# parity problem without "T" perm ?



## Eaudevian (May 18, 2009)

hello there
i m quite new in blindfold, and, altought i know how to do a "T" perm to handle with parity problems, i wonder if there is another systematic method to handle with those parity problems, without knowing any perm alg ? :confused:
(maybe the answer is obvious, and its just curiosity, because "T" is not that hard ...)


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## byu (May 18, 2009)

Well, if you have odd party, turning a quarter turn fixes it, but I don't know if that's what you're looking for.T isn't the only parity fix. Y, R, J, etc all work

Oh, and this should be in the Blindfold Cubing section.


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## Eaudevian (May 18, 2009)

my question was about permutation parity. i know T, Y, J etc. work, but I was wondering if it is possible to avoid using any of them, even if that hypothetical solution would be longer to solve (supposing this solution exists...). i was thinking about commutators or other things for exemple...

this question has no other interest than to avoid memorizing a 14-moves alg such as T.


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## cmhardw (May 18, 2009)

Eaudevian said:


> my question was about permutation parity. i know T, Y, J etc. work, but I was wondering if it is possible to avoid using any of them, even if that hypothetical solution would be longer to solve (supposing this solution exists...). i was thinking about commutators or other things for exemple...





byu said:


> Well, if you have odd party, turning a quarter turn fixes it, but I don't know if that's what you're looking for.



Brian actually already answered your question, but let me elaborate. Parity is caused because the scramble performs an odd number of quarter turns on the cube. To fix this, you must perform an odd number of quarter turns on the cube, making the total number even.

So, one method to avoid parity, is to memorize the cube *as if you have done a quarter turn of the U layer*. Remember that actually doing moves on the cube during memorization is instant grounds for disqualification on that solve. So you would have to mentally imagine that you had done a quarter turn of a layer, I recommend the U layer since it would be easy to see and visualize. Then you memorize the cube as normal, only you memorize what the cube will look like after your quarter turn.

After you put on the blindfold you perform that quarter turn you memorized first, then you solve as normal. You will never have a permutation parity on 3x3x3 if you do this.

Practically speaking, most people just use a PLL alg to fix parity. I don't think one of these methods is inherently better or easier than another, it's just that most people use PLL algs. If you were to start right now with that other variation, memorizing as if the cube is off by a quarter turn, then I think that method could be equally as fast if practiced sufficiently.

Hope that helps,
Chris


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## DavidWoner (May 18, 2009)

It also depends on your method. If you use M2 and Classic Pochman corners then you can fix parity with U' F2 U M2 U' F2 U. This is way better than using R/T/Y perms etc.


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## Eaudevian (May 18, 2009)

thanks all these answers have made things very clear to me!

but, if i use the "one quarter turn of U" method to fix the parity problem, doesn'it means that I must detect the parity *before * I memorize the cube ? in that case it causes me trouble, because normally I detect the parity at the end of the memorization ! where is my mistake ?


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## cmhardw (May 18, 2009)

Eaudevian said:


> thanks all these answers have made things very clear to me!
> 
> but, if i use the "one quarter turn of U" method to fix the parity problem, doesn'it means that I must detect the parity *before * I memorize the cube ? in that case it causes me trouble, because normally I detect the parity at the end of the memorization ! where is my mistake ?



You would have to detect parity before memorizing. The way to do this is to quickly trace through the cycles of the pieces without memorizing. Depending on your method you would have to see how many swaps you have to do, i.e. basically use whatever your method does to discover parity, but do it without memorizing pieces. This will tell you whether you have parity or not, and will tell you if you should memorize with or without the single U quarter turn.

The cons of this are that tracing the cycles like this is time lost doing essentially nothing. This is one of the main reason people don't use this method. If you train yourself to do this very quickly, then it can be seen as a memory "primer" for the actual memorization. You would do this tracing on the corners obviously, since there are fewer of them and you could detect parity quicker.

It's all a matter of perspective. Setting up the parity pieces into a PLL sometimes takes time. Tracing pieces for the "memorize with a single quarter turn applied" method takes time as well. It all depends on which method fits your style best.

Chris


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## AvGalen (May 18, 2009)

Eaudevian said:


> my question was about permutation parity. i know T, Y, J etc. work, but I was wondering if it is possible to avoid using any of them, even if that hypothetical solution would be longer to solve (supposing this solution exists...). i was thinking about commutators or other things for exemple...
> 
> this question has no other interest than to avoid memorizing a 14-moves alg such as T.


Parity means you have to switch 2 edges and 2 corners.

Commutators usually just cycle either edges or corners so normally you couldn't solve parity with commutators. (Please don't attack this point, we are dealing with someone that doesn't want to learn 1 14 move T-Perm)

The shortest PLL-alg I know to fix parity is a 10 move J-Perm (very fast as well)

The shortest way to solve parity is by performing 1 quarter-turn. That cycles 4 edges and 4 corners so if you had a parity before the quarterturn it would be gone after it. The easiest way to test this is by doing a J or T-Perm on a 2x2x2. Because there are no edges only 2 corners are swapped (parity). After a U or U' you get a nice 3-cycle of corners (A-Perm). If you would do the same experiment with a 3x3x3 and would just look at the edges (ignore the parity on the corners) you woud notice the same effect (Parity become U-Perm, H-Perm or Z-Perm)

And Chris, analysing before memoing would be a waste in 50% of all cases. Because time is running always I don't think that method would be any good
[off-topic] For 4x4x4 the same system could be used for avoiding parity. 15 seconds inspection is barely enough for this so nobody does it. Also, it is hard and only helps in 50% of all cases[/off-topic]


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## Eaudevian (May 18, 2009)

thanks to all, I will try this ! good afternoon


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## cmhardw (May 18, 2009)

AvGalen said:


> And Chris, analysing before memoing would be a waste in 50% of all cases. Because time is running always I don't think that method would be any good



True, I agree completely. However I think with training that identifying parity could be done in sub-3 seconds every time. This would mean approximately 3 seconds lost in 50% of cases and 3 seconds lost tracing and approximately 3-4 seconds gained but not executing a parity alg with setups in 50% of cases. I find this to be

0.5 * (3) + 0.5 * (3 - 3.5) = 1.25 seconds increase in your average solving time. I consider this negligible for a beginner/intermediate BLD solver, which I think the poster qualifies for. I don't think any expert would use this method, since it is a net loss of time. However, for most people I think the time lost is negligible.

Chris


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## AvGalen (May 18, 2009)

cmhardw said:


> AvGalen said:
> 
> 
> > And Chris, analysing before memoing would be a waste in 50% of all cases. Because time is running always I don't think that method would be any good
> ...


3 seconds for analysing 20 pieces by a beginner/intermediate BLD solver?
I would need at least 15 seconds to do that (I suck, I know)


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## Stefan (May 18, 2009)

Somebody needs to ask the obvious question...

*Why?*


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## cmhardw (May 18, 2009)

AvGalen said:


> 3 seconds for analysing 20 pieces by a beginner/intermediate BLD solver?
> I would need at least 15 seconds to do that (I suck, I know)



The beauty of it though is that the corner parity matches the edge parity, and you would know this at the scramble. So you can trace the corners only (8 pieces vs. 20) and figure out if the corners alone have parity. If they do, the whole cube does, so you could adjust your memorization accordingly.

I'm at work right now, so I can't try this until I get home, but I'll bet you I can correctly determine parity sub-4 using this method. With sufficient training I think sub-3 would be possible. I am assuming that this would become the beginner/intermediate solver's sole method, and thus they would be getting a lot of practice at doing this.

I'll post an average tonight or tomorrow giving this a try.

Chris


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## Eaudevian (May 18, 2009)

> 0.5 * (3) + 0.5 * (3 - 3.5) = 1.25 seconds increase in your average solving time. I consider this negligible for a beginner/intermediate BLD solver, which I think the poster qualifies for



however, the loss of time should be also depending on the level of the cuber ! I guess I would loose 10s or more, rather than 1.25 .
but the principle of that solution is cool, and it saves moves


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## Mike Hughey (May 18, 2009)

cmhardw said:


> AvGalen said:
> 
> 
> > 3 seconds for analysing 20 pieces by a beginner/intermediate BLD solver?
> ...



I couldn't resist trying. Here are my results (avg. 10 of 12); (N) = no parity, (P) = parity:
11.55 (P), 36.81 (N), 11.92 (P), 14.89 (N), 14.67 (P), 11.53 (P), (11.25) (N), 11.75 (P), 18.56 (N), 14.05 (P), (DNF) (N but I thought it was P), 13.08 (P) = *15.88*.

I would scramble, then determine parity, then stop the timer, then solve all the corners except twisted inactive pieces and/or parity to make sure I was right about the parity. It was good BH corners practice. 

Note that I probably lost a few seconds on each solve properly orienting the cube to begin with. I don't think I ever before appreciated how much time I lose in a solve properly orienting even a 3x3x3. It's certainly several seconds. 

Chris, I think you're a lot better than me at this. I'm still slow tracing corners by sticker. I've been doing OP for so long, it's a big change to switch to tracing by sticker.


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## Eaudevian (May 18, 2009)

it may be obvious, but I remark that there is no need to turn U at the very beginning : it can be done after the orientation step and before the permutation step, so memorizing the orientation can be done as usual (of course I assume the solving method is a beginner method that doesn't imply to orient while permuting ...)


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## Stefan (May 18, 2009)

Again: Why? Why do you insist on doing it without a PLL alg? Besides, T perm only needs 11 moves.


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## AvGalen (May 18, 2009)

cmhardw said:


> AvGalen said:
> 
> 
> > 3 seconds for analysing 20 pieces by a beginner/intermediate BLD solver?
> ...


As Stefan pointed out with just 3 letters, this topic was obviously bad for the brains. How could I have missed such a simple concept :confused:


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## Eaudevian (May 18, 2009)

> Again: Why? Why do you insist on doing it without a PLL alg? Besides, T perm only needs 11 moves.




maybe for some reason that is similar to the reason why some strange guys want to scramble a multicoloured cube, and rearrange it again and again lol


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## Mike Hughey (May 18, 2009)

Eaudevian said:


> > Again: Why? Why do you insist on doing it without a PLL alg? Besides, T perm only needs 11 moves.
> 
> 
> 
> ...



Exactly! It might be kind of silly to calculate the parity in advance like this, but I have to admit it was kind of fun doing that average of 12 determining parity. I'm really looking forward to seeing Chris's results.


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## Stefan (May 18, 2009)

Eaudevian said:


> > Again: Why? Why do you insist on doing it without a PLL alg? Besides, T perm only needs 11 moves.
> 
> 
> maybe for some reason that is similar to the reason why some strange guys want to scramble a multicoloured cube, and rearrange it again and again lol


Was hoping you'd actually answer the question so we could give better answers. But it's ok if you don't want that.


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## AvGalen (May 18, 2009)

StefanPochmann said:


> Eaudevian said:
> 
> 
> > > Again: Why? Why do you insist on doing it without a PLL alg? Besides, T perm only needs 11 moves.
> ...


The topic starter already gave 2 answers:


> and its just curiosity, because "T" is not that hard ...)


and


> this question has no other interest than to avoid memorizing a 14-moves alg such as T.


His curiosity is probably satisfied by now and maybe he already learned an 11 move Blind-T-Perm, or the usual 14 move Speed-PLL-T-Perm, or maybe even a FMC 10 move-PLL-T-Perm (cancel the AUF)


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## cuBerBruce (May 18, 2009)

AvGalen said:


> His curiosity is probably satisfied by now and maybe he already learned an 11 move Blind-T-Perm, or the usual 14 move Speed-PLL-T-Perm, or maybe even a FMC 10 move-PLL-T-Perm (cancel the AUF)



Just to be clear, there is no 10-move (face-turn metric) T-Perm that changes the parity. An AUF is needed to make a 10-move T-Perm into the conventional T-Perm case that swaps two corners and swaps two edges (and thus, changes parity). So Stefan is correct in saying that an 11-move T-Perm is needed (for the context of the question that was asked).


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## AvGalen (May 18, 2009)

cuBerBruce said:


> AvGalen said:
> 
> 
> > His curiosity is probably satisfied by now and maybe he already learned an 11 move Blind-T-Perm, or the usual 14 move Speed-PLL-T-Perm, or maybe even a FMC 10 move-PLL-T-Perm (cancel the AUF)
> ...


I completely agree. That is why I added the context (optimal blind, speed, fmc) for those T-Perms (11, 14, 10).

The T-Perm and the T-Perm with U2 need 11 moves. (These are the ones that change the parity)
The T-Perm with U and the T-Perm with U' can be done in 10 moves. (These are the ones that don't change the parity, or rather: These are the ones that change the parity with the T-Perm, but then it gets changed again with the quarterturn U/U')


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## cmhardw (May 19, 2009)

Ok here's my average. To be perfectly honest tonight was my roommate's birthday and we went out drinking tonight. I'm still buzzing a bit when I took this average. I found a couple things when doing this. This was harder than I thought it would be, and I think maybe sub-4 is a bit faster than I thought at first. I can see getting sub-5 with practice, but sub-4 seems like it might take a lot of training.

07.03, 05.20, 06.05, (08.30), 06.62, 05.97, 07.78, 05.80, 05.22, 04.76, 05.17, (04.72) = 5.96

Some things to point out:
1) These times represent how long it took me to determine whether or not there was parity.
2) I made no attempt to memorize the cycles, I simply traced the permutations of the pieces visually and determined if it would take an odd or even number of transpositions to solve.
3) I think I can do faster when at my peak, but I think sub-4 would take ridiculous practice to achieve. Sub-5 should be easy with a couple weeks practice, but sub-4 might be fairly difficult to achieve.

--edit--
After looking back in this thread I feel I should mention that I did not pre-orient the cube before tracing the cycles. This is because a quarter turn cube rotation is an even permutation if viewed as a permutation on corners. I did start with the cube in a random position each time, but traced it as if it was already in my solved orientation.


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## Mike Hughey (May 19, 2009)

cmhardw said:


> After looking back in this thread I feel I should mention that I did not pre-orient the cube before tracing the cycles. This is because a quarter turn cube rotation is an even permutation if viewed as a permutation on corners. I did start with the cube in a random position each time, but traced it as if it was already in my solved orientation.



Yeah. That's more fair. What I did wasn't really fair to the idea, because I did waste some time preorienting the cube. My times would probably have been several seconds faster if I hadn't done that.

Anyway, those are some pretty nice times, Chris. It would take me a lot of practice to get as good as you at it.


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## mrCage (May 19, 2009)

Hi 

I dont even trace parity for fewest moves. There i could analyse parity by looking at the scrambling algorithm (number of quarterturns).

And indeed, why trace the parity, it comes out from under the carpet eventually ;-)

Per


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## Stefan (May 19, 2009)

cmhardw said:


> I did not pre-orient the cube before tracing the cycles. This is because a quarter turn cube rotation is an even permutation if viewed as a permutation on corners. I did start with the cube in a random position each time, but traced it as if it was already in my solved orientation.


Ha. Just learned something new, thanks. I knew the cornerParity=edgeParity mentioned earlier in this thread, but I wasn't aware you could ignore the centers and just look for cornerParity like you did there. That doesn't work for edges, though, but of course you wouldn't want to check those anyway. Still... at some point you have to care about the centers so this is a neat trick for parity detection but not for overall solving.


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## Eaudevian (May 19, 2009)

> I dont even trace parity for fewest moves. There i could analyse parity by looking at the scrambling algorithm (number of quarterturns).



ho no !

WCA rule for fewest moves :
"- The solution of the competitor must not be in any way related to the scrambling algorithm. Penalty: disqualification of the solve."


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## AvGalen (May 19, 2009)

Eaudevian said:


> > I dont even trace parity for fewest moves. There i could analyse parity by looking at the scrambling algorithm (number of quarterturns).
> 
> 
> 
> ...


Please define related. Sometimes my solution starts/ends with the same move(s) as the scramble by accident.


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## Eaudevian (May 19, 2009)

> Please define related. Sometimes my solution starts/ends with the same move(s) as the scramble by accident.



you are right, i don't know what does mean "related" in that context ... 
(http://www.worldcubeassociation.org/regulations/#fewestmovessolving)

anyway, analysing parity by looking at the scrambling algorithm doesn't sound to me like an "accident" !


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## Stefan (May 19, 2009)

Wait... you weren't kidding about that rules violation?


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## AvGalen (May 19, 2009)

StefanPochmann said:


> Wait... you weren't kidding about that rules violation?


Apparently he wasn't 

First: Why would that be cheating
Second: How could anyone prove I "cheated"
Third: For such a weird topic, some very interesting things were mentioned. Half of this topic could be moved to the "cube theory" subforum


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## cmhardw (May 19, 2009)

Mike Hughey said:


> Anyway, those are some pretty nice times, Chris. It would take me a lot of practice to get as good as you at it.



Mike, to be fair remember that I used to practice this on 4x4x4. A few years ago I was convinced that counting cycles during inspection was a viable way to avoid OLL parity when solving the 4x4x4 for speed. I used to practice trying to count the parity of the wings within the 15 seconds. I never made it of course, but I feel that was useful practice for trying to count the corner parity using essentially the same method.

And if anyone is wondering I don't think counting cycles is a viable way to avoid parity on 4x4, unless you truly dedicated years to learning how to count cycles quickly.

Chris


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## fanwuq (May 20, 2009)

I got 6.53 for a best RA of 12 in a session of 17 that was 7.21. Best single was 5.24. Not bad for over a month without practice. I wouldn't be surprised if Ville, Rowe, or anyone else who can already memo sub-20 do this in sub-4.
I think this method would be usable. The tough part for me would be memorizing from a turned position.


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## blah (May 20, 2009)

Average: 4.79
5.71, 4.75, (3.91), (6.20), 5.02, 4.29, 5.65, 4.29, 4.56, 4.20, 5.19, 4.21

I haven't done a single BLD solve since my last (unofficial) competition, which was more than a month ago. (Unless you count the 2/3 multiBLD that I did last week for a friend, which took something like 20 minutes ) Conclusion: Ville/Rowe can sub-3 with a bit of practice.


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## Eaudevian (May 21, 2009)

what do you think about this for solving parity problems :

for memorization :
1. memorize the corners normally (and thus, detecting parity)
2. in case of parity, mentally turn the U face
3. memorize the edges (according to the new position engendered by the U-turn)

for solving :
1. solve all corners (except 2 of them in case of parity)
2. turn the U face so that 1 corner is solved and 3 remaining corners can be solved with a 3-cycle
3. solve the edges

(unhappy this is a simple case, where a U-turn can solve a corner while leading to a 3-cycle position . )


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## fanwuq (May 21, 2009)

Eaudevian said:


> what do you think about this for solving parity problems :
> 
> for memorization :
> 1. memorize the corners normally (and thus, detecting parity)
> ...



No.

Memo:
1. count corner cycles
2. Mentally picture U turn
3. memo edges
4. memo corners
Solve:
1. U turn
2. solve corners
3. Solve edges

The way I currently do is
Memo:
1. memo edges
2. memo corners
Solve:
1. solve all even corners
2. solve all edges
3. parity fix alg
4. solve last corner if it is odd.

I'm now liking this count cycles method, I'm going to try it out. Solving last corner + parity alg probably takes me longer than 6 seconds, so I should try this AUF method instead.
However, odd parity only happens 1/2 the time and this is a waste on good parity cases. Only singles count for BLD, so perhaps this is worth it. If they start counting averages, I would consider this.


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