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A Collection of Cubing Curiosities

cmhardw

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#23
Also, I'm not so sure about some of your attributions. But maybe I'm just jealous I didn't suggest them first. :p

Regarding Hardwick's conjecture: I checked up to n=54 over four years ago when Chris brought up the n=3 constant; see this post; I don't recall Michael posting on this, but maybe I'm just missing something.
Lucas, my apologies. I likely misremembered who had done the analysis (I'm the one who mentioned Michael Gottlieb in my post to Macky). Michael, did you do any analysis on this as well? Apologies if I have not given credit where credit is due, that was not my intention.
 

macky

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Thread starter #27
Added more. Thanks for your contributions.

I think he meant to write [R U R2, R U2 R2]. The Sune is one of the most important algs in cubing, and it is curious that the alg itself can be written as a commutator (because it's not obvious at a glance).
See http://www.speedsolving.com/forum/showthread.php?5783-Math-Problem-12
ah, I see. Did someone show that the commutators themselves are closed under composition? I remember reading something like this. In that case, I would mention the Sune is a representative non-obvious example.

Erm, what do you mean he found it? This is an old trick for FM. It also applies to L R F2 R B L' U2 L B' R2 F L' which is oriented with r U' L' as well others I'm sure.
I'd be interested in seeing some more.


Also, I'm not so sure about some of your attributions. But maybe I'm just jealous I didn't suggest them first. :p
Yeah, for things that multiple people have known for a while, I want to replace the "suggested by" with just a nameless link to the source post. On the other hand (not really a reply to your comment), I think "popularized by" should stay; if Feliks really did popularize that one case enough case to turn that trick into common knowledge, then he deserves a mention, like with Rowe's E perm. In any case, speak up if there's any doubt.
 
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#28
Lucas, my apologies. I likely misremembered who had done the analysis (I'm the one who mentioned Michael Gottlieb in my post to Macky). Michael, did you do any analysis on this as well? Apologies if I have not given credit where credit is due, that was not my intention.
I don't remember doing any analysis on this.


Another curiosity: certain algs can be done on only the top face of a bigger cube simply by replacing some of the moves. For instance, RwURw'U'Rw'FRw2U'Rw'U'RwURw'F'. The canonical Y perm works too, and Fw2UM'U2MUFw2. This is somewhat surprising since many common/fast algs do not do this. The R'U2RU2 R perm doesn't work, or the 2-gen U perm and the RU2R' style J perm doesn't although the RUR'F' one does. The MU H-perm works, the 2-gen one *almost* works (it does the intended effect plus two edge 2-cycles), and the RLU2 one almost works as well if you do it right. I'm still not really sure why some algs work and others don't, but it's definitely curious.

EDIT: Oh yeah, something else that I think I discovered: any PLL (any ZBLL, actually) can be done completely 2-gen plus exactly one F and one F'. The same thing occurs for D/D', B/B', and L/L'.
 
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#29
RU'r'U'M'UrUr' is a bit magical for LSE - much shorter/faster than any <MU> one (somewhat unique in this respect), but doubt this warrants inclusion in the list.
Are you including recognition time when you say "faster"? Because surely, when using freecenters, the five move MU'M'UM' (UL/UR at UL and DF) and M'U'M'UM' (UL/UR at UL and UB) can be performed faster than the nine move RrUM. Even M'U2M'UMUM'UM' (UL/UR at UF and UB), which is the longest freecenter six-flip, is pretty fast.

Including recognition time though, it may be quicker to use your RU'r'U'M'UrUr' instead of searching for UL and UR to save four moves.

I hate to not add anything to the topic. I tried, but nothing came to mind.
 
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