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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 5:15 pm 
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schuma wrote:
In the applet I can't find this "Rex dodecahedron", the one on the top right corner in this photo. It's a vertex turning dodecahedron. Did I miss it or is it not there yet? This puzzle is close to mass production and I think it's a good idea to have it in GB. Thanks.
It's not there although it's exactly the same puzzle as 2.1.1 with different stickers and just a combination of 1.2.2 and 1.2.3 without corners.

In general, I think there are a ton of great puzzles that have one curvy cut and one straight cut. Will's Helicopter 3x3x3 is a good example of this (Gelatinbrain added it as 3.5.4).

By mixing curvey cuts with straight (or almost straight cuts) you can get puzzles like Sharon's CopterMinx http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1646. The curvy cuts allow you to eliminate the many small pieces you sometimes get when you have straight cuts.

I sure would like to see more puzzles in the 3.4.X series that have curved and straight cuts.

Though I'm not really in a position to be asking for new puzzles with fewer than half solved :oops: .

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 5:37 pm 
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Katja and Brandon, you are right on that the Rex Dodecahedron is nothing but a sticker mod of 2.1.1. Looking at these two puzzles I feel 2.1.1 is so complicated and the Rex Dodecahedron is much nicer. Now I wish mf8 make that puzzle in an icosahedral shape because FTI means much more.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 5:51 pm 
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schuma wrote:
Katja and Brandon, you are right on that the Rex Dodecahedron is nothing but a sticker mod of 2.1.1. Looking at these two puzzles I feel 2.1.1 is so complicated and the Rex Dodecahedron is much nicer. Now I wish mf8 make that puzzle in an icosahedral shape because FTI means much more.

They have 2.1.3 in the works.

Image

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 23, 2011 6:00 pm 
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schuma wrote:
Katja and Brandon, you are right on that the Rex Dodecahedron is nothing but a sticker mod of 2.1.1. Looking at these two puzzles I feel 2.1.1 is so complicated and the Rex Dodecahedron is much nicer. Now I wish mf8 make that puzzle in an icosahedral shape because FTI means much more.


If everything goes right ("right" from my point of view) mf8 will bring us 2.1.3 which is the same too, except that it has face triangles like 2.1.2 also. Wether 2.1.3 , 2.1.2 or 2.1.1 is visually most appealing is a matter of taste. I can't even really tell.
I guess having always 5 of these triangles the same color like on the rex dodecahedron does make the solve considerably more relaxed than solving an FTI like 2.1.1.
Although as the cut gets deeper or non pillowed, the adding of corners to the dodecahedron is "worse" than having icosahedral tips that need to be orientated. I find.

edit: some of this was just posted by Brandon.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 9:53 am 
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It happened again.
This time it wasn't my fault. All of 1.4.4 solved except for little triangles. In 50 moves less than last time. This time I wake up at 3:30 am by some windows startup sound and wonder what the heck is going on. I thought I had just dreamed it but when I walked to my computer and turned on the screen I figured it had infact just rebooted for some friggin reason I can't explain!
Probalby some unimportant update that just gets applied reboots unless you klick "restart later".
How dare any machine impose such hastle on me? I am supposed to decide if and when it get's restarted, not that it doesn't get restarted by itself. The point of having a message for the user is that he might not be there! Whoever implemented this into windows was out of his mind.
This was the last straw for now.
I won't solve any puzzles for a while because I have got a project to do for uni and leaving the applet running for days apparently doesn't work due to digital animosity of my pc against me.
It probably laughed the whole night even after I then turned it off.

And I couldn't even sleep again for at least 20 minutes because I was so angry.

I won't be out of the forum or this discussion threat though. :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 1:30 pm 
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Dear Gelatin Brain,
My internet cut out right before I finished the solve. Is this why the Certificate came up? Can you enter my score manually?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 2:10 pm 
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Wow, big news. GB is invading 4D by adding two tessaracts, 8.1.1 and 8.1.2. Thanks a lot!

I wish there is going to be macros for them. GB, do you think if it's easy to add macros to them?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 3:49 pm 
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bmenrigh wrote:
Please keep the counter-examples coming, I need more things to think about :lol:

How about this one on the megaminx. I mainly use it to solve the last edges on my tuttminx.

((F',C),A'2,(C',F)),B,((F',C),A2,(C',F)),B',

I think this is
[[ (F',C) : A'2 ], B]

The only oddities about this that I can think of is that F & C are independent of each other and have no overlap. It's almost like you're doing a slice move if that helps you reason your way out of why it doesn't fit your pattern.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 10:36 pm 
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schuma wrote:
Wow, big news. GB is invading 4D by adding two tessaracts, 8.1.1 and 8.1.2. Thanks a lot!
This is amazing. And my 3 months long holiday just started :D They do look freighting without macros, but I'm sure that it's doable (maybe I'll regret saying this when I start solving :P). Schuma, did you solve them yet?
alaskajoe wrote:
It happened again. This time it wasn't my fault.
I've lost a few big solves too. I spent 4 hours on 1.2.7 to then have the applet crash on me. It's really upsetting! I hope you have better luck next time :D


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 10:53 pm 
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Katja wrote:
This is amazing. And my 3 months long holiday just started :D They do look freighting without macros, but I'm sure that it's doable (maybe I'll regret saying this when I start solving :P). Schuma, did you solve them yet?


I haven't solved them here, but I've solved the 8.1.1 (2x2x2x2) using other softwares (MC4D and Magic Puzzle Ultimate(MPUlt)) with macros. I know people solving it without macros so it's proved to be feasible. I've also done a blindfolded solution of it using macros. By BLD I mean memorizing it, switching all the colors to black (colors can be changed in MC4D and MPUlt), then solving it.

About 8.1.2, I haven't solved it in any software. I've solved a shallow cut version of it though.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 11:02 pm 
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Katja wrote:
schuma wrote:
Wow, big news. GB is invading 4D by adding two tessaracts, 8.1.1 and 8.1.2. Thanks a lot!
This is amazing. And my 3 months long holiday just started :D They do look freighting without macros, but I'm sure that it's doable (maybe I'll regret saying this when I start solving :P). Schuma, did you solve them yet?
It is really great to see these puzzles. I'm really not sure what 8.1.2 is. It doesn't really seem like it is cell or vertex or edge turning based on the way the cuts work.

I dunno about everyone else but I normally ignore the white arrows around the puzzles but in the in the 8.1.X series they do 4D rotations which is really useful. I also really like that we can see the hidden cell on the other view pane.

Now, on 8.1.1 a cube (cell) is the equivalent of a "face" on a 3D puzzle. There are 24 ways to turn the cell that seem like they should all be considered "1 move". You can reach all 24 of these moves via the 3 axis of 90-degree twists so the puzzle isn't missing any moves. The issue is that to reach some of the 24 orientations for a single cell you must use more than one move the way the program counts them right now.

As for supporting macros, that would be great considering the shortest routine I have to invert a corner is 106 moves (although I know how to shorten it some, even that is still way too long to do by hand). A notation has to be made first before macros can be done.

I'd suggest naming 12 of the orientations of the cube 1 - 12 and then the other 12 can be '1 - '12. Then the notation would be something like A5, B3, A'5, B'3 to do a [1,1] commutator. The only strange thing that this would cause is that clicking on one axis of a cell might progress with A, A2, A'1, <no move> but another axis of the same cell might progress with A4, A5, A'4, <no move>.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Nov 25, 2011 11:13 pm 
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bmenrigh wrote:
It is really great to see these puzzles. I'm really not sure what 8.1.2 is. It doesn't really seem like it is cell or vertex or edge turning based on the way the cuts work.


Brandon, you have excluded all the incorrect possibilities. In 8.1.2 the axes are passing through the 2D face centers so I'll call it face-turning. It's a deep cut face turning tessaract. I call 8.1.1 cell-turning. People use different terms here. In Andrey's MPUlt, 8.1.1 is called face-turning and 8.1.2 is called ridge-turning (RT). Gelatinbrain apparently grouped both of them under a category called "face turning". 8.1.2 can be found in the most recent version of MPUlt, v1.09, 4D/Cubebased/4D_half_RT. I guess I'll try it first in MPUlt because of its automatic undo-setup feature.

References:

The link of MPUlt:

http://astr73.narod.ru/MPUlt/MPUlt.html

MC4D:

http://www.superliminal.com/cube/cube.htm

4D cubing yahoo group:

http://games.groups.yahoo.com/group/4D_Cubing/

edit: after a closer look at 8.1.2 I found that it may not be equivalent to 4D_half_RT in MPUlt, because the moves in 8.1.2 are limited to 90 deg turns. In 4D_half_FT one is allowed to swap two complete cells affecting some partial cells. This is not allowed in 8.1.2. If one define a "turn" as "take out part of the puzzle, rotate it, and put it back", this swapping move should be allowed.

Currently I don't know if one can use a sequence of 90 deg turns to simulate that move. If so, just like 8.1.1 is equivalent to MC4D (as Brandon explained), the limitation doesn't change the space of states. If not, these two puzzles will be functionally different.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 12:33 am 
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bmenrigh wrote:
I'd suggest naming 12 of the orientations of the cube 1 - 12 and then the other 12 can be '1 - '12. Then the notation would be something like A5, B3, A'5, B'3 to do a [1,1] commutator. The only strange thing that this would cause is that clicking on one axis of a cell might progress with A, A2, A'1, <no move> but another axis of the same cell might progress with A4, A5, A'4, <no move>.


The notation I used in my notes is as follows:

The move by right clicking the face Y of cell (cube) X is represented by XY.

The names of cells are U,D,R,L,F,B, and C (for center or core) and I (for inverted center). The names of faces can be U,R,F. (clicking on D/L/B is nothing but the inverse of clicking U/R/F, so D, L, B are redundent.)

For example, right clicking the front face of the front cell is FF. Left clicking the right face of the left cell is LR'. So if you keep right-clicking on FF, the moves are FF, FF2, FF', <no move>. I found this notation natural.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 12:41 am 
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schuma wrote:
The notation I used in my notes is as follows:

The move by right clicking the face Y of cell (cube) X is represented by XY.

The names of cells are U,D,R,L,F,B, and C (for center or core) and I (for inverted center). The names of faces can be U,R,F. (clicking on D/L/B is nothing but the inverse of clicking U/R/F, so D, L, B are redundent.)

For example, right clicking the front face of the front cell is FF. Left clicking the right face of the left cell is LR'. So if you keep right-clicking on FF, the moves are FF, FF2, FF', <no move>. I found this notation natural.
This is pretty natural but it isn't conducive to collapsing two clicks, one on each axis into one move. For example, the move FF, FU doesn't map into any F{U,D,R,L,F,B} but it would map into some numbering scheme. Maybe I'm in the minority in wanting all 24 cell moves to be counted as one move?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 12:54 am 
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bmenrigh wrote:
This is pretty natural but it isn't conducive to collapsing two clicks, one on each axis into one move. For example, the move FF, FU doesn't map into any F{U,D,R,L,F,B} but it would map into some numbering scheme. Maybe I'm in the minority in wanting all 24 cell moves to be counted as one move?


Yeah, (FF, FU) is like turning the F cell around the BRD corner. I would call it FBRD. Turning around an edge of a cell may be FFR. This variable-length notation is a bit cumbersome and works best only for the 90 deg turns.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 1:45 pm 
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schuma wrote:
bmenrigh wrote:
It is really great to see these puzzles. I'm really not sure what 8.1.2 is. It doesn't really seem like it is cell or vertex or edge turning based on the way the cuts work.


Brandon, you have excluded all the incorrect possibilities. In 8.1.2 the axes are passing through the 2D face centers so I'll call it face-turning. It's a deep cut face turning tessaract. I call 8.1.1 cell-turning. People use different terms here. In Andrey's MPUlt, 8.1.1 is called face-turning and 8.1.2 is called ridge-turning (RT).

In my view, 8.1.1 & 8.1.2 are both deep-cut(2-layer) face-turning puzzles, because they share the same set of axes of rotation.
In the 3D world, for each of three axes, there is only one perpendicular plane that cuts a cube into two equal halves. But this is not the case in the 4D space.
There are infinite number of "hyper-planes" "perpendicular" to any given axis. The double-quoted words are not official terms, and maybe the analogy to 3D is not appropriate here.
Each face center of a unit tesseract can be represented by a vector composed of one "1", two "0"s and one variable.
for example, 3 front faces of the central cell in the picture below are respectively
F0: (z=1 , y=? , x=0 , w=0)
F1: (z=1 , y=0 , x=? , w=0)
F2: (z=1 , y=0 , x=0 , w=?)
Attachment:
temp0.gif
temp0.gif [ 7.37 KiB | Viewed 7466 times ]

Then the planes to cut the tesseract into two equal halves are represented by simple equations:
F0: z = ±a·y
F1: z = ±a·x
F2: z = ±a·w

In 8.1.1, the constant "a" equals 0. And in 8.1.2, it is 1.
If the "a" equals 0.5, the cut of each cell will look like this.
Attachment:
temp1.gif
temp1.gif [ 1.77 KiB | Viewed 7466 times ]


For tne notation of macros, I'm thinking to asign 'A' to 'H' to each of 8 cells.

Image

So tht two sides of each face are represented by a combination of
two characters.
Image

An edge is represented by 3 characters and a vertex by 4.
It's a little cumbersome to type, but I think the basical rule is simple enough.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 3:10 pm 
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Gelatinbrain,

I like your notation. I think it's clear and intuitive. But as for the geometry, I do have a different opinion. It has to do with the locations of F0, F1, F2. Let's use your notation to continue the discussion.

In my understanding, the whole tessaract is the set of points satisfying: x,y,z,w in the interval [-1,1]. Trying to be consistent with your definition of x,y,z,w, let's say cell A is the set of points satisfying z=1, and x,y,w in the interval [-1,1]. The center of cell A has coordinates (z=1,y=0,x=0,w=0). Similarly, cell G is defined as the set of points satisfying y=1, and x,z,w in [-1,1].

Now what is the point F0? I view F0 as the center of the 2D face that is where cells A and G touches. In the illustration cells A and G are not touching each other but it's only for convenience of illustration. In the ideal model A and G touch each other at the face {z=1, y=1, x and w in [-1,1]}. So F0 is (z=1,y=1,x=0,w=0).

The hyperplane that is perpendicular to the line connecting F0 and the origin (0,0,0,0) must be y=-z, with no ambiguity. This type of cuts leads to 8.1.2. Since F0 is the center of a 2D face, I call 8.1.2 "face turning".

I've said that the center of cell A is (z=1,y=0,x=0,w=0). The hyperplane that is perpendicular to the line connecting it and the origin (0,0,0,0) is z=0, with no ambiguity. This type of cuts leads to 8.1.1. And since the center of cell A is the center of a cell, I call 8.1.1 "cell turning".

The above is my understanding of the geometry.

The relation to your understanding:

In your description, the point F0 is (z=1,y=a,x=0,w=0). I've replaced the "?" by the symbol "a". This version of F0 may be anywhere between the center of cell A and the center of the intersection of cells A and G. So it seems like what you call face "AG" and face "GA" are not necessarily touching each other. When a=1 they are touching indeed and that's my view, and the puzzle is 8.1.2. When a=0, the three points F0, F1, and F2 collapse to a single point (z=1,y=0,x=0,w=0); the whole cell A collapses to that point. I call that point the center of cell A and the puzzle is 8.1.1. Since there's no longer any faces on the cell, F0,F1,F2 are no longer "face-center" but "cell-center". So I call it a "cell turning" puzzle.

What do you think of it? Do you buy my terminology?

But buy it or not, the puzzles are working well no matter by what they are called. Thanks.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 6:39 pm 
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schuma wrote:
Now what is the point F0? I view F0 as the center of the 2D face that is where cells A and G touches. In the illustration cells A and G are not touching each other but it's only for convenience of illustration. In the ideal model A and G touch each other at the face {z=1, y=1, x and w in [-1,1]}. So F0 is (z=1,y=1,x=0,w=0).


I buy your definition. It's much clearer.
You are right. the coordinate of Center of face F0 is (1,1,0,0).
I meant by my notation (z=1 , y=? , x=0 , w=0), the axis that passes through (1,1,0,0) and (0,0,0,0).
But if 'y' varies independent of 'z', the line is no longer straight or we cannot call two lines the same.
So my following description is clearly wrong.
There are infinite number of "hyper-planes" "perpendicular" to any given axis.
:oops: :oops: :oops: :oops: :oops:
Altough the defenition of perpendicularity in 4D space is not yet clear for me.


On another note:
Boublez, can you PM me the text of your certificate rather than the screenshort?
The letters are too small to read.
Thanks.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Nov 26, 2011 8:04 pm 
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gelatinbrain wrote:
I buy your definition. It's much clearer.


Thank you Gelatinbrain.

I just solved the 8.1.2 puzzle, not using GB, but MPUlt, because the latter one has macros. Now I'm pretty sure that the limitation to only 90 deg turns doesn't make the space of states any smaller, because using 90 deg turns one can do arbitrary 3 cycles and thus is definitely able to simulate the swapping move. But since the simulation is not straightforward, constructing algorithms in Gelatinbrain appears to be a little bit different from doing it in MPUlt.

edit: I also solved 8.1.1 in GB, without macros. It's actually not that hard... Only 263 moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 27, 2011 10:24 pm 
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schuma wrote:
I just solved the 8.1.2 puzzle, not using GB, but MPUlt, because the latter one has macros.
Nice going, schuma! Can you tell us anything about the difficulty of the solve?
schuma wrote:
I also solved 8.1.1 in GB, without macros. It's actually not that hard... Only 263 moves.
I was absolutely not expecting a low move count on that puzzle. I think I have to give it a try soon.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 27, 2011 10:42 pm 
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Katja,

8.1.1 has only 16 pieces after all. According to MC4D hall of fame <http://www.superliminal.com/cube/halloffame.htm> the shortest solution has only 59 moves by Remigiusz Durka. As Brandon said, the method of move counting is a little bit different there.

I think 8.1.2 is quite hard. My method is not efficient at all. But the move count is like 30000. The only pure 3-cycle I can construct now is about 200 moves long.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 27, 2011 10:51 pm 
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schuma wrote:
I also solved 8.1.1 in GB, without macros. It's actually not that hard... Only 263 moves.
I should be possible to place at least 4 of the 16 pieces with intuition. After that, the best commutator I have is a [[1,1],[1:1]] == [4,3] == [6,1] == 14 moves. Unfortunately one of the 1-move portions of the [1,1] is the twist of a cell around a corner which is counted as 2 moves by Gelatinbrain's program so the routine is actually 18 moves.

To twirl two corners about one of their corners (120 degree rotation) the best I have is also [[1,1],[1:1]]] but one of the 1-moves in the [1:1] is again, a cell twist about a corner so the whole thing gets counted as 20 moves.

To invert a corner, well, I only know how to build that off of my corner twirl routine so it would be [14,3] but it would be counted as [20,5] == 50 moves.

263 moves seems rather good considering the length of these routines. I'm not sure I'm up to the task without macros.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Nov 27, 2011 11:45 pm 
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bmenrigh wrote:
I should be possible to place at least 4 of the 16 pieces with intuition. After that, the best commutator I have is a [[1,1],[1:1]] == [4,3] == [6,1] == 14 moves. Unfortunately one of the 1-move portions of the [1,1] is the twist of a cell around a corner which is counted as 2 moves by Gelatinbrain's program so the routine is actually 18 moves.

To twirl two corners about one of their corners (120 degree rotation) the best I have is also [[1,1],[1:1]]] but one of the 1-moves in the [1:1] is again, a cell twist about a corner so the whole thing gets counted as 20 moves.


Your algorithms are shorter than mine. I'm curious about this: if you apply these algorithms to 3^4 but not 2^4, are they clean 3-cycles of the 4C pieces?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 28, 2011 12:07 am 
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schuma wrote:
Your algorithms are shorter than mine. I'm curious about this: if you apply these algorithms to 3^4 but not 2^4, are they clean 3-cycles of the 4C pieces?

Yup, totally pure on a 3^4 too.

I find MC4D great because I can do the vertex-twists of cells in a single click without much thought and I find Gelatinbrain's implementation great because I can see the 8th cell. I find myself switching back and forth.


Edit: Gelatinbrain added notation and macro support to 8.1.X :D Thank you so much, I'll solve it when I'm not so tired!

Here is my 3-cycle [AE', AG', CA, AG, AE, CA', FE, HB', FE', CA, AE', AG', CA', AG, AE, FE, HB, FE'].

Note the AE' AG' just simulate a vertex twist of the A cell.

If we break it up a little bit:

X == [(AE', AG'), CA, (AG, AE), CA'] == [4,1]
Y == [FE, HB', FE'] == [1:1]

By replacing the HB' in Y with with a vertex twist in H instead of a face twist in H you can twirl two corners.

I invert a single corner by building off of the twirl routine. There is a technique I discovered on 3.11.1 to twist a single corner sphere that involved a conjugate of X, Y, X' where the Y was a re-orientation of the puzzle and not an actual move. I suspect the same is possible on 8.1.1 and that would make inverting a corner much more efficient.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 28, 2011 3:26 pm 
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bmenrigh wrote:
I find MC4D great because I can do the vertex-twists of cells in a single click without much thought and I find Gelatinbrain's implementation great because I can see the 8th cell. I find myself switching back and forth.

Concurrence is always good for users, isn't it? :lol:

Two vertex turn sequences, for example [AE',AG'] and [AG',AE'] don't always lead to the same result. It's true with 8.1.1 and the MC4D hypercubes, but not with 8.1.2, neither with some special case of what schuma calls cell-turn puzzles. For example,4D version of the circle cube. That complicates the vertex-turn support.
Another reason why I don't support the vertex turn is I want to reserve the vertex notations for real vertex-turn hypercubes.
I'm not sure yet, but the deepcut vertex-turn tesseract will be composed of cells looking like the helicopter cube.
The shallow-cut ones may have 64 axes of rotation. Even if the tesseract has only 16 vertices, each 4d-vertex has tetrahedral symmetry, hence 16x4 hyperplanes to cut.
Imagine the complexity... :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 28, 2011 11:07 pm 
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I just solved 8.1.1 and in general, I really like the interface and notation. Now that I have solved it, I don't mind so much that cells are restricted to 90 degree twists. It had almost no impact on my move count and I wound up with a 478 move solve :oops: .

I thought I could solve 8 of the corners in a single cell via intuition rather easily but that required too much thought so I solved 3 and then cycled the rest. I don't have a lot of 4D intuition so I need more practice to be able to place 8 corners.

Gelatinbrain, do you think your puzzle engine will be able to support polytopes like the 6-cell or 24-cell?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 28, 2011 11:43 pm 
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bmenrigh wrote:
I thought I could solve 8 of the corners in a single cell via intuition rather easily but that required too much thought so I solved 3 and then cycled the rest. I don't have a lot of 4D intuition so I need more practice to be able to place 8 corners.


I solve the first 8 pieces as follows: First gather eight yellow (or your other fav color) stickers in a cell, using intuition. Then put the cell at the center, solve it like a 2x2x2, where FH=R, GH=U, EH=F, etc. This step affects the other unsolved 8 pieces. Since the algorithms for 3D cube have been optimized through years, they are quite efficient. At the end of this step one piece may need to be turned by 120 deg. In this case just leave it and later rotate it together with one of the other pieces.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Nov 28, 2011 11:46 pm 
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schuma wrote:
I solve the first 8 pieces as follows: First gather eight yellow (or your other fav color) stickers in a cell, using intuition. Then put the cell at the center, solve it like a 2x2x2, where FH=R, GH=U, EH=F, etc. This step affects the other unsolved 8 pieces. Since the algorithms for 3D cube have been optimized through years, they are quite efficient. At the end of this step one piece may need to be turned by 120 deg. In this case just leave it and later rotate it together with one of the other pieces.

Dang I should have thought of this too as I have experimented with this technique for solving the first half of the 3^4. I don't feel so bad about my move count now, my technique was much worse. Thanks for keeping me on my toes!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 29, 2011 1:17 am 
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Bug report: In 8.1.1 and 8.1.2, notations HD and HC are inconsistent with the name of the cells. They should be swapped. Thanks.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Nov 29, 2011 2:01 am 
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Hi Gelatinbrain,

I just solved 8.1.2. But the solved state is not recognized. Could you please add it to the record manually?

Please find attached the screenshot, showing the solved state. It took me 00:37:25, and 33854 steps. Almost all of them are macro moves. Thanks.


Attachments:
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Screenshot002.png [ 71.81 KiB | Viewed 7219 times ]

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Nov 30, 2011 2:28 am 
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Gelatinbrain, when I PM'd you my certificate for 1.1.14 I must have made a mistake typing it or something because the solve has still not apeared on the board and my 1.1.27 solve has. Here's the screen shot, I hope that helps as I'd rather not solve it again. Sorry for the inconvenience and thanks in advance.
Attachment:
Skjermbilde 2011-11-28 kl. 17.46.30.png
Skjermbilde 2011-11-28 kl. 17.46.30.png [ 84.17 KiB | Viewed 7115 times ]


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 06, 2011 1:11 pm 
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With the Help of Bmenrigh, I have been learning the basics of puzzle solving. He has taught me commutators, conjugates, and other solving techniques. For a few weeks all I was really interested in was finding out algorithms for puzzles, but Brandon and Katjas constant nagging :wink: finally made me see if I could apply what I had been learned.

3.4.1 (the skewb plus 2x2x2) was a puzzle that had always been interested in, and it seemed like a really great place for me to start. After finding the algorithms I needed, I went and completed my first solve (355 moves) I first solved the corners, then the centers) I was happy i solved my first puzzle on gelatinbrain, but I was not 100% satisfied.

I went on to use the same method (corners followed by centers) to get solves of 188 and 160 moves. I still wanted a bit more. After consulting Brandon again, he explained how to use the algorithms I had in a more efficient way and apply them to a reduction solve.

My first reduction solve was 95 moves, which broke Brandons record(100)! I then tried a few more solves and ended up with 95 again followed by a 93. I'll break down the method I used to solve here:

-Check for corner twist problem in the 2x2 (hopefully there IS one)
-undo all moves
-fix the corner twist on one of the four axis' in the way which is most advantageous (1 move)
-at this point I had 7 centers placed correctly
-reduce the puzzle into a 2x2 (68 moves, 69 total)
-solve the 2x2 (24 moves, 93 total)

93 moves for this puzzle is good, but I (along with Brandon) think a solve could be somewhere around 75 moves total. My 2x2 solve was 24 moves, which is pretty terrible (i just don't know how to solve them better). A great 2x2 solve should be something like 12-14 moves. Additionally, I was not very strict with the reduction conjugates I ran. Sometimes I only placed 2 pieces at a time. If I had devoted more time to the solve I'm guessing I can remove a full 3 cycle. with set-ups, that's about 10 moves. Doing the reduction better, along with an improved 2x2 solve, should yield a solve that's roughly 20 moves less.

I'm hoping someone goes out there and does it!


P.S. does anyone know of a good guide on how to solve a 2x2 with a low move count?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 07, 2011 4:43 pm 
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Hi gingervergo. Congratulations to your 93 moves on 3.4.1.
You can check the twist of the 3.4.1 corners easily without doing one move by means of their up/down color. (in the picture: white/yellow)
Attachment:
3_4_1.PNG
3_4_1.PNG [ 43.1 KiB | Viewed 6890 times ]
Today I solved it and I used Katja's move-sequence for the X-faces. It can be shortened from a [5,1] to a [1:5] which is 5 moves lesser when reducing to a 2x2x2. I had a fortunate solve with 98 moves and 03:45 time. But I guess, your 93 moves is nearly optimal.

I like your puzzles at shapeways. I have a question, what means "break in" for a puzzle?
Stefan.
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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 07, 2011 5:05 pm 
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Stefan Schwalbe wrote:
Hi gingervergo. Congratulations to your 93 moves on 3.4.1. [,,,] But I guess, your 93 moves is nearly optimal.
I just did it in 67 moves 8-)

1) Count the corner twist
2) Free-form reduce to a 2x2x2 keeping track of how you are changing the twist of the puzzle
3) When it starts to get too hard to free-form it, get the twist back to zero the best you can and then switch to a [1:5] conjugate
4) Solve 2x2x2

I reduced the puzzle in 50 moves and did a 17-move 2x2x2 solve.

Stefan, congrats on overtaking me, and Julian (and Michael soon I'm sure) in fewest move records! You truly are a great solver. You should try out the 3.4.X series, it isn't fair that I have all those records :lol:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 07, 2011 5:40 pm 
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Hi Brandon, today I noticed your 3.4.* rankings. You made the 1st place in so many fewest moves rankings. Did you using shorter move sequences or/and are your stratgies better? Congratulations for that. :D Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 07, 2011 5:43 pm 
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Stefan Schwalbe wrote:
I like your puzzles at shapeways. I have a question, what means "break in" for a puzzle?
Stefan.
BTW Agamemnon is me.


Breaking in a puzzle just means using it until it's worn out just a little (maybe a handfull solves) so it's not as stiff anymore. Of course you don't want to use any lubrication for this yet. Only after it's done.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 07, 2011 5:47 pm 
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bmenrigh wrote:
You should try out the 3.4.X series, it isn't fair that I have all those records :lol:
:lol: But I feel, you deserve those records all. :D Stefan.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 07, 2011 6:02 pm 
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Stefan Schwalbe wrote:
Hi Brandon, today I noticed your 3.4.* rankings. You made the 1st place in so many fewest moves rankings. Did you using shorter move sequences or/and are your stratgies better? Congratulations for that. :D Stefan.
I worked VERY HARD on the 3.4.X series, often spending more time searching for routines on the puzzle than actually solving it.

I solved every puzzle from 3.4.1 to 3.4.21 using either reduction to a 2x2x2 or to a 3x3x3. I think most other solvers were not using reduction which made most of the records quite easy to claim.

For all of the puzzles that have the equivalent of 3x3x3 centers (3.4.6, 3.4.7, 3.4.8, 3.4.11, etc.) I first got the centers into the correct color scheme, then I fixed the overall corner twist, and then I went about reducing the puzzle while maintaining the position of the centers and maintaining the overall twist of the corners. The only puzzle that has a parity you can't predict and avoid or fix easily is 3.4.5 (the 3x3x3 centers can be in odd permutations).

I did not work very hard to be efficient during the reduction phase or the 3x3x3 solving phase and instead just relied on short routines and a more efficient method. Equipped with the exact same routines most people would beat my move-counts just because I wasn't very careful.

Also, I used conjugates rather than commutators as much as possible. I tried to find routines that were all face-moves for X, and a vertex move for Y. As you pointed out on 3.4.1, this allows you to truncate the commutator to a Y X Y' conjugate, often saving a lot of moves.

My best two records of the series are 3.4.17 and 3.4.20. I spent about 3 hours searching for how to do those puzzles more efficiently. The pieces that make up the 3x3x3 edges are really hard to do efficiently.

I saved all of my routines so if you have questions about specific puzzles I'd be happy to share my thoughts and ideas on the puzzle.

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Last edited by Brandon Enright on Thu Dec 08, 2011 2:58 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 08, 2011 12:41 am 
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gingervergo wrote:
93 moves for this puzzle is good, but I (along with Brandon) think a solve could be somewhere around 75 moves total.
Once again, you really have the potential to become a great solver and I'm sure all of us here in the solving thread would love for you to stick around :D
Stefan Schwalbe wrote:
I had a fortunate solve with 98 moves and 03:45 time.
Congratulations on your fast solve, Stefan! My 5 minute solve was done corners then x-centers, and I actually recorded the solve. If I want to beat your time (and I do :P) I think I have to use reduction as well.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 09, 2011 3:47 pm 
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Katja wrote:
If I want to beat your time (and I do ) I think I have to use reduction as well.
Good luck, Stefan. 8-)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 10, 2011 6:43 am 
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I need help finding 8.1. puzzles. Where are they I don't see them.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 10, 2011 6:53 am 
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Darren Grewe wrote:
I need help finding 8.1. puzzles. Where are they I don't see them.
You can access them through the "File" menu, in the top left corner. Then see under "new puzzles" or "tesseract".


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 11, 2011 5:29 pm 
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Well I finally have GelatinBrain. Took me forever, but I finally have it. I have never been able to access it on any computer I have used, my school computer, my old computer, my personal computer, my friends, etc. I have re-installed java, changed security, all sorts of things. I still can't get it to work online. I finally just installed it.

Anyway I chose The helicopter dodecahedron as my first puzzle. I have made it this far on intuition. just need to figure out how to orient the corners. I am so happy I finally have this program.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 11, 2011 5:43 pm 
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Muffet wrote:
Well I finally have GelatinBrain. Took me forever, but I finally have it. I have never been able to access it on any computer I have used, my school computer, my old computer, my personal computer, my friends, etc. I have re-installed java, changed security, all sorts of things. I still can't get it to work online. I finally just installed it.
Yeah, installing it is the way to go. The Java <-> Browser interaction is terrible.

Muffet wrote:
Anyway I chose The helicopter dodecahedron as my first puzzle. I have made it this far on intuition. just need to figure out how to orient the corners. I am so happy I finally have this program.

Looking good.

If you get stuck on the corners, here are a few hints in hard-to-read font:

"""The trick to orienting pieces on most puzzles is to find a way to isolate a piece, then take it out of place and put it back in with a different orientation. Then you undo your isolating routine, then you undo your orientation changing.

For example, you can isolate a corner with [BC, BH, BC]
And then you can change the orientation with [AB, AF, FE, JF, FI, BF, BA]
And then undo the isolation: [BC, BH, BC] and then undo the orientation [BA, BF, FI, JF, FE, AF, BA]
"""

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 11, 2011 5:46 pm 
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I have written a simple script to help pretty-print Gelatinbrain's macro move-sequences as well as invert and mirror routines. You can see it here: http://www.brandonenright.net/cgi-bin/gb_util.pl

Eventually it will be able to deconstruct your routine if it follows "standard form" and tell you what the form is. In the future it may also support []xN notation such as [A, B, A', B']x3.

If the program needs more features let me know.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 11, 2011 5:55 pm 
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That is great Brandon! If I ever get to solving again this will be VERY useful!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 11, 2011 6:43 pm 
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bmenrigh wrote:
I have written a simple script to help pretty-print Gelatinbrain's macro move-sequences as well as invert and mirror routines. You can see it here: http://www.brandonenright.net/cgi-bin/gb_util.pl

Eventually it will be able to deconstruct your routine if it follows "standard form" and tell you what the form is. In the future it may also support []xN notation such as [A, B, A', B']x3.

If the program needs more features let me know.


Thank you very much! I've been doing this manually for years! This thing is very useful!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 11, 2011 9:28 pm 
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I notice that if you click a middle layer on 3.1.2 (3x3x3), the applet freezes. I don't know if the same bug exists for other puzzles or not.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 12, 2011 4:06 pm 
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schuma wrote:
I notice that if you click a middle layer on 3.1.2 (3x3x3), the applet freezes. I don't know if the same bug exists for other puzzles or not.

I was so sure I had done that before. But I just checked and really surprised noticed that you are right. It's really not just you.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 12, 2011 6:17 pm 
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bmenrigh wrote:
I have written a simple script to help pretty-print Gelatinbrain's macro move-sequences as well as invert and mirror routines. You can see it here: http://www.brandonenright.net/cgi-bin/gb_util.pl

Eventually it will be able to deconstruct your routine if it follows "standard form" and tell you what the form is. In the future it may also support []xN notation such as [A, B, A', B']x3.

If the program needs more features let me know.


Hi Brandon, I have a few selfish requests about this app. I wonder if you can make these:

(1) It would be great if you can add a comma at the end of each output sequence, like "[R, U, R', U']," rather than "[R, U, R', U']". For a single sequence it doesn't matter if this comma exists or not. But when you cascade several sequences together, you need to add these commas (except for the last one), otherwise the applet doesn't do anything. For this reason in my notes I always end a sequence with a comma.

(2) The current mirror function for cube is left<->right. The plane of symmetry is passing the centers of F, U, B, D. This is very natural and useful. But, can you add another kind of mirror with respect to the viewpoint in GB, where the plane of symmetry is passing through the FR and BL edges, namely, front<->right, back<->left? Sometimes I find this kind of mirroring more direct. Also, for the octahedral puzzles, this kind of mirroring is more intuitive. I think it's good to keep these two kinds of mirroring.

(3) Can you add a button to clear the input box?

Thanks a lot.

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