it isn´t. You say "The logical pair white/red to which the arrows are pointing is virtually connected to the location under the green centre (and we know this not a centre at all but 1/3 part of a corner of the inner 2x2x2)". I don´t get an idea of virtual centers at all. What´s so virtual about them? I imagine two inner edges as one piece, whose orientation is determined by its permutation (and vice versa). I don´t see what holographic virtual face centers are.
It seems to be more a language problem than a real disagreement. I want to quote a bit more of that old thread
....
Now I want to convince you that we have to view an inner edge pair as a kind of "virtual centre piece".

The logical pair white/red to which the arrows are pointing is virtually connected to the location under the green centre (and we know this not a centre at all but 1/3 part of a corner of the inner 2x2x2)

I've found this quote in the thread about "Most entertaining puzzles"
bmenrigh wrote:
For me the most entertaining from a twisty-puzzle perspective is the Crazy 4x4x4 II. Those virtual face centers (I like to think of them as "holographic" pieces) are a real brain twister.
...

Isn't that nicely worded?
If you can develop that holographic view - looking through the square centre and recognizing the "virtual centre" underneath - you can solve the puzzle like a Supercube!

We can say "inner edge pair" = "virtual centre" = normal centre on a Supercube.

....
I think we agree that the pair of triangles as indicated by the arrows is equivalent to a real centre on a 4x4x4 Super cube. This pair is certainly a real piece but it looks different from a normal 4x4x4 centre, allright. In the term "virtual centre piece" I have used the word "virtual" in a common language sense.
It has probably nothimg to do with "virtual" pieces in the sophisticated discussions of Carl Hoff, Andreas Nortmann, Matt Galla ...
I have to admit that I never really tried to understand these theoretical discussions and concepts.
What I meant was just: The pair of triangles is logically identical to a Super 444 centre, but looks different and is not a real centre in the sense of physical representation - therfore "virtual".
Brandon's "holographic view" is nothing else than imagining the piece being visible on top of the physical centre location - or underneath if you will. It's just a visual aid.
bcube wrote:
....
Brandon Enright wrote:
Did you figure out what those pieces are or did you just come up with a method of cycling them?
From the beginning I was thinking about them as centers (based on knowledge from normal 4x4x4 and crazy 4x4x4 I). Before Konrad stepped in, I thought 1 center is formed by two triangles (so far so true). That´s why I wrote "they kind of support my theory that I failed to 3-cycle only 3 of them" because you just can´t cycle 1.5 centers. Initially I thought two neighbouring triangles in a circle form that center (which is the reason I was stuck for a long time). When Konrad gave me that hint and I realized 1 center is formed by other two triangles. Then it was obvious to me what needs to be done. Since Cage method requires to cycle centers at the of the solve, I am kind of pushed to cycle them . So yes, I figured out (from my point of view, which is different from Konrad´s and yours) what those pieces are but also yes, I came up with method of cycling them.
P.S. I am looking forward to getting your "little help" (which is in fact BIG help) in the future. I prepare to solve 4x4x4 supercube, pyramorphix, AI 4x4x4 cube, ultimate skewb and gear pyraminx. If I get stuck, you will be first who will know it
Do you still think, we have a different view?
("my point of view, which is different from Konrad´s and yours")

Why did you talk abot 1.5 centers?You said above "Initially I thought two neighbouring triangles in a circle form that center"

BTW, is "your" in your PS above plural, or do you mean Brandon or Konrad in singular?

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 Post subject: Re: Can I solve XX if I can solve YY?Posted: Mon Jul 07, 2014 2:42 am

Joined: Fri Apr 25, 2014 2:04 am
I do understand nothing about "complex puzzles" or "pieces without volume" and so on myself.
I'm just a guy who likes solving physical puzzles. I use sometimes puzzle simulators as an aid, but I'm not so much in group theory and specialties like "grip analysis".

Same here.

The pair of triangles is logically identical to a Super 444 centre, but looks different and is not a real centre in the sense of physical representation - therfore "virtual".
Brandon's "holographic view" is nothing else than imagining the piece being visible on top of the physical centre location - or underneath if you will. It's just a visual aid.

Aha. Got it now. Thank you for explanation/clarification.

Do you still think, we have a different view?

Not anymore. I guess that´s a good thing.

Why did you talk about 1.5 centers?You said above "Initially I thought two neighbouring triangles in a circle form that center"

Argh , my mistake . Let me rewrite the story behind it using solving phases:

1.) I can solve everything but triangles (the point when I started this thread)
2.) (labelled as "initial" in my previous post) While fiddling with triangles, I tried to 3-cycle them using algorithm known from normal 4x4x4/crazy 4x4x4 I. First I thought I ended up with 2 3-cycles. Since there were two of them, it implies that one 3-cycle of them represents 3/2 = 1.5 centers on normal 4x4x4/crazy 4x4x4 I (the other one would represent the rest, i.e. 3/2 = 1.5 centers). Realizing that, I was starting to think two triangles are one piece.
3.) the rest is written above

is "your" in your PS above plural, or do you mean Brandon or Konrad in singular?

It is meant to be plural. After all, rayray_2561 was the first one who actually helped me

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