# Can odd parity be detected in a big cube, prior to being solved?



## Christopher Mowla (Oct 1, 2009)

..


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## Stefan (Oct 1, 2009)

Yes.


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## Logan (Oct 1, 2009)

StefanPochmann said:


> Yes.



+1


Short and to the point. I like it Stefan!


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## Stefan (Oct 1, 2009)

I did add the link, though (getting old and soft). Suggesting that understanding what permutation parity actually is should allow him to understand *how* to determine it. Though that page at one point also explicitly tells how to do it.


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## mrCage (Oct 1, 2009)

StefanPochmann said:


> Yes.


 
I'd just like to add my personal opinion. For speeding purposes early determining or eliminating this parity would be useless. Too much time spent on something that is easily fixed at a later stage. For fewest moves it might be useful. But who fewest moves solves larger cubes anyway???

Per


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## AvGalen (Oct 1, 2009)

mrCage said:


> ...But who fewest moves solves larger cubes anyway???
> 
> *Per*


Did you just answer your own question?


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## elcarc (Oct 1, 2009)

I think its possible, but not practical if you cant do it quickly during inspection.


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## mrCage (Oct 1, 2009)

AvGalen said:


> mrCage said:
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> > ...But who fewest moves solves larger cubes anyway???
> ...


 
Wrong! I have occasionaly done a few movecounts of seminormal solves. That's all actually. It takes more than enough time to fm a normal 3x3x

Per


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## AvGalen (Oct 1, 2009)

mrCage said:


> AvGalen said:
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> > mrCage said:
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No need to put Per at the end of your post than.
Hardly anyone ever did serious 4x4x4 FMC. We had it in the weekly competition for a while and "all" solutions were just optimised centers, optimised pairing and optimised 3x3x3.
There has been some work on 4x4x4 optimal solvers, but computers aren't powerful enough for optimal. The best I have seen was a 5-step "Thistlethwaite" like solution with removal of obvious cancellations.

I don't think anyone will ever really care about 4x4x4 FMC. I certainly don't, just as you don't and we are 3x3x3 FMC lovers


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## Mike Hughey (Oct 1, 2009)

AvGalen said:


> mrCage said:
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> > AvGalen said:
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You say that as if you're somehow sure that "optimised centers, optimised pairing and optimised 3x3x3" is a bad method. I'm not so sure I believe that. Especially if we're talking an FMC with a time deadline, such as the 2.5 hours you had on the weekly competition, I think it's at least *possible* that this might be the very best possible system for doing 4x4x4 FMC. I'm not saying it is the best - it probably isn't - but it might be the best, and I don't think anyone knows enough to say for sure otherwise.

By the way, I think it's funny that it's very possibly true (thanks to the weekly competitions) that I've done more 4x4x4 FMC solves than anyone else in the world.  (Pity I didn't get very good at it.)


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## cmhardw (Oct 1, 2009)

Mike Hughey said:


> You say that as if you're somehow sure that "optimised centers, optimised pairing and optimised 3x3x3" is a bad method. I'm not so sure I believe that. Especially if we're talking an FMC with a time deadline, such as the 2.5 hours you had on the weekly competition, I think it's at least *possible* that this might be the very best possible system for doing 4x4x4 FMC. I'm not saying it is the best - it probably isn't - but it might be the best, and I don't think anyone knows enough to say for sure otherwise.



I wish I had more time to practice this, but I think for 4x4x4 FMC that a good method would be to use nested pre-moves to build tons of easy pseudo blocks and to solve this way. At the end you would undo all of the premoves done at the beginning. This way you could reduce centers by solving any blocks together to be a "pseudo-center", or you could solve kinda like K4 by building pseudo blocks the whole time and doing more of a direct solve.

I have no idea how easy this method is to use in a 2.5 hour time limit, but the idea has always interested me. One day I'll try a couple solves to see if it really has any potential.

Chris


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## AvGalen (Oct 1, 2009)

3 times optimised reduction certainly seems like an easy way to get pretty decent 4x4x4 FMC solutions within a time limit but there would surely be better methods.

What about this (step 1 will be the hard part):
1) Setup to 2x2x2
2) Solve 2x2x2
3) Solve 3x3x3
This is based on a famous cheating scramble where you scramble a 4x4x4 or 5x5x5 like a 3x3x3 (outer layers only) first and then you scramble it like a 2x2x2 (double layers only)


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## joey (Oct 2, 2009)

I always detect parity before the cube is solved.


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## anythingtwisty (Oct 2, 2009)

Me too. Weird...


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## mrCage (Oct 2, 2009)

cmhardw said:


> Mike Hughey said:
> 
> 
> > You say that as if you're somehow sure that "optimised centers, optimised pairing and optimised 3x3x3" is a bad method. I'm not so sure I believe that. Especially if we're talking an FMC with a time deadline, such as the 2.5 hours you had on the weekly competition, I think it's at least *possible* that this might be the very best possible system for doing 4x4x4 FMC. I'm not saying it is the best - it probably isn't - but it might be the best, and I don't think anyone knows enough to say for sure otherwise.
> ...


What happened to our co-operative 4x4x4 solves from yrs ago?? You never completed your part!!:fp

Per


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## mrCage (Oct 2, 2009)

joey said:


> I always detect parity before the cube is solved.


Does it help you timewise in any way whatsoever, or is it just fun to do??

Per


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## qqwref (Oct 2, 2009)

joey said:


> I always detect parity before the cube is solved.



Ah, I try to do that, but sometimes I don't notice the parity until after I solve the cube!


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## Kian (Oct 2, 2009)

mrCage said:


> joey said:
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> > I always detect parity before the cube is *solved.*
> ...



Note the bolded word. .


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## mrCage (Oct 3, 2009)

Kian said:


> mrCage said:
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> > joey said:
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Misread it. Thought you meant before solving starts. OKie dokie then ... It should at least be detected before stopping the timer


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## AvGalen (Oct 3, 2009)

mrCage said:


> Kian said:
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> > mrCage said:
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Parity SHOULD at least be detected before stopping the timer.....but I missed diagonal PLL parity on a 4x4x4 solve last weekend in Poland, even after checking


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## KwS Pall (Nov 5, 2009)

If you know the quater inner moves done in scramble you can solve odd parity while solving 3rd center!
I did sub 1 while counting moves and I do sub 55 regulary without counting  all at home or school


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## LNZ (Nov 5, 2009)

I did some internet research into God's algorithm for the 4x4x4 cube and it has been shown that the maximum half turn metric turns to optimally solve a 4x4x4 cube is between 30 and 68. As the 4x4x4 cube has about 7x10^45 possible states, progress in this area will be painfully slow.

For a real 4x4, I can't detect parity from a scrambled cube. But I can see it after solving the first three layers through.


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## Themancube (Nov 6, 2009)

Anyway give me your average move of fewest move 2x2x2 only ?


http://www.youtube.com/watch?v=fhXnBI7JSV0


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## hawkmp4 (Nov 6, 2009)

KwS Pall said:


> If you know the quater inner moves done in scramble you can solve odd parity while solving 3rd center!
> I did sub 1 while counting moves and I do sub 55 regulary without counting  all at home or school



Well of course you can. That's trivial and frankly, useless.


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## Stefan (Nov 7, 2009)

LNZ said:


> I did some internet research into God's algorithm for the 4x4x4 cube and it has been shown that the maximum half turn metric turns to optimally solve a 4x4x4 cube is between 30 and 68.


How was that lower bound determined?


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## Derrick Eide17 (Nov 7, 2009)

StefanPochmann said:


> LNZ said:
> 
> 
> > I did some internet research into God's algorithm for the 4x4x4 cube and it has been shown that the maximum half turn metric turns to optimally solve a 4x4x4 cube is between 30 and 68.
> ...



sighkick powurz ob vee is lee


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## Lucas Garron (Nov 7, 2009)

StefanPochmann said:


> LNZ said:
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> > I did some internet research into God's algorithm for the 4x4x4 cube and it has been shown that the maximum half turn metric turns to optimally solve a 4x4x4 cube is between 30 and 68.
> ...


So I wonder, too. I don't remember what we got when I helped qq, but if I'm not being silly, a lower bound of 32 on 4x4x4 is easy (fix DBL, 9 generators with 3 turn possibilities each).


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## cuBerBruce (Nov 7, 2009)

Lucas Garron said:


> StefanPochmann said:
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> > LNZ said:
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LNZ should have been more specific on what he/she was allowing for single moves. It appears to me that LNZ is not using the same "half turn metric" as defined in the WCA regulations.

For lower bounds I concur that 32 is an easy lower bound if you are only considering single-layer turns or only "twists" (twisting the cube along only one cut-plane at a time).

Using <U, u, d', Uud', Uu, ud', R, r, l', Rrl', Rr, rl', F, f, b', Ffb', Ff, fb'>, I came up with 29 as a lower bound (allowing half-turns as single moves) if I set up my recurrence relations correctly. This set of moves is what I've called "block turns."

The upper bound of 68 I'm assuming is from my analysis showing 68 block turns suffice, but I later improved that to 67 in this thread.


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