## 4x4x4 parity

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### 4x4x4 parity

Can anyone tell me if it's possible to spot and fix a parity error in the pairing edges stage?
cube2cube

Posts: 36
Joined: Sun Jun 27, 2010 8:00 am

### Re: 4x4x4 parity

Yes.  But I just deleted my whole post about it because my description about how to avoid it sucked.
OsyenVyeter

Posts: 156
Joined: Fri Oct 17, 2008 4:13 am

### Re: 4x4x4 parity

I'm really desperate to avoid the parity, could you briefly explain the method to me? It would make my day and I'd be able to sleep easy.

cube2cube

Posts: 36
Joined: Sun Jun 27, 2010 8:00 am

### Re: 4x4x4 parity

I first pair up the top edge pieces and place them.  I then pair up the middle edge pieces (you dont have to place them just yet)  then you pair up the bottom edge pieces.

At this point you can then place 2 of the middle layer edge pairs into their proper spots.  Have all the bottom edge pairs ORIENTED, but they DONT have to be placed.

As for the other 2 middle layer edge pairs that werent placed lets call them the blue/red and the blue/orange pairs.  this would mean that they share blue in common.

So having the blue side facing us when we look at the under side we would want to have it so that our 2 middle edge pairs are blue.  if you find it impossible to have it so that all your bottom edge pairs are oriented AND to have your blue edge pairs be blue- then you have now detected that revenge parity is occuring.  Thus you can just fix it.  All before you even have to place all 4 of your edge pair sets and place the bottom edge pairs too.
OsyenVyeter

Posts: 156
Joined: Fri Oct 17, 2008 4:13 am

### Re: 4x4x4 parity

Excellent! Thankyou very much. That makes alot of sense, I knew there would be a way to prevent parity. Your method certainly beats learning that 15 moves long algorithm, and seems not too difficult to do and with a little practice will become second nature. I'll give it a go and let you know how it works out. Many thanks again. Cheers!!!
cube2cube

Posts: 36
Joined: Sun Jun 27, 2010 8:00 am

### Re: 4x4x4 parity cube2cube

If it doesnt much work out I can make a youtube video.  If indeed needed, tell me your top/first color that you work on so that I can make it better make sense for you.
OsyenVyeter

Posts: 156
Joined: Fri Oct 17, 2008 4:13 am

### Re: 4x4x4 parity cube2cube

Thanks, that would be great. I'm going to try it out in the next couple of days, I do most of my cubing in the evenings when it's all quiet. Hopefully It will work, I don't see why it shouldn't, but I'll let you know. I always start with white first, even when I'm doing the 3x3x3, I just find it alot easier for some reason. Thanks again. Ttfn
cube2cube

Posts: 36
Joined: Sun Jun 27, 2010 8:00 am

### Re: 4x4x4 parity cube2cube

Hi there, good news, it worked for me 3 times in a row and then the fourth time it was the corners that messed up. There were 3 corners out of place, I managed to get one of them but the other two were completely unsolvable. So I scrambled it up again and re-did it and it worked out just fine. So I think maybe placing the corners first would solve that problem, at least they would be relatively in the right place that they wouldn't be a problem. So well done! I think you may have solved the 4x4x4 parity problem. You should maybe write a book. ;)
cube2cube

Posts: 36
Joined: Sun Jun 27, 2010 8:00 am

### Re: 4x4x4 parity cube2cube

'You should maybe write a book. ;)'
Why?  His 'detection' is not in any way, more clever than simple observation from solving the first 3 layers and seeing that there is either one or 3 flipped edges in the last layer.

'I think you may have solved the 4x4x4 parity problem.'
No, not really.  He only made things more complicated than the 3X3X3 reduction method to see that there is parity for a given reduced 4X4X4.

'So I scrambled it up again and re-did it and it worked out just fine.'
Why shouldn't it?  After solving the centers, pairing all edges, and solving like a 3X3X3, you should see if the cube has parity or not, right?  There is no difference looking at it the way he is telling you.

Honestly, what might interest you is how to solve the 4X4X4 cube using the Cage Method and/or K4 Methods.  With the K4 Method, PLL parity is not really a parity, and, in the Cage Method, OLL parity cannot be avoided, however, OLL parity algorithms can be avoided entirely to solve the cube (even if there is OLL parity in the cube).

Parity can be detected even if no edges have been paired at all.  The process of doing this, however, is not fun and takes a while to compute (although you will get faster at it if you practice enough:  some can do it in 30 seconds).  A concept from mathematics is involved, but a relatively simple one.  As a matter of fact, this process can be applied to every orbit of higher order cubes up to NXNXN (there is no reason it shouldn't be either:  every orbit is treated the same way).
cuber969

Posts: 22
Joined: Fri Apr 23, 2010 9:33 pm

### Re: 4x4x4 parity cube2cube

Ha ha ha well it seems I found myself quite a fan in cuber969.  The only
thing I concede is that my method of SOLVING revenge parity isnt as
efficient as it could stand to be, but the detection is fine. (though I didnt bother telling him on how to solve Ill grant you.) I thought Id first see if He'd do well enough with just detection first and then feed him solution too if needed. Which is why Im so proud of him.

but as for Cube2cube - 2 corners on a revenge... yes .  Though many people dont know it can happen on a revenge Ive seen that. I even once out of curiosity went on a 'how to solve a revenge' calculator and it was under the impression that 2 bad corners was a mathematical impossibility.  I know how to solve it, but Id reccomend elsewhere for that - if at all possible. (being that the method for how I solve cubes was discovered by myself, it isnt the most efficient method out there)

In other news my newest cube is definately arriving today or tommorow according to my tracking info.  Im getting a 'crazy 3x3' (mercury edition)  For those who dont know- crazy 3x3 is a normal 3x3 but it has a circle cut on all the faces.  So now theres 8 additional pieces on each face.  And because its of the mercury edition only the white circle actually turns with the whole side, the rest of the circles - were you to try and rotate them will just stay in place irrespective of your moves.
OsyenVyeter

Posts: 156
Joined: Fri Oct 17, 2008 4:13 am

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