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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 22, 2010 8:09 pm 
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Cool. I think there is a lot more to be found. Most of the CPU time is spent twisting so adding more patterns to search for doesn't slow things down much. What are the remaining two center patterns? I'll program them in. Also if there are any other center paterns you want improved I can add them too.

In a day or two I'll start my machine on a 50+ hour 9-move search for routines so the more things I check for the better.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 22, 2010 8:31 pm 
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bmenrigh wrote:
What are the remaining two center patterns? I'll program them in. Also if there are any other center paterns you want improved I can add them too.
Double swap A <--> B, D <--> E takes me 14 moves to do without affecting any pieces in the G-L half, and I have nothing at all for double swap C <--> D, E <--> F.

Ideally I'd like to fix the following patterns without disturbing the G-L half of the puzzle; the numbers of moves in brackets are my shortest algo length when disturbing one corner, followed by my shortest algo length when not disturbing any corners:

A <--> B, C <--> D (9/16)
A <--> B, C <--> E (9/18)
A <--> B, C <--> F (7/16)

Thanks!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 6:33 am 
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bmenrigh wrote:
Each face added is 38x longer in processing time [...]
My program is decent at canceling symmetries to reduce the search space [...]
In a day or two I'll start my machine on a 50+ hour 9-move search for routines so the more things I check for the better.
Out of curiosity, where does the 38 come from? It seems to me that because moves of opposite faces are equivalent if we ignore puzzle rotations, and presumably all puzzle rotations/orientations need to be catered for in the pattern checking, your program only needs to twist 6 of the 12 faces. For example, just twist A to F and leave G to L alone.

So each new move can be one of a maximum of 20 possibilities: one of the 5 faces/axes not twisted on the previous move, multiplied by 4 degrees of turn. 2 possibilities for the 1st move (72 degrees or 144 degrees), 8 possibilities for the 2nd move (4 degrees of turn, adjacent or non-adjacent face from the first face), then 20 possibilities for each move after that, if one ignores symmetric duplication from the third move onwards. At least, I think that's right...


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 11:16 am 
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Julian wrote:
bmenrigh wrote:
Each face added is 38x longer in processing time [...]
My program is decent at canceling symmetries to reduce the search space [...]
In a day or two I'll start my machine on a 50+ hour 9-move search for routines so the more things I check for the better.
Out of curiosity, where does the 38 come from? It seems to me that because moves of opposite faces are equivalent if we ignore puzzle rotations, and presumably all puzzle rotations/orientations need to be catered for in the pattern checking, your program only needs to twist 6 of the 12 faces. For example, just twist A to F and leave G to L alone.

So each new move can be one of a maximum of 20 possibilities: one of the 5 faces/axes not twisted on the previous move, multiplied by 4 degrees of turn. 2 possibilities for the 1st move (72 degrees or 144 degrees), 8 possibilities for the 2nd move (4 degrees of turn, adjacent or non-adjacent face from the first face), then 20 possibilities for each move after that, if one ignores symmetric duplication from the third move onwards. At least, I think that's right...
I appreciate your thinking about this! I should have started by saying that just because I have written a program doest' mean the program is all that good.

I wasn't sure how I was going to handle completely solving a puzzle yet so I decided I'd optimize for just finding useful routines. It recognizes useful routines by just counting how many centers and how many corners are out of place and if they are below a threshold it spits out the move sequence. I pop that sequence into the applet to see what it does. For this criteria I don't have to try all puzzle orientations.

Currently the first face to turn is fixed at 0 (white) since orientation doesn't matter. I have restricted the second face to be either adjacent to white (just light blue), not adjacent to white (just dark blue) or opposite white (yellow). I recognized that on a deep cut puzzle like the Pentultimate you don't need to turn the opposite face of the previous face so I cull yellow from the second turn possibilities. For all subsequent moves the restrictions are 1) Don't turn the same face you just turned, 2) Don't turn the opposite face of what you just turned. This leaves 10 faces each with 4 possible turns or 40x per move.

Each move is a cost of 40x but likely because of nice spacial locality in the searching the CPU cache gives me a bit of a boost.

I was thinking more generically about how to find routines that just a deep cut puzzle but you're absolutely right, I only need to twist half the puzzle which should get me to 20x per move.

When I programmed in your pattern last night I realized I needed to remove the fixed "start on white" reference so all orientations would be tried. Needless to say the program didn't make much progress...

I'll implement your deep cut idea right away! Too bad this won't help us for some of the other puzzles...


Edit: For solving a puzzle I was thinking of pre-computing all useful routines found in a previous run and then using those and just brute-forcing the setup moves. The trouble though is that if I search for routines in a fixed orientation I don't know how to map that routine into a different orientation. I was thinking of using spherical coordinates and giving each face a phi and a theta value and then reorienting would just add or subtract from the values and I could remap face numbers in this way. That way I could have a routine [A1, B2] and apply it as [L1, H1]. Ideas?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 3:05 pm 
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With regards to commutators and brute-forcing possibilities, am I correct in assuming that different commutator constructions can move different patterns?

That is, if I have a (6,2) commutator are there sequences it can do that a (7,1) can not? My gut tells me "yes" and that if I want to try all length 16 commutators I have to try all constructions (4,4), (5,3), (6,2), (7,1). For some reason my critical thinking an reasoning is having trouble tackling this problem.

EDIT: turns out to have a simple answer. (7,1) and (6,2) can reach different positions. The proof is by contradiction.

Assume you have a (4,2) commutator (A B C D, E F) then it is this sequence: [A, B, C, D] [E, F], [D', C', B', A'], [F', E']

Now assume that it is a (5, 1) then it must be (A B C D E, F) but that results in this sequence:

[A, B, C, D, E], [F], [A', B', C', D', E'], [F']

Of course, this sequence is not the original sequence -- proving that it isn't of the form (5,1).

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 5:59 pm 
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bmenrigh wrote:
Assume you have a (4,2) commutator (A B C D, E F) then it is this sequence: [A, B, C, D] [E, F], [D', C', B', A'], [F', E']

Now assume that it is a (5, 1) then it must be (A B C D E, F) but that results in this sequence:

[A, B, C, D, E], [F], [A', B', C', D', E'], [F']

Of course, this sequence is not the original sequence -- proving that it isn't of the form (5,1).


Although the first and the second sequences are different, it is possible that they end up having the same effect, isn't it? You need to show that all the sequences that have the same effect of the original (4,2) sequence is not in the form of (5,1). It seems pretty hard.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 6:39 pm 
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schuma wrote:
bmenrigh wrote:
Assume you have a (4,2) commutator (A B C D, E F) then it is this sequence: [A, B, C, D] [E, F], [D', C', B', A'], [F', E']

Now assume that it is a (5, 1) then it must be (A B C D E, F) but that results in this sequence:

[A, B, C, D, E], [F], [A', B', C', D', E'], [F']

Of course, this sequence is not the original sequence -- proving that it isn't of the form (5,1).


Although the first and the second sequences are different, it is possible that they end up having the same effect, isn't it? You need to show that all the sequences that have the same effect of the original (4,2) sequence is not in the form of (5,1). It seems pretty hard.
Well I'm sure there are (4,2) and (5,1) sequences that do have identical effects. I guess all my construction showed is that there are sequences that are reachable via one commutator construction that aren't in another.

I suppose can prove this computationally though. I'll code something up.

Edit: Even length-4 commutators produce a lot of output! I did (2,2) and (3,1).

In total, the (2,2) commutators can reach 177881 unique positions. The (3,1) commutators can reach 177861 unique positions. There are 12960 positions only reachable by the (2,2) routines and 12940 routines only reachable by the (3,1) routines. There are 164921 reachable by both.

I suspect as the length of the commutator increases the number of positions only reachable by a certain form of commutator increases dramatically. Maybe the intersection increases at the same rate keeping the relative non-overlap percent roughly the same?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 7:30 pm 
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This post is meant to keep track of useful/short Pentultimate center routines that my program finds.

UPDATE: all shortest routines that leave a half unchanged have been found.

There are two ways I will list a routine here. The first is that it performs one of the 9 center cycles/swaps and performs no more than 1 corner 3-cycle. Or, it performs one of the 9 center 3-cycles and it leaves an entire half of the puzzle (centered around any face) unchanged.


Things I have tried:
* All sequences of length 4-6. There aren't any useful center routines less than length 7.
* All sequences of length 7.
* All sequences of length 8.
* All sequences of length 9.


Things I am trying:
* I'm searching for shortest commutators


A --> B --> C --> A:
* There are exactly 30 sequences of length 8 that meet the criteria. Here are a few:

L-half unchanged: [A1, B3, A1, F4, B3, F1, A1, B2] or [F3, A1, E4, F3, E1, A1, F2, A1] or [E4, F1, E1, F4, E1, A1, E4, A4]
K-half unchanged: [A2, B1, F1, A3, F4, B1, A3, B1] or [B1, F2, B1, D1, B3, D4, B1, F3] or [F4, D4, C1, D1, F1, D4, C4, D1] or [E3, A1, B4, A3, E1, A1, E2, B1]
J-half unchanged: [B2, C1, E1, C3, E4, C1, B3, C1] or [F1, B4, F4, D1, F1, B1, F4, D4] or [E4, C4, E1, C1, E1, F4, A4, F1]

* There are exactly 84 sequences of length 9 that meet the criteria. 28 around each of the J, K, and L halves.


A --> C --> F --> A:
* There are exactly 7 sequences of length 8 that meet the criteria. All leave the K-half unchanged. Here are a few:

K-half unchanged: [F4, D4, C1, A4, C4, D1, F1, D1] or [E1, C1, E1, F4, A4, F1, E4, C4] or [D1, E1, B4, E4, D4, E1, B1, E4] or [C1, E1, A1, F1, E4, F4, C4, E4]

* There are exactly 54 sequences of length 9 that meet the criteria. Here are a few:

L-half unchanged: [B4, F1, A2, F2, A3, F4, B2, F3, B4] or [F1, D2, F2, A2, F3, D3, F2, A3, F2] or [E1, F1, C1, F4, C4, F4, E1, A1, E3]
Single-corner-3-cycle: [E4, B3, F4, D2, E1, B3, F4, D2, E2] or [D2, E2, C4, B3, D1, E2, C4, B3, D4]


B --> C --> D --> B:
* There are exactly 7 sequences of length 8 that meet the criteria. Here are a few

L-half unchanged: [B1, F1, B4, F1, A1, F4, A4, F4] or [F1, A1, B1, D1, B4, D4, F4, B4] or [E4, A4, E4, A1, E1, D4, E1, D1] or [D4, E4, B4, D4, B1, D1, A1, E1]

* There are exactly 54 sequences of length 9 that meet the criteria. Here are a few:

J-half unchanged: [A1, B4, C3, B3, C2, B1, A3, B2, A1] or [B1, E1, B1, C3, B4, E4, B1, C2, B3] or [F1, E1, A4, E4, F1, C1, F1, C4, F3]


B --> D --> E --> B:
* There are exactly 3 sequences of length 8 that meet the criteria:

L-half unchanged: [C2, A3, C3, F2, C2, A2, C3, F3] and [C3, F3, A4, C3, F3, A4, C3, F3] and [C3, F3, A2, F2, C2, F3, A3, F2]

* There are exactly 30 sequences of length 9 that meet the criteria. Here are a few:

Single-corner-3-cycle: [F2, A4, E2, A1, E3, C4, E2, C1, F1] or [F2, B1, F2, B4, A3, E1, A2, E4, F1]


C <--> D, E <--> F:
* There are exactly 4 sequences of length 8 that meet the criteria:

L-half unchanged: [B1, F1, A4, F4, B4, C4, A1, C1] and [B4, C4, A1, C1, B1, F1, A4, F4] and [F1, A1, F4, B4, C4, A4, C1, B1] and [C4, A4, C1, B1, F1, A1, F4, B4]

* There are exactly 18 sequences of length 9 that meet the criteria.


A <--> B, D <--> E:
* There are exactly 2 sequences of length 7 that meet the criteria:

L-half unchanged: [B2, A4, B1, A1, B1, A4, B2] and [B3, A1, B4, A4, B4, A1, B3]

* There are exactly 8 sequences of length 8 that meet the criteria but all leave the L-half unchanged which is covered by the length 7 sequences.

* There are exactly 12 sequences sequences of length 9 that meet the criteria.


A <--> B, C <--> D:
* There are exactly 8 sequences of length 8 that meet the criteria. Here are a few:

L-half unchanged: [A1, E1, A4, E4, A4, F4, A1, F1] or [F4, A4, F1, A1, E1, A1, E4, A4]
J-half unchanged: [B1, C4, B4, C4, E4, B1, E1, C1] or [F4, E4, C1, E1, A1, F1, E4, C4] or [C1, E1, F4, A4, E4, C4, E1, F1]

* There are exactly 24 sequences of length 9 that meet the criteria. 12 of them around each of the L and J halves.


A <--> B, C <--> E:
* There are exactly 2 sequences of length 9 that meet the criteria:

L-half unchanged: [E1, B1, F1, B4, A1, B1, F3, B4, E4] and [E1, B1, F2, B4, A4, B1, F4, B4, E4]


A <--> B, C <--> F:
* There are exactly 8 sequences of length 8 that meet the criteria. Here are a few:

L-half unchanged: [F1, E2, F1, E4, F4, A1, E3, F4] or [F1, E2, A4, F1, E1, F4, E3, F4] or [C4, D3, A1, C4, D4, C1, D2, C1]
K-half unchanged: [F4, D3, A4, C1, B1, C4, D2, F1] or [F4, D3, C1, B4, C4, A1, D2, F1] or [C1, E2, F4, B1, F1, A4, E3, C4]

* There are exactly 8 sequences of length 9 that meet the criteria. 4 around each of the K and L halves.

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Last edited by Brandon Enright on Thu Aug 26, 2010 10:43 am, edited 33 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 8:21 pm 
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Brandon, thanks for the update. I've been experimenting some more tonight, and I have found two new center-swapping algos you can cross off the list:

A <--> B, C <--> D in 8 moves (no change to L-centered half)
[A', E', A', E, A, I, E, I']

A <--> B, C <--> E in 9 moves (no change to L-centered half)
[E, K, A2, K', A', K, A', K', E']

So the three I'm still stuck on are:
A <--> B, D <--> E
A <--> B, C <--> F
C <--> D, E <--> F

Edit: I can do them in 16 moves with no change to the L-centered half by combining two 8-move algos, but I'm hoping there's a way to push that 16 down a bit. And fixed the face colors in green.


Last edited by Julian on Wed Aug 25, 2010 6:07 pm, edited 2 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 8:51 pm 
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bmenrigh wrote:
The trouble though is that if I search for routines in a fixed orientation I don't know how to map that routine into a different orientation. I was thinking of using spherical coordinates and giving each face a phi and a theta value and then reorienting would just add or subtract from the values and I could remap face numbers in this way. That way I could have a routine [A1, B2] and apply it as [L1, H1]. Ideas?
I would store the mappings for all 60 puzzle orientations in lookup tables. It would be extra work to create the tables in the first place, but it would make the checks faster -- as soon as a puzzle state fails the criteria against a solved orientation due to too many pieces out of position, we move to check against the next solved orientation. So we'd just be comparing arrays in a loop without any extra calculation.

By the way, how are you checking the corners? If we aren't looking for corner twisting algos (we don't care about the reason why a corner isn't fully correct, just that it isn't), we can label the 60 corner stickers uniquely and move them around with each twist, but we only need to compare 20 of them, one for each corner, against the solved orientations.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Aug 23, 2010 9:11 pm 
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Julian wrote:
bmenrigh wrote:
The trouble though is that if I search for routines in a fixed orientation I don't know how to map that routine into a different orientation. I was thinking of using spherical coordinates and giving each face a phi and a theta value and then reorienting would just add or subtract from the values and I could remap face numbers in this way. That way I could have a routine [A1, B2] and apply it as [L1, H1]. Ideas?
I would store the mappings for all 60 puzzle orientations in lookup tables. It would be extra work to create the tables in the first place, but it would make the checks faster -- as soon as a puzzle state fails the criteria against a solved orientation due to too many pieces out of position, we move to check against the next solved orientation. So we'd just be comparing arrays in a loop without any extra calculation.
Yeah I was thinking I'd pre-compute the lookup table at the start of the program with a bit of spherical coordinate math and then use that as a lookup table.
Julian wrote:
By the way, how are you checking the corners? If we aren't looking for corner twisting algos (we don't care about the reason why a corner isn't fully correct, just that it isn't), we can label the 60 corner stickers uniquely and move them around with each twist, but we only need to compare 20 of them, one for each corner, against the solved orientations.
Right now the program treats the the corners as just 60 stickers. So to check for a 3-cycle I'm checking that the number of out-of-place corner stickers is <= 9.

I haven't profiled my code (yet) but I'm almost certain the CPU is > 95% spent doing the twists rather than checking the state of the puzzle. Short-circuiting the comparison checking as soon as a threshold is crossed wouldn't be a big saver.

The short loops are all unrolled and branch-free by the compiler so doing short-circuit checks and possible branches would most likely be slower. I'll run my code through gprof and figure out what I need to optimize. Lookup tables for the twisting will probably be a big win.

My code will make you want to pour acid in your eyes but if you want to take a look, it's up at http://noh.ucsd.edu/~bmenrigh/dodeca_solver/dodeca.c. The code will get cleaner and more generic when I'm done tweaking and testing. Eventually I want it to be able to handle more than just the Pentultimate.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 24, 2010 1:42 am 
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Julian wrote:
Brandon, thanks for the update. I've been experimenting some more tonight, and I have found two new center-swapping algos you can cross off the list:

A <--> B, C <--> D in 8 moves (no change to G-centered half)
[A', E', A', E, A, I, E, I']

A <--> B, C <--> E in 9 moves (no change to G-centered half)
[E, K, A2, K', A', K, A', K', E']

So the three I'm still stuck on are:
A <--> B, D <--> E
A <--> B, C <--> F
C <--> D, E <--> F

Edit: I can do them in 16 moves with no change to the G-centered half by combining two 8-move algos, but I'm hoping there's a way to push that 16 down a bit.


Here is A <-->B, D <--> E pure:
[B1, C4, F4, A4, B3, F1, A1], [C4], [A4, F4, B2, A1, F1, C1, B4], [C1]
or
[B4, F1, C1, A1, B2, C4, A4], [F1], [A1, C1, B3, A4, C4, F4, B1], [F4]


Here is A <-->B, C <--> E pure:
[D4, C1, E1, B1, D2, C4, D4], [F4], [D1, C1, D3, B4, E4, C4, D1], [F1]
And not pure:
[C2, F1, D4, B1, D4, B4, D4], [F4], [D1, B1, D1, B4, D1, F4, C3], [F1]


I'm disappointed there aren't shorter routines. I didn't find the routines that don't move pieces in the G-centered half because I'm only checking the bottom half. I don't have a good way to check all of the halves other than coding up a special case for all 12. It seems commutators aren't the best way to go for these cases.

I will update my previous post with this info.

Edit: my program must have had a bug. There are shorted sequences. I don't know why I didn't find them before.

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Last edited by Brandon Enright on Wed Aug 25, 2010 1:39 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 24, 2010 2:44 pm 
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bmenrigh wrote:
Here is A <-->B, D <--> E pure:
[B1, C4, F4, A4, B3, F1, A1], [C4], [A4, F4, B2, A1, F1, C1, B4], [C1]
or
[B4, F1, C1, A1, B2, C4, A4], [F1], [A1, C1, B3, A4, C4, F4, B1], [F4]


Here is A <-->B, C <--> E pure:
[D4, C1, E1, B1, D2, C4, D4], [F4], [D1, C1, D3, B4, E4, C4, D1], [F1]
And not pure:
[C2, F1, D4, B1, D4, B4, D4], [F4], [D1, B1, D1, B4, D1, F4, C3], [F1]


I'm disappointed there aren't shorter routines. I didn't find the routines that don't move pieces in the G-centered half because I'm only checking the bottom half. I don't have a good way to check all of the halves other than coding up a special case for all 12. It seems commutators aren't the best way to go for these cases.
But those algos you've found are impressively insane -- how much chance would a human have of discovering them? Changing two centers in a half with a simultaneous corner 5-cycle around a large ring for the 7 moves of (7,1)?! Your program has already found a very useful 8 move algo for swapping centers... it's really tricky moving around centers without disturbing lots of corners. The Pentultimate is probably the closest dodeca puzzle to the Rubik's Cube, along with the obvious Megaminx, in terms of many useful algos being non-commutators and difficult for humans to find.

I experimented more this evening and found a sort-of commutator to do A <--> B, D <--> E in 14 moves:

/* Pull a corner from an otherwise unchanged half */
D, C, A, C', A', D',
/* Move corner to the same relative position if the puzzle is mirrored through its correct position */
A,
/* Make the mirrored inverse of the first 6 moves to reattach the corner */
F',A',B',A,B,F,
/* Undo the 7th move to reposition two centers correctly in the changed half */
A'

Thanks for sharing your code. I must confess that I have never written anything in the C family, but I think I could follow what each part did.

Edit: I also just found an alternative 10 move algo for A --> F --> C --> A, a (4,1) commutator:
[D', J, D, J'], [B], [J, D', J', D], [B']


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 24, 2010 4:35 pm 
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Julian wrote:
I experimented more this evening and found a sort-of commutator to do A <--> B, D <--> E in 14 moves:

/* Pull a corner from an otherwise unchanged half */
D, C, A, C', A', D',
/* Move corner to the same relative position if the puzzle is mirrored through its correct position */
A,
/* Make the mirrored inverse of the first 6 moves to reattach the corner */
F',A',B',A,B,F,
/* Undo the 7th move to reposition two centers correctly in the changed half */
A'
This is extremely impressive. What made you apply the inverted mirror routine? I could code up something to do X Y m(X)' Y and various combinations easily. It should find this routine and hopefully many more.

Julian wrote:
Edit: I also just found an alternative 10 move algo for A --> F --> C --> A, a (4,1) commutator:
[D', J, D, J'], [B], [J, D', J', D], [B']
I really doubt I'll be able to beat (4,1) without changing the bottom half but perhaps I should try to improve some of the other short patterns? Let me know if you have any > 8 move patterns that I'm not already working on.

My program just found a cool (4,4) routine that doesn't change anything in the bottom half: [D4, F1, D1, F4], [C4, B1, C1, B4], [F1, D4, F4, D1], [B1, C4, B4, C1]. I like this because length 4 routines are nice and short and easy to understand.

I'm thinking about how to handle the super-Pentultimate. Keeping track of the center twist shouldn't be too hard. You can't use a straight commutator to twist a single center (it will always twist in pairs) but I'm thinking a conjugate such as X, Y, X' or X, Y x n, X' where n is some number like 2 or 3 might do it.

I'd love to solve Doug's 24-move single-center-twist challenge on 2.2.3. Tackling the super-Pentultimate centers seems like a good way to start.

(I will keep updating my above post with center pattern routines as my servers find things or I exhaust classes of algorithms.)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 24, 2010 7:28 pm 
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bmenrigh wrote:
What made you apply the inverted mirror routine?
It was spotting symmetric cancellations that allowed me to find my first solution to the Pentultimate, so the idea has always stuck in my head.

(Around two years ago when I was getting into Gelatinbrain, I started doodling with 2-gen sequences on the Pentultimate. [A,C,A,C',A',C'] didn't seem to give me anything, but before I gave up on it I tried repeating it, and I noticed that [A,C,A,C',A',C']x2 produced 4 corner swaps. Applying the same 12 moves reflected left-right [A',F',A',F,A,F]x2 resulted in 2 corner swaps plus a 3-cycle around the top face. Applying the inverse of the first 12 moves then the inverse of the second 12 moves finally gave a pure 3-cycle in 48 moves. It was a bit crazy but it enabled me to solve the Pentultimate for the first time.)

Also I sometimes use [4] + [1] + m[4]' to slot in one of corners 6-10 from an adjacent position when solving the first half of the Pentultimate.

bmenrigh wrote:
Let me know if you have any > 8 move patterns that I'm not already working on.
Here's a list of all 9 centre-perm patterns with my current best algo length that leaves the L-centered half intact:

A --> B --> C --> A: 8 moves
A --> C --> F --> A: 9 moves
B --> C --> D --> B: 8 moves
B --> D --> E --> B: 11 moves
A <--> B, C <--> D: 8 moves
A <--> B, C <--> E: 9 moves
A <--> B, C <--> F: 16 moves
A <--> B, D <--> E: 14 moves
B <--> C, D <--> E: 16 moves

At the risk of sounding pessimistic, I'm only expecting improvements to be possible with the last three patterns marked in bold, and I have a sneaking feeling the best possible sequences could be 11 or 12 moves long. However, when all 9 move sequences have been examined, there could a surprise in store to prove me wrong, or with a single setup and undo move, a [9] could become an [11] to take care of one or more of the stubborn three patterns.

bmenrigh wrote:
I'd love to solve Doug's 24-move single-center-twist challenge on 2.2.3.
Same here! I've always had the idea that it could be [8 moves]x3, because of the hint he gave with it ("cycling larger groups of pieces"). Each group of 8 moves does a cycle with a side-effect of spinning a piece 2/5, so at the end you have a spin of 6/5 = 1/5 -- maybe?

Edit: Fixed face names in green


Last edited by Julian on Wed Aug 25, 2010 6:04 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 24, 2010 7:55 pm 
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Julian wrote:
bmenrigh wrote:
What made you apply the inverted mirror routine?
It was spotting symmetric cancellations that allowed me to find my first solution to the Pentultimate, so the idea has always stuck in my head.

(Around two years ago when I was getting into Gelatinbrain, I started doodling with 2-gen sequences on the Pentultimate. [A,C,A,C',A',C'] didn't seem to give me anything, but before I gave up on it I tried repeating it, and I noticed that [A,C,A,C',A',C']x2 produced 4 corner swaps. Applying the same 12 moves reflected left-right [A',F',A',F,A,F]x2 resulted in 2 corner swaps plus a 3-cycle around the top face. Applying the inverse of the first 12 moves then the inverse of the second 12 moves finally gave a pure 3-cycle in 48 moves. It was a bit crazy but it enabled me to solve the Pentultimate for the first time.)

Also I sometimes use [4] + [1] + m[4]' to slot in one of corners 6-10 from an adjacent position when solving the first half of the Pentultimate.
Yeah makes a lot more sense now. When I was getting started 8 months ago I was trying things like this too with only mild success. Now that my (N,1) and (N,3) commutator-finding strategy is tried and true I've lost a lot of inventiveness. I'm really enjoying tackling the the Pentultimate computationally because I feel like it allows me to apply creativity without getting frustrated by failure.
Julian wrote:
bmenrigh wrote:
Let me know if you have any > 8 move patterns that I'm not already working on.
Here's a list of all 9 centre-perm patterns with my current best algo length that leaves the G-centered half intact:

A --> B --> C --> A: 8 moves
A --> B --> F --> A: 9 moves
B --> C --> D --> B: 8 moves
B --> D --> E --> B: 11 moves
A <--> B, C <--> D: 8 moves
A <--> B, C <--> E: 9 moves
A <--> B, C <--> F: 16 moves
A <--> B, D <--> E: 14 moves
B <--> C, D <--> E: 16 moves

At the risk of sounding pessimistic, I'm only expecting improvements to be possible with the last three patterns marked in bold, and I have a sneaking feeling the best possible sequences could be 11 or 12 moves long. However, when all 9 move sequences have been examined, there could a surprise in store to prove me wrong, or with a single setup and undo move, a [9] could become an [11] to take care of one or more of the stubborn three patterns.
Yeah it won't hurt to try. I'll get these programmed in and my CPUs spinning shortly. Should I also weight the G-centered half importantly? Right now I'm only weighting the L (bottom) half.

Julian wrote:
bmenrigh wrote:
I'd love to solve Doug's 24-move single-center-twist challenge on 2.2.3.
Same here! I've always had the idea that it could be [8 moves]x3, because of the hint he gave with it ("cycling larger groups of pieces"). Each group of 8 moves does a cycle with a side-effect of spinning a piece 2/5, so at the end you have a spin of 6/5 = 1/5 -- maybe?
I'm glad we're thinking along the same lines.

I feel like it has to be of a conjugate form like X Y X' where X could be zero moves. I think the Y part has to be made up of and A x 2 or A x 3 part. For example, on 1.2.1 [ACD,ABC,ACD',ABC]x2 will spin a corner. This routine or a minor varition works on many of the vertex turning puzzles. It also works on the face-turning octahedrons and icosahedrons because they are the dual of vertex-turning puzzles.

I hadn't realized that there was an excess of 1 twist. If it is A x N then A producing 2 twists and N=3 would work nicely. The reason I have X and X' in this is that I suspect setup moves would be required to help contain the mess caused by twisting to a small area.

It would take me a few hours to modify my current program to try to handle a super-1.1.4 which should get the job done. It wont happen until this weekend at the earliest though.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Aug 24, 2010 8:20 pm 
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bmenrigh wrote:
Should I also weight the G-centered half importantly? Right now I'm only weighting the L (bottom) half.
When looking for center-swapping algos that leave half of the puzzle intact, I think the only way to be sure of finding all possible useful algos is to check all 12 halves of the puzzle for an intact half at the end of a twisting sequence, and nothing else. There will be few sequences that meet this criterion, and there's only a 1/72 chance that the centers of the other half haven't moved around! I realize it would probably be a lot of extra work to map all 12 halves though.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 25, 2010 1:47 am 
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Julian wrote:
bmenrigh wrote:
Should I also weight the G-centered half importantly? Right now I'm only weighting the L (bottom) half.
When looking for center-swapping algos that leave half of the puzzle intact, I think the only way to be sure of finding all possible useful algos is to check all 12 halves of the puzzle for an intact half at the end of a twisting sequence, and nothing else. There will be few sequences that meet this criterion, and there's only a 1/72 chance that the centers of the other half haven't moved around! I realize it would probably be a lot of extra work to map all 12 halves though.
I'm too tired to track it down now now but I must have had a bug in my bottom-half checking code that was missing some sequences. I implemented checks for all 12 halves and in doing so must have fixed the bottom half bug because I made big improvements on the routines :twisted:. At this point only A <--> B, C <--> E is left for my program to find and I know it doesn't have a solution of length 8 or less and you already know a length-9 solution. I'm running length-9 anyways to see what surprises are in store.

Also, the routines you said didn't change the G-centered half... When I pop them into they applet the don't change the L-centered (bottom half). I hope I'm not doing something wrong.

Edit: yup, found the bug. Stupid mistake. I guess it doesn't matter now since the code that replaced it is more generic and works.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 25, 2010 7:21 am 
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bmenrigh wrote:
I implemented checks for all 12 halves and in doing so must have fixed the bottom half bug because I made big improvements on the routines :twisted:. At this point only A <--> B, C <--> E is left for my program to find and I know it doesn't have a solution of length 8 or less and you already know a length-9 solution. I'm running length-9 anyways to see what surprises are in store.
I've just seen your updated results and I can't wait to try the algos out this evening. Humanly possible and computerly possible are clearly two very different things! Just 7 moves for A <-->B, D <--> E with no change to the other half?! Can't wait to see how that works.

bmenrigh wrote:
Also, the routines you said didn't change the G-centered half... When I pop them into they applet the don't change the L-centered (bottom half). I hope I'm not doing something wrong.
Sorry that was my mistake, thinking that G was opposite A rather than L opposite A. I'll edit my recent posts this evening to avoid confusion to other readers.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 25, 2010 3:57 pm 
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Julian wrote:
I've just seen your updated results and I can't wait to try the algos out this evening. Humanly possible and computerly possible are clearly two very different things! Just 7 moves for A <-->B, D <--> E with no change to the other half?! Can't wait to see how that works.
I just played a bit with the routine and I'm impressed! It's totally cool and very easy to understand. A human could come up with it -- not that any of us should have come up with it. I'm sure that if everybody had a Pentultimate on their shelf, like the Rubik's cube, this would be a well-known routine.
Julian wrote:
bmenrigh wrote:
Also, the routines you said didn't change the G-centered half... When I pop them into they applet the don't change the L-centered (bottom half). I hope I'm not doing something wrong.
Sorry that was my mistake, thinking that G was opposite A rather than L opposite A. I'll edit my recent posts this evening to avoid confusion to other readers.
Don't worry about it. I'll fix my quotes of your posts later too. I'm glad I've finally got rid of all of the major bugs in my program. I can't believe how many issues I've had that stopped me from finding routines.

Now I need to enhance it and add a bunch more bugs!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 25, 2010 5:18 pm 
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bmenrigh wrote:
Julian wrote:
I've just seen your updated results and I can't wait to try the algos out this evening. Humanly possible and computerly possible are clearly two very different things! Just 7 moves for A <-->B, D <--> E with no change to the other half?! Can't wait to see how that works.
I just played a bit with the routine and I'm impressed! It's totally cool and very easy to understand. A human could come up with it -- not that any of us should have come up with it. I'm sure that if everybody had a Pentultimate on their shelf, like the Rubik's cube, this would be a well-known routine.
I had a similar reaction. Pull off a block, break it up, spin the pieces around together, put them back again, spin the block back, and push it back; and in the meantime, on the other half: A <-->B, D <--> E. It's 2-gen and only 7 moves, and if more people played with a Pentultimate regularly, I'm sure it would have been found and shared. And the first algo you give for B --> D --> E --> B is a little 3-gen (3,1) commutator! Fascinating block-moving stuff in all of the algos.

Apology: due to a silly late night blunder on my part, I mislabeled one of the perms in a previous post, resulting in a duplication of patterns. A --> B --> F --> A should have been:
A --> C --> F --> A

I have a 9 move algo for that one. Would you mind re-running your magic prog to see if there is a 7 or 8 move algo for it, please?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Aug 25, 2010 5:45 pm 
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Julian wrote:
I had a similar reaction. Pull off a block, break it up, spin the pieces around together, put them back again, spin the block back, and push it back; and in the meantime, on the other half: A <-->B, D <--> E. It's 2-gen and only 7 moves, and if more people played with a Pentultimate regularly, I'm sure it would have been found and shared. And the first algo you give for B --> D --> E --> B is a little 3-gen (3,1) commutator! Fascinating block-moving stuff in all of the algos.
Yeah the routines are great to play with. Cool stuff. I don't think the forum is the best place for a master list of algos but I'll put together a list and host it somewhere. Maybe in a week or so when I have more results and more time.
Julian wrote:
Apology: due to a silly late night blunder on my part, I mislabeled one of the perms in a previous post, resulting in a duplication of patterns. A --> B --> F --> A should have been:
A --> C --> F --> A

I have a 9 move algo for that one. Would you mind re-running your magic prog to see if there is a 7 or 8 move algo for it, please?
Oops, yeah, in my late-night-stupor I didn't notice either. Fixed and re-running. 6 and 7 go fast. 8 takes a while and 9 takes many hours.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 26, 2010 1:35 pm 
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new puzzles up 3.10.1 & 3.10.1b. This should be interesting


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Aug 26, 2010 2:01 pm 
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boublez wrote:
new puzzles up 3.10.1 & 3.10.1b. This should be interesting


Yes they are interesting. I recommend everybody to try them. General N*M*K sliding cube can be played using the program called Gliding Cube, which can be found here:

http://www.glidingcube.com/

Although I can solve 2x2x2 and 3x3x3 sliding cube, I haven't figure out how to solve 1x1x2. This is really annoying.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Aug 27, 2010 9:48 pm 
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I've been working on Doug's 2.2.3 / super 1.1.4 center twist parity fix challenge a bit. Before you laugh me right off the forum with this 168 move sequence:
Attachment:
doug_2_2_3.png
doug_2_2_3.png [ 118.28 KiB | Viewed 4804 times ]
Let me just say that I think I'm pretty close! My 168 moves is actually a 24 move routine applied 7 times. The 24 move routine is actually just a 6 move conjugate routine applied 4 times. The 24 moves come pretty close. Most edges and corners stay fixed but 7 edge-corner pairs get 7-cycled. I'm pretty sure that if I add 2 more moves to my 6-routine and apply it 3 times rather than 4 I can eliminate this extra cycling and be done in 24 moves.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 29, 2010 8:45 pm 
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Hey this is mostly directed at Julian since I see him use it but what does the N-gen terminology mean? I see 2-gen, 3-gen, etc. It seems to apply to non-commutator sequences.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 29, 2010 10:25 pm 
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A 2-gen alg uses only two faces, e.g on a 3x3x3 that would be an alg that used only the R and U (or any two) faces. Or at least that is what i always thought it meant. I'm sure you can guess what 3- gen means and so on :wink:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Aug 29, 2010 10:38 pm 
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My program solved Doug's challenge pure 8-)
Attachment:
doug_pure.png
doug_pure.png [ 24.47 KiB | Viewed 4761 times ]
I added center-orientation tracking to my Pentultimate solver and started looking for center twist sequences. I set it up to look for sequences of length 6 applied 4 times and length 8 applied 3 times. A few pure, single-center-twist Penultimate sequences were found and one of them applies pure to 2.2.3 too. Although this sequence is pure and Doug's 5-cycled the inner triangles, I'm sure the construction is very similar to Doug's. He was right that this is "large block" cycling and I'm quite surprised a human would figure this technique out.

What I was trying by hand never moved the corner to be twisted out of place, it only twisted it in place. I haven't tried all possible routines so I can't be sure but it seems moving it out of place and then back in place is a requirement.

My sequences is 8 moves x 3 and the 8 moves don't use any slices (since I found it on a super-Pentultimate).

I keep applying the 8 moves of this sequence over and over to observe how elegantly they work together -- I'm very impressed Doug found something like this. No wonder he issued the challenge!

The sequence I found seems similar to a conjugate sequence construction (X Y X'). The only thing stopping it from being a conjugate is that there is a setup twist that doesn't get undone [W X Y X']x3.

According to Elwyn (thanks!), the sequence is 3-gen.

Edit: Much to my surprise the sequence works and is pure on the super-Megaminx (1.1.1b) and its dual 2.2.2/2.2.1. The shallow cuts make the sequence much easier to understand. I'd suggest working on 2.2.2 as the "wedge group" corner-edge-corner pieces on that puzzle match up nicely with how you move the groups of pieces on 2.2.3.

Rather than looking at this routine as one large routine, it is easier to think of it as one conjugate that gets applied 3 times. A twist is done before (or after) each conjugation so that some of the pieces being cycled are changed each time. That is, [W, [X Y X']] x 3.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Sep 04, 2010 3:15 pm 
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I've been running my Pentultimate program trying to find pure corner 3-cycles but unfortunately there aren't any of length 9 or shorter and the shortest commutator-based routines are 14 moves.

I've thrown a bunch of CPU power at the 10 move sequences though and found some routines. There aren't any really nice, 3-adjacent corner cycles of ten moves but there are a handful of other patterns. Here they are with a screenshot for each pattern type. In categorizing them I've ignored clockwise versus counter-clockwise and I haven't paid any attention to what happens to the corner's orientations.

These routines only twist the first 6 faces. It may be easier to understand how these routines work by treating one or more of the twists as actually twisting the opposite face and reorienting of the puzzle, and then all subsequent moves in the routine have to be reoriented to adjust for the reorienting.

This is the complete list of all unique 10 move 3-cycles.

Tall triangle:
Attachment:
tall_triangle.png
tall_triangle.png [ 55.81 KiB | Viewed 4726 times ]
[A1, B2, A4, D1, B2, C4, B3, C1, D4, B3]
[A1, B2, D4, A1, B2, A4, F3, D1, A4, F3]
[A2, B1, E4, F2, D1, F3, D4, E1, F3, B4]
[A2, B1, E4, F2, E1, F3, B4, E1, A3, E4]
[A3, B4, D1, C3, D4, C2, B1, D4, A2, D1]
[A3, B4, D1, C3, E4, C2, E1, D4, C2, B1]
[A4, B3, A1, E4, B3, F1, B2, F4, E1, B2]
[A4, B3, E1, A4, B3, A1, C2, E4, A1, C2]


Left lopsided tall triangle triangle:
Attachment:
left_lopsided_tall_triangle.png
left_lopsided_tall_triangle.png [ 56.2 KiB | Viewed 4726 times ]
[A1, B4, D2, A1, E3, A4, B1, E3, A4, D2]
[A1, B4, D2, B1, E3, A4, B1, E3, B4, D2]
[A3, B1, A2, B4, D1, C2, B4, C3, B1, D4]
[A3, B1, F2, E4, D1, F2, D4, F3, E1, B4]
[A4, B2, A1, B3, E4, F1, B3, F4, B2, E1]
[A4, B2, D1, B3, D4, A1, B3, E4, B2, E1]
[A4, B3, A1, C2, E4, A1, C2, A4, B3, E1]
[A4, B3, E1, C2, E4, A1, C2, E4, B3, E1]



Right lopsided tall triangle triangle:
Attachment:
right_lopsided_tall_triangle.png
right_lopsided_tall_triangle.png [ 55.52 KiB | Viewed 4726 times ]
[A1, B3, A4, B2, D1, C4, B2, C1, B3, D4]
[A1, B2, A4, F3, D1, A4, F3, A1, B2, D4]
[A1, B2, D4, F3, D1, A4, F3, D1, B2, D4]
[A1, B3, E4, B2, E1, A4, B2, D1, B3, D4]
[A2, B4, A3, B1, E4, F3, B1, F2, B4, E1]
[A2, B4, C3, D1, E4, C3, E1, C2, D4, B1]
[A4, B1, E3, A4, D2, A1, B4, D2, A1, E3]
[A4, B1, E3, B4, D2, A1, B4, D2, B1, E3]


Less tall triangle:
Attachment:
less_tall_triangle.png
less_tall_triangle.png [ 56.41 KiB | Viewed 4726 times ]
[A1, B3, A4, D1, B3, A4, F2, A1, D4, F2]
[A1, B3, E4, F1, B3, F4, B2, E1, A4, B2]
[A2, B4, D1, C2, B4, C3, B1, D4, A3, B1]
[A2, B4, D1, C2, D4, A3, B1, E4, F3, E1]
[A3, B1, E4, F3, B1, F2, B4, E1, A2, B4]
[A3, B1, E4, F3, E1, A2, B4, D1, C2, D4]
[A4, B2, A1, E4, B2, A1, C3, A4, E1, C3]
[A4, B2, D1, C4, B2, C1, B3, D4, A1, B3]


Left lopsided less-tall triangle:
Attachment:
left_lopsided_less_tall_triangle.png
left_lopsided_less_tall_triangle.png [ 56.09 KiB | Viewed 4726 times ]
[A3, B4, A2, D1, B4, C2, B1, C3, D4, B1]
[A3, B4, C2, B1, D4, A2, F1, E3, F4, D1]
[A4, B1, E2, B4, E3, A1, C4, E3, C1, E2]
[A4, B1, E2, F4, E3, F1, B4, E3, A1, E2]


Right lopsided less-tall triangle:
Attachment:
right_lopsided_less_tall_triangle.png
right_lopsided_less_tall_triangle.png [ 55.96 KiB | Viewed 4726 times ]
[A1, B4, D3, B1, D2, A4, F1, D2, F4, D3]
[A1, B4, D3, C1, D2, C4, B1, D2, A4, D3]
[A2, B1, A3, E4, B1, F3, B4, F2, E1, B4]
[A2, B1, F3, B4, E1, A3, C4, D2, C1, E4]


It will take about 20 days to run through the length 11 routines. I'm hoping there are more useful cycles of length 11 beyond just the 6 patterns above.

Unless my logic is faulty, there are no more than 36 unique 3-corner patterns. That's ignoring how the three corners get oriented along the cycle. It also isn't canceling any additional rotational symmetries there may be.

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Last edited by Brandon Enright on Mon Sep 13, 2010 10:56 pm, edited 3 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Sep 04, 2010 6:26 pm 
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1.1.7 Pentultimate - cycling 3 corners pure
bmenrigh wrote:
I've thrown a bunch of CPU power at the 10 move sequences though and found some routines. There aren't any really nice, 3-adjacent corner cycles of ten moves but there are a handful of other patterns.
Fascinating, mystical routines!

bmenrigh wrote:
Unless my logic is faulty, there are no more than 36 unique 3-corner patterns. That's ignoring how the three corners get oriented along the cycle. It also isn't canceling any additional rotational symmetries there may be.
Yes, and taking account of canceling rotational symmetries, I count 25 patterns:

(ABC, ABF, xxx) = 8 patterns (6 if we ignore reflective symmetries)
(ACD, AEF, xxx) = 12 patterns (8 if we ignore reflective symmetries)
(ABC, DEK, xxx) and (ABF, DEK, xxx) = 5 patterns (3 if we ignore reflective symmetries)

So if we ignore reflective symmetries too, we have 17 patterns. However, this is assuming that the corners we want to cycle could be anywhere. But if we are solving the last 15 corners, with 5 corners already solved around a face, that comes down to 10 patterns (5 + 5 + 0 in the above breakdown). And if we assume we are solving the last 10 corners with one hemisphere solved, that comes down to 5 patterns (3 + 2 + 0). Given how amazingly efficient these routines are, it would probably be better to cycle the last 15 corners rather than spend time solving corners 6-10 one by one, so we would be looking for 10 patterns.

Thinking about orientations, 2 patterns have 3-way rotational symmetry, so they only have 3 orientation possibilities: no twists needed, all corners twist the same way, or two twist in opposite directions. 4 patterns have reflective symmetry, so they have 6 orientation possibilities (the corner in the reflecting plane either twists or it doesn't, and either way there are 3 possibilities for the other two, because the twist of the 3rd corner is determined by the twist of the other two). The other 4 patterns have 3^2 = 9 orientation possibilities. That gives 2*3 + 4*6 + 4*9 = 66 patterns to optimize, including orientation but excluding mirror images. Phew!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 05, 2010 1:30 am 
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Well if people couldn't tell the whole programming and looking for algs conversation got a bit over my head. Nice to see you found some shorter algs.


I'd be very happy if anyone got sub 100 on it, i like to get an idea of what the human limit is to solving a puzzle excluding extreme luck like solving half the pentultimate and getting a second half skip or something hahaha i'd say Julian's luck for his record came would be about the limit of normal luck hahaha. Though in this case the solver would have just a little help from a computer it's just to find an alg and i mean more the actual solving process isn't done by a solving program. And i can now be pretty confident it's around 100 for the pentultimate.

I only use 2 algs when i solve it though so i doubt i'll get near that without learning a lot more for both centres and corners and a decent amount of luck.

Uni is far too hectic for me to spend much time solving for now anyway, i did start 1.1.42 using something close to my 1.1.17 method and got the hard part (the two colour pieces crouped into megaminx corners with no parity) out of the way in around 150 moves (no parity is always nice, especially when i think there's a very high chance of it on this puzzle) but then couldn't remember an alg and couldn't tell if it was working on the scrambled puzzle so i gave up. It and 1.1.17 will get done next i just don't know how soon.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 05, 2010 6:21 am 
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Brandon, I've been playing around this morning with your new Pentultimate pure corner cycling algos. Here are examples of how we can use 2 setup moves to give 3 out of the 6 orientation patterns for the tricky adjacent corners perm:

bmenrigh wrote:
Less tall triangle:
[A1, B3, A4, D1, B3, A4, F2, A1, D4, F2]
With I2, A3 before and A2, I3 after, with a move overlap we have an adjacent corner cycle in 13 moves (hypotenuse traveler doesn't twist, other two corners twist).
bmenrigh wrote:
Right lopsided tall triangle triangle:
[A1, B3, A4, B2, D1, C4, B2, C1, B3, D4]
With L3, G1 before and G4, L2 after, we have another adjacent corner cycle in 14 moves (no corners twist). And the same algo but with C2, E4 before and E1, C3 after gives all corners twisting against the perm, in this case, twisting clockwise in a counterclockwise perm.

If we allow ourselves a 14 move experimental limit, to see how many of the 66 corner cycling patterns we can find within that, the (6,1) commutators may come into play, depending on what you find for N=11. The (6,1) commutator with 72 degree 7th and 14th moves can give what I call the "starfish" perm, because I think it looks like a 3-pointed starfish, with perfect 3-way rotational symmetry. And your "lopsided less-tall triangle" patterns are just 1 move away from a different orientation pattern for the starfish, e.g. take the "right lopsided less-tall triangle" and twist the brown face counterclockwise 72 degrees. So we quickly have 2 out of 3 of the starfish patterns.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 05, 2010 10:11 pm 
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Hey Julian, thanks a ton for your input on this. I hope to classify all 66 sequences but I'm pretty sure I'm going to need your help with the orientation related stuff. I just have no intuition on how to track the orientation of pieces when the cycle isn't all on one face. I feel like there is some fixed reference plane that needs to be used but I just don't know how to pick one and stick with it for the cycles that are spread across more than one face.

To save classification time your choice of excluding mirror symmetries is a good idea. I'm going to post the patterns and include symmetries but we should probably just ignore either the left or right versions for looking an the corner orientations.

I'm also pretty sure there will be patterns that aren't reachable in 11 moves and I'm almost certain there will be orientation variations for patterns that aren't reachable in 11 moves. 11-move routines will trickle in over the next two weeks or so. 12 moves would take my server about 350 days. I have 1000 cpu-hours of "super computer" time (a 256-node, 8 cpu/node cluster) but I wouldn't be able to complete the 12 moves in my time allotment. To do 12 moves I'm going to need donated CPU time.

Your idea of using setup moves on the 10 and 11 move sequences will work but it seems easier to make new patterns with setup moves rather than orientation variations on a particular pattern. To complete all 66 I figure a handful of sequences are going to use a lot of setup moves and be pretty far from optimal.

When you have the time, can you pop some of the found routines into the applet and annotate what happens to the corner orientations in the cycle? I think using your notes will give me a better idea of how to spot the orientations myself.

Finally, you said two patterns have 3-way rotational symmetry but I can only spot 1 pattern with that property. There is a pattern that looks like it has 3-way rotational symmetry (my "Big triangle" pattern in the next post) but I think it actually only has mirror symmetry. I think the hypotenuse of the triangle is a tiny bit different than the legs of the triangle. Is there some other pattern I'm missing?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Sep 05, 2010 10:28 pm 
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This post is meant to record all the 11-move pure corner 3-cycles for the Pentultimate/1.1.7. I am including cycles/patterns that are achievable in 10 moves because these routines may have different effects on the corner orientations. I will edit this post as my program finds more routines. If there are better names for these patterns let me know in a PM and I'll change the name here. Eventually I want to update each of these routines with annotation about how the corner orientations change in the cycle.

This is the complete list of all unique 11 move 3-cycles.

Big Triangle:
Attachment:
big_triangle.png
big_triangle.png [ 56.24 KiB | Viewed 4669 times ]
[A1, B1, A2, B4, D1, C2, B4, C3, B1, D4, A2]
[A1, B1, F2, E4, D1, F2, D4, F3, E1, B4, A2]
[A2, B4, D1, C3, E4, C2, E1, D4, C2, B1, A1]
[A2, B4, D1, C3, D4, C2, B1, D4, A2, D1, A1]
[A3, B1, E4, F2, E1, F3, B4, E1, A3, E4, A4]
[A3, B1, E4, F2, D1, F3, D4, E1, F3, B4, A4]
[A4, B4, A3, B1, E4, F3, B1, F2, B4, E1, A3]
[A4, B4, C3, D1, E4, C3, E1, C2, D4, B1, A3]


Right-lopsided tall triangle:
Attachment:
right_lopsided_tall_triangle.png
right_lopsided_tall_triangle.png [ 55.52 KiB | Viewed 4669 times ]
[A1, B1, E3, A4, D2, A1, B4, D2, A1, E3, A3]
[A1, B1, E3, B4, D2, A1, B4, D2, B1, E3, A3]
[A1, B1, E4, F2, E1, F3, B4, E1, A3, E4, A1]
[A1, B1, E4, F2, D1, F3, D4, E1, F3, B4, A1]
[A2, B1, E3, A4, D2, A1, B4, D2, A1, E3, A2]
[A2, B1, E3, B4, D2, A1, B4, D2, B1, E3, A2]
[A2, B2, A4, F3, D1, A4, F3, A1, B2, D4, A4]
[A2, B2, D4, F3, D1, A4, F3, D1, B2, D4, A4]
[A3, B1, E3, A4, D2, A1, B4, D2, A1, E3, A1]
[A3, B1, E3, B4, D2, A1, B4, D2, B1, E3, A1]
[A3, B2, A1, B3, E4, F1, B3, F4, B2, E1, A1]
[A3, B2, D1, B3, D4, A1, B3, E4, B2, E1, A1]
[A3, B2, A4, F3, D1, A4, F3, A1, B2, D4, A3]
[A3, B2, D4, F3, D1, A4, F3, D1, B2, D4, A3]
[A4, B1, A2, B4, D1, C2, B4, C3, B1, D4, A4]
[A4, B1, F2, E4, D1, F2, D4, F3, E1, B4, A4]
[A4, B2, A4, F3, D1, A4, F3, A1, B2, D4, A2]
[A4, B2, D4, F3, D1, A4, F3, D1, B2, D4, A2]
[A4, B4, D3, C1, D2, C4, B1, D2, A4, D3, A2]
[A4, B4, D3, B1, D2, A4, F1, D2, F4, D3, A2]


Left-lopsided tall triangle:
Attachment:
left_lopsided_tall_triangle.png
left_lopsided_tall_triangle.png [ 56.2 KiB | Viewed 4669 times ]
[A1, B1, E2, B4, E3, A1, C4, E3, C1, E2, A3]
[A1, B1, E2, F4, E3, F1, B4, E3, A1, E2, A3]
[A1, B3, E1, C2, E4, A1, C2, E4, B3, E1, A3]
[A1, B3, A1, C2, E4, A1, C2, A4, B3, E1, A3]
[A1, B4, A3, B1, E4, F3, B1, F2, B4, E1, A1]
[A1, B4, C3, D1, E4, C3, E1, C2, D4, B1, A1]
[A2, B3, A4, B2, D1, C4, B2, C1, B3, D4, A4]
[A2, B3, E4, B2, E1, A4, B2, D1, B3, D4, A4]
[A2, B3, E1, C2, E4, A1, C2, E4, B3, E1, A2]
[A2, B3, A1, C2, E4, A1, C2, A4, B3, E1, A2]
[A2, B4, D2, A1, E3, A4, B1, E3, A4, D2, A4]
[A2, B4, D2, B1, E3, A4, B1, E3, B4, D2, A4]
[A3, B3, E1, C2, E4, A1, C2, E4, B3, E1, A1]
[A3, B3, A1, C2, E4, A1, C2, A4, B3, E1, A1]
[A3, B4, D2, A1, E3, A4, B1, E3, A4, D2, A3]
[A3, B4, D2, B1, E3, A4, B1, E3, B4, D2, A3]
[A4, B4, D2, A1, E3, A4, B1, E3, A4, D2, A2]
[A4, B4, D2, B1, E3, A4, B1, E3, B4, D2, A2]
[A4, B4, D1, C3, E4, C2, E1, D4, C2, B1, A4]
[A4, B4, D1, C3, D4, C2, B1, D4, A2, D1, A4]


Arc of the Pentultimate:
Attachment:
arc_of_the_pentultimate.png
arc_of_the_pentultimate.png [ 56.4 KiB | Viewed 4669 times ]
[A1, B1, F3, B4, E1, A3, C4, D2, C1, E4, A1]
[A1, B1, A3, E4, B1, F3, B4, F2, E1, B4, A1]
[A1, B4, A2, D1, B4, C2, B1, C3, D4, B1, A2]
[A1, B4, D1, C2, B4, C3, B1, D4, A3, B1, A1]
[A1, B4, D1, C2, D4, A3, B1, E4, F3, E1, A1]
[A1, B4, C2, B1, D4, A2, F1, E3, F4, D1, A2]
[A2, B1, E4, F3, B1, F2, B4, E1, A2, B4, A1]
[A2, B1, E4, F3, E1, A2, B4, D1, C2, D4, A1]
[A2, B2, A1, E4, B2, A1, C3, A4, E1, C3, A2]
[A2, B2, D1, C4, B2, C1, B3, D4, A1, B3, A2]
[A2, B3, E1, A4, B3, A1, C2, E4, A1, C2, A2]
[A2, B3, A1, E4, B3, F1, B2, F4, E1, B2, A2]
[A3, B2, D4, A1, B2, A4, F3, D1, A4, F3, A3]
[A3, B2, A4, D1, B2, C4, B3, C1, D4, B3, A3]
[A3, B3, E4, F1, B3, F4, B2, E1, A4, B2, A3]
[A3, B3, A4, D1, B3, A4, F2, A1, D4, F2, A3]
[A3, B4, D1, C2, B4, C3, B1, D4, A3, B1, A4]
[A3, B4, D1, C2, D4, A3, B1, E4, F3, E1, A4]
[A4, B1, F3, B4, E1, A3, C4, D2, C1, E4, A3]
[A4, B1, E4, F3, B1, F2, B4, E1, A2, B4, A4]
[A4, B1, E4, F3, E1, A2, B4, D1, C2, D4, A4]
[A4, B1, A3, E4, B1, F3, B4, F2, E1, B4, A3]
[A4, B4, A2, D1, B4, C2, B1, C3, D4, B1, A4]
[A4, B4, C2, B1, D4, A2, F1, E3, F4, D1, A4]


Left-lopsided less-tall triangle:
Attachment:
left_lopsided_less_tall_triangle.png
left_lopsided_less_tall_triangle.png [ 56.09 KiB | Viewed 4669 times ]
[A1, B1, E4, F3, B1, F2, B4, E1, A2, B4, A2]
[A1, B1, E4, F3, E1, A2, B4, D1, C2, D4, A2]
[A2, B2, A1, B3, E4, F1, B3, F4, B2, E1, A2]
[A2, B2, D1, B3, D4, A1, B3, E4, B2, E1, A2]
[A3, B1, F3, B4, E1, A3, C4, D2, C1, E4, A4]
[A3, B1, A3, E4, B1, F3, B4, F2, E1, B4, A4]
[A3, B2, A1, E4, B2, A1, C3, A4, E1, C3, A1]
[A3, B2, D1, C4, B2, C1, B3, D4, A1, B3, A1]
[A3, B4, D3, B1, D2, A4, F1, D2, F4, D3, A3]
[A3, B4, D3, C1, D2, C4, B1, D2, A4, D3, A3]
[A4, B2, D4, A1, B2, A4, F3, D1, A4, F3, A2]
[A4, B2, A4, D1, B2, C4, B3, C1, D4, B3, A2]


Right-lopsided less-tall triangle:
Attachment:
right_lopsided_less_tall_triangle.png
right_lopsided_less_tall_triangle.png [ 55.96 KiB | Viewed 4669 times ]
[A1, B3, E1, A4, B3, A1, C2, E4, A1, C2, A3]
[A1, B3, A1, E4, B3, F1, B2, F4, E1, B2, A3]
[A2, B1, E2, B4, E3, A1, C4, E3, C1, E2, A2]
[A2, B1, E2, F4, E3, F1, B4, E3, A1, E2, A2]
[A2, B3, E4, F1, B3, F4, B2, E1, A4, B2, A4]
[A2, B3, A4, D1, B3, A4, F2, A1, D4, F2, A4]
[A2, B4, A2, D1, B4, C2, B1, C3, D4, B1, A1]
[A2, B4, C2, B1, D4, A2, F1, E3, F4, D1, A1]
[A3, B3, A4, B2, D1, C4, B2, C1, B3, D4, A3]
[A3, B3, E4, B2, E1, A4, B2, D1, B3, D4, A3]
[A4, B4, D1, C2, B4, C3, B1, D4, A3, B1, A3]
[A4, B4, D1, C2, D4, A3, B1, E4, F3, E1, A3]


Starfish:
Attachment:
starfish.png
starfish.png [ 56.25 KiB | Viewed 4669 times ]
[A1, B2, A1, B3, E4, F1, B3, F4, B2, E1, A3]
[A1, B2, D1, B3, D4, A1, B3, E4, B2, E1, A3]
[A2, B4, D3, B1, D2, A4, F1, D2, F4, D3, A4]
[A2, B4, D3, C1, D2, C4, B1, D2, A4, D3, A4]
[A3, B1, E2, B4, E3, A1, C4, E3, C1, E2, A1]
[A3, B1, E2, F4, E3, F1, B4, E3, A1, E2, A1]
[A4, B3, A4, B2, D1, C4, B2, C1, B3, D4, A2]
[A4, B3, E4, B2, E1, A4, B2, D1, B3, D4, A2]]


Left flat tall triangle:
Attachment:
left_flat_tall_triangle.png
left_flat_tall_triangle.png [ 56.58 KiB | Viewed 4580 times ]
[A1, B2, A1, E4, B2, A1, C3, A4, E1, C3, A3]
[A1, B2, D1, C4, B2, C1, B3, D4, A1, B3, A3]
[A2, B2, D4, A1, B2, A4, F3, D1, A4, F3, A4]
[A2, B2, A4, D1, B2, C4, B3, C1, D4, B3, A4]


Right flat tall triangle:
Attachment:
right_flat_tall_triangle.png
right_flat_tall_triangle.png [ 56.46 KiB | Viewed 4356 times ]
[A3, B3, E1, A4, B3, A1, C2, E4, A1, C2, A1]
[A3, B3, A1, E4, B3, F1, B2, F4, E1, B2, A1]
[A4, B3, E4, F1, B3, F4, B2, E1, A4, B2, A2]
[A4, B3, A4, D1, B3, A4, F2, A1, D4, F2, A2]


Tall triangle:
Attachment:
tall_triangle.png
tall_triangle.png [ 55.81 KiB | Viewed 4622 times ]
[A1, B4, D1, C3, E4, C2, E1, D4, C2, B1, A2]
[A1, B4, D1, C3, D4, C2, B1, D4, A2, D1, A2]
[A2, B1, A2, B4, D1, C2, B4, C3, B1, D4, A1]
[A2, B1, F2, E4, D1, F2, D4, F3, E1, B4, A1]
[A3, B4, A3, B1, E4, F3, B1, F2, B4, E1, A4]
[A3, B4, C3, D1, E4, C3, E1, C2, D4, B1, A4]
[A4, B1, E4, F2, E1, F3, B4, E1, A3, E4, A3]
[A4, B1, E4, F2, D1, F3, D4, E1, F3, B4, A3]

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Last edited by Brandon Enright on Sat Sep 11, 2010 12:55 pm, edited 10 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 06, 2010 7:09 am 
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bmenrigh wrote:
I just have no intuition on how to track the orientation of pieces when the cycle isn't all on one face. I feel like there is some fixed reference plane that needs to be used but I just don't know how to pick one and stick with it for the cycles that are spread across more than one face.
Yes, when the corners are on different faces, terms like "clockwise" lose their meaning and it's tough keeping track of the orientations. We could designate one sticker of one corner as the reference point and then show the orientation by the ordering of the stickers, for example, your Big Triangle cycle in your next post could be (BIH, GDC, EJF), showing that sticker B of corner BIH moves to sticker G of corner CGD moves to sticker E of corner EJF.

bmenrigh wrote:
When you have the time, can you pop some of the found routines into the applet and annotate what happens to the corner orientations in the cycle? I think using your notes will give me a better idea of how to spot the orientations myself.
I can put together a notated list of the 66 patterns, sure.

bmenrigh wrote:
Finally, you said two patterns have 3-way rotational symmetry but I can only spot 1 pattern with that property. There is a pattern that looks like it has 3-way rotational symmetry (my "Big triangle" pattern in the next post) but I think it actually only has mirror symmetry. I think the hypotenuse of the triangle is a tiny bit different than the legs of the triangle. Is there some other pattern I'm missing?
If you move the right hand triangle of your Big Triangle pattern over to Turquoise/D.Green/D.Blue (ACD), that's the other one.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 06, 2010 6:01 pm 
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1.1.7 Pentultimate corner patterns

I missed quite a few corner patterns when I was peering at my Pyraminx Crystal the other evening! I now count 16 distinct patterns where all corners are visible in the left half:

* = Has reflective symmetry
** = Has rotational symmetry

A = (ABC,ACD,AFB) *
B = (ABC,ADE,AFB) *
C = (ABC,CGD,AFB)
D = (ABC,DGK,AFB)
E = (ABC,DKE,AFB) *
F = (BIH,BHC,DGK)
G = (BIH,BHC,DKE)

H = (BHC,ACD,AFB) ** Starfish
I = (BHC,DKE,AFB) Lopsided tall triangle
J = (BHC,ACD,BFI) Lopsided less tall triangle
K = (BHC,ADE,BFI) * Less tall triangle
L = (BHC,CGD,BFI) * Arc of the Pentultimate
M = (BHC,DGK,BFI) Flat tall triangle
N = (BHC,DKE,BFI) * Tall triangle

O = (BIH,CGD,AEF) **
P = (BIH,CGD,EJF) * Big triangle


Suggested naming scheme for the patterns including orientation (3 possibilities for **, 6 for *, 9 for the rest):

A1-A6
etc.

111 patterns in total now. Later this week I'll list them and I'll show which pattern goes with which algo that you've already posted.


Last edited by Julian on Mon Sep 06, 2010 6:40 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Sep 06, 2010 6:34 pm 
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Julian wrote:
1.1.7 Pentultimate corner patterns
[...snip...]
That makes 111 patterns in total. Later this week I'll list them and I'll show which pattern goes with which algo that you've already posted.
Thanks for coming up with the naming, I think this is a good scheme. I like that you've grouped them based on the distance between the first two corners and then ordered them based on the distance to the third corner. That should make looking them up faster. 111 still isn't bad and it's nice that it's too much more than Fridrich's PLL+OLL. Especially when the goal is fewest moves and they can just be looked up in a table rather than memorized.

I can't be certain but I think I've already hit all of the reachable 11-move patterns. It's going faster than I was expecting. I've been profiling my code (GCC rocks!) and making improvements and I've already sped up the code by about 20%. I'm pretty sure I can get another 70-90% speedup with a twist() enhancement involving self-modifying-code (via pointer twiddling) and lookup tables. If it works out I'll probably be able to enlist a few more servers worth of resources and crunch through all the 12-move routines in a month.

Edit: the twist() lookup table worked and the code is about 100% faster (takes half the time). With significant effort, 12 moves is within the reach of brute force now.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 07, 2010 1:57 pm 
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Attachment:
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stefan.jpg [ 7.29 KiB | Viewed 4344 times ]

Hello, Agamemnon is my name on gelatinbrains rankings, and I'm now a member of the twistypuzzles.com forum, thanks again to gelatinbrain for inviting me.

About the gelatinbrain puzzles:
First I want to tell you a few words what I think about the Gelatinbrain - Virtual-Magic-Polyhedra puzzles. The two-sides view, this kind of move triggering, where the moves are indicated before on MouseOver and the snapping to view-orientations, the lot's of puzzles, especially new puzzles, the internet competition rankings makes gelatinbrain for me the best puzzle simulator. I have much fun playing with this programm. Each time, I reach an aim on it, it makes me proud, and I continue on this endless road.

About commutators and other basics:
I don't know, what I would do without the help of this commutator trick ( A, B, A', B' ). Maybe I could not solve one single puzzle. I learned this about 10 years before along with other basics from the "usefull mathematics" on Jaap's Puzzle Page. Letter notation, even and odd parity, use of reverse move sequences, the conjugator ( S, A, S' ), disjoint cycle notation, repeatation tricks with different lengths cycles, I use all that, and much of it I really learned first from Jaap's Puzzle Page. Thank you Jaap!

About impressing rankings on gelatinbrains ranking page:
Some of your rankings impressed me really and I would like to know how this were done. I have previously tried to crack some of your records on the ranking page and sometimes I did it. I do not use secret allgorithms, and so I'm free to tell my approaches on request - I hope I can do that in a way, that is understandable.

Thank you to Brandon Enright, who has first noticed me on this forum.

So, that's it for now
Your's Stefan Schwalbe.


Gelatinbrain's Magic Polyhedra
Jaap's Puzzle Page


Last edited by Stef-n on Fri Jan 24, 2014 3:24 pm, edited 3 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 07, 2010 5:13 pm 
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Welcome to the forum, Stefan. :D
I'm really impressed that you and schuma have already solved the new sliding circle cube(3.10.3).
I didn't expect anyone to solve this so soon. I, myself I have no clue at all :oops:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Sep 07, 2010 10:17 pm 
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Welcome to this forum, Stefan. I am pretty sure that you do have the ability to solve most of the GB puzzles.

Gelatinbrain: solving (3.10.3) is fun and different from previous puzzles, because that is like mixing the rolls of center pieces and edge pieces. It reminds me of the idea here:

viewtopic.php?f=9&t=17890&p=227531&hilit=mixup#p227531

The basic idea seems to be: when you turn the middle layer by 45 degrees, centers become edges and edges become centers. In face wwwmwww did say this would be a great gelatinbrain's applet.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 08, 2010 7:42 am 
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I'm going to add my welcome and say i'm very impressed with all your 2.1.x records especially and the fact that, unless i am mistaken, you have solved all 4.x.x and gained records for quite a few of them!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 08, 2010 3:35 pm 
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Hey Stefan, welcome! I agree with Elywn that your 2.1.x and your 4.3-7.x solves are phenomenal and your time and move counts make them that much more impressive.

Your solving strategy seems to be to go after the hardest puzzles first. I'm pretty sure none of Gelatinbrain's puzzles are out of your reach.

I'm looking forward to seeing more of your solves and hearing about your solving strategies.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Sep 08, 2010 7:21 pm 
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Welcome Stefan! I've been noticing more and more Agamemnon Harmagedon solves and I have been hoping that you would join and start posting here. You have set us tricky least move targets for 2.1.x, 4.3.1, 4.6.2, 4.7.2, etc.

Many puzzles have had solutions or hints posted in this thread by the person who got the record, but those posts can't be found easily using the search because GB puzzle names like 1.3.1 aren't recognized as search words. If you are interested in hints for particular puzzles, please list them here, because I can remember roughly which page they were on and I can give links.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 2:42 am 
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Hi Stefan, welcome to the forum :D Though I haven't exactly contributed with much to this thread, at least not compared to other members, I would like to say that I'm glad someone of your skill have joined. I've been browsing the records lists seeing your name and wondering who you were, and why you weren't on the forum (at least not to my knowledge). I think it will be great having your advise!

Also, at the moment I'm extremely busy with uni and work. So I've had no time at all for puzzle solving, virtual and non-virtual. But before the enormous work load at uni truly hit me, I was browsing this thread looking for ideas or inspiration to make new commutators for puzzles I already know how to solve (as I've started to get drawn into solving for fewest moves). One of Michael's 1.1.4 commutators caught my eye, as the beginning of it is precisely the same as my center switcher on puzzles like 1.1.4, 1.1.5, 1.1.20 etc. I tried it out on those puzzles and frankly I quite liked it, so I got it memorized and experimented a bit with it and discovered that it works also on the Pentultimate. Applied it gives this result:
Attachment:
1.1.7 commutator.jpg
1.1.7 commutator.jpg [ 51.53 KiB | Viewed 4455 times ]
The sequence is:
/*000000*/C',
/*000001*/F,
/*000002*/C,
/*000003*/F',
/*000004*/D',
/*000005*/F,
/*000006*/C',
/*000007*/F',
/*000008*/C,
/*000009*/D,
/*000010*/B',
/*000011*/E,
/*000012*/B,
/*000013*/D',
/*000014*/C',
/*000015*/F,
/*000016*/C,
/*000017*/F',
/*000018*/D,
/*000019*/F,
/*000020*/C',
/*000021*/F',
/*000022*/C,
/*000023*/B',
/*000024*/E',
/*000025*/B,

I don't know if this is any help to your Pentultimate outline, Brandon? I haven't gotten the chance to browse through all your pictures and results so you might already have this pattern included. At least I found it interesting. Also I would believe I now know how to solve it, though I have known about this commutator for two weeks or so, I have decided not to use it yet. My pride will be wounded if I would have to use someone else's solution to solve it :oops: So basically I'm sharing this in hope that this might be of help to yours and Julian's outline.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 3:10 am 
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Hey Katten, that's quite a beefy routine! The pattern you have there I've been calling "Arc of the Pentultimate". I'm not sure if I have that exact orientation pattern that your routine has though. The goal of my program is to find what is basically the optimal equivalent of Fridrich's OLL and PLL for the Pentultimate. I'm not sure what the fewest number of moves for the shortest routine will be but my guess is 14-16. Beyond 12 we'll be forced to add setup moves to complete the list.

If I were you I'd look for a length 16-20 corner 3-cycle and solve it with that. Most of the easy-to-find commutator based routines have a ((1,1),1) commutated-commutator in them. In the routine you posted, [C',F,C,F',D',F,C',F',C,D] is exactly a ((1,1),1) sequence.

The Pentultimate is a very hard puzzle -- one of the hardest of the 1.1.x series for sure. I look forward to seeing your name go up on the solver's list :D

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 2:13 pm 
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Thank you for all your welcomes. I took pleasure in it. It's great to be here, together with you great guys. I'm going to answer your posts in more detail, but not all at once.

When I first visited gelatinbrains rankings page in about Feb. 2009 , I was amazed that some puzzles were solved at all. For instance the 1.1.5 puzzle wich was supposed by me to be very hard or impossible to solve. (I did know this puzzle from my own puzzle-simulations, but I never solved it.) I thought: hey, they have proved that it is possible. This gave me really a kick.
And than I started with it. If I rember, the 2.1.1 was my first success. I continued than with 2.1.2 and 2.1.3. I played it several times. My time came down to 1 hour or so. Some times later I cracked the 1.1.5. These 60 tip pieces are not easy to solve. With a clean 3-cycle it is possible.
Now I look always first for such clean 3-cycles. At least, they must not change already solved pieces. I create first an order: for instance solve all edge-pieces, than solve all corner-pieces. While I solve the edge-pieces, I have not to care at all for any corner-piece. But when the edges are finished, and I'm going to solve the corner-pieces, I must care for the edges. So, for the edges I need a commutator, that is clean for edge-pieces but it can scramble any corner pieces without harm. but for the corners I need a clean commutator, which does'nt change the edge-pieces. I look than to find the necessary move-sequences and than I try my first solve. It's always the same.
But the puzzles are not the same. I often find new things in it. For instance multiple appearance-pieces.
The edge-faces of the Circle-FTO (GB 4.1.11) are such pieces. That are 8 pieces, which appear each 3 times. You can also say, that are triplets. They do not permutate, but can be oriented 3 ways.
More tricky are the small corner-faces of the 5.1.18. That are 6 pieces with 2 far appearances. If you see 12 pieces in it, you are fooled. That happend exactly to me, when I tried to solve the 5.1.18. After two hours of searching for a clean 3-cycle I gave up, and googeled 5.1.18. I found a post by Julian, in which he saw 6 pairs in them. And than I remembered suddenly multiple appearance pieces. I did know that, but I forgot to check it. If you try to do something impossible you can really waste hours and get angry. Much like the odd parity problem.

gelatinbrain wrote:
I'm really impressed that you and schuma have already solved the new sliding circle cube(3.10.3).


Gelatinbrain: the 3.10.3 has a piece-type with 192 members. You need great endurance to solve that. I used: F, B,U4,B', R,F',R',F, B, F',R,F,R', U'4, R,F',R',F, B', F',R,F,R', F', to solve the 192 pieces one by one.

schuma wrote:
Welcome to this forum, Stefan. I am pretty sure that you do have the ability to solve most of the GB puzzles.

schuma: I will have to prove that. You have solved all puzzles. That's great, great, great.

Elwyn wrote:
I'm going to add my welcome and say i'm very impressed with all your 2.1.x records especially and the fact that, unless i am mistaken, you have solved all 4.x.x and gained records for quite a few of them!


Elwyn: Thank you. I'm really proud of that. It nourishes my brain.

bmenrigh wrote:

Hey Stefan, welcome! I agree with Elywn that your 2.1.x and your 4.3-7.x solves are phenomenal and your time and move counts make them that much more impressive.

Your solving strategy seems to be to go after the hardest puzzles first. I'm pretty sure none of Gelatinbrain's puzzles are out of your reach.

I'm looking forward to seeing more of your solves and hearing about your solving strategies.


Brandon: Thank you too. I would start with the Spheres than. But they are to hard. For wich puzzle you want to hear my soving strategies first? Hey, you try to find a Friedrich-like method for the Pentultimate? Thats surely not easy.

Julian wrote:
Welcome Stefan! I've been noticing more and more Agamemnon Harmagedon solves and I have been hoping that you would join and start posting here. You have set us tricky least move targets for 2.1.x, 4.3.1, 4.6.2, 4.7.2, etc.

Many puzzles have had solutions or hints posted in this thread by the person who got the record, but those posts can't be found easily using the search because GB puzzle names like 1.3.1 aren't recognized as search words. If you are interested in hints for particular puzzles, please list them here, because I can remember roughly which page they were on and I can give links.


Julian: Thank you for your offer. Your move-counts are impressing.

Katten wrote:
Hi Stefan, welcome to the forum :D Though I haven't exactly contributed with much to this thread, at least not compared to other members, I would like to say that I'm glad someone of your skill have joined. I've been browsing the records lists seeing your name and wondering who you were, and why you weren't on the forum (at least not to my knowledge). I think it will be great having your advise!



Katten: Thank you.


Sorry if I was to short with some of you,
That's it for now,

Stefan.


Last edited by Stef-n on Fri Sep 10, 2010 4:21 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 4:15 pm 
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Julian wrote:
but those posts can't be found easily using the search because GB puzzle names like 1.3.1 aren't recognized as search words.

At google, type "1.3.1" site:http://twistypuzzles.com, for exemple.
Just in case you don't know. 8-)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 5:22 pm 
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Stefan Schwalbe wrote:
But the puzzles are not the same. I often find new things in it. For instance multiple appearance-pieces. The edge-faces of the Circle-FTO (GB 4.1.11) are such pieces. That are 8 pieces, which appear each 3 times. You can also say, that are triplets. They do not permutate, but can be oriented 3 ways. More tricky are the small corner-faces of the 5.1.18. That are 6 pieces with 2 far appearances. If you see 12 pieces in it, you are fooled. That happend exactly to me, when I tried to solve the 5.1.18. After two hours of searching for a clean 3-cycle I gave up, and googeled 5.1.18. I found a post by Julian, in which he saw 6 pairs in them. And than I remembered suddenly multiple appearance pieces. I did know that, but I forgot to check it. If you try to do something impossible you can really waste hours and get angry. Much like the odd parity problem.
I love these types of pieces. When you finally spot how they are connected it's a :idea: moment.

On this website the user wwwmwww calls those pieces "virtual pieces" but virtual seems like the wrong word. I prefer to think of them as "holographic pieces" where you have to think of them as being located in one place on the puzzle but they have parts of them that are projected out like a hologram to other locations. Most of the circle puzzles have these types of pieces. It is funny you should bring up the Circle FTO though because I've examined those circle pieces for more than an hour and I see how some are paired up and others indicate the orientation but I haven't been able to figure out how to actually solve the puzzle. Perhaps I need to revisit... Julian helped me figure out 5.1.18 too but I can't figure out how to move the paired pieces in 5.1.19.

On the topic of virtual/holographic pieces, take a look at 3.2.10, it has these pieces in a rather cool (to me) way.


Stefan Schwalbe wrote:
Brandon: Thank you too. I would start with the Spheres than. But they are to hard. For wich puzzle you want to hear my soving strategies first? Hey, you try to find a Friedrich-like method for the Pentultimate? Thats surely not easy.
The spheres are hard. Bandaging moves screw up my ability to make consistent routines.

I want to hear about your 2.1.1 solve strategy and solve order. Are your routines more efficient than mine posted here: http://www.twistypuzzles.com/forum/viewtopic.php?f=8&p=211229?

That is: center diamonds ((1,1), 3), center triangles ((1,1),1) and small two-color triangles ((1,1),3), where the (1,1) can sometimes be shortened to just 3 moves? Those 60 tiny 2-color triangles take me forever. Sometimes I have to use 8-10 setup moves to get them in the right position and orientation.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 6:05 pm 
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Stefan Schwalbe wrote:
But the puzzles are not the same. I often find new things in it. For instance multiple appearance-pieces.
The edge-faces of the Circle-FTO (GB 4.1.11) are such pieces. That are 8 pieces, which appear each 3 times. You can also say, that are triplets. They do not permutate, but can be oriented 3 ways.
More tricky are the small corner-faces of the 5.1.18. That are 6 pieces with 2 far appearances. If you see 12 pieces in it, you are fooled. That happend exactly to me, when I tried to solve the 5.1.18. After two hours of searching for a clean 3-cycle I gave up, and googeled 5.1.18. I found a post by Julian, in which he saw 6 pairs in them. And than I remembered suddenly multiple appearance pieces. I did know that, but I forgot to check it. If you try to do something impossible you can really waste hours and get angry. Much like the odd parity problem.


About the multiple appearance-pieces, the most fascinating puzzle is 3.2.10. Many pieces are locked with each other. Once you figure out the relative movement between them, you will find that this is nothing but a:

skewb ultimate

But the hard part is to recognize the equivalency relation between the pieces of 3.2.10 and the pieces of that puzzle. This is a completely different challenge.


Puzzle 3.4.24 also has many multiple appearance-pieces. I had to do a thorough analysis for the movement of all kinds of pieces. The basic principle is that if two pieces can be moved by the same set of turns, they belong to one multiple appearance-piece.

For example, I wrote down: each curved isosceles triangle can be moved by three face-turns (the three faces are around a vertex, call it vertex-A) and four vertex-turns (the four vertices are those vertices that are far away from vertex-A). The set of such three faces and four vertices has a three-fold rotational symmetry with respect to the line connecting vertex-A and the center of cube. Therefore, this set of turns will not only affect one curved isosceles triangle, but also two more triangles. These three triangles have a three-fold rotational symmetry with respect to the same line. Therefore they are actually one multiple appearance-piece.

I think this is a systematic method to recognize multiple appearance-pieces. I used this analysis a lot for 3.4.24. Eventually 3.4.24 cannot be reduced to any puzzle I'm familiar with. So I have to find some commutators to solve it.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Sep 09, 2010 7:47 pm 
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Stefan Schwalbe wrote:
gelatinbrain wrote:
I'm really impressed that you and schuma have already solved the new sliding circle cube(3.10.3).
Gelatinbrain: the 3.10.3 has a piece-type with 192 members. You need great endurance to solve that. I used: F, B,U4,B', R,F',R',F, B, F',R,F,R', U'4, R,F',R',F, B', F',R,F,R', F', to solve the 192 pieces one by one.
That is a clever algo. I couldn't find a pure algo to cycle smaller pieces on 3 different faces but I have found a pure commutated commutated commutator :) where 2 pieces are on the same face: (((L3, F), R'), U2). Setups are going to be tricky.

Stefan Schwalbe wrote:
For wich puzzle you want to hear my soving strategies first?
I'd like to read about your methods for 4.3.1 and 4.5.2, please.

gelatinbrain wrote:
At google, type "1.3.1" site:http://twistypuzzles.com, for exemple.
Just in case you don't know. 8-)
Thanks!


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