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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Aug 28, 2011 12:24 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Katja wrote:
Hey guys,

The parity in this photo is the only parity that I could never understand and therefore never find a solution to. Normally I'd just scramble the puzzle and try again, but I'm getting pretty sick of doing that for every puzzle this occurs in. For the normal 4x4x4, I can solve the two other parities; the one where two edges need switching and when two edge pairs need switching (in the final stage of the last layer). But I just cannot solve this parity. I do understand why I get the parity, but I still can't use that knowledge to actually solve it. Does anyone know how to fix this and maybe also explain the logic behind how the fix was found?
Attachment:
Skjermbilde 2011-08-28 kl. 19.41.00.png
EDIT: The puzzle is 3.1.21, but discard the fact that this is a circle puzzle. This just happened to be the latest puzzle I encountered the parity on, and I didn't want to start solving a standard 4x4x4 just to get a screenshot. I'm asking about the parity in general, not in relations to the puzzle in this photo.

Hi Katja, hopefully I can give you a satisfactory answer.

First, as I think you're aware, a 3-cycle is an even permutation whereas a 4-cycle is an odd permutation. The reasoning for this is that if the only operation you could do is swap two pieces, then to make a 3-cycle you'd have to use 2 swaps and to make a 4-cycle you'd have to use 3 swaps. 2 swaps is an even number of swaps, 3 swaps is an odd number. Because of this, if you are using 3-cycles only which do an even number of swaps, if the puzzle needs an odd number of swaps you'll run into a parity where only 1 swap is needed at the end.

So, given the above, lets talk about a regular 4x4x4 and the parity case where you have two edges swapped across from each other. Since they are in the same slice you can do a quarter-turn of that slice which does a 4-cyle of the edges and breaks the centers of the puzzle. Since the centers have indistinguishable pieces you can re-solve them.

Here is an annotated sequence that does just that:

/* Do a slice move to break 4 edges (4-cycle) */
R'&2,
/* Do a setup + [1,[1:1]] 3-cycle to fix two broken edges */
F', [R&2, [D', R', D], R'&2, [D', R, D]], F,
/* Do several 3-cycles of the center pieces to fix centers */
[B, D&2, B'&2, F&2, D'&2, B'2, D&2, B&2, F'&2, D'2&2, B'&2, F&2, D&2, B'2, D'&2, B&2, F'&2, D&2, B', U, B'&2, U'&2, D&2, B&2, U'2, B'&2, U&2, D'&2, B&2, U'2, R, L, U'2, L', R', U, R, L, U'2, L', R']

I have annotated it as though it is creating the parity case rather than fixing it.

If you understand this then note that with two setup moves you can swap to edges that are next to each other rather than across from each other:

/* Setup moves to move edges next to each other to across from each other */
R'2&4, B'2,
/* Parity fix from above */
[R'&2, F', R&2, D', R', D, R'&2, D', R, D, F, B, D&2, B'&2, F&2, D'&2, B'2, D&2, B&2, F'&2, D'2&2, B'&2, F&2, D&2, B'2, D'&2, B&2, F'&2, D&2, B', U, B'&2, U'&2, D&2, B&2, U'2, B'&2, U&2, D'&2, B&2, U'2, R, L, U'2, L', R', U, R, L, U'2, L', R'],
/* Undo setup moves */
B'2, R'2&4

So as you can see, the parity case where two edges are swapped and the parity case where and edge group appears flipped are really the same parity case, just two different views of it.

Now, the screenshot you have adds an additional twist to the issue. On GB 3.1.9 (the Crazy 4x4x4 I) the edge parity cases are impossible once you have solved the inner 2x2x2. The reason is that the face moves of the inner 2x2x2 are the slice moves of the 4x4x4. If you have solved the 2x2x2 then it is in an even permutation which means the slices moves must be in an even permutation. If you were to use the parity fix on 3.1.9 t would cause a quarter-turn in one of the faces of the 2x2x2. The parity of the edges is connected to the parity of the 2x2x2. If you solve the 2x2x2 you won't get a parity in the 4x4x4 edges.

Now, since the screenshot you provided was for 3.1.21 things get extra complicated. The circle pieces of 3.1.21 are edges of an inner 3x3x3 and by the same reasoning, if you do the parity fix above you will put a quarter-turn in that 3x3x3. But, unlike the 2x2x2 corners, the 3x3x3 edges can be in a odd permutation because you can't see the centers or corners of the 3x3x3 so all the parity restrictions on the edges are lifted. It is possible to resolve the parity in the 3x3x3 edges without affecting the outer 4x4x4 edges.

_________________
Prior to using my real name I posted under the account named bmenrigh.

Last edited by Brandon Enright on Tue Feb 28, 2012 7:22 pm, edited 2 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Aug 28, 2011 2:45 pm

Joined: Mon Jul 21, 2008 4:52 am
Location: Brighton, UK
Katja wrote:
Does anyone know how to fix this and maybe also explain the logic behind how the fix was found?
The one I used to use for the 4x4x4 was (r U2)*4 r. Like quite a few people (I'm guessing), I tried the repeating sequence to see if it led to anything interesting, then after the 9th move I noticed that the centers looked okay and there was a 4-cycle of edges: an odd permutation. Doing setups and two regular 3-cycles after that, it took me 33 moves in all to fix the situation shown in your screenshot, where the Fu and Uf cubies are swapped.

I found a quicker fix online a few years ago. I don't know who found it originally, but here is a possible way it might have developed...

We have a [3,3] commutator to cycle 3 edge cubies on the U face of a 4x4x4, based on tweaking the (U2 M U M U M) (U2 M' U M' U M') edge flip algo for the 3x3x3:

[U2 l U2, r' U2 r], or in full: (U2 l U2 r' U2 r) (U2 l' U2 r' U2 r).

In Gelatinbrain notation this is: U'2,L&2,U'2,R'&2,U'2,R&2,U'2,L'&2,U'2,R'&2,U'2,R&2

Now, to get an odd permutation we need to avoid the symmetry of this algo, with its even number of 90 degree slice moves. How about we start off with this algo but in the 2nd half, when the first slice move comes along, we make a face move instead?

(U2 l U2 r' U2 r) U2 F2

Let's try to fix the centers in a small number of moves:

(U2 l U2 r' U2 r) U2 F2 r F2 l'

In Gelatinbrain notation: U'2,L&2,U'2,R'&2,U'2,R&2,U'2,F'2,R&2,F'2,L'&2

Apart from a pair of center pieces on the F and B face swapping places, that would be perfect, as just 2 edge pieces have swapped places. Now can we find some setups so that the swap of the center pieces becomes invisible? Yes, we can -- added in red below:

(r2 B2) (U2 l U2 r' U2 r) (U2 F2 r F2 l') (B2 r2)

In Gelatinbrain notation: R2&2,B2,U'2,L&2,U'2,R'&2,U'2,R&2,U'2,F'2,R&2,F'2,L'&2,B2,R2&2

So now we have a parity fix of 15 moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Aug 28, 2011 4:08 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
bmenrigh wrote:
Katja wrote:
Hey guys,

The parity in this photo is the only parity that I could never understand...

Hi Katja, ...Now, the screenshot you have adds an additional twist to the issue. On GB 3.1.9 (the Crazy 4x4x4 II)
3.1.9 is Crazy 4x4x4 Type I, right? I had been confused by the screenshot, because I had never seen 3.1.21 (it is not on the Internet index page, as far as I can see) and I assumed at the first glance that the screenshot is Crazy 444 Type I and there
bmenrigh wrote:
the edge parity cases are impossible once you have solved the inner 2x2x2.
bmenrigh wrote:
...Now, since the screenshot you provided was for 3.1.21 things get extra complicated. The circle pieces of 3.1.21 are edges of an inner 3x3x3
As I cannot play with 3.1.21, this is hard to understand for me. As I see 24 circle pieces, I need to see 12 pairs building the edges of the 3x3x3. I know the Crazy Type I, II,III, only.
I'm tired now and hope to understand it tomorrow.

_________________

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Aug 28, 2011 4:27 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Hi Konrad, you're right, I meant Crazy 4x4x4 I and not type II for GB 3.1.9 -- I edited my post.

On 3.1.9 the circles in a face turn as the slice under those circles turn and so they form 2x2x2 corners. On 3.1.21 they do not so they form 3x3x3 edges. As for the program not working, have you tried to download a local copy and run it directly without using a web browser? If not I'd be happy to help you. It solves all of the dumb Java signing problems that are imposed when you run Java in a web browser.

Julian: impressive explanation of how to intuitively develop the 4x4x4 parity routine. I had dissected the sequence to see why it worked but I had always wondered how it was found. I always assumed computer search. Great explanation!

_________________
Prior to using my real name I posted under the account named bmenrigh.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 02, 2011 1:06 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Hi Brandon,

I think I understand the thing about the 3x3x3 edges on 3.1.21.
I cannot play with it, because
- it is not on the index page here http://users.skynet.be/gelatinbrain/App ... .htm#Cubes
- the downloadable does not run on my W7/64bit notebooks (I have tried it on three, it runs only on one of them - unfortunately the notebook of my daughter in London
(Gelatinbrain assumes that it has to do with the video driver, but the two notebooks it does not run on are quite different, one Fujitsu, one Lenovo Thinkpad - and the notebook of my daughter is a Thinkpad as well, but a high end professional version)

I'm still struggling with the theory:
OK, I solve the 444 parity first, shown on Katja's screenshot. This will leave the 3x3x3 edges in an odd permutation (like turning a single face on a 3x3x3 by 90 degrees). Now, when I solve this 3x3x3 edge parity, I have to turn the inner slices of the 444 again. How can I be sure, that an odd permutation of the 3x3x3 edges (I'm talking about the pieces inside the circle of 3.1.21, not the visible 3x3x3 edge pairs) will not induce an odd permutation of the 444 edges again?
I have tried to simulate it on a normal 444 using a VOID 333 sequence to correct the imaginary (= not visible on a normal 4x4x4) odd 333 edges permutation. I think this might work, but I'm struggling to understand why

_________________

Last edited by Konrad on Fri Sep 02, 2011 2:09 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 02, 2011 1:45 pm

Joined: Sat Jun 11, 2011 2:34 pm
I'm not entirely sure that I understand you problem but Ill give it a go.
are you saying that when you correct the 444 orientation parity you get a permutation parity of the 333 edge pairs?
If so, you can use this algorithm to correct the parity and not affect the permutation of the 333 edges.
(Small letters = slice moves)
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2.

If i'm wrong, I am sorry for posting this, but I think I have it sorted.

_________________
I am a fan of the Face turning Dodecahedrons

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 02, 2011 1:55 pm

Joined: Sun Aug 29, 2010 1:56 pm
I'm still struggling with the theory:
OK, I solve the 444 parity first, shown on Katja's screenshot. This will leave the 3x3x3 edges in an odd permutation (like turning a single face on a 3x3x3 by 90 degrees). Now, when I solve this 3x3x3 edge parity, I have to turn the inner slices of the 444 again. How can I be sure, that an odd permutation of the 3x3x3 edges will not induce an odd permutation of the 444 edges again?
I have tried to simulate it on a normal 444 using a VOID 333 sequence to correct the imaginary odd 333 edges permutation. I think this might work, but I'm struggling to understand why

You have to turn the inner slices of the 444 again, but an even number of times (double moves count 2).
You need not to change the paritiy of the 444 wings, because the odd permutation of the reduced 333 edges is even for the permutation of the 444 wings.
Attachment:

444wedge.png [ 6.71 KiB | Viewed 6091 times ]

A single slice move is the only way to change the parity of the 444 wings, and you don't need it.

Last edited by Stef-n on Fri Sep 02, 2011 2:39 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 02, 2011 2:28 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Hi Stefan and MaelSTRoM,

I'm not talking about the reduced 3x3x3 edges (edge pairs on the 4x4x4), I'm talking about the pieces inside the circle of the very specific circle cube 3.1.21. (As you have seen above it is not a Crazy 4x4x4 Type I and I do not think that a physical puzzle exists representing 3.1.21. A slice move on 3.1.21 does not turn the circle pieces of the adjacent outer face, as on Type I.)
The circle pieces of 3.1.21 act as circle corners on a regular 3x3x3 circle cube, while you can not see any centres or corners. And you see the 3x3x3 edges of 3.1.21 in this circle representation, only. You cannot see anything of them on a normal 444.
Brandon has explained it above. My problem is, that this puzzle seems to exist in the downloadable version only and it does not run on my notebooks.

EDIT: The behaviour on the two notebooks (both W7 /x64) is quite different, though:
- On the Fujitsu notebook, nothing visible happens (no error message, just NOTHING)
- On the Lenovo, the .exe starts and I can select a puzzle, but after that the application crashes.

_________________

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 02, 2011 3:30 pm

Joined: Sun Aug 29, 2010 1:56 pm
Hi Stefan and MaelSTRoM,

I'm not talking about the reduced 3x3x3 edges (edge pairs on the 4x4x4), I'm talking about the pieces inside the circle of the very specific circle cube 3.1.21.

I hope this time I understood what you meant. Sorry for my last post. A position with all circle pieces look solved can be wrong, in case the 444-wings are odd in permutation. This is because there are 3x4 equal circle pieces and you don't see its permutation parity. When I solve the inner circle pieces, I also care for the permutation parity of the 444-wings. A late repair will be expensive (I don't know how many moves). Of course this will be of no use, if you cannot play 3.1.21. I'm sad about that, my version runs.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 02, 2011 5:36 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
I'm still struggling with the theory:
OK, I solve the 444 parity first, shown on Katja's screenshot. This will leave the 3x3x3 edges in an odd permutation (like turning a single face on a 3x3x3 by 90 degrees). Now, when I solve this 3x3x3 edge parity, I have to turn the inner slices of the 444 again. How can I be sure, that an odd permutation of the 3x3x3 edges (I'm talking about the pieces inside the circle of 3.1.21, not the visible 3x3x3 edge pairs) will not induce an odd permutation of the 444 edges again?
I have tried to simulate it on a normal 444 using a VOID 333 sequence to correct the imaginary (= not visible on a normal 4x4x4) odd 333 edges permutation. I think this might work, but I'm struggling to understand why

Hi Konrad, this is a subtle question which has what I think is a subtle answer.

You are correct that when you fix the 4x4x4 edge-wing parity with a quarter-turn of one of the 4x4x4 slices you are changing the parity of the inner 3x3x3 edges too. If you were to fix the odd-permutation of the inner 3x3x3 edges with a 4x4x4 slice move (which is a face move on the inner 3x3x3) you would again break the 4x4x4 edge-wing pieces.

The trick is to "turn" the middle slice of the 3x3x3 just like you do with the void cube parity. The subtle trick is that there is no middle layer to turn because this is a 4x4x4 and not a 5x5x5 so you have to simulate turning the middle slice by turning up all of the faces and slices and doing a puzzle re-orientation.

Remember back when you were discussing the Dino + 3x3x3 you provided this Void-cube parity fix:
[R, F', L2, F2, U', D, R', F, B', D', F2, D, F']

Observe that on a 4x4x4 if you want to operate on the inner 3x3x3 you need to hold both the outer face and the slice and turn the puzzle like a 2x2x2. Here is the routine:
[R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]

And the effect is:
Attachment:

3.1.21_3x3x3_parity.png [ 6.61 KiB | Viewed 6059 times ]

If you are having trouble figuring out what is going on here, check out what the routine does on 3.1.14 which has the 3x3x3 edges visible as well as the 5x5x5 slice layer that is missing on the 4x4x4.

EDIT: I forgot to mention that there is another type of weirdness in the 3x3x3 edges on 3.1.21 too. Notice that there are two of each edge. That is, there are two white-yellow edges, two orange-red edges, etc. This is because you are looking at the sides of the edges rather than the two faces of the edge. Because of this, if you swap two edges with the same colors and flip their orientations it looks as though nothing has happened. If it looks like you have a permutation parity, you can solve it through re-orientation and some 3-cycles. The circle cubes are awesome

_________________
Prior to using my real name I posted under the account named bmenrigh.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sat Sep 03, 2011 5:49 am

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
Thanks Brandon & Julian! That made a lot of sense and I think I should be able to solve this parity from now on. I was pretty shocked to see that it could be solved in 15 moves though

Generally, even if I understand why the parity occurs and theoretically what it takes to fix it, I still find it hard to construct the appropriate sequence sometimes. I will usually be able to, but sometimes I will have to re-solve some of the previous steps because I have failed to make the fix pure.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sat Sep 03, 2011 4:01 pm

Joined: Sun Aug 29, 2010 1:56 pm
bmenrigh wrote:
Observe that on a 4x4x4 if you want to operate on the inner 3x3x3 you need to hold both the outer face and the slice and turn the puzzle like a 2x2x2. Here is the routine:
[R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]

Hello again, I have repeated this routine 12 times to get the 3.1.21 look solved again. It is not simply doing a swap or a 3-cycle.

Edit: Which was wrong because I had to do a y rotation of the whole puzzle after the routine (thanks for the help of Konrad) . It does a clean swap!! Well done - Brandon.

I have found today a clean [5,1] for the circle pieces, wich I want to intodruce here:
F'&2,
U,D',R&2,U',D,
F&2,
U,D',R'&2,U',D,
It does:
Attachment:

circle-pcs-3 cycl.png [ 10.61 KiB | Viewed 6021 times ]

Katja's position was:
Attachment:

2wingsswapped.png [ 10.53 KiB | Viewed 6021 times ]

Julian wrote:
In Gelatinbrain notation: R2&2,B2,U'2,L&2,U'2,R'&2,U'2,R&2,U'2,F'2,R&2,F'2,L'&2,B2,R2&2

Then it looks so:
Attachment:

afterthe15mvs.png [ 10.71 KiB | Viewed 6020 times ]

and then perform the [5,1] two times with setups:
U&2, U', D, F&2, U, D', R&2, U', D, F'&2, U, D', R'&2, U'&2, B&2, R&2, B'&2, D, U', R&2, D', U, B&2, D, U', R'&2, D', U, R'&2, B'&2,
gives 45 moves.

Im a bit confused about this puzzle, because I still don't know the best way to solve it. I'm not happy of having to swap pieces I already solved.

Last edited by Stef-n on Sat Sep 03, 2011 6:22 pm, edited 3 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sat Sep 03, 2011 5:09 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Stefan Schwalbe wrote:
bmenrigh wrote:
Observe that on a 4x4x4 if you want to operate on the inner 3x3x3 you need to hold both the outer face and the slice and turn the puzzle like a 2x2x2. Here is the routine:
[R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]

Hello again, I have repeated this routine 12 times to get the 3.1.21 look solved again.

Brandon's sequence swaps two of the inner 3x3x3 edges, while doing a virtual y' at the same time.
If you do [R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]
y (and repeat)
[R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]
the cube is solved again.
Stefan Schwalbe wrote:
...I have found today a clean [5,1] for the circle pieces, wich I want to intodruce here:
F'&2,
U,D',R&2,U',D,
F&2,
U,D',R'&2,U',D,
Here is my solution (after the 15 move 444 parity fix):

If you count Brandon's fix as 13 moves (e.g. R&3 = R, R&2 counted as 1 move) you can swap two edges (z' , [R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]), add a pure 3-cycle of 3 edges (R&3,U'&3,R&3,U&3,R&3,U&3,R&3,U'&3,R'&3,U'&3,R2&3 adopted from the well known 3x3x3 edges 3-cycle R, U', R,U,R,U,R,U',R',U',R2) and you are done with 24 moves after the 4x4x4 parity fix (Julian's sequence).

_________________

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sat Sep 03, 2011 5:38 pm

Joined: Sun Aug 29, 2010 1:56 pm
Brandon's sequence swaps two of the inner 3x3x3 edges, while doing a virtual y' at the same time.
If you do [R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]
y (and repeat)
[R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]
the cube is solved again.

You are right. And now I get a problem with my theory. How can this routine swap two inner 333 edges without swaping two 444 edge wings? I thought this is not possible. ??? Maybe I was wrong.
Yes, when you turn the whole puzzle by 90 degrees, this is like having 3 4-cycles of the inner 333 edges, and 6 4-cycles of the 444 wings and this is the answer. The inner 333 edges make an odd permutation and the 444 wings make an even permutation. Thank you. Now I understand this.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sat Sep 03, 2011 11:42 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Stefan Schwalbe wrote:
Brandon's sequence swaps two of the inner 3x3x3 edges, while doing a virtual y' at the same time.
If you do [R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]
y (and repeat)
[R&3, F'&3, L2&3, F2&3, U'&3, D&3, R'&3, F&3, B'&3, D'&3, F2&3, D&3, F'&3]
the cube is solved again.

You are right. And now I get a problem with my theory. How can this routine swap two inner 333 edges without swaping two 444 edge wings? I thought this is not possible. ??? Maybe I was wrong.
Yes, when you turn the whole puzzle by 90 degrees, this is like having 3 4-cycles of the inner 333 edges, and 6 4-cycles of the 444 wings and this is the answer. The inner 333 edges make an odd permutation and the 444 wings make an even permutation. Thank you. Now I understand this.

I was out most of the day so I couldn't respond. I'm glad you figured it out. Konrad and I had PM-based discussion of the specifics of the routine and 3.1.21 and 3.1.14

I think 3.1.14 is a great puzzle to illustrate what is going on with the 3x3x3 parity sequence fix because it has the extra hidden layer that isn't there on 3.1.21

Borrowing the image that Konrad made (I'm pretty sure he's okay with me using it ), the parity fix for the 3x3x3 edges does this on the 3.1.14 puzzle:
Attachment:

3.1.14Brandon.jpg [ 39.95 KiB | Viewed 5981 times ]

The reason I suggested looking at 3.1.14 is that it has every piece of a 3x3x3 and every piece of a 5x5x5 plainly visible so it is easier to see why the parity fix for the 3x3x3 edges works without affecting the 4x4x4 at all.

Here is a diagram of the pieces on 3.1.14:
Attachment:

3.1.14_diagram.png [ 19.2 KiB | Viewed 5981 times ]

I have labeled each sticker of a piece once.

1: 3x3x3 / 5x5x5 centers
2: 3x3x3 edges
3: 3x3x3 corners
4: 5x5x5 middle edges
5: 5x5x5 wing-edges
6: 5x5x5 corners
7: 5x5x5 x centers
8: 5x5x5 + centers

So as you can see, 3.1.14 has every piece that 3.1.21 has and more.

So why does the 3x3x3 edge parity fix work on 3.1.21 without affecting any of the 4x4x4 pieces? Well if you perform the fix on 3.1.14 you can see that it only affects the middle slice layer shared by the 3x3x3 and 5x5x5. It changes the parity of the centers, 5x5x5 and 3x3x3 edges, and 5x5x5 + centers.

But, the 3.1.21 puzzle doesn't have any of those pieces except the 3x3x3 edges. I think watching how the routine works on 3.1.14 is a very good demonstration of what is happening on 3.1.21 and why it has no effect on the 4x4x4 in 3.1.21

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Sep 04, 2011 4:11 am

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Thank you very much for your great explanation and for sharing what you have told me via PM with the others.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Sep 04, 2011 10:08 am

Joined: Sun Aug 29, 2010 1:56 pm
I'm still busy with the 3.1.21.
I had a new idea while I was out.
-Solve the wings and the corners like a 444 without centers.
-Solve the circle pieces with a [1,1]
-Solve the (bitten) face-corners with a [3,1]
It avoids the wing-parity fix we have worked out (~40 moves) and seems to be easier, but I'm not sure.
Thank you.

I like your 3.1.14 diagram. It makes me think of 3.1.14 as a combination of a 3x3x3 and a 5x5x5 - amazing. A solve might be a bit harder, than solving a 3x3x3 and a 5x5x5 separate.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 4:36 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
From the evil laboratory of Dr. Gelatinbrain comes a set of 4 new puzzles
Attachment:

gb_3.12.9_madness.png [ 24.9 KiB | Viewed 5821 times ]

3.12.9 through 3.12.12 which turn in a similar manner to some of the other 3.12.X puzzles but look more like the 3.11.X puzzles.

Thank you!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 4:59 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
I can't tell the difference between 3.12.9 and 3.12.11. I also don't know the difference between 3.12.10 and 3.12.12. What are the differences?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 5:03 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
schuma wrote:
I can't tell the difference between 3.12.9 and 3.12.11. I also don't know the difference between 3.12.10 and 3.12.12. What are the differences?
Yeah me either but I thought that was just from my cursory click-through of them. Upon more clicking I can't find a difference either.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 5:12 pm

Joined: Thu May 31, 2007 7:13 pm
Location: Bruxelles, Belgium
bmenrigh wrote:
schuma wrote:
I can't tell the difference between 3.12.9 and 3.12.11. I also don't know the difference between 3.12.10 and 3.12.12. What are the differences?
Yeah me either but I thought that was just from my cursory click-through of them. Upon more clicking I can't find a difference either.

3.12.11 & 3.12.12 have an extra cubie at the core while 3.12.9 & 3.12.19 cores are void.

Brandon, how do you detect every update in 3 minutes?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 5:22 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
gelatinbrain wrote:
3.12.11 & 3.12.12 have an extra cubie at the core while 3.12.9 & 3.12.19 cores are void.
Brandon, how do you detect every update in 3 minutes?

Thanks. I see. It'so easy to miss the core in the default point of view.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 6:33 pm

Joined: Mon Jul 21, 2008 4:52 am
Location: Brighton, UK
I have to go to bed now, but I just wanted to pop in and say:

Gelatinbrain -- thank you and congratulations on 500+ puzzles!

That's an amazing puzzle shown in the screenshot in Brandon's post.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 6:39 pm

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
The new puzzles could not have been better timed; as I will be on my mid-semester break at 5 pm today

Thanks Gelatinbrain! And congratulations indeed

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 7:08 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
gelatinbrain wrote:
Brandon, how do you detect every update in 3 minutes?
Obsession

Actually I wrote a script to monitor the webserver timestamp for polyhedra.jar and if the timestamp changes I download polyhedra.jar and check it against a cryptographic hash on file. If the hash is different then my script extracts the jar and does some analysis on the compiled classes to detect what puzzles were added.

Code:
From: Gelatinbrain Update Notice <gb_update@brandonenright.net>
Subject: Gelatinbrain update notice
Date: Tue, 13 Sep 2011 21:25:07 +0000
X-Mailer: MIME::Lite 3.027 (F2.78; T1.29; A2.06; B3.08; Q3.08)

The timestamp on http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/joglx/polyhedra.jar was updated.
New date: Tue, 13 Sep 2011 21:20:28 GMT
New md5:  b86dde90cdb02efaabdcaf0292fcfc2e

The new puzzles appear to be:
+3.12.10
+3.12.11
+3.12.12
+3.12.9

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 13, 2011 8:22 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
bmenrigh wrote:
Actually I wrote a script to monitor the webserver timestamp for polyhedra.jar and if the timestamp changes I download polyhedra.jar and check it against a cryptographic hash on file. If the hash is different then my script extracts the jar and does some analysis on the compiled classes to detect what puzzles were added.

Actually a few GB solvers are receiving the alert email. Although GB himself never needs it, it would be funny if he's the last one to know about it.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 14, 2011 12:18 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Hi fellow twisty puzzle solvers! It is a bit out of the scope of this thread but hopefully once is okay. I have made a "how to solve twisty puzzles" Youtube video using 1.4.14 as an example.

The reason I point this out here is that I think we all go through roughly the same thought process in our heads when we are faced with a new puzzle but I thought it would still be useful to share my own thought process.

I chose 1.4.14 as the basis for the video because I think it's a big but medium difficulty puzzle that can highlight some of the various ideas without being too tedious with the nitty-gritty details of how to find a particular sequence.

Because the video is meant to highlight a thought process rather than how to solve 1.4.14 specifically I didn't have any notes or anything like that. It is my hope that this will be a more accurate representation of the discovery process than a pre-made list of talking points. It also made the video way longer that I would have liked (47 minutes).

I hope that you all will find it useful and I especially hope that you guys will think about better ways to approach the puzzle and puzzles like it and bring those up here. I know I have a lot to learn!

Gelatinbrain, thank you for making such a great program and congratulations on your 500th puzzle discovery!

Best,

Brandon

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 14, 2011 3:03 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Hi Gelatinbrain,

I just solved 3.12.9. The internet connection of my PC was down. So I copied the certification code and am sending them via my phone. I've got two codes for the solve.

-------
1764ab9f093fb776e42f727aa1bc436e
91f3234285f40bd926474c7886f20db9
46788ce116dd2c6798e731fd1a3534e4
19cd32a7584fb09d623bc497686dd04f
-------
eb9d52e472c941e6740e5383584fb09d
6214c4af682fd09b64c3c89f613dc276
89e71356a1b2436e91f52343855d0bda
26b34c7986f20db946738ce916912cb3
-------

I hope at least one of them works. It's pretty hard indeed.Â

-- schuma

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Thu Sep 15, 2011 1:11 pm

Joined: Sun Aug 29, 2010 1:56 pm
Dear Gelatinbrain, congratulations on your 500th puzzle. This programm is a great thing for me, thank you very much.
Hi schuma, can you help me on solving the new puzzle? I have found nothing until now.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Thu Sep 15, 2011 1:42 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Stefan Schwalbe wrote:
Hi schuma, can you help me on solving the new puzzle? I have found nothing until now.

Hi Stefan, here are some hints.

First, in 3.12.9, every small cubie can move independently and three cycles of small cubies exist. There's no orbits or pairs or any other fancy stuff.

Second, I found this algorithm useful:

[F',B,R,B',F],U,[F',B,R',B',F],U',

because it only affects the four 2x2x2 on the equator. In order to construct a pure 3-cycle, I use the above sequence as X, and a setup version of it as Y and do XYX'Y'.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Thu Sep 15, 2011 4:15 pm

Joined: Sun Aug 29, 2010 1:56 pm
Thank you schuma for your last post. It helped me a lot. I've found now a pure 3-cycle with 56 moves.
I'll have to make that convenient. I don't know.
I have to swap pieces and to care for the orientation of the pieces...
Now I spent two hours on it and that's enough for today.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Sep 18, 2011 1:30 pm

Joined: Sun Aug 29, 2010 1:56 pm
3.12.9 solved
Attachment:

solved.PNG [ 191.29 KiB | Viewed 5618 times ]

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Sun Sep 18, 2011 8:56 pm

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
Stefan Schwalbe wrote:
3.12.9 solved
Congratulations! To both you and schuma for solving these They don't make sense to me at all.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 20, 2011 1:06 pm

Joined: Sun Aug 29, 2010 1:56 pm
Katja wrote:
Stefan Schwalbe wrote:
3.12.9 solved
Congratulations! To both you and schuma for solving these They don't make sense to me at all.

Thank you Katja.
Yes, after I got a routine that cycles 3 cubies, and a 3-steps setup strategy it was a bit like other puzzles, where you had to solve piece by piece. Also thanks to the great help of schuma.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Tue Sep 20, 2011 5:09 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Katja wrote:
Stefan Schwalbe wrote:
3.12.9 solved
Congratulations! To both you and schuma for solving these They don't make sense to me at all.

Thank you.

By the way GB just added a new puzzle, 3.9.4. It looks like an easy one. I hope its simple form doesn't fool me.

edit: I just solved 3.9.4. It's richer than I thought because there are more possibilities for orienting a 3D object than for 2D object.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 5:47 am

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
Gelatinbrain, can you please add a helicopter (more specifically the curvy helicopter cube) + 3x3x3 cube? When I saw this today, I felt a need to solve it because it looks so cool. Also, someone else from that thread has suggested that this be added to your collection of puzzles

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 8:52 am

Joined: Sun Aug 29, 2010 1:56 pm
Hi schuma, it seems, that at 3.12.10 the 24 inner cubies go never outside. have you found out the same?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 1:23 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Stefan Schwalbe wrote:
Hi schuma, it seems, that at 3.12.10 the 24 inner cubies go never outside. have you found out the same?

Yeah, sure. The inner pieces can be easily solved as a 2x2x2. 3.12.12 is more clear about it.

So 3.12.10 has less pieces to solve than 3.12.9.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 1:27 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Hi Gelatinbrain, for the new puzzle 3.9.3, should we

(1) solve all the 5x5x5 pieces completely, or
(2) only the 5x5x5-3x3x3 pieces on the surface completely, or
(3) only the stickers on the surface,

before the solution gets recognized? Thanks. Different requirements may lead to different strategies, you know.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 4:05 pm

Joined: Thu May 31, 2007 7:13 pm
Location: Bruxelles, Belgium
schuma wrote:
Hi Gelatinbrain, for the new puzzle 3.9.3, should we

(1) solve all the 5x5x5 pieces completely, or
(2) only the 5x5x5-3x3x3 pieces on the surface completely, or
(3) only the stickers on the surface,
Only the stickers on the surface matter.
Katja wrote:
Gelatinbrain, can you please add a helicopter (more specifically the curvy helicopter cube) + 3x3x3 cube?

3.5.4

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 4:25 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
gelatinbrain wrote:
Katja wrote:
Gelatinbrain, can you please add a helicopter (more specifically the curvy helicopter cube) + 3x3x3 cube?

3.5.4

So many beautiful puzzles in this update! I'm very pleased with all of the new tetrahedra lately. I finally figured out the Skewb / Skewb variants so I solved your 5.1.20 and 5.1.21 last night. Also, I really love the 1.2.X series so more puzzles there is great. There is a cut depth slightly deeper than 1.2.8 that adds the triangle pieces from 1.2.9. Is that puzzle too big for you to feel comfortable adding? I want to finish off the 1.2.{7,8,9} puzzles soon and it would be nice to do a "Master 1.2.9".

Code:
+1.2.37
+1.2.38
+1.2.39
+1.2.40
+1.2.41
+1.2.42
+1.2.43
+1.2.44
+1.2.45
+1.2.46
+1.2.47
+3.5.4
+5.1.29
+5.1.30
+5.1.31
+5.1.32
+5.1.33
+5.1.34

Also, a follow up to schuma's question. The Dino Cube can be solved into it's mirror and you recognize it as solved. Do the Starminx and other puzzles that have that property? I don't think it is needed but it would be nice to know.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 6:09 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
bmenrigh wrote:
Is that puzzle too big for you to feel comfortable adding?

If he feels comfortable adding it, do you feel comfortable solving it?
I probably won't feel comfortable

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 8:50 pm

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
gelatinbrain wrote:
3.5.4
Thank you! I like it a lot!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 9:41 pm

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
I just solved 3.9.4 but the applet didn't recognize the solved state. I finished at 689 moves and 30 minutes. I forgot to take a screen capture proving it, because I hit initialize assuming I had done something wrong, like not solving the inside stickers, but I just saw Gelatinbrain's post saying that's not necessary.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Wed Sep 21, 2011 11:51 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Katja wrote:
I just solved 3.9.4 but the applet didn't recognize the solved state. I finished at 689 moves and 30 minutes. I forgot to take a screen capture proving it, because I hit initialize assuming I had done something wrong, like not solving the inside stickers, but I just saw Gelatinbrain's post saying that's not necessary.

I also solved 3.9.4 and it was recognized. When I ask GB about inside stickers I was talking about 3.9.3 but not 3.9.4. In 3.9.4 you do need to worry about the orientation of the slates between the cubes, because the sides of them can be seen from outside. There is essentially no inside sticker on 3.9.4.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Thu Sep 22, 2011 3:12 am

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
schuma wrote:
I also solved 3.9.4 and it was recognized. When I ask GB about inside stickers I was talking about 3.9.3 but not 3.9.4. In 3.9.4 you do need to worry about the orientation of the slates between the cubes, because the sides of them can be seen from outside. There is essentially no inside sticker on 3.9.4.
Oh really? That't strange. Maybe I did do something wrong then. I really should have screen captured it. I guess I'll just have to solve it again

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Thu Sep 22, 2011 8:27 pm

Joined: Tue Feb 16, 2010 12:15 pm
Location: Sandnes, Norway
Stefan, how did you solve 3.9.4 in so few moves?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Thu Sep 22, 2011 9:21 pm

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
schuma wrote:
bmenrigh wrote:
Is that puzzle too big for you to feel comfortable adding?
I probably won't feel comfortable
Anything that slow schuma is a good puzzle.

I was pulling data from rankings page so I could track my progress while I'm not in the top 20 for puzzle solved and noticed a few oddities.
1) Some of the dates when puzzles were solved don't make sense. Here's the out of range ones
Code:
puzzle   solver   scramble   moves   date
2.1.6   Agamemnon   500   1543   0000-00-00
3.7.6b   GuiltyBystander    500    90    0000-00-00
1.4.1   Bishibosh   500   676   2001-00-21
3.2.18   Sjoerd   500   818   2001-00-22
1.1.29   Agamemnon   500   231   2001-12-01

2) The second oddity I saw is that schuma is the top 50 of every puzzle except the move count for megaminx. I think this means we need more puzzles like the megaminx

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Fri Sep 23, 2011 6:10 am

Joined: Sun Aug 29, 2010 1:56 pm
Katja wrote:
Stefan, how did you solve 3.9.4 in so few moves?

Hello Katja. This was actually my second solve. My movecount was 157. I guess someone will soon replace it
Attachment:

3.9.4.PNG [ 11.75 KiB | Viewed 5217 times ]

Now, I hope I can help:
(If you're not sure: I solved the inner parts in permutation and orientation as well as the outer parts.) Started with one cubie, than the neighbor-cubie and so on.
For clean cycling 3 parts I used: [1:1] or [1,1]. At the same time I cared for getting the parts right twisted into it's positions, or I had to twist them later.
For clean twisting 2 parts I used: 3, 4 or 5 moves:
When you have to twist two parts on a cubie, maybe the URF-cubie, you can bring them one after another to the down position of the URF-cubie, and use an D and an D' move of the DFR cubie without changing any of the other parts of the puzzle.

Thank you.
You'll have to highlight some of the text.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion ThreadPosted: Mon Sep 26, 2011 5:57 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
GB, thank you for adding the new puzzle 3.13.1. It's unique in the way that the inverse of URF is not URF'. I don't even know a good way to invert a sequence. So I just used an algorithm several times as its inverse. But it's not that hard to solve. I think somebody will solve it using very few moves.

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