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Speedcubing: Solving the Rubik's Cube > Speedcubing > 4x4x4 parity fix


Title: 4x4x4 parity fix


karthikputhraya - July 3, 2007 09:25 AM (GMT)
I learnt to do the 4x4x4 recently.I learn from bigcubes.com.
But I think we can correct the OLL parity before finishing solving it like a 3x3.
I do a 4 look LL 3x3.So when I have finished my F2L I correct the parity then and there by looking at the number of correctly oriented edges in the LL.
What do you think about this?

Erik - July 3, 2007 11:25 AM (GMT)
I think it's quite undoable, you'd have to count all edges and besides that, we don't have a better parity alg than the normal one so it wouldn't be any faster too :unsure:

karthikputhraya - July 3, 2007 12:16 PM (GMT)
Counting edges is not a problem at all!
I said that we count edges after F2L i.e the edges in the LL.If there is an odd number of correct edges,then there is OLL parity.So we can correct the OLL parity after F2L.
If we were to correct OLL parity after fully solving like 3x3 (using the algo given in bigcubes.com) then we will be left with an un-oriented LL,which has to be corrected again.
So if I am not wrong, correcting OLL parity after F2L results in solving the OLL only once and not twice,thus saving time.
Please correct me if there is any flaw in my argument.

AvGalen - July 3, 2007 12:26 PM (GMT)
This might be possible if you are an extremely fast roux solver, or a 3-cycle (orient first) blindfolded solver with a very bad/slow parity fix.

If you could count edge-orientation in sub-5 seconds and fix parity in 2 seconds (I don't think such a fast fix exist. I figure it would require at least 5 moves, including 3 slice moves. Probably way more) you will still spend at least 5 seconds on parity, EVEN IF YOU DON'T HAVE PARITY!

The only way to avoid parity is to spend all your inspection time on parity analysis AND use a corners first (cage) and orientation preserving method.

Either I have a pretty good idea how parity works, or my brain is dead after 2.5 hours of sleep in 2.5 days.

AvGalen - July 3, 2007 12:37 PM (GMT)
karthikputhraya wrote something while I was typing.....

You can do 1 of 4 things:
1) Check/Solve parity really early during the solve, when it takes fewer moves (maybe, see above)
2) Check for OLL-parity after F2L. If you have it, fix it using the faster OLL+PLL parity fix. This will give you PLL-parity if you didn't have it and it will make you skip PLL-parity if you had it. Either way, you have 50% chance of getting PLL-parity, but you have saved some time because of the faster OLL+PLL parity fix. This is the method I use.
3) Solve the cube all the way through OLL. Now check for OLL and PLL parity and fix it with only 1 parity alg, then do PLL. This is harder to recognise, but fast because you use 1 parity fix and you don't have to worry about distroying PLL. I think this is the fastest method
4) Solve the cube all the way through OLL+PLL. Parity will be very easy to recognise now, but to solve it without destroying OLL and PLL you will have to learn more parity-fixes and they will be slower. This is a method most beginners will use, but they will end up destroying OLL and/or PLL because they don't know the exact parity-fix.

Erik - July 3, 2007 12:58 PM (GMT)
QUOTE (karthikputhraya @ Jul 3 2007, 12:16 PM)
Counting edges is not a problem at all!
I said that we count edges after F2L i.e the edges in the LL.If there is an odd number of correct edges,then there is OLL parity.So we can correct the OLL parity after F2L.
If we were to correct OLL parity after fully solving like 3x3 (using the algo given in bigcubes.com) then we will be left with an un-oriented LL,which has to be corrected again.
So if I am not wrong, correcting OLL parity after F2L results in solving the OLL only once and not twice,thus saving time.
Please correct me if there is any flaw in my argument.

but... we already do this (correct OLL parity after F2L)

karthikputhraya - July 3, 2007 01:27 PM (GMT)
Oh!Fine.
I dint know that.
As Arnaud said that most beginners follow step 4,I used to follow that,screwing up my OLL.So I thought that doing that differently would help.
Arnaud:Why not do this way.
F2L-->Fix OLL parity if any-->OLL--Fix PLL parity if any.

AvGalen - July 3, 2007 01:57 PM (GMT)
karthikputhraya and Erik, I think you actually agree on this. You both seem to prefer option 2 (see above). I think the misunderstanding was that karthikputhraya maid it sound like he wanted to do OLL-parity before the 3x3x3 part.
QUOTE
But I think we can correct the OLL parity before finishing solving it like a 3x3


But on bigcubes.com they also hint at beginners to solve the 3x3x3 entirely and then fix parity/parities. (http://bigcubes.com/4x4x4/finalsolve.html)

karthikputhraya: F2L-->Fix OLL parity if any-->OLL--Fix PLL parity if any
That is exactly what option 2 is. I just recommend to use the OLL+PLL-parityfix to fix the OLL-parity because it is faster.

Erik - July 3, 2007 02:07 PM (GMT)
:D

PJK - July 3, 2007 05:00 PM (GMT)
I think you are referring to ways of recognizing the parity. Whenever I solve, I do the F2L, then recognize the top pattern, if I don't recognize it, it is a parity, so I fix it. Then I oriente it all, and permute/fix PLL parity. I can solve the 3x3 stage in 30 seconds or less almost every time, which is actually pretty slow, but good enough ;) If I can get my pairing+centers down to 40 seconds, that will be sub-70 average ;) Anyways, keep up the practice and good luck.

karthikputhraya - July 3, 2007 06:36 PM (GMT)
I was doing exactly what PJK does.But now I think I will switch to what Arnaud does ;)

AvGalen - July 4, 2007 01:29 PM (GMT)
PJK: Are you saying you can see if a 4x4x4 has no parity, OLL parity, PLL parity or OLL+PLL parity just by recognizing the top pattern after OLL? There are over 1000 no-parity cases for the last layer and (I guess) over 3000 parity cases. Recognizing that (fast) would be a very desirable skill.

Off course, you can see if you have OLL parity really fast (odd number of oriented edges). And you can see if you have PLL parity by checking if you don't have 1 of the 21 regular PLL-case, but that is very hard to recognize before doing OLL.

PJK - July 4, 2007 10:26 PM (GMT)
Arnaud, no, I just recognize the OLL parity, then fix, then see if I have a PLL, and then fix/not. But I just saw your post, and then read on bigcubes about just using the quicker double parity alg. I have no idea why I wasn't doing that before. I will now use that. Thanks

karthikputhraya - July 5, 2007 05:22 AM (GMT)
What is the probability of having a PLL parity??(Not ONLY PLL but PLL with or without OLL)

AvGalen - July 5, 2007 05:31 AM (GMT)
25% no parity
25% only OLL parity
25% only PLL parity
25% both OLL and PLL parity

so
25% no parity
75% parity

and
50% OLL parity (with or without PLL parity)
50% PLL parity (with or without OLL parity)




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