Sunday, 30 June 2013

Lock 250+ and the Generation Lock ...



A few weeks ago Wil Strijbos sent out one of his customary email newsletters with a bunch of puzzles available for sale. One of the puzzles that caught my eye was one that I'd been meaning to get for a little while called the Lock 250+, so I asked Wil to put one aside for me and he duly brought it over when he came to join us at MPP11. 


It's a neat looking lock-shaped n-ary puzzle made by Jean Claude Constantin in laser-cut plywood. The outer panels are all veneered and it looks reasonably innocuous - although there's an ominous clue in the name that there may well be c.250 moves to open (and then another 250 moves to close) this puzzle. Looking between the slots in the sides you can see a series of internal plates that are moved up and down through the interactions of the steel sliders. The bottom slider is pretty much free to move left and right all of the time and the plates interact to allow each successive slider to move one place until it completes a full transit, allowing the next slider to move one space along... repeat until open...


At MPP11 Kevin had brought his copy along and reckoned that once you got into the rhythm of a particular n-ary puzzle, they became pretty mechanical and didn't take long to solve at all... mere minutes for this little 250-ish move version...


At that point Kevin made a fatal mistake - he engaged Wil in a conversation about the fact that the highest order n-ary puzzle currently out there was "only" around 4000-odd moves (the 7-ary Kugellager puzzle) - now I knew what was coming (having seen the monster the night before) and played along a little coaxing him to suggest just how high he might like to go... he plumped for c.6000 moves... and with that Wil introduces a special collectors' edition fresh from the Constantin workshop - dubbed the Generation Lock, it's a slightly larger version of the Lock 250+ .... slightly larger... OK, I lied ... it's huge! (and we all know that size isn't everything...)
 

So how do they compare?


Lock 250+ has 4 sliders ... three of them have 6 positions each and the bottom one shuttles between the two extremes freely... the Generation Lock also has a bottom slider that shuttles between the two end positions freely, however it has a further 7 sliders each with 15 positions... so similar then?


Well, yes - in the same way that the Spirit of St Louis is similar to an F14... 

Think about the number of discrete positions and moves on the Lock 250+ : each of the three main sliders has 6 positions (including the start position), so each has to make 5 moves... and each one relies on the previous slider having done one complete left/right transition also taking 5 moves (except the bottom trivial slider) ... so I think that means that in total you need [2*(5^3) + 1] moves, or roughly 251 of them - which sort of lines up with the thing's name, so my sums may be right... but I'm not good with sums, so don't take my word for it... OK, so assuming that you can do roughly one move per second, you can open little brother in a little over 4 minutes... [See below for the right figures!]


Now let's consider big brother - 15 positions gives us 14 required moves per slider, and 7 sliders means that the total number of moves required should be of the order of [2*(14^7) +1], which is a bit larger ... about 210 million moves ... and if that doesn't quite put it in perspective, at a move per second on average, that's 6.7 YEARS - AS LONG AS YOU NEVER TAKE A BREAK[See below for the right figures!]


OK, hopefully that makes the point - it is totally BONKERS! 


So bonkers in fact that you're probably never ever going to actually solve this one - not in one generation anyway ... see where the name comes from now? 


Having introduced it to us, a couple of us duly threw some cash at Wil and ended up taking home a really unique, if not totally bonkers puzzle lock...


I've spent a little while exercising the mechanism. (I don't think you ever seriously set about trying to open things like this, you can only hope to exercise the mechanism a little in the right direction and head towards the solution... but I suspect that it's not going to feel like it's coming closer for a very long time!)


Since acquiring our Generation Locks, Wil's been back in touch with us to let us know that the locks will have their name laser-etched on the front in future and he's given us a fantastic suggestion for the puzzle equivalent of a log-book to track who has helped us to ultimately open our Generation Locks. 

Given that it's going to take many, many years to open, what better way to track your puzzling meetings than have everyone put in a couple of moves on the puzzle and sign the log-book ... so I think that I shall be instituting exactly such a rule for all visitors to the puzzle cave... and sit back and watch my puzzling mates open this monster for me ... over the next forty years or so!

________________________


ERRATUM - Thanks to Goetz Schwandtner for pointing out (very nicely) that all my calcs were totally wrong! And that there are one or two subtle differences in how the mechanisms work so that they actually behave slightly differently ... the net upshot of which is that Lock 250+ could in fact have been called Lock 310, and the Generation Lock requires about 341 million moves... or 10.8 years at my mythical move-a-second - read his analysis over here.  Thanks Goetz!!

18 comments:

  1. Very nice article, Allard!

    However, I will have to correct the number of moves, as I have found them out to be a bit higher than the 210 million moves that have been my previous estimate, too. If you are not afraid of a formal analysis, please read more here: http://www.schwandtner.info/publications/GenerationLock.pdf

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    1. Thanks Goetz! Corrections added... :-)

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  2. I definitely want to get the Lock 250+ (310), but I fear it's going to be rather short and tempt into buying the Generation. The only problem is, I will want to open the Generation myself!!!! Therefore I can see myself wasting a large portion of my life and God only knows to what consequences ......

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  3. If it takes so many moves to solve the Generation Lock, how is the puzzle assembled in the first place? Is must have parts that unscrew, or something?

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    1. It looks like there are four rivets, or possibly screws, one in each corner.

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    2. Yip - all the silver rivets can be unscrewed - including the sliders...

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    3. If you can unscrew them with your fingernail, there you go. Solved! ;-)

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    4. Yip - it becomes a 16 move puzzle that way (unscrew & remove the 8 slider screws)... unless of course someone's been at the Loctite!

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  4. You'd better hope that your puzzler friends don't make a mistake or you'll be many moves in and not know which way to go! It could be decades before you know one way or the other!

    Kevin
    Puzzlemad

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    1. Yeah, I'm sure none of them would do THAT on purpose! :-)

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    2. While the Lock 250+ may seem a bit chaotic at some points of the solution (because of some reversed layer of teeth in it), the Generation Lock is perfectly regular. You only have to quickly analyze the position, then decide for opening or closing the lock and on you go! ;)

      The algorithm in the article on my home page may help you with this. :)

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  5. Before buying one I would be tempted to ask the seller to show me it works properly...

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  6. Two questions come to mind:
    1) Based on the concerns about accidentally reversing direction raised above, is it possible to mark the lock in some way so as to indicate the proper unlocking direction or next move?
    2) Anyone want to make a jig, with some kind of automated controller (say a Lego Mindstorms or other microcomputer) to set running to open the lock mechanically?

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    1. ...it would be pretty simple to indicate direction, I think - you could always stick a piece of masking tape with an arrow on it next to a slider... and hope no-one flips it around...

      ...had a similar thought about a mindstorm controller myself ... but it would still end up running for years!

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    2. You have to define a front face and then keep track on which side the top rivet starts and move all rivets to the opposite side.
      Since it is a "Generation" Lock I will literally scratch a mark at the point where I stop the top rivet and then hand it over to my children.

      By the way loctite could be good idea for the rivets

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    3. Interesting thoughts. Never seen such discussions for any other puzzle! :)

      Actually, you can do without any marks: Just peek into the inside of the lock through the slots, then you will see where the gaps in the shackle plate are. All the rivets will have to end up in that position for the shackle to come out, so that would be your goal position. The rest is just analysis of the current position. ;)

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  7. Wow! That's a great idea to get everyone to do a move every so often.

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