# Message #3934

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Physical 2x2x2x2 - Canonical moves

Date: Fri, 05 Jan 2018 18:43:44 -0800

Hello Joel,

It appears that If we only care about not getting out of the legal set of states, then no compensating twists are required for #9 at all. Although I don’t know how to do it, I’m guessing that you could twist a single end cap of a solved puzzle and then solve it using only moves 1-8. In other words, it’s similar to flipping a single piece in that it can be justified as a legitimate macro move but just feels like it’s gone too far, whereas moves #4 and 5 are so much simpler that they feel OK.

So it sounds like your answer to my main question of how to describe #9 is that any sequence of them on a half puzzle is fine so long as you keep track of the twists mod 4 and make any compensating twist on the other half when you’re done.

I’d still love to know where you draw the lines delineating primitive moves and canonical moves. I’d also love to hear from more people on this as well as any suggested reordering of these numbers or any additional moves that belong here. I agree with Marc that it’s fine to end up with multiple rule sets. I’d just love to first establish how much we already agree upon.

Thanks,

-Melinda

On 1/5/2018 9:10 AM, Joel Karlsson joelkarlsson97@gmail.com [4D_Cubing] wrote:

>

>

> 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 <mailto:melinda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com <mailto: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 <mailto: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 <mailto:whotyjones@gmail.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com <mailto:4D_Cubing@yahoogroups..com>>:

>>

>> Oops! Looks like the link has an extra period in it 🙂 https://www.youtube.com/watch?v=fYxn4wPe2ZE <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 <mailto:melinda@superliminal.com> [4D_Cubing] <4D_Cubing@yahoogroups.com <mailto: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

>>

>>

>

>

>

>

>