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 Post subject: Checking for flipped edgesPosted: Sun Jul 21, 2013 4:36 am

Joined: Mon Feb 28, 2011 4:54 am
Hi all

Is there a way to look at any scrambled 3x3x3 cube and work out how many edges need flipping, based on sticker colours etc?

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 6:20 am

Joined: Fri Apr 01, 2011 10:58 am
Location: Stockholm, Sweden
Yes there is.

Put your green center at the front, and the yellow on the top (these colors are just an example. It works with any centers as long as you decide on an orientation (note that the sticker colors you use may vary depending on orientation)).

Now look at all the white/yellow edges. If a yellow/white edge is on the top or bottom layers, with the sticker facing up or down the piece is oriented correctly. The same goes for a white/yellow edge piece on the E layer with the yellow/white sticker facing back/front. If a yellow/white edge piece doesn't meet any of these conditions it is not oriented correctly

For the last four edge pices you do basically the same thing, with blue and green instead of white and yellow. If one of these pieces are on the top/bottom layer with the blue/green sticker facing up/down, the piece is oriented correctly. If one of these pieces are on the equator with the sticker facing back/front the piece is also correctly oriented.

So to conclude this there are four rules for telling how an edge piece is oriented:
1. Yellow/white on top/bottom - Piece oriented correctly.
2. Yellow/white on E, on back/front - Piece oriented correctly
3. Blue/green without white/yellow, on top/bottom - Piece oriented correctly.
4. Blue/green without white/yellow, on E, on back front - Piece oriented correctly.

I hope this helps, if it's too messy or something, just ask and I will try to clarify.

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 7:31 am

Joined: Mon Feb 28, 2011 4:54 am
Ah, got it! Thankyou very much. I knew they had to be flipped in pairs, but wasn't sure how. Much apprecaited.

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 9:14 am

Joined: Fri Apr 01, 2011 10:58 am
Location: Stockholm, Sweden
I'm glad to be able to help!

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 9:43 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I think the answer is relative: If you do the twist `U`, `you have flipped 4 edges`. According to their permutation they are 90* out (but in solving LL most solvers would not see any `flipping` in this situation. But: Every flipped edge `in place` takes 3X 90* twists to put back. I think the question is ambiguous.

Cheers,
Burgo.

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 12:17 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Burgo wrote:
I think the answer is relative: If you do the twist `U`, `you have flipped 4 edges`. According to their permutation they are 90* out (but in solving LL most solvers would not see any `flipping` in this situation. But: Every flipped edge `in place` takes 3X 90* twists to put back. I think the question is ambiguous.

Agreed. The definition of "flipped" (or twist) is dependent on the initial labels and what permutation the puzzle is in. You can sum up the total twist of the edges modulo 2 and track total twist (which is constant for the edges and corners on a 3x3x3) but whether a piece is twisted in some spot other than its solved spot is entirely definitional.

For a puzzle like the 4x4x4 which can be reduced to a 3x3x3, once you've reduced it you can say unambiguously and absolutely regardless of initial definition whether a single edge-group will be twisted in place. All this count says though is that there must be one twisted edge-group, you still have control during the reduced 3x3x3 solve to choose which one.

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 4:51 pm

Joined: Mon Feb 28, 2011 4:54 am
Burgo wrote:
I think the question is ambiguous.
bmenrigh wrote:
Agreed.

Gentlemen,

The question isn't remotely ambiguous to me! Temeraire understood what I was asking and Temeraire's answer told me completely what I needed to know.

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 6:04 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
rline wrote:
The question isn't remotely ambiguous to me! Temeraire understood what I was asking and Temeraire's answer told me completely what I needed to know.

You asked "Is there a way to look at any scrambled 3x3x3 cube and work out how many edges need flipping, based on sticker colours etc?" and the answer is that most positions do not have a unique answer. If you use Temeraire's algorithm you will get an answer but most of the time it's not a unique answer.

Allow me to illustrate.

First, lets say that a F turn doesn't flip any pieces:
Attachment:

flip_f.png [ 5.65 KiB | Viewed 1935 times ]

Now, if a single F turn doesn't flip any pieces, then F2 and F' also do not. Applying F twice or three times or any number of times won't flip any pieces if a single F won't.

Second, lets say that a R turn doesn't flip any pieces:
Attachment:

flip_r.png [ 5.63 KiB | Viewed 1935 times ]

Following the same logic from the F turn, R2 and R' also don't flip any pieces.

Third, lets say that a U turn doesn't flip any pieces:
Attachment:

flip_u.png [ 5.52 KiB | Viewed 1935 times ]

Of course, U2 and U' also don't flip any pieces.

As you can see in these screenshots, it's easy to say that for each position shown, none of the edges have been flipped.

So if F, R, and U don't flip any pieces then applying the sequence FRU shouldn't flip any either:
Attachment:

flip_fru.png [ 5.79 KiB | Viewed 1935 times ]

But as you can see, the Green-White edge has definitely been flipped which implies at least one other edge has been flipped too.

Worse, if we have a flipped edge then we know at least one of our F, R, or U turns must have flipped edges. Which turn was it? There isn't a uniquely correct answer. You get to pick. All we know is that simultaneously saying F, R, and U turns each don't flip pieces is inconsistent. At least one of them must flip at least two edges. Which one flips which two edges is up to you and the definition you choose to use.

So for each of my F, R, and U screenshots, there are three possible answers. You could say that there are 0 flipped edges, 2 flipped edges, or 4 flipped edges. So if I pick an algorithm like Temeraire's but it arrives at a different number of flipped edges, we're both right and both wrong. Most positions have multiple answers and any algorithm that only provides one is incomplete or incorrect or simply misleading.

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 Post subject: Re: Checking for flipped edgesPosted: Sun Jul 21, 2013 6:21 pm

Joined: Sat Sep 15, 2012 7:42 am
Brandon and Burgo, I think maybe you're reading too much into this. The question seems only relevant if your cube carries restrictions [either physical or self-imposed] on which faces can turn. If you're limited to, say, 2 adjacent faces [as on some bandaged cubes, the Petrus method for the 3x3, or a reduction solve of the Uranus Crazy 3x3x3], it's easy to identify edges are "good" and which are "bad" - that is, edges that will need to be flipped at some point. The same concept extends to 3 or 4 faces not meeting at a corner. In these situations, the orientation cannot change in the sense that no permutation that returns an edge to the original position will also change it's orientation. To orient a "bad" edge in situations like this, you MUST utilize a third face around a corner somewhere [or slice moves with some bandaged cubes]. To discuss orientations appearing to be flipped while in other positions is meaningless as it will always be oriented correctly when it is positioned correctly. The restrictions on the faces preserves some concept of "absolute" orientation on edges.

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 Post subject: Re: Checking for flipped edgesPosted: Mon Jul 22, 2013 2:18 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
The initial question probably needed more context, but, it’s nice to have the conversation, and it’s nice to consider people’s answers. I certainly try to learn constantly from this wonderful site, where so many people have so much to offer. The original question didn’t mention bandaging, but the implication of bandaging is obviously not withheld either.

It’s probably more pertinent to ask for a definition of a flipped edge first. I think the most reasonable definition of a flipped edge is: An edge piece that is in odd permutation from it’s solved state; and a non-flipped edge is therefore in even permutation from it’s solved state. But like I said earlier, this definition doesn't really fit most people's paradigm.

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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)

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 Post subject: Re: Checking for flipped edgesPosted: Mon Jul 22, 2013 3:09 am

Joined: Mon Feb 28, 2011 4:54 am
themathkid wrote:
Brandon and Burgo, I think maybe you're reading too much into this.
Yes, I think so.

Burgo wrote:
The initial question probably needed more context
Fair enough too

OK. The context is simply this: I'm working on the L-cube, where it's possible at the end to get a flipped edge, with all other edges in place correctly. I showed the picture of this on the 3x3x5 thread. So my thought was to see whether I could figure out early on, whether I would end up with the single flipped edge, and therefore avoid it. Temeraire's answer enabled me to do exactly this. I hope this clears things up and sorry for any confusion.

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 Post subject: Re: Checking for flipped edgesPosted: Mon Jul 22, 2013 8:47 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
rline wrote:
OK. The context is simply this: I'm working on the L-cube, where it's possible at the end to get a flipped edge, with all other edges in place correctly. I showed the picture of this on the 3x3x5 thread. So my thought was to see whether I could figure out early on, whether I would end up with the single flipped edge, and therefore avoid it. Temeraire's answer enabled me to do exactly this. I hope this clears things up and sorry for any confusion.

You're going for what I'd call the parity of flipped edges .

Every position has a unique and unambiguous edge flip parity. As I think you figured out, Assign a non-flipped edge a 0, a flipped edge a 1, add them all up and mod by 2. If you end with a 0 then you won't run into a single flipped edge issue.

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 Post subject: Re: Checking for flipped edgesPosted: Mon Jul 22, 2013 5:11 pm

Joined: Mon Feb 28, 2011 4:54 am
bmenrigh wrote:
Every position has a unique and unambiguous edge flip parity. As I think you figured out, Assign a non-flipped edge a 0, a flipped edge a 1, add them all up and mod by 2. If you end with a 0 then you won't run into a single flipped edge issue.

Yes, I already knew they needed to be flipped (as in my definition) in groups of 2, so I just wanted to be able to tell how many were "currently" flipped.

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 Post subject: Re: Checking for flipped edgesPosted: Mon Jul 22, 2013 6:05 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
rline wrote:
Yes, I already knew they needed to be flipped (as in my definition) in groups of 2, so I just wanted to be able to tell how many were "currently" flipped.

This is where the confusion happened in the first place. You can't know how many are flipped. All you can know is if an even number or an odd number are flipped (zero is even). I'm glad it worked out.

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 Post subject: Re: Checking for flipped edgesPosted: Wed Jul 24, 2013 7:09 pm

Joined: Wed Jan 09, 2013 8:39 am
Hello,

I would like to show how I view this "edge flipped" issue. I think posts showed the problem from different points of view, I simply want to add mine.

I'm open to criticism especially knowing that the posters of this thread are incredibly more advanced than me, solving-wise (read: burgo, rline) and theory-wise (read: bmenright).

To flip an edge we need to turn at least three faces around a corner, say FUR.
So supposing to "remove" one of these turns we can define which edges are flipped and which are not.

For example let's say we can't turn R or L by 90*, R2 L2 are ok. This way we can never flip an edge and we can say that all edges keeps the same flipped state. Another way to see this is to define an edge as "correct" or "unflipped" if it can be put correctly flipped in his spot by just doing U,D,F,B,R2,L2 turns.
With this restriction/definition a turn of U,D,F,B doesn't flip any edge, an R2 or L2 turn doesn't flip any edge but a turn of R or L flips 4 edges at once.

This is the same "thing" that the Human Thistlethwaite Algorithm does
I already posted a link to it because I liked that idea:
http://www.ryanheise.com/cube/human_thistlethwaite_algorithm.html

The first step of such algorithm is to orient all edges and put the cube into the subgroup
G1=<U,D,F,B,R2,L2> After achieving such goal edges are never flipped again and the rest of the cube is solved with just U,D,F,B,R2,L2 turns.
To orient all edges the key is to put flipped edges (according above definition) to R (or L) face and then do an R (or L) turn.
Example: if only 2 edges need to be flipped:
- Leave only 1 of the 2 flipped edges on R
- Turn R (3 edges become flipped, 1 becomes unflipped on R)
- Put the second flipped edges in place of the unflipped edge on R (4 flipped edges now on R)
- Turn R, now all edges are unflipped.

This definition is arbitrary, the same we could do considering F,B as the faces that "flip" edges.
This is in fact what the "definition" of Temeraire did. According his configuration (F-green, U-yellow, ...) a turn of U or R doesn't flip edges, F instead flips 4 edges:

Quote:
So to conclude this there are four rules for telling how an edge piece is oriented:
1. Yellow/white on top/bottom - Piece oriented correctly.
2. Yellow/white on E, on back/front - Piece oriented correctly
3. Blue/green without white/yellow, on top/bottom - Piece oriented correctly.
4. Blue/green without white/yellow, on E, on back front - Piece oriented correctly.

I really hope this is not too confusing.

Bye

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 Post subject: Re: Checking for flipped edgesPosted: Thu Jul 25, 2013 3:39 am

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Friends,

Burgo wrote:
If you do the twist `U`, `you have flipped 4 edges`

Yep, I agree.
Rule:
An edge is flipped if the distance (= quarterturns) to solve this piece is odd !
------------------------------------------------------------------------------
This picture shows this rule. Every quarter turn has different orientation.

Attachment:

cube.png [ 16.86 KiB | Viewed 1678 times ]

A F turn causes 4 differences. F R causes 6 differences.

Cheers,
Andrea

PS: There is no confusion. To check each edge, you solve only this edge and count the quarter-turns. If the number of quarter-turns odd then the edge is flipped.
Example:
Attachment:

cube2.png [ 17.16 KiB | Viewed 1668 times ]

Left Up edge (blue white) to solve only this piece use U' R' F'.
These are 3 Quarter turns, so the edge is flipped. ( Ok, you can see it directly that the piece is flipped, but this shows rule)
R U ( yellow orange) to solve it you need R and R . The number of quarter-turns is even. So the Yellow / orange edge is not flipped.

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