4x4 and parity for fairly new cubers

[thornomad]

Hello everyone. First post.

This past summer I taught myself and then my eight year old son how to solve the 3x3 Rubik's Cube. Since then he has gotten a lot better. Over the holidays, we got a 2x2 cube and a 4x4 Cube. We've got the 2x2 Cube figure it out, however, still working on the 4x4.

My question is about the parity. But before I get to that I believe my question actually starts about the 3x3 Cube.

When we learned the 3x3 I followed a couple different beginner methods. The one we finally settled on has us solving the last layer by first forming a correctly positioned and correctly oriented yellow cross and then solving the corners (first positioning the corners and then orienting them as the final step). Not sure what this approach is called. I did notice, later, that other beginner methods approach the last layer differently -- first solving for the orientation of the yellow face, and then the positioning of all the pieces. I think this is referred to as OLL then PLL (which is different, if I understand it, than how I learned).

This leads me back to the question of parody in the 4x4 Cube. When I search online I feel like I find all of the parity Solutions for the 4x4 reference the OLL and then PLL methods -- That is, the method that my son and I did not learn.

Do you recommend we take a step back and learn this method for solving the last layer of the 3x3 cube before moving back to the 4x4?

Or are there guides to solving parity with the method that we learned already for the 3x3 Cube?

Am just curious if I am on the right track with my understanding of all this. We have made some changes already to how we solve the F2L in hopes of getting faster … but want to make sure we are approaching it right.

 

[xyzzy]

Welcome to the forums!

> Do you recommend we take a step back and learn this method for solving the last layer of the 3x3 cube before moving back to the 4x4?

If you intend to get into speedcubing seriously (or at least semi-seriously), then yes, I'd highly recommend learning (beginner versions of) OLL and PLL. It's not that your current method is bad or anything; it's just that it doesn't extend cleanly into more advanced LL methods, so you'd have to relearn a lot of things. Might as well get it out of the way earlier.

There's also an additional complication with an edges-first last layer method when it comes to parity on big cubes.

The general approach to solving big cubes is to group up all of the centres first, then group up all of the edges, then solve it like a 3×3×3. There are two different "parity" situations that can arise at this point: "OLL parity" (odd number of flipped edges) and "PLL parity" (odd number of swaps of corners and edge pairs). The names of these situations are just what they are, names. You'll still have a chance of encountering them even if you use a method that doesn't involve the OLL and PLL steps.

OLL parity requires a really long and annoying alg (15 to 17 moves, depending on who you ask), but essentially what the alg does is that it flips one edge and rearranges the other last layer pieces a bit. This integrates into the edges-first last layer method cleanly. Just do the OLL parity alg when you have one or three flipped edges, then proceed to solve the edges as usual.

It's PLL parity that's problematic. While the PLL parity alg is much shorter (6 to 8 moves, again depending on who you ask), it swaps two edge pairs with each other. The way you'd handle this with an edges-first method is to finish solving your edges first (doing OLL parity if necessary), then trying to solve your corners only to find that you have an "impossible" situation (e.g. you need to swap two corners); at that point you'd do the PLL parity alg, and now your edges are messed up and you need to solve them again. In a sense, the PLL parity alg will destroy progress in your solve if you use an edges-first method, and I don't know about you, but this would certainly seem very frustrating to me.

This wouldn't be an issue with the OLL+PLL last layer method that most people use these days. Do OLL parity if necessary, then do OLL, then do PLL parity if necessary, then do PLL. Done. No destruction of progress.

 

[Solvador Cubi]

A couple of usual algs for 4x4 parity fixing:

OLL (flips the UF edge pair): r U2 x (r U2 r U2) r' U2 l U2 r' U2 r U2 r' U2 r'

PLL (swaps positions of the UF & UB edge pairs): u2 r2 U2 2R2 U2 r2 u2
or this one: 2R2 U2 2R2 u2 2R2 2U2 (or written with different notation: r2 U2 r2 Uw2 r2 u2 )


-= Solvador Cubi

 

[thornomad]

If you intend to get into speedcubing seriously (or at least semi-seriously), then yes, I'd highly recommend learning (beginner versions of) OLL and PLL. It's not that your current method is bad or anything; it's just that it doesn't extend cleanly into more advanced LL methods, so you'd have to relearn a lot of things. Might as well get it out of the way earlier.

Me personally? Probably sort of maybe not. But my son might be interested. He can do the cube in about a minute twenty with the current approach we have. He has fast fingers. Me it takes 2-3 minutes. We had been working on F2L and doing a more intuitive approach of solving both the white corners and the second layer simultaneously (instead of in stages). He is getting faster at that.

It's PLL parity that's problematic. While the PLL parity alg is much shorter (6 to 8 moves, again depending on who you ask), it swaps two edge pairs with each other. The way you'd handle this with an edges-first method is to finish solving your edges first (doing OLL parity if necessary), then trying to solve your corners only to find that you have an "impossible" situation (e.g. you need to swap two corners); at that point you'd do the PLL parity alg, and now your edges are messed up and you need to solve them again. In a sense, the PLL parity alg will destroy progress in your solve if you use an edges-first method, and I don't know about you, but this would certainly seem very frustrating to me.

Thanks for taking the time to explain that in such detail; that sounds exactly like what I've been experiencing! Added to that it's hard to find actual diagrams showing the current state of the cube at that point because I think the OLL to PLL route is more popular.

This wouldn't be an issue with the OLL+PLL last layer method that most people use these days. Do OLL parity if necessary, then do OLL, then do PLL parity if necessary, then do PLL. Done. No destruction of progress.

That makes sense. All right! I think I at least know what's going on. Since we are already learning new algorithms for the 4x4 maybe we will finish with memorizing the two parity cases and just deal with the destruction for the time being. Then take a step back and work on learning a new method for the 3x3 (OLL to PLL) and then we can apply it to the 4x4 cube.

Thanks so much for such a detailed explanation of everything! Really appreciate it.

 

[thornomad]

OLL (flips the UF edge pair): r U2 x (r U2 r U2) r' U2 l U2 r' U2 r U2 r' U2 r'

PLL (swaps positions of the UF & UB edge pairs): u2 r2 U2 2R2 U2 r2 u2
or the same but written with different notation: 2R2 U2 2R2 u2 2R2 2U2

Thanks for adding these here for my reference. I have to look up all these notations again because the 4x4 added some complexity to my old brain. Will bookmark this and come back with a notation dictionary and give it a whirl.