Thread: "A Hyperminx solution approach (was Thibaut Kirchner)"

From: "Roice Nelson" <roice3@gmail.com>
Date: Wed, 17 Sep 2008 21:03:53 -0500
Subject: A Hyperminx solution approach (was [MC4D] Thibaut Kirchner)




Hey Nelson,

So in short, my thought was to take advantage of solving one of the simpler
puzzles first as a path towards solving the full puzzle. This would have 2
big advantages. The first is that for the majority of the solution, one
would work with a smaller number of colors. The second (less obvious but
possibly more dramatic) is that the number of moves to do a full solution
would decrease, and here is a little more explanation on that...

In computer science, a classic problem is sorting an array of numbers, and
there are slower and faster ways to do it. If you have 8 items in a list,
it doesn't matter so much how you sort because the cost difference, although
there, won't balloon to extreme proportions. But when you have 15x as many
items in the list (120), the way you sort becomes more important (often the
slowness of an approach doesn't scale linearly, so instead of being 15x
slower, it might be 225x slower). There is something called "quick sort",
which (roughly speaking) doesn't sort items in a list one by one, but first
moves items into the general area they will ultimately go, and later makes
further passes to complete the sorting in the smaller areas. What I'm
describing as a suggested approach isn't really a quicksort, but is loosely
based on the idea of moving pieces to an area, then working on the smaller
areas later.

I should point out I don't think it would be necessary to fully solve the
smaller puzzle. It could be a waste of time to worry about orientations at
that stage, and so maybe better to focus only on positions since the pieces
will have to be moved around again later. On the other hand, orienting them
early on could make later work easier. I'm not sure what I would do on that
yet.

I think the rings or 4-cube cells puzzles might be best suited as the puzzle
to solve first, because unlike the layers puzzle, the different sets are
more similar. The tori puzzle might be a bad choice because it is only
breaking the world up into 2 big areas, but maybe the gains would still be
as big - I'm not sure. The antipodal puzzle is truly a bad choice though
because the sets of similarly colored cells are not connected.

You could also choose to do it in 3 steps. You could do the tori puzzle,
then switch to the rings or 4-cube cells puzzle, then finally switch to the
full puzzle. Note that after the first step of moving pieces into the
correct areas of the tori puzzle, you have only really actively moved half
of the puzzle pieces, yet the other half are in their area now as well. In
effect, you have obtained a lot of work for free!

Now, when you switch puzzles in the program, it currently resets the puzzle
(maybe this should change), so you can't do what I'm describing with the
UI. But you can edit the integer representing the puzzle type in the log
file at any point and it would work. Even on the simpler puzzles, the
internal state representation still contains the full 120 colors on all the
cells. I intentionally made that the case, knowing this meant log files
that have solved one of the easier puzzles still won't look very pristine.

That's it. I could analyze the benefits further (actually try to estimate
what the differences in moves required might be), but these are my loose
thoughts on it so far, and I have the feeling that the benefits in
time-complexity of solution are definitely worth it.

Roice



On 9/16/08, thibaut.kirchner wrote:
>
> Hello to all of you.
> I'm Thibaut Kirchner, nearly 21 years old, and live near Paris, France.
> I'm student in maths and computer science (fifth year after in
> superior). Since a few days, I'm the 84th person having solved a 3^4
> hypercube (actually, I've solved two of them).
>
> I'm interested in solving puzzles which look like the traditional 3^3
> cube since March, when a friend of mine taught me to solve the 3^3 and
> the Pyraminx (at the French Open 2008).
> Then I found how to solve the Megaminx, and then the 4^3 and 5^3 cubes
> (parity errors were the more difficult).
> I've been to some WCA competitions, but, if I like solving faster and
> faster the same puzzles, what I really enjoy is to find methods and
> algorithms to solve new puzzles. When I discovered Gelatinbrain
> (http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/) and
> rediscovered the 3^4 hypercube (another friend of mine, Ilia Smilga,
> solved it a few years ago, and I had heard of it), I decided to solve
> as much puzzles from there as possible.
>
> Now, I'm working at solving the 4^4 Hypercube and the Magic 120-Cell.
> I believe I have a complete method to do them, the only thing I need
> to complete the solution is some time, since it takes me a few minutes
> to find some piece in this maelstrom of colors.
> I expect to come with a full solution of the 4^4 in a few months, and
> as for the Magic 120-Cell... It won't be sooner than in a few years,
> since it is really an enormous puzzle.
>
> I'm looking forward to speaking about methods to solve the 3^4
> hypercube, but before, I have some questions:
> - I read that we don't have a complete proof for the number of states
> of the Magic 120-Cell (would you mind if I call it Hyper-megaminx?
> Sounds better to me), because we don't have enough formulas to orient
> all the pieces as we conjecture we can. Is it still true today? What
> cases remain to be treated? To solve the 3^4 hypercube, I found (or
> rather adapted from the 3^3 cube) and used a few formulas to orient
> different pieces, and I'm almost sure (and absolutely sure for the
> 4-stickered and 3-stickered pieces) they can be adapted for the
> Hyper-megaminx.
> - Can someone do a program to manipulate a Hyper-pyraminx (based on
> the 4D-simplex as the Pyraminx is based on the 3D-simplex), or
> Super-hypercubes (as hypercubes but center pieces are somehow oriented)?
>
> Thibaut.
>
> PS: Thank you for your invitation here.
>
>
>

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Hi Thibaut,

 

Welcome!  There are a lot of topics floating around (thanks for t=
he parity writeup by the way), but here I'm only replying about your de=
sire to tame Magic120Cell, which we've also been calling Hyperminx.&nbs=
p; I just uploaded a single line code change to the Hyperminx program which=
I think could greatly help anyone attempting a full solution.  The ch=
ange is that when you switch puzzle types, e.g. from a 2-color puzzle to a =
12-color puzzle, the internal state of the puzzle won't reset. &nb=
sp;I am copying an email below that I sent to Nelson a few months ago descr=
ibing the motivation for this.  I still haven't quantified the ben=
efit I perceive would come from this approach, but it hopefully might turn =
a "taking years" solution into a "taking months" one...=



 

All the best,

Roice

 

---------- Forwarded message ----------
>From: Roice Nelson <:roice@gravitation3d.com" target=3D"_blank">roice@gravitation3d.com>=


Date: Jun 2, 2008 8:16 PM

Subject: Re: One more suggestion
To: Nelson Garcia <:spel_werdz_rite@hotmail.com" target=3D"_blank">spel_werdz_rite@hotmail.com=
>

 

Hey Nelson,

 

So in short, my thought was to take advantage of solving one of the si=
mpler puzzles first as a path towards solving the full puzzle.  This w=
ould have 2 big advantages.  The first is that for the majority of the=
solution, one would work with a smaller number of colors.  The second=
(less obvious but possibly more dramatic) is that the number of moves to d=
o a full solution would decrease, and here is a little more explanation on =
that...  



 

In computer science, a classic problem is sorting an array of numbers,=
and there are slower and faster ways to do it.  If you have 8 items i=
n a list, it doesn't matter so much how you sort because the cost diffe=
rence, although there, won't balloon to extreme proportions.  But =
when you have 15x as many items in the list (120), the way you sort be=
comes more important (often the slowness of an approach doesn't scale l=
inearly, so instead of being 15x slower, it might be 225x slower). There is=
something called "quick sort", which (roughly speaking) doesn=
9;t sort items in a list one by one, but first moves items into the general=
area they will ultimately go, and later makes further passes to complete t=
he sorting in the smaller areas.  What I'm describing as a suggest=
ed approach isn't really a quicksort, but is loosely based on the idea =
of moving pieces to an area, then working on the smaller areas later.



 

I should point out I don't think it would be necessary to fully so=
lve the smaller puzzle. It could be a waste of time to worry about orientat=
ions at that stage, and so maybe better to focus only on positions since th=
e pieces will have to be moved around again later.  On the other hand,=
orienting them early on could make later work easier.  I'm not su=
re what I would do on that yet.



 

I think the rings or 4-cube cells puzzles might be best suited as the =
puzzle to solve first, because unlike the layers puzzle, the different sets=
are more similar.  The tori puzzle might be a bad choice because it i=
s only breaking the world up into 2 big areas, but maybe the gains would st=
ill be as big - I'm not sure.  The antipodal puzzle is truly =
a bad choice though because the sets of similarly colored cells are not con=
nected.



 

You could also choose to do it in 3 steps.  You could do the tori=
puzzle, then switch to the rings or 4-cube cells puzzle, then finally swit=
ch to the full puzzle.  Note that after the first step of moving piece=
s into the correct areas of the tori puzzle, you have only really actively =
moved half of the puzzle pieces, yet the other half are in their area now a=
s well. In effect, you have obtained a lot of work for free!



 

Now, when you switch puzzles in the program, it currently resets the p=
uzzle (maybe this should change), so you can't do what I'm describi=
ng with the UI.  But you can edit the integer representing the puzzle =
type in the log file at any point and it would work.  Even on the simp=
ler puzzles, the internal state representation still contains the full 120 =
colors on all the cells.  I intentionally made that the case, knowing =
this meant log files that have solved one of the easier puzzles still won&#=
39;t look very pristine.



 

That's it.  I could analyze the benefits further (actually tr=
y to estimate what the differences in moves required might be), but these a=
re my loose thoughts on it so far, and I have the feeling that the benefits=
in time-complexity of solution are definitely worth it.



 

Roice

 



On 9/16/08, =
thibaut.kirchner
<t=3D"_blank">thibaut.kirchner@yahoo.fr> wrote:
=20
0px 0.8ex;border-left:#ccc 1px solid">


:0px;margin:0px;width:470px;padding-top:0px">

Hello to all of you.
I'm Thibaut Kirchner, nearly 21 years old, a=
nd live near Paris, France.
I'm student in maths and computer scienc=
e (fifth year after in
superior). Since a few days, I'm the 84th per=
son having solved a 3^4


hypercube (actually, I've solved two of them).

I'm intereste=
d in solving puzzles which look like the traditional 3^3
cube since Marc=
h, when a friend of mine taught me to solve the 3^3 and
the Pyraminx (at=
the French Open 2008).


Then I found how to solve the Megaminx, and then the 4^3 and 5^3 cubes
(=
parity errors were the more difficult).
I've been to some WCA compet=
itions, but, if I like solving faster and
faster the same puzzles, what =
I really enjoy is to find methods and


algorithms to solve new puzzles. When I discovered Gelatinbrain
(=3D"http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/" target=
=3D"_blank">http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/<=
/a>) and


rediscovered the 3^4 hypercube (another friend of mine, Ilia Smilga,
sol=
ved it a few years ago, and I had heard of it), I decided to solve
as mu=
ch puzzles from there as possible.

Now, I'm working at solving t=
he 4^4 Hypercube and the Magic 120-Cell.


I believe I have a complete method to do them, the only thing I need
to =
complete the solution is some time, since it takes me a few minutes
to f=
ind some piece in this maelstrom of colors.
I expect to come with a full=
solution of the 4^4 in a few months, and


as for the Magic 120-Cell... It won't be sooner than in a few years,>since it is really an enormous puzzle.

I'm looking forward to s=
peaking about methods to solve the 3^4
hypercube, but before, I have som=
e questions:


- I read that we don't have a complete proof for the number of statesr>of the Magic 120-Cell (would you mind if I call it Hyper-megaminx?
Sou=
nds better to me), because we don't have enough formulas to orient


all the pieces as we conjecture we can. Is it still true today? What
cas=
es remain to be treated? To solve the 3^4 hypercube, I found (or
rather =
adapted from the 3^3 cube) and used a few formulas to orient
different p=
ieces, and I'm almost sure (and absolutely sure for the


4-stickered and 3-stickered pieces) they can be adapted for the
Hyper-me=
gaminx.
- Can someone do a program to manipulate a Hyper-pyraminx (based=
on
the 4D-simplex as the Pyraminx is based on the 3D-simplex), or


Super-hypercubes (as hypercubes but center pieces are somehow oriented)?>
Thibaut.

PS: Thank you for your invitation here.

iv>
>



------=_Part_21458_1121849.1221703433490--




From: Melinda Green <melinda@superliminal.com>
Date: Wed, 17 Sep 2008 19:42:59 -0700
Subject: A Hyperminx solution approach (was [MC4D] Thibaut Kirchner)



Roice,

You already implemented the show-the-cubie-that-goes-here functionality,
right? In other words, the compliment to the
show-me-where-this-cubie-belongs feature. Without this, I suspect that a
great deal of a potential solver's time would be spent searching. Even
still I expect it will take months but at least the bulk of the mindless
work can be eliminated.

-melinda

Roice Nelson wrote:
> Hi Thibaut,
>
> Welcome! There are a lot of topics floating around (thanks for the
> parity writeup by the way), but here I'm only replying about your
> desire to tame Magic120Cell, which we've also been calling Hyperminx.
> I just uploaded a single line code change to the Hyperminx program
> which I think could greatly help anyone attempting a full solution.
> The change is that when you switch puzzle types, e.g. from a 2-color
> puzzle to a 12-color puzzle, the internal state of the puzzle won't
> reset. I am copying an email below that I sent to Nelson a few months
> ago describing the motivation for this. I still haven't quantified
> the benefit I perceive would come from this approach, but it hopefully
> might turn a "taking years" solution into a "taking months" one...
>
> All the best,
> Roice
>
> ---------- Forwarded message ----------
> From: *Roice Nelson* > >
> Date: Jun 2, 2008 8:16 PM
> Subject: Re: One more suggestion
> To: Nelson Garcia > >
>
>
> Hey Nelson,
>
> So in short, my thought was to take advantage of solving one of the
> simpler puzzles first as a path towards solving the full puzzle. This
> would have 2 big advantages. The first is that for the majority of
> the solution, one would work with a smaller number of colors. The
> second (less obvious but possibly more dramatic) is that the number of
> moves to do a full solution would decrease, and here is a little more
> explanation on that...
>
> In computer science, a classic problem is sorting an array of numbers,
> and there are slower and faster ways to do it. If you have 8 items in
> a list, it doesn't matter so much how you sort because the cost
> difference, although there, won't balloon to extreme proportions. But
> when you have 15x as many items in the list (120), the way you
> sort becomes more important (often the slowness of an approach doesn't
> scale linearly, so instead of being 15x slower, it might be 225x
> slower). There is something called "quick sort", which (roughly
> speaking) doesn't sort items in a list one by one, but first moves
> items into the general area they will ultimately go, and later makes
> further passes to complete the sorting in the smaller areas. What I'm
> describing as a suggested approach isn't really a quicksort, but is
> loosely based on the idea of moving pieces to an area, then working on
> the smaller areas later.
>
> I should point out I don't think it would be necessary to fully solve
> the smaller puzzle. It could be a waste of time to worry about
> orientations at that stage, and so maybe better to focus only on
> positions since the pieces will have to be moved around again later.
> On the other hand, orienting them early on could make later work
> easier. I'm not sure what I would do on that yet.
>
> I think the rings or 4-cube cells puzzles might be best suited as the
> puzzle to solve first, because unlike the layers puzzle, the different
> sets are more similar. The tori puzzle might be a bad choice because
> it is only breaking the world up into 2 big areas, but maybe the gains
> would still be as big - I'm not sure. The antipodal puzzle is truly a
> bad choice though because the sets of similarly colored cells are not
> connected.
>
> You could also choose to do it in 3 steps. You could do the tori
> puzzle, then switch to the rings or 4-cube cells puzzle, then finally
> switch to the full puzzle. Note that after the first step of moving
> pieces into the correct areas of the tori puzzle, you have only really
> actively moved half of the puzzle pieces, yet the other half are in
> their area now as well. In effect, you have obtained a lot of work for
> free!
>
> Now, when you switch puzzles in the program, it currently resets the
> puzzle (maybe this should change), so you can't do what I'm describing
> with the UI. But you can edit the integer representing the puzzle
> type in the log file at any point and it would work. Even on the
> simpler puzzles, the internal state representation still contains the
> full 120 colors on all the cells. I intentionally made that the case,
> knowing this meant log files that have solved one of the easier
> puzzles still won't look very pristine.
>
> That's it. I could analyze the benefits further (actually try to
> estimate what the differences in moves required might be), but these
> are my loose thoughts on it so far, and I have the feeling that the
> benefits in time-complexity of solution are definitely worth it.
>
> Roice




From: "Roice Nelson" <roice3@gmail.com>
Date: Wed, 17 Sep 2008 22:30:02 -0500
Subject: Re: A Hyperminx solution approach (was [MC4D] Thibaut Kirchner)



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Yep, shift+ctrl+clicking does the piece finding functionality, and
left/right clicking distinguishes between the two complementary cases you
mention...
Roice


On Wed, Sep 17, 2008 at 9:42 PM, Melinda Green wrote:

> Roice,
>
> You already implemented the show-the-cubie-that-goes-here functionality,
> right? In other words, the compliment to the
> show-me-where-this-cubie-belongs feature. Without this, I suspect that a
> great deal of a potential solver's time would be spent searching. Even
> still I expect it will take months but at least the bulk of the mindless
> work can be eliminated.
>
> -melinda
>
>
> Roice Nelson wrote:
> > Hi Thibaut,
> >
> > Welcome! There are a lot of topics floating around (thanks for the
> > parity writeup by the way), but here I'm only replying about your
> > desire to tame Magic120Cell, which we've also been calling Hyperminx.
> > I just uploaded a single line code change to the Hyperminx program
> > which I think could greatly help anyone attempting a full solution.
> > The change is that when you switch puzzle types, e.g. from a 2-color
> > puzzle to a 12-color puzzle, the internal state of the puzzle won't
> > reset. I am copying an email below that I sent to Nelson a few months
> > ago describing the motivation for this. I still haven't quantified
> > the benefit I perceive would come from this approach, but it hopefully
> > might turn a "taking years" solution into a "taking months" one...
> >
> > All the best,
> > Roice
> >
> > ---------- Forwarded message ----------
> > From: *Roice Nelson*
> > >>
> > Date: Jun 2, 2008 8:16 PM
> > Subject: Re: One more suggestion
> > To: Nelson Garcia
> > >>
> >
> >
> > Hey Nelson,
> >
> > So in short, my thought was to take advantage of solving one of the
> > simpler puzzles first as a path towards solving the full puzzle. This
> > would have 2 big advantages. The first is that for the majority of
> > the solution, one would work with a smaller number of colors. The
> > second (less obvious but possibly more dramatic) is that the number of
> > moves to do a full solution would decrease, and here is a little more
> > explanation on that...
> >
> > In computer science, a classic problem is sorting an array of numbers,
> > and there are slower and faster ways to do it. If you have 8 items in
> > a list, it doesn't matter so much how you sort because the cost
> > difference, although there, won't balloon to extreme proportions. But
> > when you have 15x as many items in the list (120), the way you
> > sort becomes more important (often the slowness of an approach doesn't
> > scale linearly, so instead of being 15x slower, it might be 225x
> > slower). There is something called "quick sort", which (roughly
> > speaking) doesn't sort items in a list one by one, but first moves
> > items into the general area they will ultimately go, and later makes
> > further passes to complete the sorting in the smaller areas. What I'm
> > describing as a suggested approach isn't really a quicksort, but is
> > loosely based on the idea of moving pieces to an area, then working on
> > the smaller areas later.
> >
> > I should point out I don't think it would be necessary to fully solve
> > the smaller puzzle. It could be a waste of time to worry about
> > orientations at that stage, and so maybe better to focus only on
> > positions since the pieces will have to be moved around again later.
> > On the other hand, orienting them early on could make later work
> > easier. I'm not sure what I would do on that yet.
> >
> > I think the rings or 4-cube cells puzzles might be best suited as the
> > puzzle to solve first, because unlike the layers puzzle, the different
> > sets are more similar. The tori puzzle might be a bad choice because
> > it is only breaking the world up into 2 big areas, but maybe the gains
> > would still be as big - I'm not sure. The antipodal puzzle is truly a
> > bad choice though because the sets of similarly colored cells are not
> > connected.
> >
> > You could also choose to do it in 3 steps. You could do the tori
> > puzzle, then switch to the rings or 4-cube cells puzzle, then finally
> > switch to the full puzzle. Note that after the first step of moving
> > pieces into the correct areas of the tori puzzle, you have only really
> > actively moved half of the puzzle pieces, yet the other half are in
> > their area now as well. In effect, you have obtained a lot of work for
> > free!
> >
> > Now, when you switch puzzles in the program, it currently resets the
> > puzzle (maybe this should change), so you can't do what I'm describing
> > with the UI. But you can edit the integer representing the puzzle
> > type in the log file at any point and it would work. Even on the
> > simpler puzzles, the internal state representation still contains the
> > full 120 colors on all the cells. I intentionally made that the case,
> > knowing this meant log files that have solved one of the easier
> > puzzles still won't look very pristine.
> >
> > That's it. I could analyze the benefits further (actually try to
> > estimate what the differences in moves required might be), but these
> > are my loose thoughts on it so far, and I have the feeling that the
> > benefits in time-complexity of solution are definitely worth it.
> >
> > Roice
>
>
>

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Yep, shift+ctrl+clicking does the piece finding functionality, and left/right clicking distinguishes between the two complementary cases you mention...

Roice



On Wed, Sep 17, 2008 at 9:42 PM, Melinda Green <
melinda@superliminal.com> wrote:


















Roice,



You already implemented the show-the-cubie-that-goes-here functionality,

right? In other words, the compliment to the

show-me-where-this-cubie-belongs feature. Without this, I suspect that a

great deal of a potential solver's time would be spent searching. Even

still I expect it will take months but at least the bulk of the mindless

work can be eliminated.



-melinda





Roice Nelson wrote:

> Hi Thibaut,

>

> Welcome! There are a lot of topics floating around (thanks for the

> parity writeup by the way), but here I'm only replying about your

> desire to tame Magic120Cell, which we've also been calling Hyperminx.

> I just uploaded a single line code change to the Hyperminx program

> which I think could greatly help anyone attempting a full solution.

> The change is that when you switch puzzle types, e.g. from a 2-color

> puzzle to a 12-color puzzle, the internal state of the puzzle won't

> reset. I am copying an email below that I sent to Nelson a few months

> ago describing the motivation for this. I still haven't quantified

> the benefit I perceive would come from this approach, but it hopefully

> might turn a "taking years" solution into a "taking months" one...

>

> All the best,

> Roice

>

> ---------- Forwarded message ----------

> From: *Roice Nelson* <roice@gravitation3d.com

> <mailto:roice@gravitation3d.com>>

> Date: Jun 2, 2008 8:16 PM

> Subject: Re: One more suggestion

> To: Nelson Garcia <spel_werdz_rite@hotmail.com

> <mailto:spel_werdz_rite@hotmail.com>>

>

>

> Hey Nelson,

>

> So in short, my thought was to take advantage of solving one of the

> simpler puzzles first as a path towards solving the full puzzle. This

> would have 2 big advantages. The first is that for the majority of

> the solution, one would work with a smaller number of colors. The

> second (less obvious but possibly more dramatic) is that the number of

> moves to do a full solution would decrease, and here is a little more

> explanation on that...

>

> In computer science, a classic problem is sorting an array of numbers,

> and there are slower and faster ways to do it. If you have 8 items in

> a list, it doesn't matter so much how you sort because the cost

> difference, although there, won't balloon to extreme proportions. But

> when you have 15x as many items in the list (120), the way you

> sort becomes more important (often the slowness of an approach doesn't

> scale linearly, so instead of being 15x slower, it might be 225x

> slower). There is something called "quick sort", which (roughly

> speaking) doesn't sort items in a list one by one, but first moves

> items into the general area they will ultimately go, and later makes

> further passes to complete the sorting in the smaller areas. What I'm

> describing as a suggested approach isn't really a quicksort, but is

> loosely based on the idea of moving pieces to an area, then working on

> the smaller areas later.

>

> I should point out I don't think it would be necessary to fully solve

> the smaller puzzle. It could be a waste of time to worry about

> orientations at that stage, and so maybe better to focus only on

> positions since the pieces will have to be moved around again later.

> On the other hand, orienting them early on could make later work

> easier. I'm not sure what I would do on that yet.

>

> I think the rings or 4-cube cells puzzles might be best suited as the

> puzzle to solve first, because unlike the layers puzzle, the different

> sets are more similar. The tori puzzle might be a bad choice because

> it is only breaking the world up into 2 big areas, but maybe the gains

> would still be as big - I'm not sure. The antipodal puzzle is truly a

> bad choice though because the sets of similarly colored cells are not

> connected.

>

> You could also choose to do it in 3 steps. You could do the tori

> puzzle, then switch to the rings or 4-cube cells puzzle, then finally

> switch to the full puzzle. Note that after the first step of moving

> pieces into the correct areas of the tori puzzle, you have only really

> actively moved half of the puzzle pieces, yet the other half are in

> their area now as well. In effect, you have obtained a lot of work for

> free!

>

> Now, when you switch puzzles in the program, it currently resets the

> puzzle (maybe this should change), so you can't do what I'm describing

> with the UI. But you can edit the integer representing the puzzle

> type in the log file at any point and it would work. Even on the

> simpler puzzles, the internal state representation still contains the

> full 120 colors on all the cells. I intentionally made that the case,

> knowing this meant log files that have solved one of the easier

> puzzles still won't look very pristine.

>

> That's it. I could analyze the benefits further (actually try to

> estimate what the differences in moves required might be), but these

> are my loose thoughts on it so far, and I have the feeling that the

> benefits in time-complexity of solution are definitely worth it.

>

> Roice


























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