My notes for using ZBF2L for the 4x4x4
This page is really meant just for me, though I include it on my page on the offhand chance that one day someone may have the interest to study it. The purpose is so that I can have a single place where I can easily tell which ZBF2L cases should have an even number of edges showing in the top layer, which ones should have an odd number showing, and which ones may have both. This will help to 1) sometimes identify the parity error before finish ZBF2L, and 2) allow myself to solve an easier ZBF2L case than I actually may have when I do have the flipped edge parity error.

I will split these into two categories, when the middle layer edge is in the middle layer, or in the top layer. For each case I find it easiest to see whether the middle layer edges is flipped or not flipped.

Middle layer edge is in the middle layer

Even parity cases: Obvious
Given a solvable 3x3x3 cube configuration, these cases must have an even number of edges showing in the top layer.

Odd parity cases: Obvious
Given a solvable 3x3x3 cube configuration, these cases must have an odd number of edges showing in the top layer.

Middle layer edge is in the last layer

I'm still working on a way to handle these cases, based on how recognition seems to go for me when solving. What I think will be useful is to look and try to identify 1) the F2L case, 2) whether the middle layer edge is flipped or not, 3) whether the number of flipped edges is even if the middle layer edge is correct or odd if the middle layer edge is flipped. I haven't practiced this method much, but it seems that it might work.

Middle layer edge correctly flipped

Even number of correctly oriented last layer edges in the last layer
Odd number of correctly oriented last layer edges in the last layer

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