HTR to FR: Using Floppy Reduction to find optimal half-turn solutions

[@lichifang632]

You know a problem is "solved" when Rodney uploads a video. Thank you soooooo much, Rodney. Beyond their effectiveness, your methods are always so elegant. Your work motivates me to a huge extent and got me from ~30 global to ~26. It's always so exciting to see new video coming out from the channel.

[@hyper-paritycorner6030]

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

[@fmcer]

Shorter equivalent scrambles for examples: 1. L2 F' L R B2 L' R' F' R2 2. F2 L2 R2 D2 L2 B2 L2 F2 U2 3. R2 B2 U2 L2 B2 U2 R2 F2 U2

[@KalinduSachinthaWijesundara]

@9:26 Example 3, how do we decide it’s odd parity when corners are 2 cycles and no edge cycles? Can you explain a bit more how that’s determined?

[@hyper-paritycorner6030]

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

[@KalinduSachinthaWijesundara]

@@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.

[@KalinduSachinthaWijesundara]

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

[@hyper-paritycorner6030]

@@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

[@ignDart]

🤔

[@louissarthou6655]

Thanks a lot for the explanations, I'll definitely try to get more comfortable with floppy reduction. I think it can be very useful when the solution to HTR is short but you can't find a straight forward way to reduce the case to something easy. I often miss "long" half turn optimals. Side note, the second case sequence is wrong by an E-slice even permuation. That doesn't affect the floppy case but it took me some time to understand what was wrong. Greetings from France

[@spencerchubb]

This is wonderful! Could I have a link to the discord server you mentioned?

[@Mmmm1ch43l]

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

[@rodrigoqteixeira]

Gonna be honest, I didn't understand a thing about the tutorial, too confuse for my brain