Thread: "2-c parity(?) problem with 4^4"

From: "deustfrr" <deustfrr@yahoo.ca>
Date: Wed, 21 Jul 2010 13:53:56 -0000
Subject: 2-c parity(?) problem with 4^4



I have a problem with the last 2 faces
http://groups.yahoo.com/group/4D_Cubing/photos/album/346940124/pic/list
reply please
(I got parental controls on time so I just type that, lolz)




From: "deustfrr" <deustfrr@yahoo.ca>
Date: Wed, 21 Jul 2010 17:57:32 +0000
Subject: 2-c parity(?) problem with 4^4



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From: "deustfrr" <deustfrr@yahoo.ca>
Date: Wed, 21 Jul 2010 23:48:17 -0000
Subject: Re: [MC4D] 2-c parity(?) problem with 4^4



I updated the pictures. The red line is the wrong piece and the green line =
are the right pieces. And, can you make a log file showing the XY moves?

--- In 4D_Cubing@yahoogroups.com, Brandon Enright wrote:
>
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>=20
> On Wed, 21 Jul 2010 13:53:56 -0000
> "deustfrr" wrote:
>=20
> > I have a problem with the last 2 faces
> > http://groups.yahoo.com/group/4D_Cubing/photos/album/346940124/pic/list
> > reply please
> > (I got parental controls on time so I just type that, lolz)
> >=20
>=20
> deustfrr,
>=20
> Your images are quite hard (for me) to see the exact problem in context.
>=20
> However, for your "1-c piece situation" image, you have what appears to
> be a blue and an orange 1-c central piece swapped. If you were solving
> purely intuitively then you may have a bit of trouble solving this but
> if you have a 3-cycle for the 1-c pieces then just swap two
> indistinguishable pieces such as two blue in the 3-cycle along with the
> orange.
>=20
> For your "2-c piece parity 1b" and "2-c piece parity 1a" images, this
> isn't really a parity but they must be solved together.
>=20
> I recently discussed a semi-generic technique for doing this on almost
> any puzzle here:
> http://www.twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D21942=
2#p219422
> The general idea is to 3-cycle your two flipped pieces along with some
> other (choice is arbitrary) piece such that one of the flipped pieces
> moves into the place of the other flipped piece (call this sequence X).
> Then flip the whole group over and put it back in place (call this Y),
> then undo X, then undo Y. This technique will work in any number of
> dimensions.
>=20
> Good luck,
>=20
> Brandon
>=20
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v2.0.15 (GNU/Linux)
>=20
> iEYEARECAAYFAkxHNRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40
> X/MAn3VzbHkYtEJCNUGeCCM5MljsXnsG
> =3DV8uU
> -----END PGP SIGNATURE-----
>




From: Chris Locke <project.eutopia@gmail.com>
Date: Thu, 22 Jul 2010 13:48:07 +0900
Subject: Re: [MC4D] 2-c parity(?) problem with 4^4



--005045013e1be7a67b048bf29fd6
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

Well, we can't exactly solve it for you, but one of the big hints that
Brandon just gave is to try to "swap two indistinguishable pieces". When
you realize the presence of indistinguishable pieces, it suddenly no longer
becomes a parity issue, but just another case to work out with your
3-cycles. Still some work left for you to figure out exactly how to use th=
e
3 cycles to get what you want done, but I think you'll feel pretty good
about it when you do figure it out. Good luck!

Chris

2010/7/22 deustfrr

>
>
> I updated the pictures. The red line is the wrong piece and the green lin=
e
> are the right pieces. And, can you make a log file showing the XY moves?
>
>
> --- In 4D_Cubing@yahoogroups.com <4D_Cubing%40yahoogroups.com>, Brandon
> Enright wrote:
> >
> > -----BEGIN PGP SIGNED MESSAGE-----
> > Hash: SHA1
> >
> > On Wed, 21 Jul 2010 13:53:56 -0000
> > "deustfrr" wrote:
> >
> > > I have a problem with the last 2 faces
> > >
> http://groups.yahoo.com/group/4D_Cubing/photos/album/346940124/pic/list
> > > reply please
> > > (I got parental controls on time so I just type that, lolz)
> > >
> >
> > deustfrr,
> >
> > Your images are quite hard (for me) to see the exact problem in context=
.
> >
> > However, for your "1-c piece situation" image, you have what appears to
> > be a blue and an orange 1-c central piece swapped. If you were solving
> > purely intuitively then you may have a bit of trouble solving this but
> > if you have a 3-cycle for the 1-c pieces then just swap two
> > indistinguishable pieces such as two blue in the 3-cycle along with the
> > orange.
> >
> > For your "2-c piece parity 1b" and "2-c piece parity 1a" images, this
> > isn't really a parity but they must be solved together.
> >
> > I recently discussed a semi-generic technique for doing this on almost
> > any puzzle here:
> >
> http://www.twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D21942=
2#p219422
> > The general idea is to 3-cycle your two flipped pieces along with some
> > other (choice is arbitrary) piece such that one of the flipped pieces
> > moves into the place of the other flipped piece (call this sequence X).
> > Then flip the whole group over and put it back in place (call this Y),
> > then undo X, then undo Y. This technique will work in any number of
> > dimensions.
> >
> > Good luck,
> >
> > Brandon
> >
> > -----BEGIN PGP SIGNATURE-----
> > Version: GnuPG v2.0.15 (GNU/Linux)
> >
> > iEYEARECAAYFAkxHNRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40
> > X/MAn3VzbHkYtEJCNUGeCCM5MljsXnsG
> > =3DV8uU
> > -----END PGP SIGNATURE-----
> >
>
>=20=20
>

--005045013e1be7a67b048bf29fd6
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

Well, we can't exactly solve it for you, but one of the big hints that =
Brandon just gave is to try to "swap two

indistinguishable pieces".=C2=A0 When you realize the presence of indi=
stinguishable pieces, it suddenly no longer becomes a parity issue, but jus=
t another case to work out with your 3-cycles.=C2=A0 Still some work left f=
or you to figure out exactly how to use the 3 cycles to get what you want d=
one, but I think you'll feel pretty good about it when you do figure it=
out.=C2=A0 Good luck!


Chris

2010/7/22 deustfrr "ltr"><deustfrr@yahoo.ca>pan>
x; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">















=C2=A0







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

I updated the pictures. The red line is the wrong piece and the gr=
een line are the right pieces. And, can you make a log file showing the XY =
moves?





--- In 4D_=
Cubing@yahoogroups.com
, Brandon Enright <bmenrigh@...> wrote:

>

> -----BEGIN PGP SIGNED MESSAGE-----

> Hash: SHA1

>

> On Wed, 21 Jul 2010 13:53:56 -0000
=3D"h5">
> "deustfrr" <deustfrr@...> wrote:

>

> > I have a problem with the last 2 faces

> > 46940124/pic/list" target=3D"_blank">http://groups.yahoo.com/group/4D_Cubin=
g/photos/album/346940124/pic/list


> > reply please

> > (I got parental controls on time so I just type that, lolz)

> >

>

> deustfrr,

>

> Your images are quite hard (for me) to see the exact problem in contex=
t.

>

> However, for your "1-c piece situation" image, you have what=
appears to

> be a blue and an orange 1-c central piece swapped. If you were solvin=
g

> purely intuitively then you may have a bit of trouble solving this but=


> if you have a 3-cycle for the 1-c pieces then just swap two

> indistinguishable pieces such as two blue in the 3-cycle along with th=
e

> orange.

>

> For your "2-c piece parity 1b" and "2-c piece parity 1a=
" images, this

> isn't really a parity but they must be solved together.

>

> I recently discussed a semi-generic technique for doing this on almost=


> any puzzle here:

> t=3D7830&p=3D219422#p219422" target=3D"_blank">http://www.twistypuzzles=
.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D219422#p219422


> The general idea is to 3-cycle your two flipped pieces along with some=


> other (choice is arbitrary) piece such that one of the flipped pieces<=
br>
> moves into the place of the other flipped piece (call this sequence X)=
.

> Then flip the whole group over and put it back in place (call this Y),=


> then undo X, then undo Y. This technique will work in any number ofr>
> dimensions.

>

> Good luck,

>

> Brandon

>

> -----BEGIN PGP SIGNATURE-----

> Version: GnuPG v2.0.15 (GNU/Linux)

>

> iEYEARECAAYFAkxHNRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40

> X/MAn3VzbHkYtEJCNUGeCCM5MljsXnsG

> =3DV8uU

> -----END PGP SIGNATURE-----

>






=20=20=20=20=20

=20=20=20=20







=20=20









--005045013e1be7a67b048bf29fd6--




From: "deustfrr" <deustfrr@yahoo.ca>
Date: Thu, 22 Jul 2010 11:52:08 -0000
Subject: Re: 2-c parity(?) problem with 4^4



That reminds me of another problem I had. I'll just say it
The first time i tried solving the 3^4 I had a 2-cycle center parity, but t=
he third time (youtube vid)I realized it was a 3-cycle. lolz=20
I'm trying it right now. I switched 4 pieces...

--- In 4D_Cubing@yahoogroups.com, Chris Locke wrote:
>
> Well, we can't exactly solve it for you, but one of the big hints that
> Brandon just gave is to try to "swap two indistinguishable pieces". When
> you realize the presence of indistinguishable pieces, it suddenly no long=
er
> becomes a parity issue, but just another case to work out with your
> 3-cycles. Still some work left for you to figure out exactly how to use =
the
> 3 cycles to get what you want done, but I think you'll feel pretty good
> about it when you do figure it out. Good luck!
>=20
> Chris
>=20
> 2010/7/22 deustfrr
>=20
> >
> >
> > I updated the pictures. The red line is the wrong piece and the green l=
ine
> > are the right pieces. And, can you make a log file showing the XY moves=
?
> >
> >
> > --- In 4D_Cubing@yahoogroups.com <4D_Cubing%40yahoogroups.com>, Brandon
> > Enright wrote:
> > >
> > > -----BEGIN PGP SIGNED MESSAGE-----
> > > Hash: SHA1
> > >
> > > On Wed, 21 Jul 2010 13:53:56 -0000
> > > "deustfrr" wrote:
> > >
> > > > I have a problem with the last 2 faces
> > > >
> > http://groups.yahoo.com/group/4D_Cubing/photos/album/346940124/pic/list
> > > > reply please
> > > > (I got parental controls on time so I just type that, lolz)
> > > >
> > >
> > > deustfrr,
> > >
> > > Your images are quite hard (for me) to see the exact problem in conte=
xt.
> > >
> > > However, for your "1-c piece situation" image, you have what appears =
to
> > > be a blue and an orange 1-c central piece swapped. If you were solvin=
g
> > > purely intuitively then you may have a bit of trouble solving this bu=
t
> > > if you have a 3-cycle for the 1-c pieces then just swap two
> > > indistinguishable pieces such as two blue in the 3-cycle along with t=
he
> > > orange.
> > >
> > > For your "2-c piece parity 1b" and "2-c piece parity 1a" images, this
> > > isn't really a parity but they must be solved together.
> > >
> > > I recently discussed a semi-generic technique for doing this on almos=
t
> > > any puzzle here:
> > >
> > http://www.twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D219=
422#p219422
> > > The general idea is to 3-cycle your two flipped pieces along with som=
e
> > > other (choice is arbitrary) piece such that one of the flipped pieces
> > > moves into the place of the other flipped piece (call this sequence X=
).
> > > Then flip the whole group over and put it back in place (call this Y)=
,
> > > then undo X, then undo Y. This technique will work in any number of
> > > dimensions.
> > >
> > > Good luck,
> > >
> > > Brandon
> > >
> > > -----BEGIN PGP SIGNATURE-----
> > > Version: GnuPG v2.0.15 (GNU/Linux)
> > >
> > > iEYEARECAAYFAkxHNRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40
> > > X/MAn3VzbHkYtEJCNUGeCCM5MljsXnsG
> > > =3DV8uU
> > > -----END PGP SIGNATURE-----
> > >
> >
> >=20=20
> >
>




From: Jonathan Mecias <jonathan.mecias001@mymdc.net>
Date: Thu, 22 Jul 2010 11:18:16 -0400
Subject: Re: [MC4D] Re: 2-c parity(?) problem with 4^4



--001636417e1b89af4a048bfb6de9
Content-Type: text/plain; charset=windows-1252
Content-Transfer-Encoding: quoted-printable

do you have a regular 4x4x4 rubiks cube at home? try playing around with
that to see what happends. Your doing great so far and dont stress it.

On Thu, Jul 22, 2010 at 7:52 AM, deustfrr wrote:

>
>
> That reminds me of another problem I had. I'll just say it
> The first time i tried solving the 3^4 I had a 2-cycle center parity, but
> the third time (youtube vid)I realized it was a 3-cycle. lolz
> I'm trying it right now. I switched 4 pieces...
>
>
> --- In 4D_Cubing@yahoogroups.com <4D_Cubing%40yahoogroups.com>, Chris
> Locke wrote:
> >
> > Well, we can't exactly solve it for you, but one of the big hints that
> > Brandon just gave is to try to "swap two indistinguishable pieces". Whe=
n
> > you realize the presence of indistinguishable pieces, it suddenly no
> longer
> > becomes a parity issue, but just another case to work out with your
> > 3-cycles. Still some work left for you to figure out exactly how to use
> the
> > 3 cycles to get what you want done, but I think you'll feel pretty good
> > about it when you do figure it out. Good luck!
> >
> > Chris
> >
> > 2010/7/22 deustfrr
>
> >
> > >
> > >
> > > I updated the pictures. The red line is the wrong piece and the green
> line
> > > are the right pieces. And, can you make a log file showing the XY
> moves?
> > >
> > >
> > > --- In 4D_Cubing@yahoogroups.com <4D_Cubing%40yahoogroups.com><4D_Cub=
ing%
> 40yahoogroups.com>, Brandon
>
> > > Enright wrote:
> > > >
> > > > -----BEGIN PGP SIGNED MESSAGE-----
> > > > Hash: SHA1
> > > >
> > > > On Wed, 21 Jul 2010 13:53:56 -0000
> > > > "deustfrr" wrote:
> > > >
> > > > > I have a problem with the last 2 faces
> > > > >
> > >
> http://groups.yahoo.com/group/4D_Cubing/photos/album/346940124/pic/list
> > > > > reply please
> > > > > (I got parental controls on time so I just type that, lolz)
> > > > >
> > > >
> > > > deustfrr,
> > > >
> > > > Your images are quite hard (for me) to see the exact problem in
> context.
> > > >
> > > > However, for your "1-c piece situation" image, you have what appear=
s
> to
> > > > be a blue and an orange 1-c central piece swapped. If you were
> solving
> > > > purely intuitively then you may have a bit of trouble solving this
> but
> > > > if you have a 3-cycle for the 1-c pieces then just swap two
> > > > indistinguishable pieces such as two blue in the 3-cycle along with
> the
> > > > orange.
> > > >
> > > > For your "2-c piece parity 1b" and "2-c piece parity 1a" images, th=
is
> > > > isn't really a parity but they must be solved together.
> > > >
> > > > I recently discussed a semi-generic technique for doing this on
> almost
> > > > any puzzle here:
> > > >
> > >
> http://www.twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D21942=
2#p219422
> > > > The general idea is to 3-cycle your two flipped pieces along with
> some
> > > > other (choice is arbitrary) piece such that one of the flipped piec=
es
> > > > moves into the place of the other flipped piece (call this sequence
> X).
> > > > Then flip the whole group over and put it back in place (call this
> Y),
> > > > then undo X, then undo Y. This technique will work in any number of
> > > > dimensions.
> > > >
> > > > Good luck,
> > > >
> > > > Brandon
> > > >
> > > > -----BEGIN PGP SIGNATURE-----
> > > > Version: GnuPG v2.0.15 (GNU/Linux)
> > > >
> > > > iEYEARECAAYFAkxHNRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40
> > > > X/MAn3VzbHkYtEJCNUGeCCM5MljsXnsG
> > > > =3DV8uU
> > > > -----END PGP SIGNATURE-----
> > > >
> > >
> > >
> > >
> >
>
>=20=20
>

--001636417e1b89af4a048bfb6de9
Content-Type: text/html; charset=windows-1252
Content-Transfer-Encoding: quoted-printable

do you have a regular 4x4x4 rubiks cube at home? try playing around with th=
at to see what happends. Your doing great so far and dont stress it.
>

On Thu, Jul 22, 2010 at 7:52 AM, deustfrr dir=3D"ltr"><deustfrr@yahoo.ca&=
gt;
wrote:

; PADDING-LEFT: 1ex" class=3D"gmail_quote">
=A0=20



That reminds me of another problem I had. I'll just say it
The fi=
rst time i tried solving the 3^4 I had a 2-cycle center parity, but the thi=
rd time (youtube vid)I realized it was a 3-cycle. lolz
I'm trying i=
t right now. I switched 4 pieces...=20



--- In com" target=3D"_blank">4D_Cubing@yahoogroups.com, Chris Locke <proje=
ct.eutopia@...> wrote:
>
> Well, we can't exactly solve =
it for you, but one of the big hints that

> Brandon just gave is to try to "swap two indistinguishable pieces=
". When
> you realize the presence of indistinguishable pieces, =
it suddenly no longer
> becomes a parity issue, but just another case=
to work out with your

> 3-cycles. Still some work left for you to figure out exactly how to us=
e the
> 3 cycles to get what you want done, but I think you'll fe=
el pretty good
> about it when you do figure it out. Good luck!

>
> Chris
>
> 2010/7/22 deustfrr <deustfrr@=
...>=20

>
> >
> >
> > I update=
d the pictures. The red line is the wrong piece and the green line
> =
> are the right pieces. And, can you make a log file showing the XY move=
s?

> >
> >
> > --- In g%40yahoogroups.com" target=3D"_blank">4D_Cubing@yahoogroups.com <4D=
_Cubing%40yahoogrou=
ps.com
>, Brandon=20



> > Enright <bmenrigh@> wrote:
> &g=
t; >
> > > -----BEGIN PGP SIGNED MESSAGE-----
> > &=
gt; Hash: SHA1
> > >
> > > On Wed, 21 Jul 2010 13:5=
3:56 -0000

> > > "deustfrr" <deustfrr@> wrote:
> > &=
gt;
> > > > I have a problem with the last 2 faces
> &=
gt; > >
> > ng/photos/album/346940124/pic/list" target=3D"_blank">http://groups.yahoo.c=
om/group/4D_Cubing/photos/album/346940124/pic/list


> > > > reply please
> > > > (I got parental con=
trols on time so I just type that, lolz)
> > > >
> >=
; >
> > > deustfrr,
> > >
> > > Your=
images are quite hard (for me) to see the exact problem in context.

> > >
> > > However, for your "1-c piece situatio=
n" image, you have what appears to
> > > be a blue and an =
orange 1-c central piece swapped. If you were solving
> > > pur=
ely intuitively then you may have a bit of trouble solving this but

> > > if you have a 3-cycle for the 1-c pieces then just swap two<=
br>> > > indistinguishable pieces such as two blue in the 3-cycle =
along with the
> > > orange.
> > >
> > >=
; For your "2-c piece parity 1b" and "2-c piece parity 1a&qu=
ot; images, this

> > > isn't really a parity but they must be solved together.<=
br>> > >
> > > I recently discussed a semi-generic tec=
hnique for doing this on almost
> > > any puzzle here:
> =
> >

> > &t=3D7830&p=3D219422#p219422" target=3D"_blank">http://www.twistypu=
zzles.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D219422#p219422
=

> > > The general idea is to 3-cycle your two flipped pieces a=
long with some

> > > other (choice is arbitrary) piece such that one of the flipp=
ed pieces
> > > moves into the place of the other flipped piece=
(call this sequence X).
> > > Then flip the whole group over a=
nd put it back in place (call this Y),

> > > then undo X, then undo Y. This technique will work in any nu=
mber of
> > > dimensions.
> > >
> > > G=
ood luck,
> > >
> > > Brandon
> > >

> > > -----BEGIN PGP SIGNATURE-----
> > > Version: Gnu=
PG v2.0.15 (GNU/Linux)
> > >
> > > iEYEARECAAYFAkxH=
NRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40
> > > X/MAn3Vz=
bHkYtEJCNUGeCCM5MljsXnsG

> > > =3DV8uU
> > > -----END PGP SIGNATURE-----
>=
; > >
> >
> >
> >
>

div>


=



--001636417e1b89af4a048bfb6de9--




From: "deustfrr" <deustfrr@yahoo.ca>
Date: Fri, 23 Jul 2010 01:12:19 -0000
Subject: Re: 2-c parity(?) problem with 4^4



I really don't know what to do about this problem. And do I only swap 2 or =
can I swap 2 pairs?

> --- In 4D_Cubing@yahoogroups.com, Chris Locke wrote:
> >
> > Well, we can't exactly solve it for you, but one of the big hints that
> > Brandon just gave is to try to "swap two indistinguishable pieces". Wh=
en
> > you realize the presence of indistinguishable pieces, it suddenly no lo=
nger
> > becomes a parity issue, but just another case to work out with your
> > 3-cycles. Still some work left for you to figure out exactly how to us=
e the
> > 3 cycles to get what you want done, but I think you'll feel pretty good
> > about it when you do figure it out. Good luck!
> >=20
> > Chris
> >=20
> > 2010/7/22 deustfrr
> >=20
> > >
> > >
> > > I updated the pictures. The red line is the wrong piece and the green=
line
> > > are the right pieces. And, can you make a log file showing the XY mov=
es?
> > >
> > >
> > > --- In 4D_Cubing@yahoogroups.com <4D_Cubing%40yahoogroups.com>, Brand=
on
> > > Enright wrote:
> > > >
> > > > -----BEGIN PGP SIGNED MESSAGE-----
> > > > Hash: SHA1
> > > >
> > > > On Wed, 21 Jul 2010 13:53:56 -0000
> > > > "deustfrr" wrote:
> > > >
> > > > > I have a problem with the last 2 faces
> > > > >
> > > http://groups.yahoo.com/group/4D_Cubing/photos/album/346940124/pic/li=
st
> > > > > reply please
> > > > > (I got parental controls on time so I just type that, lolz)
> > > > >
> > > >
> > > > deustfrr,
> > > >
> > > > Your images are quite hard (for me) to see the exact problem in con=
text.
> > > >
> > > > However, for your "1-c piece situation" image, you have what appear=
s to
> > > > be a blue and an orange 1-c central piece swapped. If you were solv=
ing
> > > > purely intuitively then you may have a bit of trouble solving this =
but
> > > > if you have a 3-cycle for the 1-c pieces then just swap two
> > > > indistinguishable pieces such as two blue in the 3-cycle along with=
the
> > > > orange.
> > > >
> > > > For your "2-c piece parity 1b" and "2-c piece parity 1a" images, th=
is
> > > > isn't really a parity but they must be solved together.
> > > >
> > > > I recently discussed a semi-generic technique for doing this on alm=
ost
> > > > any puzzle here:
> > > >
> > > http://www.twistypuzzles.com/forum/viewtopic.php?f=3D8&t=3D7830&p=3D2=
19422#p219422
> > > > The general idea is to 3-cycle your two flipped pieces along with s=
ome
> > > > other (choice is arbitrary) piece such that one of the flipped piec=
es
> > > > moves into the place of the other flipped piece (call this sequence=
X).
> > > > Then flip the whole group over and put it back in place (call this =
Y),
> > > > then undo X, then undo Y. This technique will work in any number of
> > > > dimensions.
> > > >
> > > > Good luck,
> > > >
> > > > Brandon
> > > >
> > > > -----BEGIN PGP SIGNATURE-----
> > > > Version: GnuPG v2.0.15 (GNU/Linux)
> > > >
> > > > iEYEARECAAYFAkxHNRsACgkQqaGPzAsl94JmswCfaN11Ja6eh2Dw6+nAFcunco40
> > > > X/MAn3VzbHkYtEJCNUGeCCM5MljsXnsG
> > > > =3DV8uU
> > > > -----END PGP SIGNATURE-----
> > > >
> > >
> > >=20=20
> > >
> >
>





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