# Message #3920

From: Roice Nelson <roice3@gmail.com>

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

Date: Fri, 05 Jan 2018 10:55:35 -0600

I don’t have an opinion on primitive vs. canonical but draw the line

between 8 and 9 for solution acceptability. IOW, I don’t consider 9

acceptable for solutions… at least if you want to claim twisting is

faithful to MC4D’s 2^4. If you want another fun puzzle, go for it.

9 clearly makes the puzzle easier to solve than in MC4D because it allows

twisting only 4 cubies at a time and dealing with resulting parity at a

later stage. A faithfully modeled twist must permute 8 cubies. I have no

issue with a "twist" being a sequence of moves but it wouldn’t be ok would

be to execute move 9, then do some other primitive twists, then execute

move 9 again to fix up parity.

It also feels like a stretch to allow doing something like Melinda

described: manipulating one 2x2x2 block intuitively, then fixing up the

parity on the other block. That is arguably a single twist but manipulates

the puzzle in a fundamentally different way than is possible in MC4D.

I think what I’m suggesting is that allowable twists should traverse the

state space graph in exactly the same way that is possible in MC4D. Hmmmm,

this might eliminate some of the other entries in the list, since I bet a

few of the twists act more like MC4D macros than single twists, so perhaps

this is overly restrictive. Maybe moves like Melinda described should be

allowed. Subtle! However, I do feel pretty strongly that move 9 should be

disallowed in isolation.

Using an even number of 9s during scrambling seems perfectly fine since the

goal of scrambling is just to get a valid puzzle state.

Best,

Roice

On Fri, Jan 5, 2018 at 1:17 AM, Melinda Green melinda@superliminal.com

[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>

>

> Wait, maybe I’ve answered my own question. If you twist the other half

> "the wrong way", you can easily reduce both to a single end cap twist of

> 180 degrees which should therefore be fine.

> -Melinda

> PS: About your notation, ‘E’ works great as an abbreviation for "End".

>

>

> On 1/4/2018 11:11 PM, Melinda Green melinda@superliminal.com [4D_Cubing]

> wrote:

>

> 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

>>

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