Thread: "16-cell FT solved"

Dear cubists,

Has it really been a year and a half since we touched the code? It
appears so. This version simply implements David Smith's near little
Goldilocks function for calculating a good number of scrambling twists
for all puzzles. You will find the new featured version here:

http://magiccube4d.googlecode.com/files/mc4d-4.0.181.jar

Please try it out with your favorite puzzles and let us know if you see
any problems. If it looks good in a few days, I'll make the "Download"
button point to it. The only problem you would even see would be if
there were too few scrambles, but you can look at the resulting log
files to see the number used, or simply run it from a command window
where it will print out the value used for each full scramble.

For the record, here is my Java implementation as some of you might like
to adapt and test with other puzzles:

public int goldilocks(int nPieces, int nFaces, int nStickers, int
n1CPieces, int d) {
double dpieces = nPieces, dfaces = nFaces, dstickers = nStickers,
d1cpieces = n1CPieces;
double aveNumTwists = (dpieces * dfaces / ((double)dstickers -
d1cpieces)) * (0.577 + Math.log(dpieces));
return (int)Math.round(aveNumTwists * (d - 1 + log4(dfaces / (2.0 *
d))));
}

private double log4(double x) {
return Math.log(x) / Math.log(4);
}

It may be too much to expect for one function to handle every possible
twisty puzzle, and David has already described some of its limitations,
but this is a noble goal to aspire to, so maybe over time will have a
fully general, well tested and reasonably simple solution. Regardless of
how far David's first shipping version takes us towards that goal, it is
definitely light years ahead of my original hack.

Thank you David!!
-Melinda

Here is my story of solving the 16-cell:

When Andrey posted MPUlt v0.1, I was impressed by the images. I decided to =
try one of the puzzles once the macro function was available. I chose the 1=
6-cell because it had relatively less colors. I love 24-cell but really hat=
e distinguishing 24 colors. I cannot even name more than 10 major colors. =
At that time I studied the types of pieces in the 16-cell. But I didn't sta=
rt looking for algorithms.

When Andrey posted MPUlt v0.2, the macro function was available. An actual =
solve became feasible for me. So I began to look for algorithms. One of the=
biggest breakthrough in searching for algos is, to find a convenient viewp=
oint. I don't like the default view of 16-cell, where I can only see eight =
cells. I found that using ctrl+left click to center a cell gave a perfect v=
iewpoint. So I setup my 3-cycle algorithms in that viewpoint. The second br=
eakthrough is that I realized all 16 cells can be grouped into two groups. =
A sticker belonging to a group-A cell never goes to a group-B cell. So we d=
on't need 16 very different colors. We only need eight very distinct colors=
. And for the other eight I use the darker versions of the same colors. It =
took me some time to customize the colors. "Viewpoint" and "color pattern",=
two important things. Last night I worked very late and found algorithms n=
eeded to solve the small pieces around corners. Those are the hard part. I =
apparently missed the usual time to bed. The result is I couldn't fall asle=
ep till 5am. I don't know if it's excitation of the new puzzle or not.=20

Today Andrey posted MPUlt v0.3, which made my study of inner pieces much ea=
sier. But even without v0.3 I was planning to solve it within one or two da=
ys. In the 16-cell there are nine types of pieces. So six levels of rank ca=
nnot fully separate all nine types. In "rank 5+" there are three types of p=
ieces, which leads to some difficulty seeing the inner corner pieces.=20

Finally it was the actual solve, which took 3 hours and 24 minutes in total=
. It was not painful.=20

Andrey, thank you for making this puzzle. Excellent piece of work!

Nan

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Hi everyone
>=20
> I've just solved 16-cell FT (cell-turning) using Andrey's MPUlt 0.3. The =
log file can be found here:=20
>
>=20
> Phew...
>=20
> MUUlt is really great! For a puzzle of this size, I can't imagine a bette=
r experience. All the turning and macros are one-click. I can use macro whe=
n defining another macro, and so on.
>=20
> Nan
>

Great!
Congratulations!

You say: "Viewpoint" and "color pattern" are important. I can't see those a=
nywhere. What dou you mean?

Ed

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Here is my story of solving the 16-cell:
>=20
> When Andrey posted MPUlt v0.1, I was impressed by the images. I decided t=
o try one of the puzzles once the macro function was available. I chose the=
16-cell because it had relatively less colors. I love 24-cell but really h=
ate distinguishing 24 colors. I cannot even name more than 10 major colors.=
At that time I studied the types of pieces in the 16-cell. But I didn't s=
tart looking for algorithms.
>=20
> When Andrey posted MPUlt v0.2, the macro function was available. An actua=
l solve became feasible for me. So I began to look for algorithms. One of t=
he biggest breakthrough in searching for algos is, to find a convenient vie=
wpoint. I don't like the default view of 16-cell, where I can only see eigh=
t cells. I found that using ctrl+left click to center a cell gave a perfect=
viewpoint. So I setup my 3-cycle algorithms in that viewpoint. The second =
breakthrough is that I realized all 16 cells can be grouped into two groups=
. A sticker belonging to a group-A cell never goes to a group-B cell. So we=
don't need 16 very different colors. We only need eight very distinct colo=
rs. And for the other eight I use the darker versions of the same colors. I=
t took me some time to customize the colors. "Viewpoint" and "color pattern=
", two important things. Last night I worked very late and found algorithms=
needed to solve the small pieces around corners. Those are the hard part. =
I apparently missed the usual time to bed. The result is I couldn't fall as=
leep till 5am. I don't know if it's excitation of the new puzzle or not.=20
>=20
> Today Andrey posted MPUlt v0.3, which made my study of inner pieces much =
easier. But even without v0.3 I was planning to solve it within one or two =
days. In the 16-cell there are nine types of pieces. So six levels of rank =
cannot fully separate all nine types. In "rank 5+" there are three types of=
pieces, which leads to some difficulty seeing the inner corner pieces.=20
>=20
> Finally it was the actual solve, which took 3 hours and 24 minutes in tot=
al. It was not painful.=20
>=20
> Andrey, thank you for making this puzzle. Excellent piece of work!
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Hi everyone
> >=20
> > I've just solved 16-cell FT (cell-turning) using Andrey's MPUlt 0.3. Th=
e log file can be found here:=20
> >
> >=20
> > Phew...
> >=20
> > MUUlt is really great! For a puzzle of this size, I can't imagine a bet=
ter experience. All the turning and macros are one-click. I can use macro w=
hen defining another macro, and so on.
> >=20
> > Nan
> >
>

Hi Eduard,

I apologize for any unclear expression. Please find illustrations here:

http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/16cellfiles/

First, I find the 4D orientation (or projection to 3D) in cellcenteredview.=
png is more convenient than that in defaultview.png, because in cellcentere=
dview.png I can see more cells. This point of view is selected by ctrl+left=
click on any cell.

Second, I find the colors in mycolor.png is more convenient to use than tho=
se in defaultcolor.png. Notice that in defaultcolor.png, there are three gr=
een colors. And they cause confusion because any green piece can go to any =
other green cell. In mycolor.png, there are only two green colors. And they=
don't cause any confusion because a light green piece never go to the dark=
green cell and vice versa. All the light red/dark red, light blue/dark blu=
e etc are similar.

I hope I made myself clear this time.

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> Great!
> Congratulations!
>=20
> You say: "Viewpoint" and "color pattern" are important. I can't see those=
anywhere. What dou you mean?
>=20
> Ed
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Here is my story of solving the 16-cell:
> >=20
> > When Andrey posted MPUlt v0.1, I was impressed by the images. I decided=
to try one of the puzzles once the macro function was available. I chose t=
he 16-cell because it had relatively less colors. I love 24-cell but really=
hate distinguishing 24 colors. I cannot even name more than 10 major color=
s. At that time I studied the types of pieces in the 16-cell. But I didn't=
start looking for algorithms.
> >=20
> > When Andrey posted MPUlt v0.2, the macro function was available. An act=
ual solve became feasible for me. So I began to look for algorithms. One of=
the biggest breakthrough in searching for algos is, to find a convenient v=
iewpoint. I don't like the default view of 16-cell, where I can only see ei=
ght cells. I found that using ctrl+left click to center a cell gave a perfe=
ct viewpoint. So I setup my 3-cycle algorithms in that viewpoint. The secon=
d breakthrough is that I realized all 16 cells can be grouped into two grou=
ps. A sticker belonging to a group-A cell never goes to a group-B cell. So =
we don't need 16 very different colors. We only need eight very distinct co=
lors. And for the other eight I use the darker versions of the same colors.=
It took me some time to customize the colors. "Viewpoint" and "color patte=
rn", two important things. Last night I worked very late and found algorith=
ms needed to solve the small pieces around corners. Those are the hard part=
. I apparently missed the usual time to bed. The result is I couldn't fall =
asleep till 5am. I don't know if it's excitation of the new puzzle or not.=
=20
> >=20
> > Today Andrey posted MPUlt v0.3, which made my study of inner pieces muc=
h easier. But even without v0.3 I was planning to solve it within one or tw=
o days. In the 16-cell there are nine types of pieces. So six levels of ran=
k cannot fully separate all nine types. In "rank 5+" there are three types =
of pieces, which leads to some difficulty seeing the inner corner pieces.=20
> >=20
> > Finally it was the actual solve, which took 3 hours and 24 minutes in t=
otal. It was not painful.=20
> >=20
> > Andrey, thank you for making this puzzle. Excellent piece of work!
> >=20
> > Nan
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > >
> > > Hi everyone
> > >=20
> > > I've just solved 16-cell FT (cell-turning) using Andrey's MPUlt 0.3. =
The log file can be found here:=20
> > >
> > >=20
> > > Phew...
> > >=20
> > > MUUlt is really great! For a puzzle of this size, I can't imagine a b=
etter experience. All the turning and macros are one-click. I can use macro=
when defining another macro, and so on.
> > >=20
> > > Nan
> > >
> >
>

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Content-Type: text/plain; charset=ISO-8859-1

On Thu, May 12, 2011 at 12:38 AM, schuma wrote:

> The second breakthrough is that I realized all 16 cells can be grouped into
> two groups. A sticker belonging to a group-A cell never goes to a group-B
> cell.


That's a really neat observation, so thanks for sharing! I would have
guessed otherwise, even knowing the 16-cell is the only "duoantiprism". I
just would have thought it to be too symmetrical of an object for this
effect (similar to how the 3^4 is a duoprism, yet is too symmetrical to
disallow pieces from moving from one "duoprism torus" to the other). I
enjoy being surprised by things like this.

Big props on your first solve too :D

seeya,
Roice

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

Hi Nan,

Sorry, I did understand the why of colorchange but not the how.
I think you have changed the color figures in "MPUlt_settings.txt"

Ed

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Hi Eduard,
>=20
> I apologize for any unclear expression. Please find illustrations here:
>=20
> http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/16cellfiles/
>=20
> First, I find the 4D orientation (or projection to 3D) in cellcenteredvie=
w.png is more convenient than that in defaultview.png, because in cellcente=
redview.png I can see more cells. This point of view is selected by ctrl+le=
ft click on any cell.
>=20
> Second, I find the colors in mycolor.png is more convenient to use than t=
hose in defaultcolor.png. Notice that in defaultcolor.png, there are three =
green colors. And they cause confusion because any green piece can go to an=
y other green cell. In mycolor.png, there are only two green colors. And th=
ey don't cause any confusion because a light green piece never go to the da=
rk green cell and vice versa. All the light red/dark red, light blue/dark b=
lue etc are similar.
>=20
> I hope I made myself clear this time.
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> >
> > Great!
> > Congratulations!
> >=20
> > You say: "Viewpoint" and "color pattern" are important. I can't see tho=
se anywhere. What dou you mean?
> >=20
> > Ed
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > >
> > > Here is my story of solving the 16-cell:
> > >=20
> > > When Andrey posted MPUlt v0.1, I was impressed by the images. I decid=
ed to try one of the puzzles once the macro function was available. I chose=
the 16-cell because it had relatively less colors. I love 24-cell but real=
ly hate distinguishing 24 colors. I cannot even name more than 10 major col=
ors. At that time I studied the types of pieces in the 16-cell. But I didn=
't start looking for algorithms.
> > >=20
> > > When Andrey posted MPUlt v0.2, the macro function was available. An a=
ctual solve became feasible for me. So I began to look for algorithms. One =
of the biggest breakthrough in searching for algos is, to find a convenient=
viewpoint. I don't like the default view of 16-cell, where I can only see =
eight cells. I found that using ctrl+left click to center a cell gave a per=
fect viewpoint. So I setup my 3-cycle algorithms in that viewpoint. The sec=
ond breakthrough is that I realized all 16 cells can be grouped into two gr=
oups. A sticker belonging to a group-A cell never goes to a group-B cell. S=
o we don't need 16 very different colors. We only need eight very distinct =
colors. And for the other eight I use the darker versions of the same color=
s. It took me some time to customize the colors. "Viewpoint" and "color pat=
tern", two important things. Last night I worked very late and found algori=
thms needed to solve the small pieces around corners. Those are the hard pa=
rt. I apparently missed the usual time to bed. The result is I couldn't fal=
l asleep till 5am. I don't know if it's excitation of the new puzzle or not=
.=20
> > >=20
> > > Today Andrey posted MPUlt v0.3, which made my study of inner pieces m=
uch easier. But even without v0.3 I was planning to solve it within one or =
two days. In the 16-cell there are nine types of pieces. So six levels of r=
ank cannot fully separate all nine types. In "rank 5+" there are three type=
s of pieces, which leads to some difficulty seeing the inner corner pieces.=
=20
> > >=20
> > > Finally it was the actual solve, which took 3 hours and 24 minutes in=
total. It was not painful.=20
> > >=20
> > > Andrey, thank you for making this puzzle. Excellent piece of work!
> > >=20
> > > Nan
> > >=20
> > > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > > >
> > > > Hi everyone
> > > >=20
> > > > I've just solved 16-cell FT (cell-turning) using Andrey's MPUlt 0.3=
. The log file can be found here:=20
> > > >
> > > >=20
> > > > Phew...
> > > >=20
> > > > MUUlt is really great! For a puzzle of this size, I can't imagine a=
better experience. All the turning and macros are one-click. I can use mac=
ro when defining another macro, and so on.
> > > >=20
> > > > Nan
> > > >
> > >
> >
>

Hi,

That's easy. Ctrl + right click a cell to change its color.

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> Hi Nan,
>=20
> Sorry, I did understand the why of colorchange but not the how.
> I think you have changed the color figures in "MPUlt_settings.txt"
>=20
> Ed
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Hi Eduard,
> >=20
> > I apologize for any unclear expression. Please find illustrations here:
> >=20
> > http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/16cellfile=
s/
> >=20
> > First, I find the 4D orientation (or projection to 3D) in cellcenteredv=
iew.png is more convenient than that in defaultview.png, because in cellcen=
teredview.png I can see more cells. This point of view is selected by ctrl+=
left click on any cell.
> >=20
> > Second, I find the colors in mycolor.png is more convenient to use than=
those in defaultcolor.png. Notice that in defaultcolor.png, there are thre=
e green colors. And they cause confusion because any green piece can go to =
any other green cell. In mycolor.png, there are only two green colors. And =
they don't cause any confusion because a light green piece never go to the =
dark green cell and vice versa. All the light red/dark red, light blue/dark=
blue etc are similar.
> >=20
> > I hope I made myself clear this time.
> >=20
> > Nan
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > >
> > > Great!
> > > Congratulations!
> > >=20
> > > You say: "Viewpoint" and "color pattern" are important. I can't see t=
hose anywhere. What dou you mean?
> > >=20
> > > Ed
> > >=20
> > > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > > >
> > > > Here is my story of solving the 16-cell:
> > > >=20
> > > > When Andrey posted MPUlt v0.1, I was impressed by the images. I dec=
ided to try one of the puzzles once the macro function was available. I cho=
se the 16-cell because it had relatively less colors. I love 24-cell but re=
ally hate distinguishing 24 colors. I cannot even name more than 10 major c=
olors. At that time I studied the types of pieces in the 16-cell. But I di=
dn't start looking for algorithms.
> > > >=20
> > > > When Andrey posted MPUlt v0.2, the macro function was available. An=
actual solve became feasible for me. So I began to look for algorithms. On=
e of the biggest breakthrough in searching for algos is, to find a convenie=
nt viewpoint. I don't like the default view of 16-cell, where I can only se=
e eight cells. I found that using ctrl+left click to center a cell gave a p=
erfect viewpoint. So I setup my 3-cycle algorithms in that viewpoint. The s=
econd breakthrough is that I realized all 16 cells can be grouped into two =
groups. A sticker belonging to a group-A cell never goes to a group-B cell.=
So we don't need 16 very different colors. We only need eight very distinc=
t colors. And for the other eight I use the darker versions of the same col=
ors. It took me some time to customize the colors. "Viewpoint" and "color p=
attern", two important things. Last night I worked very late and found algo=
rithms needed to solve the small pieces around corners. Those are the hard =
part. I apparently missed the usual time to bed. The result is I couldn't f=
all asleep till 5am. I don't know if it's excitation of the new puzzle or n=
ot.=20
> > > >=20
> > > > Today Andrey posted MPUlt v0.3, which made my study of inner pieces=
much easier. But even without v0.3 I was planning to solve it within one o=
r two days. In the 16-cell there are nine types of pieces. So six levels of=
rank cannot fully separate all nine types. In "rank 5+" there are three ty=
pes of pieces, which leads to some difficulty seeing the inner corner piece=
s.=20
> > > >=20
> > > > Finally it was the actual solve, which took 3 hours and 24 minutes =
in total. It was not painful.=20
> > > >=20
> > > > Andrey, thank you for making this puzzle. Excellent piece of work!
> > > >=20
> > > > Nan
> > > >=20
> > > > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > > > >
> > > > > Hi everyone
> > > > >=20
> > > > > I've just solved 16-cell FT (cell-turning) using Andrey's MPUlt 0=
.3. The log file can be found here:=20
> > > > >
> > > > >=20
> > > > > Phew...
> > > > >=20
> > > > > MUUlt is really great! For a puzzle of this size, I can't imagine=
a better experience. All the turning and macros are one-click. I can use m=
acro when defining another macro, and so on.
> > > > >=20
> > > > > Nan
> > > > >
> > > >
> > >
> >
>

Nan, congratulations with this solve!
Nice to see that somebody beat me in my program :)=20
I started with 24-cell, and now struggling with central 2C pieces - witho=
ut macros - just to understand the geometry of the puzzle. And pieces often=
go in the wrong places - so probably I don't see all connections between c=
ells.
As for incomplete orbits of stickers - it's a property of many puzzles: F=
TO, cell-turn douprisms, cell-turn bitruncated 4D simplex, and probably a l=
ot of others. I thought that 24-cell will have three sets of cells, but it'=
s not the case.

In next version I'll do checkboxes for 10 or 12 ranks of stickers.
Are there any ideas what new puzzles to include in it? Better from tesserac=
t/cross or 24-cell families - now I'm not ready to calculate irrational coo=
rdinates of axes of simplex or 600-cell...=20=20=20

Good luck!
Andrey


--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Here is my story of solving the 16-cell:
>=20
> When Andrey posted MPUlt v0.1, I was impressed by the images. I decided t=
o try one of the puzzles once the macro function was available. I chose the=
16-cell because it had relatively less colors. I love 24-cell but really h=
ate distinguishing 24 colors. I cannot even name more than 10 major colors.=
At that time I studied the types of pieces in the 16-cell. But I didn't s=
tart looking for algorithms.
>=20
> When Andrey posted MPUlt v0.2, the macro function was available. An actua=
l solve became feasible for me. So I began to look for algorithms. One of t=
he biggest breakthrough in searching for algos is, to find a convenient vie=
wpoint. I don't like the default view of 16-cell, where I can only see eigh=
t cells. I found that using ctrl+left click to center a cell gave a perfect=
viewpoint. So I setup my 3-cycle algorithms in that viewpoint. The second =
breakthrough is that I realized all 16 cells can be grouped into two groups=
. A sticker belonging to a group-A cell never goes to a group-B cell. So we=
don't need 16 very different colors. We only need eight very distinct colo=
rs. And for the other eight I use the darker versions of the same colors. I=
t took me some time to customize the colors. "Viewpoint" and "color pattern=
", two important things. Last night I worked very late and found algorithms=
needed to solve the small pieces around corners. Those are the hard part. =
I apparently missed the usual time to bed. The result is I couldn't fall as=
leep till 5am. I don't know if it's excitation of the new puzzle or not.=20
>=20
> Today Andrey posted MPUlt v0.3, which made my study of inner pieces much =
easier. But even without v0.3 I was planning to solve it within one or two =
days. In the 16-cell there are nine types of pieces. So six levels of rank =
cannot fully separate all nine types. In "rank 5+" there are three types of=
pieces, which leads to some difficulty seeing the inner corner pieces.=20
>=20
> Finally it was the actual solve, which took 3 hours and 24 minutes in tot=
al. It was not painful.=20
>=20
> Andrey, thank you for making this puzzle. Excellent piece of work!
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Hi everyone
> >=20
> > I've just solved 16-cell FT (cell-turning) using Andrey's MPUlt 0.3. Th=
e log file can be found here:=20
> >
> >=20
> > Phew...
> >=20
> > MUUlt is really great! For a puzzle of this size, I can't imagine a bet=
ter experience. All the turning and macros are one-click. I can use macro w=
hen defining another macro, and so on.
> >=20
> > Nan
> >
>