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How To: Solve 4x4 orientation parity intuitively

Christopher Mowla

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I guess it's good to revisit old (but good) topics!

Perhaps you can also make an intermediate video which explains that if you set up the centers in the 2R slice with 2R2 F2 U2 and then do the extra quarter turn and undo those moves, [2R2 F2 U2: 2R], then all you have to do is 2L' U2 2L 2R U2 2R' to completely restore the centers. This is simply because we put the colors of two adjacent centers in slice 2R first. That way, we only can messup two composite center's centers. Similarly, we can put two opposite composite centers' centers in slice 2R: [2R' e2: 2R] F2 2L2 F2 2L2 OR [2R' U2 2R' F2 U2 2R' B2: 2R] m2 2U2 m2 2U2.

Regarding the adjacent composite center case, if we do the premove F2 before we do the two adjacent-center switching algorithm, we get a 2-cycle: [r2 F2 U2: 2R] F2 (2L' U2 2L) (2R U2 2R') F2. I explain this concept in this post, and then in this post I show how to modify the algorithm to create a single dedge flip. (This would be too advanced for a beginner's video.) [r2 F2 U F' R' F R2 U: 2R] F2 (2L' U2 2L) (2R U2 2R') F2

Of course, I don't know if you recall my video on this topic, where we go all the way and just make use of some move sequence which does the effect of 2F2 2U' 2R2 u2 s' on slice 2R, so that we don't have to solve back centers at all when we apply the quarter turn. (I recently did a write-up in this post of this center-setup concept, which includes information on how to set up the centers for ODD-layered cubes as well and also gives a good summary of pretty much everything I ever did with the concept.)

Although definitely too advanced for most people (but I thought you might be interested, PJK) is to study this algorithm, as it's based off of Bruce Norskog (cuBerBruce's) (15,15) single parity algorithm (which is definitely too complicated to understand . . . hence why I made a more manageable - although longer - analogue which illustrates how Bruce's algorithm actually fixes parity). Specifically, notice that I begin with an inner slice 2R turn and do 3x3x3 M U moves only to until the first Uw2. The 1x2 center block formation allows us to ONLY use three inner slice 2R turns but yet still deal with the centers in a more "linear" path as you portray in this video. But as the added bonus, the dedges are preserved as well. I really think this alternate way to deal with centers (and maintaining dedge pairs) is truly a beautiful concept. I felt as though "I saw it all" when I understood how that worked! As I emphasized in my video, it's not the moves themselves that are important (in this particular case, the two sequences of M and U moves), but the pattern they setup.

If my MU algorithm is too complicated to grasp at first, you can simply study how r U' R U' 2R' D' R D' r (or any algorithms in this section of the 4x4x4 parity algorithms wiki page) fixes edge parity (but it "completely ignores" the centers). Then if we simply use one half turn in the 9 move sequence, we can use what can be thought of as an intuitive approach to fixing parity. (See this old post for details.)

But that's all I know of (besides making direct algorithms or algorithms which, if repeated, create OLL parity, of course).
 
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