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Check out docs.google.com/document/d/1_NMlyPh2Ifd1E0ivos-15Sp-by-KPxoOsj9JD4pJuHI/edit#heading=h.3km7zdqm21jw

The HTR Theory video/doc is an application of corner swap insertions. The optimal HTR sequences were found by taking the optimal corner-only sequences and inserting corner swaps (and slices) to fix the edges. Once you understand how corner swaps work, you can usually find optimal HTR intuitively, instead of having to memorize each case.

@@hyper-paritycorner6030 Thank you for the answer. and for the tips. it's already becoming more intuitive now. for all the cases i can understand intuitiveley, i don't have to memorize the alg. :-) My confusion still is, that in the corner swap insertion video you always did two corner swap insertions. the second one put the cube back in its orientation/state as before, so the transcription part ended there and the following sequence didn't need to be transcribed. In the HTR-Theory video there is no second CS-Insertion, which is more understadable to me. Why do this second CS-Insertion? just to end the need to transcribe after?

@@megaigor2000 Sometimes the HTR alg will have two corner swaps (e.g. U B2 R2 U’ L2 B2 U) but more often only one is needed, and the second corner swap, if any, would be part of the HTR finish. In fact, corner swaps are kind of like parity: From any DR starting position, you can always fully solve the corners with at most one corner swap. If your position requires zero corner swaps to solve the corners, but you need one to bring the edges into HTR, then you will need a second corner swap after HTR.

@@hyper-paritycorner6030 Thanks a lot - this is very insightfull! So if i understand it right, in this video you always needed to take two insertions, because the starting point was a corner skeleton and the goal was to optimize the edges. in this context you had to do two, because inserting only one would disturb the pairity. right?

@@megaigor2000 Exactly right.

See the explanation here: docs.google.com/document/d/1HjS92UBCeCasbW44ezE0fjt5vmWQvlfkaC4rA113nmw/edit#heading=h.khhb6f4vryse

The easiest way to check parity is to solve just the corners. Add the number of U2 moves you used to the number of E-layer edge swaps remaining. In this case, you can solve the corners with R2 B2 U2, leaving a 3-cycle in the E layer. So that's 1 + 2 = odd parity

@@hyper-paritycorner6030Thank you very much for the explanation. 😊Somehow, it was not clear in the video what you actually counted. Maybe because you just visualised the corner solution and what happens to the edge pieces when solving the corners. Or is there any other way of checking parity? At first, I thought you were doing something like BLD tracing for the corners.

What I didn’t understand is “the parity of one of the two HTR-invariant corner tetrads”

@@KalinduSachinthaWijesundara The two tetrads are UFR-UBL-DFL-DBR and UFL-UBR-DFR-DBL. Since you're in HTR, any corner cycles will stay within one of the tetrads. Each half turn swaps one pair in each tetrad, so both tetrads always have the same parity and you only need to count one of them. In this example, one tetrad has a 2-cycle and one has a 4-cycle, so it's odd party. In this video, I determine parity that way using BLD tracing, but nowadays I think it's faster to solve the corners as described in the previous comment

🤔

In the "exclusive" case, if you try to form bars with the the bad FB stickers, you will find that the bad UD stickers are split 3/1 between the top and bottom faces, and vice versa. So it's not possible to form bars with both the bad UD and the bad FB stickers simultaneously. The good case is named "same" because you can form both sets of bars simultaneously, with the bad UD and the bad FB stickers on the same cubelets

If the perpendicular bars are on the same layer, then a U move stays at BS2, but there's only one BS2. If you're having trouble finding the half-turn setups that take you to somewhere that the maze says you should be able to go to, then R2 U2 F2 will often work.

Here, the "corner skeleton" is what brings the corners into HTR after the cube is already in DR.

@@hyper-paritycorner6030 thanks

It's a good case if you can split up the two bad F/B stickers (1 on U and 1 on D) while still forming a bar/slash pattern with the U/D stickers. This sets up a transition to bars + bars, which is impossible in the bad case.

That's right. I have another guide coming out that will cover edges.

It's always possible, using at most 4 extra moves beyond what's needed to solve the corners. If you set up the edges so that you have 4 bad edges after the first quarter turn, you can always bring them to the same face using half turns.

I’ll have to get my head around that one. Do you insert slices and R2 F2 R2s to force 4 bad edges? I’ll have to feed Nissy some HTR-2qt skeletons and see if I can understand how it works. Thanks Rodney.

@@edladd212 To manipulate the edges, you're always inserting slices and corner swaps (R2 F2 R2). At HTR-2qt, just make sure that your bad edges are split evenly between the U and D layers when you make the first quarter turn. That will ensure you have 4 bad edges at HTR-1qt.

@@rodneykinney4714 Thanks for the tips. I found my first direct finish with this just now, but it still feels a bit like trial and error :D

there's a link in the "detailed explanation" document in the description

Depending on the edges, the optimal HTR might use a non-optimal corner skeleton. Sometimes the optimal HTR uses 2 extra quarter turns, but it's more common to go 2qt -> 4qt than 3qt -> 5qt. Those solutions will be harder to find, so it might be better to move to another DR than to search for solutions that use non-optimal corner skeletons.

This morning, I found the origin of this issue problem myself. After contemplating for three days that there must be another special case with both a good and a bad option, I discovered that the supposedly bad option I was dealing with was physically not possible! :-) This was due to the fact that I had only mentally considered those cases. I had set it up just in my mind without considering whether the situation could actually occur in reality. I am relieved that the mystery is solved."

Well that a relief that there are no holes in this method

Also I want to know whether DR corner solution or hyper parity was better (fewest move), or they equal and I can pick whatever I want

If there are any NISS moves in the DR portion of the skeleton, you can invert them and apply them after the normal moves in the DR portion to get a non-NISSed skeleton.

Thanks! I definitely would not have gotten so far on this problem without the group's energy and ideas.

Those names are supposed to identify the points in the maze. ST = Solved/Top. BB = Bars/Bars, BS = Bar/Slash. Not very clear, I admit. Maybe I should have just gone with A/B/C!

So I've been playing around with this method for a couple of days, and I'm currently getting ~30 move solutions. I can imagine this will quickly get better, as I'm quite slow right now and one hour is not enough time for me to explore a lot of different hyper-parity continuations after DR. But this is promising!

Where did you learn DR

@@alexting827 Mainly using drive.google.com/drive/folders/1mppifILqu9Bu2phr8zhXGcXasBsSkv_S?usp=sharing

hi

Awesome. Let me know how things go!

Ha! I didn't even think of that.