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 Post subject: Trigears
PostPosted: Sun Nov 30, 2008 1:33 pm 
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Location: Marin, CA
Updated: now with video, see it here: http://www.youtube.com/watch?v=ONYN8yAEfpA

This isn't a twisty puzzle, but it's a puzzle of mine and may be of interest to some people here:
Attachment:
trigears.jpg
trigears.jpg [ 89.25 KiB | Viewed 2666 times ]

You can get it and see more information here (sorry for the 3d printed prices): http://puzzlepalace.com/viewPuzzle.php5?id=200643


Last edited by Bram on Sun Mar 01, 2009 11:41 am, edited 1 time in total.

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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 6:44 pm 
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Ooo. Very nice puzzle. Looks quite fun to mess around with. :D

Could you bring it to the next puzzle meeting in Berkeley?

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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 8:53 pm 
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If I have one - the prototype is in europe right now.


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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 9:08 pm 
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It can't be that hard, can it? I think there are only 48 different ways to arrange them, right?

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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 9:09 pm 
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how many teeth in each gear??

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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 9:23 pm 
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Justin B wrote:
I think there are only 48 different ways to arrange them, right?

This sounds right. There are 8 different ways to orient the wheels and 3!=6 different ways to place them so 6*8=48 appears to be correct. However, there are really only 2 positions because all the rest reduce to rotations of the puzzle. so there are then 8*2=16 positions. However, this is assuming that the 3 positions for the wheels are all the same. If they are at different heights or something then there _are_ 48 positions.

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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 9:49 pm 
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Danny Devitt wrote:
Justin B wrote:
I think there are only 48 different ways to arrange them, right?

This sounds right. There are 8 different ways to orient the wheels and 3!=6 different ways to place them so 6*8=48 appears to be correct. However, there are really only 2 positions because all the rest reduce to rotations of the puzzle. so there are then 8*2=16 positions. However, this is assuming that the 3 positions for the wheels are all the same. If they are at different heights or something then there _are_ 48 positions.


I was assuming they were at different heights or distances from the center when I calculated that.

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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 10:53 pm 
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Location: Marin, CA
If you look closely you'll notice that the teeth in the gears are irregular, so the orientations of each gear matter. On top of that, each gear can be flipped over, and the order in which the gears go through the middle can be either ABC or ACB, so that's 2*2*2*2*12*15*20 = 57600 total possible positions (the stand only lets each gear go in one of the three holders, and the numbers of teeth on the gears are 12, 15, and 20). On top of that, it's fairly tricky to get the pieces put in in a particular position, due to how the gears have to all kind of go in at once, and if you're trying to go through possibilities systematically you tend to lose your place when you take the gears out to reposition them.

There are other mitigating factors which make the number of possibilities fairly under control if you analyze it a bit, which I won't go into because it's a spoiler, but I can tell you that simply messing with this puzzle trying to find a solution randomly feels fairly hopeless, and that proper analysis can make finding the solution completely reasonable.


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 Post subject: Re: Trigears
PostPosted: Sun Nov 30, 2008 11:00 pm 
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Okay, I knew it had to be harder than that.

Excellent design, as always.

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 Post subject: Re: Trigears
PostPosted: Sun Mar 01, 2009 1:38 pm 
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A bit of a bump here, but I added a video (see the first post for a link).


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 Post subject: Re: Trigears
PostPosted: Sun Mar 01, 2009 2:23 pm 
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Oskar was very enthusiastic when showing it at the IPP last August.
And I cannot blame him, as it is an excellent concept. Well done Bram!

:)


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 Post subject: Re: Trigears
PostPosted: Sun Mar 01, 2009 5:11 pm 
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Joined: Sun Dec 07, 2008 6:42 pm
Bram wrote:
Updated: now with video, see it here: http://www.youtube.com/watch?v=ONYN8yAEfpA

This isn't a twisty puzzle, but it's a puzzle of mine and may be of interest to some people here:
Attachment:
trigears.jpg

You can get it and see more information here (sorry for the 3d printed prices): http://puzzlepalace.com/viewPuzzle.php5?id=200643



Technically, it is a twisty puzzle, as to tell if you have the solution you have to "twist" the gears(twist is used instead of spin in this case)

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