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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 26, 2008 8:18 pm 
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AndrewG wrote:
This morning I just looked at some edge-turning dodeca- and icosahedra.

For the dodecahedra:
Depth 69 and 180 are present.
Depth 35 (roughly) is another good puzzle, roughly equivalent to a Bevel cube.
I do not see much else interesting here, except possibly something in the 158-179 range, possibly with some pieces unstickered.

For the icosahedra:
Depth 23, 34, 44, and 50 are definitely of interest, they resemble the Octahedral puzzles.
69, 83, and 90 are of interest also, although they might be pushing the envelope a bit more than we're ready for at this point (but hey, if a year ago we would have known what would have been accomplished by now, we'd be shocked)
Depth 180 is already present.

All of these are out of 360 (I looked at them on the Ultimate magic cube program).
Interesting! Please could you post little images of what these look like? (Those of us without a high-end graphics card can't run UMC.)

P.S. I like the term "quantum operation", and I look forward to reading your comparison of the move lengths of some puzzles.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 26, 2008 10:59 pm 
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Second Unsolved List - 6 puzzles
having algorithms for the solution
Image2.4.1 - Solution lost, Image 4.3.4 - The solution exists
Image 1.2.6b - his brother (1.2.6) is solved, here all is similar, Image 1.2.10 - his brother (1.2.3) is solved, here all is similar
Image 4.3.5 - solution there, Image 4.5.2 - solution there

(IMHO: 1.2.6b, 1.2.10 - medium, 2.4.1, 4.3.4 - hard, 4.3.5, 4.5.2 - easy)
------------------------------------------------------------
1 puzzle not in rank list - 2.4.1
------------------------------------------------------------
One Man List - 36 puzzles
Only 1 man has made it, probably this list is interesting to someone
1.2.3, 1.2.4, 1.2.5, 1.2.6, 1.2.7, 1.2.8, 1.2.11
1.3.1, 1.3.2, 1.3.3, 1.3.7, 1.3.8, 1.4.2
2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.5, 2.3.1
3.3.4, 3.4.3, 3.4.4, 3.4.6, 3.4.7, 3.4.9
3.6.2, 3.6.4, 3.6.5, 4.3.2, 4.5.1, 4.7.2
6.1.1, 6.1.3, 6.2.1, 6.2.2, 6.2.3, 6.2.4
------------------------------------------------------------
The list with all riddles reminds me a big raw diamond,
ranking-list is cut brilliant where each puzzle is a separate side,
All of us together process it, each new record in the general list is a sweep of a cutter,
Some sides are already polished, and some still wait for you!

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Last edited by grigr on Sun Feb 08, 2009 10:48 pm, edited 7 times in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 27, 2008 1:05 am 
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Julian wrote:
grigr wrote:
It is interesting to me why nobody has solved 1.3.7?

Or all have lost interest to socer-balls?
I was leaving 1.3.7 for Danny, but as he's said "eventually", I've gone for it. 1309 moves, in 2 hours 45 mins.

I didn't realize you were waiting, if I knew I would have told you to go for it. Your time and move count will most likely both be much better than mine anyway. And I still feel good that (I think) I was the first to figure out a solution, even if I didn't actually use it first.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 27, 2008 7:37 am 
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Danny Devitt wrote:
Julian wrote:
I was leaving 1.3.7 for Danny, but as he's said "eventually", I've gone for it. 1309 moves, in 2 hours 45 mins.

I didn't realize you were waiting, if I knew I would have told you to go for it. Your time and move count will most likely both be much better than mine anyway. And I still feel good that (I think) I was the first to figure out a solution, even if I didn't actually use it first.

You almost certainly were the first. I didn't click on 1.3.7 until last night, because I tend to shy away from soccerballs after my brain-melting experience with 1.1.14. It was a case of, "If I can't figure out a solution in an hour, I'll just leave it for much later." Fortunately, because I'd already come across the thin pieces 5 times already (2.1.1-2.1.3, 1.2.3 & 1.2.11), and the centers and diamond edges are easy, I didn't have much new work to do.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 27, 2008 1:03 pm 
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Julian, I have attached a file of some of the puzzles I mentioned. From left to right, top to bottom, they are:
23, 34, 44,
50, 69, 90

They're all to just the closest integer, so there are some abberations. I left 83 out, there are some pretty tiny pieces on that one.

23 is analagous to E60 on the octahedron, which isn't on gelatinbrain (but it also probably worthwhile)
34 is analagous to E90 on the octahedron, which is the first one on GB, 4.3.1
44 is looks like E 108 (I think) on the octahedron, which is also absent
50 looks like 4.3.2.
69 occurs when the cut passes through some corners
90 occurs when the several cuts meet halfway along an edge. I think it does involve some pretty tiny pieces which UMC blacks out for you but I'm not sure if gelatinbrain would want to do this.

For the last two I left a slice highlighted in the picture.

On some of these icosahedra a few more pieces show up around corners which are not present on the octahedra.

I haven't really done much more with "quantum operations" yet, but for the SuperX and Bevel+Dino (I call it "Vestar") hybrids I did several solves and collected data which allowed me to calculate an average number of moves used per piece in each step, which I think could also be a good measure of difficulty because it takes into account how many setup moves are used and how many pieces each three-cycle actually solves (on some puzzles this is 2+, on some it is probably only about 1.5)

Go here:
http://www.geocities.com/sxsk17/umcproj ... ehome.html
Click on the pages for SuperX (5th one down) and Vestar (bottom), then on the left click on "Analysis, Tips & Tricks)
I've also collected the same type of data for the "SuperO" (2x2x2+Skewb) but haven't written a webpage yet.


Attachments:
IcosaE's.jpg
IcosaE's.jpg [ 107.67 KiB | Viewed 3596 times ]

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 27, 2008 5:58 pm 
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You have made 2 mistakes on your web page thats in the last post and they are Adam Cowan not Adam Zamora made the Helicopter Cube and Super X Cube.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 9:59 am 
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AndrewG wrote:
Julian, I have attached a file of some of the puzzles I mentioned. From left to right, top to bottom, they are:
23, 34, 44,
50, 69, 90

They're all to just the closest integer, so there are some abberations. I left 83 out, there are some pretty tiny pieces on that one.

23 is analagous to E60 on the octahedron, which isn't on gelatinbrain (but it also probably worthwhile)
34 is analagous to E90 on the octahedron, which is the first one on GB, 4.3.1
44 is looks like E 108 (I think) on the octahedron, which is also absent
50 looks like 4.3.2.
69 occurs when the cut passes through some corners
90 occurs when the several cuts meet halfway along an edge. I think it does involve some pretty tiny pieces which UMC blacks out for you but I'm not sure if gelatinbrain would want to do this.

For the last two I left a slice highlighted in the picture.

On some of these icosahedra a few more pieces show up around corners which are not present on the octahedra.
Thanks! I'd be happy to see E34, E44, E50 & E69 added to 2.3.x. I think the small pieces of E23 would be too small to see properly in GB, and E90 has 362 pieces, which is probably too many for humans to endure (by comparison, 4.7.2 has 280 pieces, and 1.2.8 has 302). Given the choice of just one, I'd ask GB to add E50. E23 = piece equivalent of face-turner 2.1.1, with an extra set of wings; E34 = 2.1.3 + extra wings; E44 = 2.1.4 + extra edges; E50 = 2.1.4. E69 would be something completely new, visually.

Could you also give us pics of the dodeca ones? I'm especially interested in the one where the cuts go right through corners, which I think would be E125.

AndrewG wrote:
I haven't really done much more with "quantum operations" yet, but for the SuperX and Bevel+Dino (I call it "Vestar") hybrids I did several solves and collected data which allowed me to calculate an average number of moves used per piece in each step, which I think could also be a good measure of difficulty because it takes into account how many setup moves are used and how many pieces each three-cycle actually solves (on some puzzles this is 2+, on some it is probably only about 1.5)
Thinking about this more, if a commutator of 30 moves is 14 + 1 + 14 + 1 where a swapped piece is isolated in 14 moves, that's a quantum operation length of 14. The rest is just single move, undo operation, undo single move.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 1:11 pm 
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grigr wrote:
1 unsolved puzzles:
1.2.8 Image
1.2.8 solved, in 3441 moves. :) I missed the latest update by a few hours, so 1.3.7 and 3.6.5 are on the rankings page now but 1.2.8 isn't. I'll try to post a solution outline for 1.2.8 sometime next week.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 1:40 pm 
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After finishing 1.2.8, I noticed how much longer my 1.2.7 solve was in comparison. After some more playing around with 1.2.7 I've found that the small wings next to the corners can be solved pure at the end in 14 moves instead of 30. That, combined with solving the corners with a shorter commutator, would enable me to re-solve 1.2.7 in under 3500 moves, even without any other improvements... but life is too short for me to put theory into practice. I'll update my solution outline for 1.2.7.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 4:03 pm 
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Thanks for weighing in Julian. I wasn't able to estimate feasibility well because I don't really do dodeca/icosahedral puzzles because I think they are long and boring :)

As for other dodecahedra, at about depth 111 the cuts coincide with corners again. I too was excited when this thought came to mind, but actually looking at the puzzle reveals that it's quite ugly.
There are (broken down by piece type)
30+60 = 90 two-color pieces
12+60+60+60+60+120+120+120= 612 one-color pieces

For 702 pieces total. One type of the pieces of which there are 120 is particularly tiny.
I guess the problem is that except for the corners, there is place where more than three cut lines intersect.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 4:12 pm 
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Also, I wasn't thinking of "quantum operation" as something which "isolating a piece" could fufill. This is because the act of isolating a piece is often allowed to leave another portion of the puzzle scrambled, so it NEEDS the undoing operation to make it a usable sequence.

Also comms are made in many different ways so I think it would be detrimental if the comms of the "form" (N+1)*2 where counted as just N. Because then the 3.3.6 three-cycle (which is an 8+8+8+8 comm) would still count as 32 while other similar-length comms would count as 14 or 15. There are various other examples like the 4+3+4+3 comm for 3.3.3 and the 10+5+10+5 comm I use for the 2x2x2+little chop which finish isolating the piece in the Y portion.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 9:22 pm 
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Julian wrote:
1.2.8 solved, in 3441 moves. :) I missed the latest update by a few hours, so 1.3.7 and 3.6.5 are on the rankings page now but 1.2.8 isn't. I'll try to post a solution outline for 1.2.8 sometime next week.

If that is the last one then what about 1.2.10? It's not on the scoreboard...

I think that the next step is to make sure everything is on the scoreboard. Also, maybe the next challenge for Julian is to do some Spheres, which no one really got except me.

So here's a list of stuff not currently on the scoreboard:
1.2.10, 4.5.2, 4.3.4, 4.3.5, 2.4.1, (and 1.2.8)
I guess it would be nice to have a summary for these if no one wants to solve/re-solve these. Eventually (like in the next 6 years), I hope to solve those - and the 30 others I have remaining.

We should have some sort of title bestowed upon whoever actually completes all 183 of the GB puzzles. (I think the 189 figure in the stats page is wrong.) Like "Grandmaster of Twisty Puzzles", similar to chess.

(Btw, in forming this list, I noticed that the number is offset in the 1.4.x. Typo here: "1.3,2". GB should fix these.)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 28, 2008 11:02 pm 
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Well I just looked back at 1.3.7. I had essentially forgotten my old solution (I have it written down somewhere though) and so I figured I'd figure out a new one. The solution I came up with this time must be far better than whatever I came up with before, because within 5 minutes I had it and it wouldn't take too terribly long. Here's what I came up with:

There are 4 piece types: pentagonal centers, triangular centers, diamond centers, and edges.

Pentagonal centers are easily solved using the built-in 3-cycle corner moves.

Edges are then solved using face moves only. This is equivalent to solving an impossiball.

Diamond centers are solved using a non-pure 3-cycle commutator (4+1+4+1=10) (technically the 4s are also commutators of 1+1+1+1)

And finally triangular centers are solved using a pure 3-cycles commutator ((4+1+4+1)+1+(4+1+4+1)+1=22) (technically the 4s are also commutators of 1+1+1+1).

The first two steps should be done in a couple minutes and then the rest all depends on luck and how good you can do set-up moves. I estimate that you could easily use no more than 25 3-cycles each for the 3rd and 4th steps. I would estimate a total move count of under 1400 moves. This seems consistent with Julian's move count as I actually think that in most cases a number around 1300 is far more likely.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 1:11 pm 
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@ Danny, I didn't see your post until this morning. thanks, I fixed my website just now.

@ Doug: lol. or maybe the forum could issue a Master's in Computer Puzzle Solving :D

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 1:33 pm 
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AndrewG wrote:
@ Danny, I didn't see your post until this morning. thanks, I fixed my website just now.


Do you mean me? Darren Grewe

viewtopic.php?p=138289#p138289

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 2:55 pm 
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haha I'm so sorry! apparently I'm no good with names at all! :(

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 3:24 pm 
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UMichSpeedCubist wrote:
If that is the last one then what about 1.2.10? It's not on the scoreboard...
1.2.10 needs fixing. It's supposed to have slice moves only (as is 1.1.8), as confirmed by the functioning and naming of 1.3.3 = 1.1.8 + 1.2.10; also the Windows standalone versions have inner slices only. It would be annoying to have to hold or weigh down the shift key throughout the solve for the "authentic 1.2.10 experience", plus someone else could then come along and knock the record down by solving it like 1.2.3, so I'm hoping GB fixes it sometime.
UMichSpeedCubist wrote:
I think that the next step is to make sure everything is on the scoreboard.
Yes, especially as we are so close now. I'll probably be able to get 4.3.4 and 4.5.2 done next weekend, as I have solutions for both and they shouldn't take that long. I'll get around to the others later in the winter, maybe even including redoing 2.4.1. I'm looking to relax with mostly shorter and easier puzzles for a while.
UMichSpeedCubist wrote:
Also, maybe the next challenge for Julian is to do some Spheres, which no one really got except me.
I once tried 6.1.1 for a while and was utterly bamboozled. Someday I'll try again.
UMichSpeedCubist wrote:
So here's a list of stuff not currently on the scoreboard:
1.2.10, 4.5.2, 4.3.4, 4.3.5, 2.4.1, (and 1.2.8)
I guess it would be nice to have a summary for these if no one wants to solve/re-solve these. Eventually (like in the next 6 years), I hope to solve those - and the 30 others I have remaining.
I think they all have summaries earlier in the thread, except for 1.2.8. 1.2.10 can be solved exactly like 1.2.3, which has a summary by me; Evgeny gave summaries for 4.3.5 and 4.5.2; and I gave summaries for 4.3.4 and 2.4.1 (well, a solution to 2.2.6 is needed to solve 2.4.1 my way, and I'm not sure if 2.2.6 ever had a summary written for it). There's also 1.2.6b, which has center pieces that require orientation, but I haven't played with it yet to see how much more is involved than with 1.2.6.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 3:32 pm 
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AndrewG wrote:
Thanks for weighing in Julian. I wasn't able to estimate feasibility well because I don't really do dodeca/icosahedral puzzles because I think they are long and boring :)

As for other dodecahedra, at about depth 111 the cuts coincide with corners again. I too was excited when this thought came to mind, but actually looking at the puzzle reveals that it's quite ugly.
There are (broken down by piece type)
30+60 = 90 two-color pieces
12+60+60+60+60+120+120+120= 612 one-color pieces

For 702 pieces total. One type of the pieces of which there are 120 is particularly tiny.
I guess the problem is that except for the corners, there is place where more than three cut lines intersect.
Yuck! Thanks, it was worth a thought.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 5:25 pm 
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AndrewG wrote:
Also, I wasn't thinking of "quantum operation" as something which "isolating a piece" could fufill. This is because the act of isolating a piece is often allowed to leave another portion of the puzzle scrambled, so it NEEDS the undoing operation to make it a usable sequence.

Also comms are made in many different ways so I think it would be detrimental if the comms of the "form" (N+1)*2 where counted as just N. Because then the 3.3.6 three-cycle (which is an 8+8+8+8 comm) would still count as 32 while other similar-length comms would count as 14 or 15. There are various other examples like the 4+3+4+3 comm for 3.3.3 and the 10+5+10+5 comm I use for the 2x2x2+little chop which finish isolating the piece in the Y portion.
I was rethinking things from the angle of "What's the longest sequence you need to figure out in order to be able to solve the puzzle?" If you manage to isolate a swapped piece in x moves, commutating to (x+1)*2 moves is a formality. For example, when solving the corners of the Super-Pentultimate without affecting the centers, x=6. Isolate a swapped corner in 6 moves and you know you're home and dry, and it never takes more than 6 moves to push any 3 corners into adjacent positions, or to push them from adjacent positions into the positions needed for the base algo. That fact might surprise a lot of people, and give them encouragement to find a/the "magic 6 move sequence". I suspect that 150+ of the GB puzzles don't require the solver to work out any sequence longer than 9 moves, where every sequence has a clearly visible subgoal, including both rehearsed and improvised sequences. I guess I've shifted to "readily understandable operation". Overheard at a puzzling symposium in the future, during a break before the Grandmaster award is presented: "So do you use the QO or RUO paradigm for measuring x?" :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 9:23 pm 
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Julian, I'm not sure what's best at the moment, but its an interesting topic and I'll be putting some thought into it soon. First, I have a few comments though.

What is the purpose of trying to define this "x"? I just spent a few hours thinking about these concepts and realized that a major problem is that I don't know exactly what result I'm searching for. Right now I'm under the impression that this will allow us to estimate the relative difficulty of puzzles. (A problem well-stated really is half solved. haha)

I do have one thing for consideration, however. I think we both agree that setup moves should be considered in some way. What I was just thinking of is whether to consider the average setup moves needed or the MOST setup moves needed. I'm still toying with my idea of using an average "moves per piece" to estimate difficulty.

The most needed could be determined exhaustively by determining setups needed for every relative position of 2 or 3 pieces, but this is probably not fun. An exact average could also be determined with even more work (lots of probability, etc etc), or an average could be experimentally determined by just doing several solves and recording the correct data.

It seems logical to me that the overall difficulty of the puzzle is more related to the most complicated case than the average case (as far as setup moves go). Figuring out the length of the most complicated case even for simple puzzles could be a huge ordeal, though, and it might be an extremely rare case anyway.


Also, I have another thought just to throw out there.
The list of puzzles on GelatinBrain (currently) is extremely arbitrary. There were some odd choices for what to include and exclude, but this is because GB made most of the applets before anyone really cared much about the subject and twisty puzzles like those on his site were not previously classified in any meaningful way. (I remember how my jaw dropped because his website was FOUND by members here, not "announced" here. It's amazing someone did so much with no community around them; he's a bit like Okamoto in that respect)

As such, GB was the first that I know of to try to organize the "universe of twisty puzzles" in a meaningful way, with his decimal-based system (1.2.2, etc). However, better systems could be established.

Once a system is established, it could be much more meaningful to talk about having solved all the members of certain groups of puzzles.

Now, naturally I recommend my system of classification :mrgreen: (which I've mentioned previously, though it hasn't attracted much attention), but there could definitely be better things out there, especially beacuse I developed my classification mainly by looking at only cubes, which hybridize in a much more aesthetically pleasing way and don't have some of the horribly intimidating puzzles present among the higher polyhedra.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 10:04 pm 
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Julian wrote:
AndrewG wrote:
Thanks for weighing in Julian. I wasn't able to estimate feasibility well because I don't really do dodeca/icosahedral puzzles because I think they are long and boring :)

As for other dodecahedra, at about depth 111 the cuts coincide with corners again. I too was excited when this thought came to mind, but actually looking at the puzzle reveals that it's quite ugly.
There are (broken down by piece type)
30+60 = 90 two-color pieces
12+60+60+60+60+120+120+120= 612 one-color pieces

For 702 pieces total. One type of the pieces of which there are 120 is particularly tiny.
I guess the problem is that except for the corners, there is place where more than three cut lines intersect.
Yuck! Thanks, it was worth a thought.

MAD puzzle


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 29, 2008 10:21 pm 
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Julian wrote:
grigr wrote:
1 unsolved puzzles:
1.2.8 Image
1.2.8 solved, in 3441 moves. :) I missed the latest update by a few hours, so 1.3.7 and 3.6.5 are on the rankings page now but 1.2.8 isn't. I'll try to post a solution outline for 1.2.8 sometime next week.

Well Done - Julian
1.2.8 - He is last hero who has surrendered before You :)
You liked travel round-the-world (Australia, China, Russia, etc.)?
Now when you will have a rest at home on holidays, you recollect those 6 which are not solved yet?
:D

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 3:39 pm 
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After typing my last post I had a fit of inspiration and typed up something last night and this morning. It's about a system to classify twisty puzzles with. Let me know what you think. It's kinda long... 8 pages, but there are also lots of pictures :) (some of which did not compress very well... but meh, they're ok)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 4:30 pm 
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grigr wrote:
2.4.1 - Solution lost
:( Here's my screenshot for 2.4.1 from November 2nd:

Image

I took extended breaks, but at least 5 hours were puzzling time. I'll try to do it again in under 5 hours in the next month or two. I solve the 2.2.6 pieces first, like a Super-Pentultimate with single-colored corners, then the two-colored "arrow" pieces non-pure with an 18-move algo, then the smaller triangles pure with a 30-move algo. The setups for the last two stages are quite mind-warping.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 6:58 pm 
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AndrewG wrote:
After typing my last post I had a fit of inspiration and typed up something last night and this morning. It's about a system to classify twisty puzzles with. Let me know what you think. It's kinda long... 8 pages, but there are also lots of pictures :) (some of which did not compress very well... but meh, they're ok)
I like! Both the overall division of puzzles into single cut, multiple cut, and hybrid, and the details of your proposed system, which could prove to be very useful for non-cube puzzles where the cuts don't fit a whole number of degrees.


Last edited by Julian on Tue Dec 30, 2008 7:45 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 7:42 pm 
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AndrewG wrote:
What is the purpose of trying to define this "x"? I just spent a few hours thinking about these concepts and realized that a major problem is that I don't know exactly what result I'm searching for. Right now I'm under the impression that this will allow us to estimate the relative difficulty of puzzles. (A problem well-stated really is half solved. haha)
I'm also looking to find a partial measure of relative difficulty.
AndrewG wrote:
I think we both agree that setup moves should be considered in some way. What I was just thinking of is whether to consider the average setup moves needed or the MOST setup moves needed. I'm still toying with my idea of using an average "moves per piece" to estimate difficulty.
My preference would be to try to estimate both average and maximum setup moves needed. Average moves per piece is another useful indicator, but I'm thinking it might underestimate the difficulty of some puzzles, especially a hybrid where most of the solve is fairly quick and easy, apart from a particular piece type that is very difficult to move around without disturbing its neighbors.
AndrewG wrote:
The most needed could be determined exhaustively by determining setups needed for every relative position of 2 or 3 pieces, but this is probably not fun. An exact average could also be determined with even more work (lots of probability, etc etc), or an average could be experimentally determined by just doing several solves and recording the correct data.
An experimental average seems good. Also, maybe an estimated maximum could be worked out for some of the more popular puzzles via collaborative "challenge-response". Hypothesis: "I reckon you never need more than 8 moves to set up any of the pieces of this puzzle." Challenge: "Okay then, how would you set up THESE? [screenshot]" Response: "I see what you mean. 10 then." OR "Like THIS."
AndrewG wrote:
It seems logical to me that the overall difficulty of the puzzle is more related to the most complicated case than the average case (as far as setup moves go).
I agree.
AndrewG wrote:
Figuring out the length of the most complicated case even for simple puzzles could be a huge ordeal, though, and it might be an extremely rare case anyway.
Yes, and I don't think calculating a precise answer would be worth the effort.
AndrewG wrote:
The list of puzzles on GelatinBrain (currently) is extremely arbitrary. There were some odd choices for what to include and exclude, but this is because GB made most of the applets before anyone really cared much about the subject and twisty puzzles like those on his site were not previously classified in any meaningful way. (I remember how my jaw dropped because his website was FOUND by members here, not "announced" here. It's amazing someone did so much with no community around them; he's a bit like Okamoto in that respect)
I share your sense of wonder, and admiration for GB. My impression is that the non-hybrids are more a complete set than the hybrids. The potential hybrids are indeed "a vast, dark world into which there has not yet been much exploration", as you say in your paper.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 7:58 pm 
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Danny Devitt wrote:
Well I just looked back at 1.3.7. I had essentially forgotten my old solution (I have it written down somewhere though) and so I figured I'd figure out a new one. The solution I came up with this time must be far better than whatever I came up with before, because within 5 minutes I had it and it wouldn't take too terribly long. Here's what I came up with:

There are 4 piece types: pentagonal centers, triangular centers, diamond centers, and edges.

Pentagonal centers are easily solved using the built-in 3-cycle corner moves.

Edges are then solved using face moves only. This is equivalent to solving an impossiball.

Diamond centers are solved using a non-pure 3-cycle commutator (4+1+4+1=10) (technically the 4s are also commutators of 1+1+1+1)

And finally triangular centers are solved using a pure 3-cycles commutator ((4+1+4+1)+1+(4+1+4+1)+1=22) (technically the 4s are also commutators of 1+1+1+1).

The first two steps should be done in a couple minutes and then the rest all depends on luck and how good you can do set-up moves. I estimate that you could easily use no more than 25 3-cycles each for the 3rd and 4th steps. I would estimate a total move count of under 1400 moves. This seems consistent with Julian's move count as I actually think that in most cases a number around 1300 is far more likely.
Suggested minor improvements: If you swap the middle two stages you can cycle the diamond centers in 8 moves, not caring what happens to the edges, then you solve the edges pure using face moves. The small triangles can be cycled slightly faster in 20 moves -- separate one from its neighbors in 4 moves, replace with a different colored one on the 5th move, undo the previous 4 moves, and then commutate to get 9+1+9+1.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 8:00 pm 
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grigr wrote:
Well Done - Julian
1.2.8 - He is last hero who has surrendered before You :)
You liked travel round-the-world (Australia, China, Russia, etc.)?
Now when you will have a rest at home on holidays, you recollect those 6 which are not solved yet?
:D
Thanks, and yes, they are not forgotten! :)


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 30, 2008 9:25 pm 
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Julian wrote:
Danny Devitt wrote:
Well I just looked back at 1.3.7. I had essentially forgotten my old solution (I have it written down somewhere though) and so I figured I'd figure out a new one. The solution I came up with this time must be far better than whatever I came up with before, because within 5 minutes I had it and it wouldn't take too terribly long. Here's what I came up with:

There are 4 piece types: pentagonal centers, triangular centers, diamond centers, and edges.

Pentagonal centers are easily solved using the built-in 3-cycle corner moves.

Edges are then solved using face moves only. This is equivalent to solving an impossiball.

Diamond centers are solved using a non-pure 3-cycle commutator (4+1+4+1=10) (technically the 4s are also commutators of 1+1+1+1)

And finally triangular centers are solved using a pure 3-cycles commutator ((4+1+4+1)+1+(4+1+4+1)+1=22) (technically the 4s are also commutators of 1+1+1+1).

The first two steps should be done in a couple minutes and then the rest all depends on luck and how good you can do set-up moves. I estimate that you could easily use no more than 25 3-cycles each for the 3rd and 4th steps. I would estimate a total move count of under 1400 moves. This seems consistent with Julian's move count as I actually think that in most cases a number around 1300 is far more likely.
Suggested minor improvements: If you swap the middle two stages you can cycle the diamond centers in 8 moves, not caring what happens to the edges, then you solve the edges pure using face moves. The small triangles can be cycled slightly faster in 20 moves -- separate one from its neighbors in 4 moves, replace with a different colored one on the 5th move, undo the previous 4 moves, and then commutate to get 9+1+9+1.


I can't seem to figure out a useful 8 move algorithm for diamonds, even if you ignore edges. And as far as the second suggestion, I again can't seem to find the algorithm either and I also realized that my algorithm is a double 2-swap instead of a 3-cycle. I've only tried for about 5 minutes just now though so don't tell me unless I ask again.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Jan 09, 2009 9:43 am 
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This thread seems very lonely since the New Year :(

Well, yesterday I was bored so I went ahead and solved the last two of the fundamental face-turning dodecahedra, so now I've solved all four. Didn't do them on gelatinbrain but they're 1.1.5 and 1.1.7 there. I'd been meaning to get around to them for quite a while, I'm just not a particular fan of the actual process of solving puzzles, I mainly like writing methods and otherwise just talking about puzzles :)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jan 11, 2009 2:01 am 
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I have no idea why I put off 1.3.7 for so long. I just solved it in 56:07 and 1550 moves. The way I wound up solving it was:

1. pentagonal centers
2. diamond centers
3. edges
4. triangular centers (and I figured out my alg was actually a 5-cycle or 6-cycle (depending if you did a 1/5 or 2/5 turn on one move) but it was only on 2 faces so it actually worked pretty well.

Also, I was solving on a mac (with a wireless mouse) but after I clicked what I thought was submit (the screen shows up behind the puzzle, if you remember) I was given a certificate... any thoughts?

c8ee77d04267f1ce54c276c614e65dcd
57a92e49d99d163bb063682ed09b6437
c897613dc27c89fa1379a1a7431791df
237a85f40bd926b34c7986f20db94673

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jan 11, 2009 2:32 am 
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Danny Devitt wrote:
I have no idea why I put off 1.3.7 for so long. I just solved it in 56:07 and 1550 moves. The way I wound up solving it was:

1. pentagonal centers
2. diamond centers
3. edges
4. triangular centers (and I figured out my alg was actually a 5-cycle or 6-cycle (depending if you did a 1/5 or 2/5 turn on one move) but it was only on 2 faces so it actually worked pretty well.

Also, I was solving on a mac (with a wireless mouse) but after I clicked what I thought was submit (the screen shows up behind the puzzle, if you remember) I was given a certificate... any thoughts?

c8ee77d04267f1ce54c276c614e65dcd
57a92e49d99d163bb063682ed09b6437
c897613dc27c89fa1379a1a7431791df
237a85f40bd926b34c7986f20db94673


i was solving the master pyraminx and 2.2.1 (centerless icosaminx) on my mac, and got 2 certificates in a row. i cant have missed submit twice, surely? :solved:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jan 11, 2009 3:14 am 
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I think it's a mac issue for a few reasons.

1) The certificate button has actually been disabled so you can't even push it if you tried
2) I've solved on a mac before and the button that you can see is definitely the submit button
3) I just went and solved a few random puzzles on a windows computer (including 2.2.1) and I wasn't given a certificate or anything weird

So then why is this happening? And will the solves still go through? If the answer to the 2nd is yes, then I don't really care, but if not then this should be fixed.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Jan 11, 2009 3:21 pm 
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Danny Devitt wrote:
I think it's a mac issue for a few reasons.

1) The certificate button has actually been disabled so you can't even push it if you tried
2) I've solved on a mac before and the button that you can see is definitely the submit button
3) I just went and solved a few random puzzles on a windows computer (including 2.2.1) and I wasn't given a certificate or anything weird

So then why is this happening? And will the solves still go through? If the answer to the 2nd is yes, then I don't really care, but if not then this should be fixed.


I just solved the lattice cube twice (Intuatively :D ) on my mac and didn't get the certificate showing. And it REALLY needs to be fixed if it happens again and the solves dont go through.

EDIT: while typing this message, the certificate just appeared :P

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Feb 08, 2009 10:47 pm 
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It is interesting to me, why anybody did not try to solve till now :?:
4.3.5, 4.5.2 - easy puzzle, or already nobody plays? :(

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 09, 2009 10:25 am 
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This may be because all of the puzzles are solved.
when I was looking through the solving forum, I noticed this topic again, and tried some more puzzles. I have finally solved the super-X, with my own, waaaay to difficult, algorithms. so now I only need to solve two more puzzles to get to the number 9 of most puzzles solved!

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 09, 2009 9:50 pm 
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Sjoerd wrote:
This may be because all of the puzzles are solved.

And who has solved all it?
6 Unsolved puzzles: 2.4.1, 4.3.4, 1.2.6b, 1.2.10, 4.3.5, 4.5.2
I have checked up these riddles do not enter in RankScore

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Feb 11, 2009 1:45 am 
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Well those ones all have known solutions so it's just a matter of putting in the time.

I haven't been doing these lately because of school... when spring break comes (or if I have a lot of spare time at some point), I'll be trying to solve a few more of these

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Feb 12, 2009 3:49 pm 
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Julian wrote:
grigr wrote:
1 unsolved puzzles:
1.2.8 Image
1.2.8 solved, in 3441 moves. :) I missed the latest update by a few hours, so 1.3.7 and 3.6.5 are on the rankings page now but 1.2.8 isn't. I'll try to post a solution outline for 1.2.8 sometime next week.


Doesn´t this mean all the puzzles are solved?

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Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Feb 12, 2009 6:45 pm 
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If you look back at his other lists, you'll see that he had a list of puzzles with no solution and a list of puzzle which do but that haven't physically been solved yet. All puzzles have solutions now, but those 6 still just need the manual work.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Feb 13, 2009 3:27 am 
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Ok, I misunderstood

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Feb 15, 2009 4:29 pm 
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grigr wrote:
Sjoerd wrote:
This may be because all of the puzzles are solved.

And who has solved all it?
6 Unsolved puzzles: 2.4.1, 4.3.4, 1.2.6b, 1.2.10, 4.3.5, 4.5.2
I have checked up these riddles do not enter in RankScore
Well, I just spent over 5 hours on 4.3.4, got within 11 pieces of solved, and clicked Clear by mistake. No way to Undo. I'll try again next weekend.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Feb 15, 2009 11:09 pm 
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Julian wrote:
Well, I just spent over 5 hours on 4.3.4, got within 11 pieces of solved, and clicked Clear by mistake. No way to Undo. I'll try again next weekend.

:(

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 16, 2009 2:37 am 
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Julian wrote:
grigr wrote:
Sjoerd wrote:
This may be because all of the puzzles are solved.

And who has solved all it?
6 Unsolved puzzles: 2.4.1, 4.3.4, 1.2.6b, 1.2.10, 4.3.5, 4.5.2
I have checked up these riddles do not enter in RankScore
Well, I just spent over 5 hours on 4.3.4, got within 11 pieces of solved, and clicked Clear by mistake. No way to Undo. I'll try again next weekend.

:( :( :(

Can someone give me a hand with the super X, i got up to here, and cannot figure out any more:
Image

-Door-

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 16, 2009 3:21 am 
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Do you want an algorithm or hint or what? I just did it in 37 moves and I highly doubt that's optimal.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 16, 2009 3:27 am 
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Danny Devitt wrote:
Do you want an algorithm or hint or what? I just did it in 37 moves and I highly doubt that's optimal.


If you want, you could give me an algorithm, but im also happy with just some tips, e.g "you need to 3-cycle ____..." or "You need to flip ____ and then 3 cycle ____..." :P

Any help is much appreciated! :)





~EDIT!~
2 Days ago, I decided i wanted to do a long solve, so i went for the Gigaminx. My first attempt, I got 1h 6m 9s, and 1656 moves. I didnt get a picture of this, and so i decided to have another go, just to get a picture! :lol: And here it is:
Image

Also, I decided to try solve the Master pyraminx crystal yesterday, and I solved it on and off throughout the day:
Image

I then tried Seriously(Without Breaks), and got this:
Image

For the Gigaminx, I solved Centers, then I did edge pairing, then I just solved like a Megaminx
For the Master Pyraminx Crystal, I First solved the centers, then I paired edges(But its quite different to gigaminx styles -- When moving edge pieces to match other edge pieces, you always move a middle edge and a small edge at the same time. You people probably know this anyway! :P ) and then solved like a Megaminx.

Kind regards,
~Door~ (Mark)

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Last edited by Door on Mon Feb 16, 2009 4:03 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 16, 2009 3:40 am 
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Door wrote:
If you want, you could give me an algorithm, but im also happy with just some tips, e.g "you need to 3-cycle ____..." or "You need to flip ____ and then 3 cycle ____..." :P

you need two 3-cycle
;)

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 16, 2009 4:08 am 
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grigr wrote:
Door wrote:
If you want, you could give me an algorithm, but im also happy with just some tips, e.g "you need to 3-cycle ____..." or "You need to flip ____ and then 3 cycle ____..." :P

you need two 3-cycle
;)


Hmm ok I'll think about it while trying to get to sleep :P I Have to close it down because i have an early day tomorrow, and I cant leave the computer on over night. Ill figure it out some time :wink: Thanks for the help, i am already thinking how to do it :)

~Mark~

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Feb 16, 2009 4:40 am 
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While trying this time to get something a bit more optimal, I managed 13. However, since I first solved into the position and then out of it differently, it is quite possible that the first few moves undid the previous ones, especially since I can't reproduce it and even more so because the super-x has even parity. The farthest I know I've gotten to is 20.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Feb 17, 2009 2:50 am 
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Location: New Zealand
Figured it out. All i did was a couple of setup moves and then used the (parity?) edge flipping algorithm.

solved first in 14 mins something, and then 4 minutes something, ill post a couple of pics when i get around to it.
I also solved the one after the Master pyraminx crystal (I Gigaminx crystal :) ?) solved in 40 something mins. Pictures soon.

I feel great to be able to solve these, even if loads of other people have solved them before :D

-Mark-

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Tony Fisher wrote:
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