Message #3921

From: Joel Karlsson <joelkarlsson97@gmail.com>
Subject: Re: [MC4D] Physical 2x2x2x2 - Canonical moves
Date: Fri, 05 Jan 2018 18:10:44 +0100

I see two options here:

If we only care about not getting out of the legal set of states it would
not matter which way the compensating twist is.

However, since it’s an elementary twist to turn both of the caps it is
possible to do a cap on twist, reorient one half of the puzzle (another
elementary twist), do another cap twist and so on to perform manipulations
on just one of the halves as a 2x2x2. If we view the manipulation of a
single half as a shortcut for this then it would indeed matter; you would
have to keep count of the twists mod 4 (counterclockwise twists increasing
the count and clockwise twists decreasing the count) and than twist a cap
on the other half corresponding to this count (so if the count ends up at 1
you should turn a cap 1*90 degrees counterclockwise). Thus, the
compensating twist at the end could be either clockwise, counterclockwise
or 180 degrees.

This comes down to personal preference and if you accept single moves that
correspond to macros or not. As stated in a previous post, it is impossible
to get the whole set of 2^4 states without allowing at least one
non-elementary move with the physical 2^4.

Best regards,
Joel

Den 5 jan. 2018 8:12 fm skrev "Melinda Green melinda@superliminal.com
[4D_Cubing]" <4D_Cubing@yahoogroups.com>:

For people making a set of moves on one half, can you just count your turns
and either make an extra turn on the other half if it’s odd? And if so,
does it matter which direction you make that twist?
Thanks,
-Melinda

On 1/4/2018 11:01 PM, Joel Karlsson joelkarlsson97@gmail.com [4D_Cubing]
wrote:

Regarding #9: to get solvable states the number of single cap twists has to
be even (a single cap twist is an odd permutation but only even
permutations are possible for the 2^4). I don’t think that a single cap
twist breaks the corner rotation restriction so as long as an even number
is used everything should be fine.

Best regards,
Joel

Den 5 jan. 2018 12:33 fm skrev "Ty Jones whotyjones@gmail.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com>:

Oops! Looks like the link has an extra period in it 🙂
https://www.youtube.com/watch?v=fYxn4wPe2ZE there’s the corrected one for
anyone too lazy

Looking forward to watching the video!

On Thu, Jan 4, 2018, 4:28 PM Melinda Green melinda@superliminal.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> First off, please check out Zander Bolgar’s lovely solution video
> <https://www.youtube..com/watch?v=fYxn4wPe2ZE> that he invited me to
> share. It’s very cool to see someone developing something like finger
> tricks and blasting through a solution. It’s very much like Bob’s
> <https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/3803>
> and Joel’s
> <https://groups.yahoo..com/neo/groups/4D_Cubing/conversations/messages/3904>
> solutions as well as Marc’s <https://www.youtube.com/watch?v=pKHU5sFaGvY>
> approach.
>
> This makes for a great launching point for questions about which moves
> should be included in a canonical set. Of course any move that results in a
> reachable state can be justified in a solution, but there’s such a spectrum
> from "obviously fine" to "obviously not". Now that we’ve gotten some
> experience with this puzzle and the practicalities of solving it, I feel
> it’s time to see if we can find some sort of natural canonical set, so I’d
> love to hear your thoughts.
>
> Here is the list of moves I know about, loosely ordered as described above:
>
> 1. Simple rotations
> 2. 90 degree twists of outer face
> 3. 180 degree twists of side face
> 4. Center face axial twist
> 5. Arbitrary half-puzzle juxtapositions
> 6. Clamshell move
> 7. Whole-puzzle reorientations
> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
> directions)
> 9. Single end cap twist (with parity restrictions?) [fine for
> scrambling]
> 10. Restacking moves [fine for scrambling]
> 11. Single piece flip
> 12. Reassemble entire puzzle
>
> I suspect the trickiest part has to do with #9 which is the one I would
> most like to nail down.
>
> I intend to create a follow-up video to talk about all of these and any
> others you can think of. The way you can help is to offer additions and
> corrections to the above list, and especially in suggesting ways to reorder
> it. Then please suggest where you’d draw three lines:
>
> - Everything above is primitive (Or "basic" or "elementary" as Joel
> calls them)
> - Everything above is canonical. IE always acceptable in solutions
> - Nothing below is acceptable in solutions.
>
> Thanks all!
> -Melinda
>