Thread: "Minimal number of pieces affected via a slice move in n-dimensions"

From: pauloliver.timmons@gmail.com
Date: 26 Sep 2019 12:59:31 +0000
Subject: Minimal number of pieces affected via a slice move in n-dimensions




From: pauloliver.timmons@gmail.com
Date: Thu, 26 Sep 2019 14:00:10 -0500
Subject: Minimal number of pieces affected via a slice move in n-dimensions



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Hi Paul,

You could make a puzzle with twisting like you describe, and I've seen one
in the past by Nate Berglund supporting that mode (it makes the puzzle
easier to solve). It breaks the analogy to the classic 3x3x3 in the sense
that such twists don't move all stickers on the face of a puzzle. A twist
like you describe would be somewhat like allowing a twist on Rubik's cube
that only affected edge pieces on a single face... "somewhat like" because
3-dimensions don't allow that without self-intersections, whereas
4-dimensions have enough space to "twist" only 2C+3C stickers on a single
face without overlap.

If you stick to the idea that a twist should affect all face stickers,
there will be no twists like you describe in any dimension... any twist
will always move pieces of every type, including corners (I'm considering
center-slice twists as twists of two faces here). MC4D and MC5D strictly
follow the analogy in this sense and don't support the twists you mention.

Of course, this can be debated. Here's quite an old thread, from 2005, that
discusses both approaches:
https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/125

Cheers,
Roice



On Thu, Sep 26, 2019 at 8:22 AM pauloliver.timmons@gmail.com [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:

> My question relates to three divisions per side.
> Is it possible to move just eight "pieces" in 4D? It looks like this
> should be possible by moving four 3-coloured cubies and four 2-coloured
> cubies (using either the smaller cube jnside or the larger outside cube).
> Slice move only so no 4-coloured pieces affected.
> Although this option is not implemented in the MC4D model ? But perhaps my
> understanding is flawed. Please can someone illuminate - I am particularly
> interested in higher than four dimensions also i.e. could one always move a
> layer just affecting eight pieces in isolation (ignoring the piece that
> exposed no stickers)
> Paul
>
>
>
> ------------------------------------
> Posted by: pauloliver.timmons@gmail.com
> ------------------------------------
>
>
> ------------------------------------
>
> Yahoo Groups Links
>
>
>
>

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Hi Paul,

You could make a puzzle with t=
wisting like you describe, and I've seen one in the past=20

by Nate Berglund supporting that mode (it makes the puzzle easier to solve)=
. It breaks the analogy to the classic 3x3x3 in the sense that such twists =
don't move all stickers on the face of a puzzle. A twist like you descr=
ibe would be somewhat like allowing a twist on=20

Rubik's cube that only affected edge pieces on a single face... "=
somewhat like" because 3-dimensions don't allow that without self-=
intersections, whereas 4-dimensions have enough space to "twist" =
only 2C+3C stickers on a single face without overlap.=C2=A0

<=
/div>
If you stick to the idea that a twist should affect all face stic=
kers, there will be no twists like you describe in any dimension... any twi=
st will always move pieces of every type, including corners (I'm consid=
ering center-slice twists as twists of two faces here). MC4D and MC5D stric=
tly follow the analogy in this sense and don't support the twists you m=
ention.

Of course, this can be debated. Here's=
quite an old thread, from 2005, that discusses both approaches:
=
cs/125">https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/=
125


Cheers,
Roice

=


class=3D"gmail_attr">On Thu, Sep 26, 2019 at 8:22 AM oliver.timmons@gmail.com" target=3D"_blank">pauloliver.timmons@gmail.com> [4D_Cubing] <lank">4D_Cubing@yahoogroups.com> wrote:
=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rg=
b(204,204,204);padding-left:1ex">My question relates to three=C2=A0 divisio=
ns per side.

Is it possible to move just eight "pieces" in 4D? It looks like t=
his should be possible by moving=C2=A0 four 3-coloured cubies and four 2-co=
loured cubies (using either the smaller cube jnside or the larger outside c=
ube). Slice move only so no 4-coloured pieces affected.

Although this option is not implemented in the MC4D model ? But perhaps my =
understanding is flawed. Please can someone illuminate - I am particularly =
interested in higher than four dimensions also i.e. could one always move a=
layer just affecting eight pieces in isolation (ignoring the piece that ex=
posed no stickers)

Paul







------------------------------------

Posted by: ">pauloliver.timmons@gmail.com

------------------------------------





------------------------------------



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From: Roice <roice3@gmail.com>
Date: Thu, 26 Sep 2019 17:50:20 -0500
Subject: Re: [MC4D] Minimal number of pieces affected via a slice move in n-dimensions



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I think that is a different move than Paul is describing. A 90 degree cente=
r-slice twist in MC4D permutes 8 3C, 8 2C, and 4 1C pieces, but I think he =
is asking about a hypothetical twist that would only affect 4 3C, 4 2C, and=
no 1C pieces.=20

Roice

> On Sep 26, 2019, at 4:45 PM, Marc Ringuette ringuette@solarmirror.com [4D=
_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>=20
>=20
>=20
> To me, the answer is a clear YES. You can do those slice moves analogous=
ly to 3D, and they make sense. It even works in MC4D as implemented.
>=20
> In the 3^4 hypercube puzzle in MC4D, f you hold down the 2 key as you cli=
ck a move with your mouse, your action will only affect slice 2 of the puzz=
le. I must made a macro with 1 move in it, an M slice move. So, MC4D se=
ems to think it's a valid single move, internally.
>=20
>=20
> Marc
>=20
>> On 9/26/2019 5:59 AM, pauloliver.timmons@gmail.com [4D_Cubing] wrote:
>> My question relates to three divisions per side.
>> Is it possible to move just eight "pieces" in 4D? It looks like this sho=
uld be possible by moving four 3-coloured cubies and four 2-coloured cubies=
(using either the smaller cube jnside or the larger outside cube). Slice m=
ove only so no 4-coloured pieces affected.=20
>> Although this option is not implemented in the MC4D model ? But perhaps =
my understanding is flawed. Please can someone illuminate - I am particular=
ly interested in higher than four dimensions also i.e. could one always mov=
e a layer just affecting eight pieces in isolation (ignoring the piece that=
exposed no stickers)
>> Paul
>>=20
>>=20
>=20
>=20
>=20
>=20

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=3Dutf-8">I think that is a different move than P=
aul is describing. A 90 degree center-slice twist in MC4D permutes 8 3C, 8 =
2C, and 4 1C pieces, but I think he is asking about a hypothetical twist th=
at would only affect 4 3C, 4 2C, and no 1C pieces. 


>Roice

On Sep 26, 2019, at 4:45 PM, Marc Ringuette =
ringuette@solarmirror.com =
[4D_Cubing] <4D_Cubing@yaho=
ogroups.com
> wrote:

=3D"ltr">






=20=20=20=20=20=20=20=20

=20=20
">
=20=20
=20=20






To me, the answer is a clear YES.  You can do those slice moves
analogously to 3D, and they make sense.  It even works in MC4D as
implemented.



In the 3^4 hypercube puzzle in MC4D, f you hold down the 2 key as
you click a move with your mouse, your action will only affect slice
2 of the puzzle.   I must made a macro with 1 move in it, an&=
nbsp; M
slice move.  So, MC4D seems to think it's a valid single move,
internally.





Marc



On 9/26/2019 5:59 AM, ailto:pauloliver.timmons@gmail.com">pauloliver.timmons@gmail.com [4D_Cu=
bing]
wrote:



-8">
 
=20=20=20=20=20=20

My question relates to three divisions per side.

Is it possible to move just eight "pieces" in 4D? It looks
like this should be possible by moving four 3-coloured
cubies and four 2-coloured cubies (using either the
smaller cube jnside or the larger outside cube). Slice
move only so no 4-coloured pieces affected.

Although this option is not implemented in the MC4D model
? But perhaps my understanding is flawed. Please can
someone illuminate - I am particularly interested in
higher than four dimensions also i.e. could one always
move a layer just affecting eight pieces in isolation
(ignoring the piece that exposed no stickers)

Paul





=20=20=20=20=20=20=20=20=20=20

=20=20=20=20=20=20
=20=20=20=20=20=20




=20=20










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From: pauloliver.timmons@gmail.com
Date: 26 Sep 2019 15:49:15 -0700
Subject: Re: [MC4D] Minimal number of pieces affected via a slice move in n-dimensions




From: pauloliver.timmons@gmail.com
Date: Fri, 27 Sep 2019 19:43:55 +0100
Subject: Re: [MC4D] Minimal number of pieces affected via a slice move in n-dimensions



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Is this the move you're talking about? If so, it's not a single move, but
can be accomplished using rkt.

~Luna

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Is this the move you're talking about? If so, it's not a single move, but can be accomplished using rkt.

~Luna


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From: pauloliver.timmons@gmail.com
Date: 28 Sep 2019 14:55:37 +0000
Subject: Re: [MC4D] Minimal number of pieces affected via a slice move in n-dimensions




From: pauloliver.timmons@gmail.com
Date: Sat, 28 Sep 2019 20:13:31 -0700
Subject: Re: [MC4D] Minimal number of pieces affected via a slice move in n-dimensions



Yahoo Groups is a very shaky and poorly supported platform, and one of the biggest problems is it's mysterious ways of handling attachments. It's therefore often preferable to link to photos and files on the web when practical.

-Melinda

On 9/28/2019 7:55 AM, pauloliver.timmons@gmail.com [4D_Cubing] wrote:
> Sorry cant view any attachment. I can see there is one there but unable to view content. II have MC4D downloaded. Am using Google chrome browser





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