Thread: "Latch Cube"

The latch cube is not 4D. I know. But does anybody of you know a good solvi=
ng description? What is the part of the 12! 12^2 edge positions which is re=
achable with this latch mechanisme? Per cents, per mils ?
If it is a very small part then I'm intested to establish the graph of thos=
e positions.

Sorry, there are 12!/2*2^11 unhindered edge positions.

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> The latch cube is not 4D. I know. But does anybody of you know a good sol=
ving description? What is the part of the 12! 12^2 edge positions which is =
reachable with this latch mechanisme? Per cents, per mils ?
> If it is a very small part then I'm intested to establish the graph of th=
ose positions.
>

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Content-Type: text/plain; charset=windows-1252
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Hi Eduard,

Here is some discussion about solving the latch cube.

http://twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D18752

I have never seen a good estimation for the number of reachable positions. =
I
only know that the superflip position (all edges are in place, but flipped)
is nonreachable. I guess the space of reachable positions is so large that
one cannot fully describe the graph. An interesting question is, how many
orbits are there for the edges. Note that this number depends on whether th=
e
corners are ignored or required to be solved, because the parity of the
corners determines the parity of the edges.

Nan

On Fri, Mar 25, 2011 at 9:31 AM, Eduard wrote:

>
>
> The latch cube is not 4D. I know. But does anybody of you know a good
> solving description? What is the part of the 12! 12^2 edge positions whic=
h
> is reachable with this latch mechanisme? Per cents, per mils ?
> If it is a very small part then I'm intested to establish the graph of
> those positions.
>
>=20=20
>

--20cf3054a043bf0c74049f50ea6e
Content-Type: text/html; charset=windows-1252
Content-Transfer-Encoding: quoted-printable

Hi Eduard,

Here is some discussion about solving the latch cube. >
18752">http://twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D18752=



I have never seen a good estimation for the number of reachable positions. =
I only know that the superflip position (all edges are in place, but flippe=
d) is nonreachable. I guess the space of reachable positions is so large th=
at one cannot fully describe the graph. An interesting question is, how man=
y orbits are there for the edges. Note that this number depends on whether =
the corners are ignored or required to be solved, because the parity of the=
corners determines the parity of the edges.


Nan

--------------030707030401090503060901
Content-Type: text/plain; charset=windows-1252; format=flowed
Content-Transfer-Encoding: 7bit

OK I'm going to embarrass myself here. I've only glanced at a couple
photos and videos of the latch cube but I can't see what makes it
different from the normal 3^3. It looks like you can make any twist you
like but to get some 90 degree twists you need just need to do a -270
degree twist. Can somebody tell me why it is interesting?

Thanks,
-Melinda

On 3/25/2011 9:16 AM, Nan Ma wrote:
>
>
> Hi Eduard,
>
> Here is some discussion about solving the latch cube.
>
> http://twistypuzzles.com/forum/viewtopic.php?f=8&t=18752
>
>
> I have never seen a good estimation for the number of reachable
> positions. I only know that the superflip position (all edges are in
> place, but flipped) is nonreachable. I guess the space of reachable
> positions is so large that one cannot fully describe the graph. An
> interesting question is, how many orbits are there for the edges. Note
> that this number depends on whether the corners are ignored or
> required to be solved, because the parity of the corners determines
> the parity of the edges.
>
> Nan
>
> On Fri, Mar 25, 2011 at 9:31 AM, Eduard > > wrote:
>
> The latch cube is not 4D. I know. But does anybody of you know a
> good solving description? What is the part of the 12! 12^2 edge
> positions which is reachable with this latch mechanisme? Per
> cents, per mils ?
> If it is a very small part then I'm intested to establish the
> graph of those positions.
>
>
>
>
>

--------------030707030401090503060901
Content-Type: text/html; charset=windows-1252
Content-Transfer-Encoding: quoted-printable




http-equiv=3D"Content-Type">


OK I'm going to embarrass myself here. I've only glanced at a couple
photos and videos of the latch cube but I can't see what makes it
different from the normal 3^3. It looks like you can make any twist
you like but to get some 90 degree twists you need just need to do a
-270 degree twist. Can somebody tell me why it is interesting?



Thanks,

-Melinda



On 3/25/2011 9:16 AM, Nan Ma wrote:
cite=3D"mid:AANLkTimsXuMNBtajoh-7GR9EfheJP+dAQcnzM+k=3DuzF7@mail.gmai=
l.com"
type=3D"cite">


Hi Eduard,



Here is some discussion about solving the latch cube.



href=3D"http://twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D=
18752">http://twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D18752=




I have never seen a good estimation for the number of reachable
positions. I only know that the superflip position (all edges are
in place, but flipped) is nonreachable. I guess the space of
reachable positions is so large that one cannot fully describe the
graph. An interesting question is, how many orbits are there for
the edges. Note that this number depends on whether the corners
are ignored or required to be solved, because the parity of the
corners determines the parity of the edges.



Nan

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Although Brandon has answered the question, I would like to show a photo of=
my Latch Cube, where the front face is locked because it has contradicting=
arrows:

Note that the top face has no arrow, and therefore it can be turned to eith=
er direction.

I don't think scrambling is as hard as Brandon described. It's impossible t=
o move it into a completely locked state (meaning no face can be turned). T=
he face of the last move can always be turned again. And I haven't run into=
a situation that only one face can be turned. I don't know if such state i=
s reachable or not.

Like Brandon, I don't enjoy solving the Latch Cube because it was full of e=
mbarrassment. I didn't like the crazy 3x3x3 series in the beginning but lat=
er I found it interesting. Here is a simulator for it: s.com/forum/viewtopic.php?f=3D1&t=3D20285>.

Nan

--- In 4D_Cubing@yahoogroups.com, Brandon Enright wrote:
>
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>=20
> On Fri, 25 Mar 2011 11:06:40 -0700 or thereabouts Melinda Green
> wrote:
>=20
> > OK I'm going to embarrass myself here. I've only glanced at a couple=20
> > photos and videos of the latch cube but I can't see what makes it=20
> > different from the normal 3^3. It looks like you can make any twist
> > you like but to get some 90 degree twists you need just need to do a
> > -270 degree twist. Can somebody tell me why it is interesting?
> >=20
> > Thanks,
> > -Melinda
>=20
>=20
> Hi Melinda,
>=20
> When I first saw the latch cube photos I came to the same conclusion.
> What happens though is that if you do a 90 degree twist on a face, the
> arrows along the side of those 4 edges will move through the 4 adjacent
> faces and for each adjacent face, if the new edge's arrow happens to be
> pointing the opposite direction from the existing arrows on that face
> then you can't turn that face anymore.
>=20
> So while you can always undo a 90 degree twist by just doing another
> 270 degrees of twisting, often the intermediate twist before you do a
> full circle will block adjacent faces from moving.
>=20
> Even scrambling the latch cube seems hard. The puzzle easily ends up
> in a bandaged face mess which makes analysis of it quite difficult.
>=20
> I really dislike this sort of bandaging. A lot of others seem
> to really like the challenge though. The Crazy 3x3x3 and Megaminx
> planet series puzzles are another such set of oddly bandaged puzzles.
>=20
> Brandon
>=20
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v2.0.17 (GNU/Linux)
>=20
> iEYEARECAAYFAk2M3WkACgkQqaGPzAsl94IMxwCgxZykcKZiNSoQ1VkKakUpoRDU
> iVsAn19wxwNm6vmtruKAqD/OS93RygIb
> =3D/Wxi
> -----END PGP SIGNATURE-----
>

The simulator is very beautiful. Thanks. I have two real "crazy" cubes and =
now the latch cube. I'm still searching a good solution description and ana=
lysis for the latch cube (both don't existe I think).

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Although Brandon has answered the question, I would like to show a photo =
of my Latch Cube, where the front face is locked because it has contradicti=
ng arrows:
>
> Note that the top face has no arrow, and therefore it can be turned to ei=
ther direction.
>=20
> I don't think scrambling is as hard as Brandon described. It's impossible=
to move it into a completely locked state (meaning no face can be turned).=
The face of the last move can always be turned again. And I haven't run in=
to a situation that only one face can be turned. I don't know if such state=
is reachable or not.
>=20
> Like Brandon, I don't enjoy solving the Latch Cube because it was full of=
embarrassment. I didn't like the crazy 3x3x3 series in the beginning but l=
ater I found it interesting. Here is a simulator for it: les.com/forum/viewtopic.php?f=3D1&t=3D20285>.
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, Brandon Enright wrote:
> >
> > -----BEGIN PGP SIGNED MESSAGE-----
> > Hash: SHA1
> >=20
> > On Fri, 25 Mar 2011 11:06:40 -0700 or thereabouts Melinda Green
> > wrote:
> >=20
> > > OK I'm going to embarrass myself here. I've only glanced at a couple=
=20
> > > photos and videos of the latch cube but I can't see what makes it=20
> > > different from the normal 3^3. It looks like you can make any twist
> > > you like but to get some 90 degree twists you need just need to do a
> > > -270 degree twist. Can somebody tell me why it is interesting?
> > >=20
> > > Thanks,
> > > -Melinda
> >=20
> >=20
> > Hi Melinda,
> >=20
> > When I first saw the latch cube photos I came to the same conclusion.
> > What happens though is that if you do a 90 degree twist on a face, the
> > arrows along the side of those 4 edges will move through the 4 adjacent
> > faces and for each adjacent face, if the new edge's arrow happens to be
> > pointing the opposite direction from the existing arrows on that face
> > then you can't turn that face anymore.
> >=20
> > So while you can always undo a 90 degree twist by just doing another
> > 270 degrees of twisting, often the intermediate twist before you do a
> > full circle will block adjacent faces from moving.
> >=20
> > Even scrambling the latch cube seems hard. The puzzle easily ends up
> > in a bandaged face mess which makes analysis of it quite difficult.
> >=20
> > I really dislike this sort of bandaging. A lot of others seem
> > to really like the challenge though. The Crazy 3x3x3 and Megaminx
> > planet series puzzles are another such set of oddly bandaged puzzles.
> >=20
> > Brandon
> >=20
> > -----BEGIN PGP SIGNATURE-----
> > Version: GnuPG v2.0.17 (GNU/Linux)
> >=20
> > iEYEARECAAYFAk2M3WkACgkQqaGPzAsl94IMxwCgxZykcKZiNSoQ1VkKakUpoRDU
> > iVsAn19wxwNm6vmtruKAqD/OS93RygIb
> > =3D/Wxi
> > -----END PGP SIGNATURE-----
> >
>

Why such beautiful simulators have no "macro possibility" ??
In my opinion before reaching such perfection in presentation the macro mus=
t be offered.

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Although Brandon has answered the question, I would like to show a photo =
of my Latch Cube, where the front face is locked because it has contradicti=
ng arrows:
>
> Note that the top face has no arrow, and therefore it can be turned to ei=
ther direction.
>=20
> I don't think scrambling is as hard as Brandon described. It's impossible=
to move it into a completely locked state (meaning no face can be turned).=
The face of the last move can always be turned again. And I haven't run in=
to a situation that only one face can be turned. I don't know if such state=
is reachable or not.
>=20
> Like Brandon, I don't enjoy solving the Latch Cube because it was full of=
embarrassment. I didn't like the crazy 3x3x3 series in the beginning but l=
ater I found it interesting. Here is a simulator for it: les.com/forum/viewtopic.php?f=3D1&t=3D20285>.
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, Brandon Enright wrote:
> >
> > -----BEGIN PGP SIGNED MESSAGE-----
> > Hash: SHA1
> >=20
> > On Fri, 25 Mar 2011 11:06:40 -0700 or thereabouts Melinda Green
> > wrote:
> >=20
> > > OK I'm going to embarrass myself here. I've only glanced at a couple=
=20
> > > photos and videos of the latch cube but I can't see what makes it=20
> > > different from the normal 3^3. It looks like you can make any twist
> > > you like but to get some 90 degree twists you need just need to do a
> > > -270 degree twist. Can somebody tell me why it is interesting?
> > >=20
> > > Thanks,
> > > -Melinda
> >=20
> >=20
> > Hi Melinda,
> >=20
> > When I first saw the latch cube photos I came to the same conclusion.
> > What happens though is that if you do a 90 degree twist on a face, the
> > arrows along the side of those 4 edges will move through the 4 adjacent
> > faces and for each adjacent face, if the new edge's arrow happens to be
> > pointing the opposite direction from the existing arrows on that face
> > then you can't turn that face anymore.
> >=20
> > So while you can always undo a 90 degree twist by just doing another
> > 270 degrees of twisting, often the intermediate twist before you do a
> > full circle will block adjacent faces from moving.
> >=20
> > Even scrambling the latch cube seems hard. The puzzle easily ends up
> > in a bandaged face mess which makes analysis of it quite difficult.
> >=20
> > I really dislike this sort of bandaging. A lot of others seem
> > to really like the challenge though. The Crazy 3x3x3 and Megaminx
> > planet series puzzles are another such set of oddly bandaged puzzles.
> >=20
> > Brandon
> >=20
> > -----BEGIN PGP SIGNATURE-----
> > Version: GnuPG v2.0.17 (GNU/Linux)
> >=20
> > iEYEARECAAYFAk2M3WkACgkQqaGPzAsl94IMxwCgxZykcKZiNSoQ1VkKakUpoRDU
> > iVsAn19wxwNm6vmtruKAqD/OS93RygIb
> > =3D/Wxi
> > -----END PGP SIGNATURE-----
> >
>

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Content-Transfer-Encoding: quoted-printable

Well, the reason was explained here:

http://twistypuzzles.com/forum/viewtopic.php?p=3D250170#p250170

Basically it's because there is another version of the applets that has
macros, for a different purpose. I agree that it would be better if it
includes macros for this version.

Nan

On Fri, Mar 25, 2011 at 4:13 PM, Eduard wrote:

>
>
> Why such beautiful simulators have no "macro possibility" ??
> In my opinion before reaching such perfection in presentation the macro
> must be offered.
>
>
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Although Brandon has answered the question, I would like to show a phot=
o
> of my Latch Cube, where the front face is locked because it has
> contradicting arrows:
> >
> > Note that the top face has no arrow, and therefore it can be turned to
> either direction.
> >
> > I don't think scrambling is as hard as Brandon described. It's impossib=
le
> to move it into a completely locked state (meaning no face can be turned)=
.
> The face of the last move can always be turned again. And I haven't run i=
nto
> a situation that only one face can be turned. I don't know if such state =
is
> reachable or not.
> >
> > Like Brandon, I don't enjoy solving the Latch Cube because it was full =
of
> embarrassment. I didn't like the crazy 3x3x3 series in the beginning but
> later I found it interesting. Here is a simulator for it: <
> http://twistypuzzles.com/forum/viewtopic.php?f=3D1&t=3D20285>.
> >
> > Nan
> >
> > --- In 4D_Cubing@yahoogroups.com, Brandon Enright wrote:
> > >
> > > -----BEGIN PGP SIGNED MESSAGE-----
> > > Hash: SHA1
> > >
> > > On Fri, 25 Mar 2011 11:06:40 -0700 or thereabouts Melinda Green
> > > wrote:
> > >
> > > > OK I'm going to embarrass myself here. I've only glanced at a coupl=
e
> > > > photos and videos of the latch cube but I can't see what makes it
> > > > different from the normal 3^3. It looks like you can make any twist
> > > > you like but to get some 90 degree twists you need just need to do =
a
> > > > -270 degree twist. Can somebody tell me why it is interesting?
> > > >
> > > > Thanks,
> > > > -Melinda
> > >
> > >
> > > Hi Melinda,
> > >
> > > When I first saw the latch cube photos I came to the same conclusion.
> > > What happens though is that if you do a 90 degree twist on a face, th=
e
> > > arrows along the side of those 4 edges will move through the 4 adjace=
nt
> > > faces and for each adjacent face, if the new edge's arrow happens to =
be
> > > pointing the opposite direction from the existing arrows on that face
> > > then you can't turn that face anymore.
> > >
> > > So while you can always undo a 90 degree twist by just doing another
> > > 270 degrees of twisting, often the intermediate twist before you do a
> > > full circle will block adjacent faces from moving.
> > >
> > > Even scrambling the latch cube seems hard. The puzzle easily ends up
> > > in a bandaged face mess which makes analysis of it quite difficult.
> > >
> > > I really dislike this sort of bandaging. A lot of others seem
> > > to really like the challenge though. The Crazy 3x3x3 and Megaminx
> > > planet series puzzles are another such set of oddly bandaged puzzles.
> > >
> > > Brandon
> > >
> > > -----BEGIN PGP SIGNATURE-----
> > > Version: GnuPG v2.0.17 (GNU/Linux)
> > >
> > > iEYEARECAAYFAk2M3WkACgkQqaGPzAsl94IMxwCgxZykcKZiNSoQ1VkKakUpoRDU
> > > iVsAn19wxwNm6vmtruKAqD/OS93RygIb
> > > =3D/Wxi
> > > -----END PGP SIGNATURE-----
> > >
> >
>
>=20=20
>

--20cf3005ddf8a8351a049f546f13
Content-Type: text/html; charset=windows-1252
Content-Transfer-Encoding: quoted-printable

Well, the reason was explained here:

.com/forum/viewtopic.php?p=3D250170#p250170">http://twistypuzzles.com/forum=
/viewtopic.php?p=3D250170#p250170

Basically it's because the=
re is another version of the applets that has macros, for a different purpo=
se. I agree that it would be better if it includes macros for this version.=



Nan