Thread: "My solution"

Hi! I was #93 on the 3^4 solution list, and I was told I had a unique solut=
ion, so I wanted to let you all know what I did. Sorry for the delay, there=
was some confusion about me getting on this group.

For an analogy, take a regular 3^3 (3d cube) and orient it so you've got a =
top and bottom and sides. Now rotate any sides 180 at a time. If you notice=
the center slice of the cube, it behaves exactly as a 3^2 puzzle, the 2d a=
nalog. If you also allow turning that center slice (reorienting the 3^2) yo=
u'll find that you only need to turn one face of the 3^3.

When you get to 4d, the extra freedom of movement makes this technique even=
more useful, as not only the center slice, but the top and bottom slices c=
an be manipulated in the same way, as long as the top (and bottom) stickies=
are the same color.

It gets a bit more complicated than that, but overall, if you're willing to=
let your turn counter rise a bit, you can solve about 90% of the 3^4 not w=
ith analogous techniques, but with IDENTICAL techniques as the 3^3. If some=
visual and control issues are resolved (especially with the 5d), this shou=
ld make it much easier for people to get started solving these puzzles.

Kyle

--- In 4D_Cubing@yahoogroups.com, "Kyle Headley" wrote:
>
> Hi! I was #93 on the 3^4 solution list, and I was told I had a unique sol=
ution, so I wanted to let you all know what I did. Sorry for the delay, the=
re was some confusion about me getting on this group.
>=20
> For an analogy, take a regular 3^3 (3d cube) and orient it so you've got =
a top and bottom and sides. Now rotate any sides 180 at a time. If you noti=
ce the center slice of the cube, it behaves exactly as a 3^2 puzzle, the 2d=
analog. If you also allow turning that center slice (reorienting the 3^2) =
you'll find that you only need to turn one face of the 3^3.
>=20
> When you get to 4d, the extra freedom of movement makes this technique ev=
en more useful, as not only the center slice, but the top and bottom slices=
can be manipulated in the same way, as long as the top (and bottom) sticki=
es are the same color.
>=20
> It gets a bit more complicated than that, but overall, if you're willing =
to let your turn counter rise a bit, you can solve about 90% of the 3^4 not=
with analogous techniques, but with IDENTICAL techniques as the 3^3. If so=
me visual and control issues are resolved (especially with the 5d), this sh=
ould make it much easier for people to get started solving these puzzles.
>=20
> Kyle
>


That sounds vey similar to my solution. I began by making one side of the =
3^4 a solid colour, without paying attention to the anything but the 2C pie=
ces, then I did the same with the opposite side. From then on, it was like=
solving three 3^3 cubes, but restricting myself to only using one working =
side and reorienting the "middle slice"(although you can use the opposite s=
ide as a working side as well without mixing anything up)

In the end you might end up with some situations that you would not get on =
a normal 3^3, such as a single disoriented edge. However, the problems alw=
ays happen in pairs, so it is easy to correct at the very end.

In that case my solution was not unique at all. Any hints on getting corner=
s to line up nicely? I was working to systematize the solution using 3d tec=
hniques, but I think I'm just trying to hard and frustrating myself.

I'm also looking forward to seeing what the additional freedom of movement =
allows in the 5d version, but I just can't make use of the control scheme i=
n MC5D. Are you able to freely rearrange the stickies? I guess that require=
s a (3+)^5.

--- In 4D_Cubing@yahoogroups.com, "Anthony" wrote:
>
> --- In 4D_Cubing@yahoogroups.com, "Kyle Headley" wrote:
> >
> > Hi! I was #93 on the 3^4 solution list, and I was told I had a unique s=
olution, so I wanted to let you all know what I did. Sorry for the delay, t=
here was some confusion about me getting on this group.
> >=20
> > For an analogy, take a regular 3^3 (3d cube) and orient it so you've go=
t a top and bottom and sides. Now rotate any sides 180 at a time. If you no=
tice the center slice of the cube, it behaves exactly as a 3^2 puzzle, the =
2d analog. If you also allow turning that center slice (reorienting the 3^2=
) you'll find that you only need to turn one face of the 3^3.
> >=20
> > When you get to 4d, the extra freedom of movement makes this technique =
even more useful, as not only the center slice, but the top and bottom slic=
es can be manipulated in the same way, as long as the top (and bottom) stic=
kies are the same color.
> >=20
> > It gets a bit more complicated than that, but overall, if you're willin=
g to let your turn counter rise a bit, you can solve about 90% of the 3^4 n=
ot with analogous techniques, but with IDENTICAL techniques as the 3^3. If =
some visual and control issues are resolved (especially with the 5d), this =
should make it much easier for people to get started solving these puzzles.
> >=20
> > Kyle
> >
>=20
>=20
> That sounds vey similar to my solution. I began by making one side of th=
e 3^4 a solid colour, without paying attention to the anything but the 2C p=
ieces, then I did the same with the opposite side. From then on, it was li=
ke solving three 3^3 cubes, but restricting myself to only using one workin=
g side and reorienting the "middle slice"(although you can use the opposite=
side as a working side as well without mixing anything up)
>=20
> In the end you might end up with some situations that you would not get o=
n a normal 3^3, such as a single disoriented edge. However, the problems a=
lways happen in pairs, so it is easy to correct at the very end.
>

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Hi Kyle,

In response to the MC5D paragraph, which of the two twisting control schemes
are you finding difficult to use, the buttons or the click twisting? If you
haven't seen it, information about both is on the feature notes
page
.

Also, I'm not sure what you are asking by "Are you able to freely rearrange
the stickies?". Could you expound? My guesses were three:

You may be referring to how to perform click twisting.
Or maybe to what happens to the puzzle stickers during a twist.
Or maybe you are wondering what possible states various piece types can get
in.

Let us know and we'll try to answer...

Take Care,
Roice


On 5/20/09, Kyle Headley wrote:
>
>
> In that case my solution was not unique at all. Any hints on getting
> corners to line up nicely? I was working to systematize the solution using
> 3d techniques, but I think I'm just trying to hard and frustrating myself.
>
> I'm also looking forward to seeing what the additional freedom of movement
> allows in the 5d version, but I just can't make use of the control scheme in
> MC5D. Are you able to freely rearrange the stickies? I guess that requires a
> (3+)^5.
> .
>
>
>

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Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

--- In 4D_Cubing@yahoogroups.com, "Kyle Headley" wrote:
>
> In that case my solution was not unique at all. Any hints on getting corn=
ers to line up nicely? I was working to systematize the solution using 3d t=
echniques, but I think I'm just trying to hard and frustrating myself.
>=20
> I'm also looking forward to seeing what the additional freedom of movemen=
t allows in the 5d version, but I just can't make use of the control scheme=
in MC5D. Are you able to freely rearrange the stickies? I guess that requi=
res a (3+)^5.
>=20
> --- In 4D_Cubing@yahoogroups.com, "Anthony" wrote:
> >
> > --- In 4D_Cubing@yahoogroups.com, "Kyle Headley" wrote:
> > >
> > > Hi! I was #93 on the 3^4 solution list, and I was told I had a unique=
solution, so I wanted to let you all know what I did. Sorry for the delay,=
there was some confusion about me getting on this group.
> > >=20
> > > For an analogy, take a regular 3^3 (3d cube) and orient it so you've =
got a top and bottom and sides. Now rotate any sides 180 at a time. If you =
notice the center slice of the cube, it behaves exactly as a 3^2 puzzle, th=
e 2d analog. If you also allow turning that center slice (reorienting the 3=
^2) you'll find that you only need to turn one face of the 3^3.
> > >=20
> > > When you get to 4d, the extra freedom of movement makes this techniqu=
e even more useful, as not only the center slice, but the top and bottom sl=
ices can be manipulated in the same way, as long as the top (and bottom) st=
ickies are the same color.
> > >=20
> > > It gets a bit more complicated than that, but overall, if you're will=
ing to let your turn counter rise a bit, you can solve about 90% of the 3^4=
not with analogous techniques, but with IDENTICAL techniques as the 3^3. I=
f some visual and control issues are resolved (especially with the 5d), thi=
s should make it much easier for people to get started solving these puzzle=
s.
> > >=20
> > > Kyle
> > >
> >=20
> >=20
> > That sounds vey similar to my solution. I began by making one side of =
the 3^4 a solid colour, without paying attention to the anything but the 2C=
pieces, then I did the same with the opposite side. From then on, it was =
like solving three 3^3 cubes, but restricting myself to only using one work=
ing side and reorienting the "middle slice"(although you can use the opposi=
te side as a working side as well without mixing anything up)
> >=20
> > In the end you might end up with some situations that you would not get=
on a normal 3^3, such as a single disoriented edge. However, the problems=
always happen in pairs, so it is easy to correct at the very end.
> >
>


Hi,
hate to say it but I've also thought of that trick, though it did take a=
few attempts to figure out how to achieve it. It can't be a bad way to so=
lve it, it let me set the fewest moves record for the 2^4 just there to 75.=
I prefer to just use it on the last face though.

It can be applied to the 5D hypercubes too, but be warned, it is very trick=
y to work. I used to for all the corner algs I have recorded, and it took =
a fair few attempts to manage it correctly. Also, I believe the 'additiona=
l freedom of movement' maybe just makes the puzzle 100 times harder. I cou=
ld also argue that the vast number of pieces moved with one turn actually h=
inders movement!

If you get stuck (which is unlikely given you have got this far already on =
your own) feel free to ask for a tip or two.

Good luck with the other hypercubes, it's good to hear from others finding =
similar strategies to these monsters!

Matthew

Hey Roice,=20

> Also, I'm not sure what you are asking by "Are you able to freely rearran=
ge
> the stickies?". Could you expound?

I was referring to a freedom of movement sequence:
3^2: unable to physically twist
3^3: center 3^2 slice can twist with the help of a single face,
other slices cannot twist in place
3^4: all 3 3^3 slices can fully twist in place with help
3^5: ?? what is left that couldn't be twisted previously?

I had speculated that in a (3+)^5 the 1-color cubies could be rearranged in=
place. This may be the reason that certain parity issues don't come up (th=
ought I haven't fully read that section of the group postings yet).

As for the control issues, I owe you a full critique/suggestion :), I'll po=
st one soon.

Kyle

--- In 4D_Cubing@yahoogroups.com, "Kyle Headley" wrote:
>=20
> I had speculated that in a (3+)^5 the 1-color cubies=20
> could be rearranged in place. This may be the reason=20
> that certain parity issues don't come up (thought I=20
> haven't fully read that section of the group postings=20
> yet).


Actually, Kyle, On a 3^n, the 1 color cubies are immovable in relation to e=
ach other. (Their "orientation" can be changed...) Look at a 3^3. If yours =
has red and orange 1 color cubies opposite of each other, you'll never be a=
ble to move them to sides next to each other. This applies to all 3^n. With=
n>4 this is extremely difficult to visualize.=20

As for the m^n (m>3 and even, n>2), the 1 color cubies CAN be "rearranged" =
in place. This is due to the multiple same color cubies. This is also the r=
eason parity issues do seem to come up (but can be trivial to solve with an=
unrestricted move set).=20

The easiest example of parity issues is with the 4^3. The rearranging of th=
e 1 color cubies is what allows the apparent single flipped edge on a 4^3. =
(An odd number of quarter twists of center slices is what creates it)

Happy n-cubing!

-Levi