Thread: "Mistake in Logic of Computation"

From: "David Smith" <djs314djs314@yahoo.com>
Date: Fri, 09 May 2008 07:40:45 -0000
Subject: Mistake in Logic of Computation



Hi everyone,

I just realized that I made an error in reasoning in my
proof of the number of permutations of Magic120Cell.
My proof by induction was completely wrong. The result
though, was correct, so the error was only one of logic.

I am sending an email to Roice with the correction,
so can update the link on his website to my writeup.
I will try not to make such errors in the future!

All the best,
David




From: "Roice Nelson" <roice3@gmail.com>
Date: Fri, 9 May 2008 09:44:09 -0500
Subject: Mistake in Logic of Computation



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Hi,

Thank you, I am glad you are liking it. Melinda had suggested doing a piece
finder where clicking on a sticker makes the program find and highlight
which sticker should ultimately go there (this would be an inverse function
to the current ctrl+shift+click capability that highlights where a clicked
sticker should go). This will be easy and I plan to do it (I'll probably
get another version out in the next week or two with that and some other
nice suggestions Melinda made). The new piece finder could highlight single
stickers or all the stickers of a piece, and I'm leaning towards the second
possibility. I think Melinda's suggestion will be a better functionality
for this puzzle than doing an MC5D-like piece finder because the latter
requires the user deal with all the face colors.

Thanks for the suggestion of numbering/patterns on stickers. I agree that
would be nice, but it will be more involved to program. So even though I
would like this too, I'm going to have to add it to the long term wish list
for now (it's going to take some investigation on my part to figure out a
good way to do it - I think the solution may likely involve texture
mapping). Hopefully the extended piece finding will be enough for the short
term. Thanks again for the feedback!

Roice

P.S. There were some ugly rendering issues I noticed since the first upload,
which are fixed. If any of you are playing with this and seeing them, you
might want to grab the latest.



On Wed, May 7, 2008 at 9:19 PM, corkle0 wrote:

> Hello Roice,
>
> I really think this is an amazing program and I will definitely
> attempt to solve it, but for me, looking at 120 different colors is
> just too confusing, so I thought it might be easier if each color had
> a number or some type of distinguishing pattern it so there wouldn't
> be so much confusion between the colors. Also, on the MagicCube5D, I
> really liked the piece finder, and I think it would make the 120 Cell
> much easier if there were a piece finder in it. Just a couple
> suggestions, but great job creating such an awesome puzzle!
>
>
> Visit Your Group
>
> All-Bran
>
> Day 10 Club
>
> on Yahoo! Groups
>
> Feel better with fiber.
> Healthy Living
>
> Learn to live life
>
> to the fullest
>
> on Yahoo! Groups.
> Best of Y! Groups
>
> Check it out
>
> and nominate your
>
> group to be featured.
> .
>
>
>

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Hi,
 
Thank you, I am glad you are liking it.  Melinda had suggested doing a piece finder where clicking on a sticker makes the program find and highlight which sticker should ultimately go there (this would be an inverse function to the current ctrl+shift+click capability that highlights where a clicked sticker should go).  This will be easy and I plan to do it (I'll probably get another version out in the next week or two with that and some other nice suggestions Melinda made).  The new piece finder could highlight single stickers or all the stickers of a piece, and I'm leaning towards the second possibility.  I think Melinda's suggestion will be a better functionality for this puzzle than doing an MC5D-like piece finder because the latter requires the user deal with all the face colors.

 
Thanks for the suggestion of numbering/patterns on stickers.  I agree that would be nice, but it will be more involved to program.  So even though I would like this too, I'm going to have to add it to the long term wish list for now (it's going to take some investigation on my part to figure out a good way to do it - I think the solution may likely involve texture mapping).  Hopefully the extended piece finding will be enough for the short term.  Thanks again for the feedback!

 
Roice
 
P.S. There were some ugly rendering issues I noticed since the first upload, which are fixed.  If any of you are playing with this and seeing them, you might want to grab the latest.



 

On Wed, May 7, 2008 at 9:19 PM, corkle0 <corkle0@yahoo.com> wrote:






Hello Roice,

I really think this is an amazing program and I will definitely
attempt to solve it, but for me, looking at 120 different colors is
just too confusing, so I thought it might be easier if each color had

a number or some type of distinguishing pattern it so there wouldn't
be so much confusion between the colors. Also, on the MagicCube5D, I
really liked the piece finder, and I think it would make the 120 Cell

much easier if there were a piece finder in it. Just a couple
suggestions, but great job creating such an awesome puzzle!




 








All-Bran

Day 10 Club



on Yahoo! Groups


Feel better with fiber.



Healthy Living

Learn to live life



to the fullest


on Yahoo! Groups.




Best of Y! Groups

Check it out



and nominate your


group to be featured.


.




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From: "spel_werdz_rite" <spel_werdz_rite@yahoo.com>
Date: Sat, 10 May 2008 15:02:34 -0000
Subject: Re: Mistake in Logic of Computation



Heh. You scared me for a minute there. I was going to feel like an
idiot for agreeing with you on the number and it turning out to be wrong.




From: "spel_werdz_rite" <spel_werdz_rite@yahoo.com>
Date: Mon, 12 May 2008 05:00:39 +0000 (GMT)
Subject: Re: Mistake in Logic of Computation



ont: inherit;'>

I know what you mean, Jay, about the dodecahedron not bei=
ng an 'immediately obvious' Platonic solid. (I think that is what you were =
getting at?) I had felt the same myself when I first came across them.=
Maybe this suprise arises as the triangle and square can tile an infinite =
2-D plane, wheras the pentagon can not. Strange, then, that the Pentagon CA=
N 'tile' a 3-D solid quite happily!


 


I fear the dual of the dodecahedron is in fact the icosohedron;&nbs=
p;while the cube and octahedron are similarly dual to each other. The tetra=
hedron IS its own dual however: possibly this is where your recollection ca=
me from?




--- On Sat, 10/5/08, Jay Berkenbilt <ejb@ql.org>=
wrote:


16,16,255) 2px solid">From: Jay Berkenbilt <ejb@ql.org>
Subject: R=
e: [MC4D] Magic120Cell Realized
To: 4D_Cubing@yahoogroups.com
Date: S=
aturday, 10 May, 2008, 3:57 PM





I have to add my voice to the rest in expression of awe at this
p=
uzzle. It's been years since I've even done mc4d -- my life has
gotten b=
usier. One day maybe I'll try it, and I'm sure I'll
eventually play arou=
nd with it just to see what it feels like. As
with many of the other par=
ticipants on this list, I have always had a
special affinity for the 120=
-cell. It always seemed to me that it
sort of snuck in to the regular po=
lyhedron list, just barely fitting,
kind of like the pentagon just barel=
y being able to be the face shape
of one of the platonic solids. :-) Do =
I recall correctly that this
polyhedron is its own dual?

> Hon=
estly, the reason I wasn't planning on working through a solution
> w=
as that I am a bit scared of the sheer number of pieces! I just
> fin=
ished up the final parts that I felt were needed for it to be
> solva=
ble today, and I actually haven't even figured out a single
>
sequence yet. So as of this evening, I only have the thoughts about
>=
; it we've discussed in the past, which is that it will be easier in
>=
; some ways than MC4D because of the larger space to sequester pieces,
&=
gt; but that it will be a big effort in time. Also, I think I am ready
&=
gt; for a bit of a rest and was too excited to share to let it sit on a
=
> shelf. Sarah will be happy to get my attention back now too since
&=
gt; I've been spending a lot of time on it lately :)

My recollection=
of solving the megaminx is that you can do all but the
last few steps a=
s localized solutions. Each twist affects such a
small number of pieces =
that the constraints don't play a big role
until the end. It seems that =
each twist would necessarily alter
pieces on the 12 adjacent cells.
<=
BR>I don't find it surprising that five random twists would result in
so=
me interacting pieces. The first twist affects pieces on 12 of
the
120 cells, not including the cell twisted. In order for the second<=
BR>twist to not interact with any pieces, it must be on a cell that is
n=
either any of the 12 affected faces nor adjacent to any of them
(except =
that it could be another twist of the first face). I'm not
sure how many=
cells that is. If you managed to get one, there are
even fewer places f=
or the third twist. It seems to me that the number
of twists after which=
there is some guaranteed interaction must be
very small....maybe three =
or four? I could probably work it out, but
I imagine others on this list=
could do it faster. My "math chops" may
be good compared to the general=
population, but not compared to many
of the readers of this list. :-)R>
Anyway, the 120 cell puzzle is a work of beauty!

--Jay

=







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