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 Post subject: Has anyone ever *solved* the 17x17x17 Over the Top puzzle?
PostPosted: Sun Mar 03, 2013 9:18 pm 
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Having recently completed my eight hour Petaminx Tutorial, I've been thinking about what it would take to record other long, big puzzle solves. It's not easy. In the short term, I'd like to tackle the Void Tuttminx and the Radiolarian 3, but what about the mighty 17x17x17, Oskar's Over the Top puzzle? Has it ever been scrambled and solved? Could it be done or would it be too stressful for the mechanism? Are the specimens too rare and valuable to play with them? I think a 17x17x17 solve video would be delightful and if one already exists, I'd sure like to see it.

Some people might wonder why I or anyone would bother with such big puzzles when there are other "more interesting" puzzles available. First, there are people who want to learn to solve these big puzzles. They don't want to figure it out, they just want to solve it. Second, these giant puzzles are interesting and attractive to many people who are not currently puzzle enthusiasts. They are big twisty ambassadors for our hobby. Finally, some of us really do enjoy solving simple, giant puzzles!

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 12:06 am 
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The only reason I could see anyone solving it is so they could say they solved it. The method used to solve it is the same as a 5x5x5, just longer and more tedious.


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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 1:01 am 
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Hi Pete,

I'm one of those who doesn't mind solving a large puzzle, over time, with a few sittings.

I think if you did want to `sit down for a solve` of the 17x17x17 you would want some sort of platform, that possibly held a corner, like RC stands do, with bearings in the base so it could be rotated around 360*. This would leave you the top 3 faces, and say 1/2 of the layers below to twist at any one time. Or maybe one that supported 2 corners and held the puzzle up, with an edge along the base, so certain slice twists might be available?

Zero gravity would be great too, maybe we could get it onto a space station some day.

Cheers,
Burgo.

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 1:59 am 
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I think an interesting theoretical question is, how many scramble steps are enough to "fully scramble" a 17x17x17.


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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 2:07 am 
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Hi Schuma,

Is that the same question as God's number?

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 2:17 am 
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schuma wrote:
I think an interesting theoretical question is, how many scramble :lol: steps are enough to "fully scramble" a 17x17x17.
Proof: 17x17x17 can take at least 379 moves Just a lower bound. It may be more.

Watching this youtube clip, it took him almost 50 seconds from the start of the first move to start the 2nd move properly. At that rate, it would take over 5 hours to scramble it.

It should be made clear that large nxnxn cubes are not hard. Lots of people have solve virtual ones much larger than 17. Speedcubing.com keeps some unofficial records. Someone did a 20x20x20 in under 2 hours. They also managed to do a 40x40x40 in just over 8 hours.

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 2:45 am 
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Pete the Geek wrote:
I think a 17x17x17 solve video would be delightful and if one already exists, I'd sure like to see it.

That would be like watching an entire series of 24, but with many more twists in the plot. :lol:

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 3:19 am 
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Burgo wrote:
Hi Schuma,

Is that the same question as God's number?

They're somewhat related but in practice the relation isn't very useful. If you had a fast "god's algorithm" implementation then the optimal scrambling strategy is to pick a element from the group at random and perform the inverse of god's algorithm to reach this state. In this way, your scramble is always less than or equal to god's number.

In practice though, we don't have god's algorithm for most puzzles so our scrambling strategy is to perform a lot of moves at random. You want to do enough moves that all resulting states are equally likely while not doing so many moves that you waste time. This has been called "Goldilocks Number" and a formula or algorithm for determining Goldilocks number for a given puzzle has been called the "Goldilocks function".

David Smith (formerly on the MC4D list) created a Goldilocks function for hypercubes and some other 4D twisty puzzles and it was integrated into MC4D. He attested to its correctness however I have some reservations and I'm not convinced that the numbers it produces approximate the optimal number.

Also, there isn't one true exact goldilocks number for all puzzles due to parity. At the very least there needs to be equal chance that your scramble uses an even number or odd numbers of moves. Of course this assumes a scramble doesn't allow duplicate moves in sequence which could wind up collapsing into a single move.

I'd certainly like to see some more work done in this area.

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 5:00 am 
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bmenrigh wrote:
David Smith (formerly on the MC4D list) created a Goldilocks function for hypercubes and some other 4D twisty puzzles and it was integrated into MC4D. He attested to its correctness however I have some reservations and I'm not convinced that the numbers it produces approximate the optimal number.

Presumably there is no function which ensures exactly equal probability for all states, so it's always going to be a trade-off between the "uniformity" of the probability distribution, and the number of moves. You would have to invent some kind of single trade-off metric to optimize, e.g., (maximum frequency - minimum frequency) / no. of moves. However, there will be many similar, but alternative metrics, so the optimum algorithm will depend on the metric you want to optimize. In other words, it depends what trade-off metric David had used to develop his function.

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 6:12 am 
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I'd love to solve one, I would not mind if it took a few hours. And I think one solve could be sufficient to completely break it in.


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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 6:27 am 
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I am pretty much past the point of wanting to solve puzzles. When I was into it though the 17x17x17 would certainly be top of my list. The satisfaction of returning so many messed up cubies to their proper position would outweigh any satisfaction I got from solving something truly new. To be honest I would have absolutely loved solving this thing and afterwards I would have wanted something even bigger to tackle. Naturally I would be using my own methods since I agree it would be boring if you were just using a copied solution.
Has anyone ever solved it? I doubt that very much. Simply because it would take way too long because of the movement.
Bizarrely I dreamt about some kind of 15x15x15 cube last night which had a price tag of £8.30.

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 6:41 am 
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Tony Fisher wrote:
Bizarrely I dreamt about some kind of 15x15x15 cube last night which had a price tag of £8.30.
If this was produced by Shapeways, then the cubie size would have to be about 0.7mm = edge length of 11mm. I'd like to see you sticker that :lol:

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 Post subject: Re: Has anyone ever *solved* the 17x17x17 Over the Top puzzl
PostPosted: Mon Mar 04, 2013 9:24 am 
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GuiltyBystander wrote:
Watching this youtube clip, it took him almost 50 seconds from the start of the first move to start the 2nd move properly. At that rate, it would take over 5 hours to scramble it.
Big Shapeways puzzles can require quite a bit of break in before they turn well. You've pointed to the heart of my question. Was this puzzle intended to be broken in and repeatedly solved. This would be a long and possibly tedious task. Videoing (I want to say "filming") would be technically challenging (everything is ONE take). Has anyone done it?

On scrambling big puzzles... I think a casual solve of a big puzzle can get away with less-than-theoretical scramble, as the act of solving the first and subsequent faces further scrambles the remaining puzzle. Still, for a puzzle that will take a week or two of evenings to solve, it makes sense to spend the first 30 or even 60 minutes on scrambling.

FWIW, I don't solve the Petaminx in one sitting or even two! The Petaminx is the biggest widely-available "simple" puzzle. It has 9 layers and 1,212 stickers to place. The Over-the-Top has 17 layers and 1,734. Daunting, but not orders-of-magnitude more.

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