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Not just challenging; I don't have any clue on how to go about doing that either! What I used was this: solving four wing pieces (the UF dedge and two other pieces), five centre pieces, and one corner piece; this was done with two small pruning tables (~4-5 million entries). I then multiplied the resulting pruning value by 2, which makes it almost certainly not optimal, and filtered the solutions (which can have up to 16 unsolved wings and 17 unsolved centres) for those that had only fixed points and 3-cycles.

Now I'm running a full optimal search (i.e. solving only the UF dedge, no restrictions on other pieces), but it's only finished exploring 25 moves so far. (The code is… not fast.) Edit: finished searching up to 27 moves now; still hasn't found anything. Edit 2: oops, found a bug—it was searching something completely different. Disregard this whole paragraph!

I mentioned in the fourth video of my 2-gen series about "Type 3" == <r,Uw> that there is room for improvement. In the video, I derived a 61 move algorithm. Below is a derivation of a 53 by simply reusing the 37 move algorithm I found which is in <r,3Uw> ("Type 2"). (An algorithm which I derived without repetition.)

Specifically,

Spoiler: Derivation

[1] Below is the algorithm which is derived by 16:03 of the video on <r,3Uw>. [Link]
r
r2 3Dw2 r2 3Dw2 r2
3Dw2 r'
3Dw2 r2 3Dw2 r' 3Dw2 r2 3Dw2
r2
r 3Dw2
r'
3Dw r 3Dw r2 3Dw' r' 3Dw' r 3Dw r 3Dw r2 3Dw' r' 3Dw' r'

I have still not been able to beat the record 102 set by xyzzy. But I have found that there is no sequence shorter than 26 moves that when repeated 3 times is a pure double edge flip on UF.

I have still not been able to beat the record 102 set by xyzzy. But I have found that there is no sequence shorter than 26 moves that when repeated 3 times is a pure double edge flip on UF.

I wrote a little routine in Mathematica earlier this year to find repeats of short sequences via a random scramble. (I did this to see if I could find alternate short move sequences to repeat 5 times to get OLL parity.) I just adjusted it to the given constraints and it is giving me move sequences with a random number of required repeats.

Below are the shortest so far (I started with "depth"/Length 8).

All of these flip a single dedge, but most do not flip the UF one. Ones which do flip the UF dedge have an * next to them. My program is finding one sequence every few seconds, on average.

It seems that algorithms of Length 8 is the minimum, but I can't prove this. I am running my solver again to see if it finds any solutions which consist of repeating an algorithm 7 moves long. In addition, I may run it for Length 30 or so to see if I can beat xyzzy's alg length.

24 is optimal for UF flip + 5-cycles. (This is assuming centres are distinguishable, as on a supercube. My code doesn't handle the normal, non-supercube case.)

Finally found one (or two). This is not necessarily optimal. It has a length of 31, but there are
move cancellations when repeating it thrice so the total length is 91.