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Megaminx ZBLL

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Feb 23, 2017
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I discovered NMLL for the 3x3 a month or two ago on the wiki. The idea is that you separate the last layer so all L-R colored stickers are on those two sides, though not necessarily permuted correctly, then solve everything with an extremely reduced subset of ZBLL. If you use phasing, it's actually <30 algorithms for a 2LLL.

Anyway, I was wondering what this would look like on the megaminx. My current vision is that L and R stickers can show up on L and R, U and F stickers can show up on U, F, BR, and BL, BR stickers can show up on U, F, and BR, and BL stickers can show up on U, F, and BL. Or possibly letting BR and BL stickers show up on the other back face as well.

Catch is, if I were to actually work this out, the easiest way I can think of would be to look at a list of ZBLL cases and simplify it. So does anyone know if a ZBLL case list exists for the megaminx, despite there apparently being 11672 mega-ZBLL cases, including mirrors, inverses, and solved?
 
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My current vision is that L and R stickers can show up on L and R, U and F stickers can show up on U, F, BR, and BL, BR stickers can show up on U, F, and BR, and BL stickers can show up on U, F, and BL. Or possibly letting BR and BL stickers show up on the other back face as well.
It's interesting to note that the first restriction (L/R facelets on L/R faces) alone is a pretty strict one: you're orienting all five corners and permuting two edges relative to a corner. Naïvely, this could take \( 3^4\cdot\binom52=810 \) cases, but we can reduce this by a bit.

We'll always have two edges "phased" (in the sense that they're not adjacent colours and also not physically adjacent) because of parity considerations, so we could pick those as our L/R colours and permute a corner relative to those two edges; this drops the case count to "only" \( 3^4\cdot5=405 \).

Adding further restrictions on bL/bR colours will increase the case count, which is probably not what you want.

Side note: Isn't megaminx PLL just 100-ish algs or something?
 
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