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 Post subject: An oversight in puzzles which have been made so farPosted: Sat Oct 22, 2011 1:11 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Here is a puzzle concept which I'm surprised hasn't been made so far.

In rashkey-style planar puzzles, it would be entirely possible to apply the shells concept to them, so that there's a higher layer which is held down by a lower layer and goes more deeply than it. In fact, it would be possible using this technique to go 'super-deep', so that the circles enclose the centers of other circles, and if you went really nuts super-duper-deep, where the circles enclose the centers of circles which aren't even their nearest ones. That seems like it would be a little nuts, but even the simplest example of a puzzle where the radius goes over another circle's center hasn't been built, and it would be straightforward to do by applying the shells concept to the plane.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Sun Oct 23, 2011 4:32 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
So is anybody going to step up to the plate and take a stab at this one? Should I have posted in the general forum instead? Is anybody out there?

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Sun Oct 23, 2011 4:38 pm

Joined: Wed Jan 07, 2009 6:46 pm
Location: San Francisco, CA
I might try making a deeper Pascal's Jumble. But it might not happen for a while, since my puzzle-designing time is rather limited by the fact that I'm in senior year of engineering school.

Thanks for the idea.

-Eitan

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Sun Oct 23, 2011 4:39 pm

Joined: Fri Feb 08, 2008 1:47 am
Location: near Utrecht, Netherlands
Question: what do these puzzles add over traditional 3D twisty puzzles? It seems most 3D puzzles can be "unfolded" onto a 2D plane and vice versa. Of course there is a problem going from 3D to 2D but you'd end up with a puzzle that behaves similarly. However, it should always be possible to fold a 2D twisty puzzle onto a sphere and end up with a regular twisty puzzles.

It's a neat idea and I will consider making a puzzle based on this but I'm a bit put off by the fact that you can easily hold a 3D puzzle and twist it naturally, while a 2D one is much harder to grip and turn and you would need handles of some sort to turn it.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Sun Oct 23, 2011 5:44 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
This is an interesting idea and I too am a bit surprised this hasn't been mentioned before. But I'm sort of in the same boat as Tom. I generally prefer 3D puzzles over 2D ones and I have a backlog of 3D ones I want to try and make. Have you bounced this idea off Oskar? Odds are he's uploading the first of these to Shapeways as I type this.

Carl

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Mon Oct 24, 2011 7:51 am

Joined: Mon Feb 06, 2006 12:52 am
I am sorry for just letting this lie here like it hasn't been there.
I at first didn't get what you were talking about. Rashkey-style planar puzzle are those where your turn circles on a little pin and they carry pieces around?
I also prefer 3d puzzles. I am crazy about the geometrie and the mechanical aspects and such. That is probably what inevitably took me here eventually (I am not saying I don't care about 2d puzzles since I am also a solver.)

Now I was wondering about one thing: If the cuts go over the next circle's center where is the above stated pin to turn?
You would either need to practise the path to be able to move the pin around rather than just turning it in place (difficulty to handle smoothly), or one could just use the puzzle like a DJ does with the disc. (I don't like that concept to much) A second idea I just have is to add pins that are arranged outside of the puzzle but in some way marked so you know which circle they move. Maybe they could be connected via gears that turn everything from the outside. (Now Oskar has take that bait. )
Although I am not sure if it is possible to have pins in some way after all. Can they leave tracks in the rotating parts? I mean there IS a center to every circle that stays relatively to the puzzle even though it is not presented by a physical piece.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Mon Oct 24, 2011 11:04 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
TomZ wrote:
Question: what do these puzzles add over traditional 3D twisty puzzles? It seems most 3D puzzles can be "unfolded" onto a 2D plane and vice versa.

Untrue! 3d puzzles max out at being deep cut, and then get shallower again if you keep going, while 2d puzzle just keep getting deeper no matter how big you make the radius. Try drawing some examples of two circles which mostly overlap and give them the possibility of rotating 90 or 60 degrees. A whole bunch of very interesting pieces get added which have no equivalent in extant puzzles, especially the ones which pass over and beyond the centers.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Mon Oct 24, 2011 11:05 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Now I was wondering about one thing: If the cuts go over the next circle's center where is the above stated pin to turn?

The pin is hidden below, and is part of the first layer, which indirectly holds in the second layer, the pieces you can actually see.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Wed Oct 26, 2011 9:10 am

Joined: Mon Feb 06, 2006 12:52 am
Ah, I see. That makes sense. That's actually something that should be made.
You said that it is impossible to get deeper cuts on a 3d puzzle after the point where they max out and get shallower again.
But what about a puzzle that has an infinite amount of sides (I am talking about sphere actually) where you can just cut away circles that reach as deeply into each other as you wish, not because the cut goes deeper into the solid but because the axis' of rotation become very numerous? I guess that would at some point be the same as your idea, except that for symmetry a LOT circles are needed to cover all the sphere's surface?
Anyway I would like to see a 2D puzzle of 3, 5 or whatever number of circles that has layers and floating pieces due to deeper cuts.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Wed Oct 26, 2011 3:10 pm

Joined: Mon Aug 27, 2007 3:50 pm
Location: Copenhagen, Denmark
Very interesting Bram!
I think I can visualize your idea and at the same time it would be really nice if you could just draw up the simplest puzzle you can imagine that still has all the specifictions it needs as well as an overly complicated one.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Wed Oct 26, 2011 4:10 pm

Joined: Thu Sep 16, 2010 4:35 am
I did a quick little thing in Illustrator to see if I could visualize a deeper-than-half cut 2D puzzle. I did two thirds deep and this is what I got.
Sorry if it's a little big.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Wed Oct 26, 2011 4:49 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
oBNoo wrote:
I did a quick little thing in Illustrator to see if I could visualize a deeper-than-half cut 2D puzzle. I did two thirds deep and this is what I got.
Sorry if it's a little big.
Boy that is alot of pieces for a puzzle with just 2 turnable layers/sections. How many turns are required just to seperate the two pieces most difficult to seperate?

And this makes me think of another reason I'm not a huge fan of planar puzzles. How would you sticker that such that each piece had a unique position and orientation?

Carl

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Wed Oct 26, 2011 5:14 pm

Joined: Sun Mar 06, 2011 12:46 pm
Location: Wichita
wwwmwww wrote:
Boy that is alot of pieces for a puzzle with just 2 turnable layers/sections.

And this makes me think of another reason I'm not a huge fan of planar puzzles. How would you sticker that such that each piece had a unique position and orientation?

Carl

I don't know if there is any good way to make every piece have a unique position and orientation. You could put arrows on the pieces and give it just enough colors to where there are no 2 pieces that can swap while having the arrows still point in the same direction.
Also, Here is another version that can make 1/3 turns that I think looks a bit nicer.

 Attachments: 's 2 wheel puzzle.jpg [ 126.5 KiB | Viewed 2662 times ]

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Wed Oct 26, 2011 10:43 pm

Joined: Thu Sep 16, 2010 4:35 am
wwwmwww wrote:
Boy that is alot of pieces for a puzzle with just 2 turnable layers/sections. How many turns are required just to seperate the two pieces most difficult to seperate?

And this makes me think of another reason I'm not a huge fan of planar puzzles. How would you sticker that such that each piece had a unique position and orientation?

Carl

I'm sure the deepness of it could be fine tuned to where it doesn't have so many pieces. Or at least to get rid of the really tiny ones.
I actually used to have an idea for a "deep cut" 2D puzzle, but it didn't involve the shells mech. I just planned on covering the circles with plexiglass and having small gaps where the puzzle could be rotated with one's fingers. Never got around to it though.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Thu Oct 27, 2011 12:15 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
The above diagram with two circles and three-fold symmetry on both is probably as simple as you can get with a super-deep cut puzzle with both circles having three-fold symmetry, but it's also possible for one circle to have three-fold and the other two-fold, or one four-fold and the other two-fold, and those might be simpler.

Also, it terms of movement if it's done in layers then it should be possible to have parts sticking out of the top layer, which should make it fairly easy to manipulate.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Thu Oct 27, 2011 7:39 pm

Joined: Tue Apr 27, 2010 10:38 am
Wow, how did I miss this thread? I've been laboriously hand drawing circle puzzles in DeltaCAD for weeks, maybe months, ever since I ordered a selection of gear puzzles from Douglas Engel. The diagrams in this thread have inspired me to finally write the program I've been dreaming of all along, to make it easier to explore the effect of different turn increments and depth of cuts. You can download it here.

It's very limited now, only supporting 3-, 4- or 6-fold symmetry and only showing half of the puzzle. This is enough to find interesting arrangements which can then be fleshed out in an actual drawing program. The controls are

q - Move circles large step closer together
w - Move circles large step farther apart
a - Move circles small step closer together
s - Move circles small step farther apart

k - Decrease turning positions (6->4->3)
l - Increase turning positions (3->4->6)

When it first loads the program defaults to 3-fold symmetry and the distance between circles equal to the radius.

The most promising candidates for physical production that I've found so far are a variation on the puzzle shown by cubedude76, which eliminates the diamond shaped pieces around the centers:

and a slightly deeper cut Rashkey:

If anyone actually tries the Circle Simulator and finds anything else interesting and/or producible please post! I hope to get 5- and 8-fold symmetry added soon, hopefully this weekend.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Thu Oct 27, 2011 7:53 pm

Joined: Thu Sep 16, 2010 4:35 am
Very nice program. In a fit of extremism, I went as deep as it would go and almost had a fully white screen.

EDIT: Found some nice 4fold depths.

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Last edited by BN on Thu Oct 27, 2011 8:02 pm, edited 1 time in total.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Thu Oct 27, 2011 7:59 pm

Joined: Tue Apr 27, 2010 10:38 am
oBNoo wrote:
Very nice program. In a fit of extremism, I went as deep as it would go and almost had a fully white screen.

Thanks! I actually had to limit it to no more than 90% overlap between circles, as past that it would go fully white, and then fully crash after recursing past about 2,500 levels deep...

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Fri Oct 28, 2011 11:28 am

Joined: Tue Apr 27, 2010 10:38 am
I've been playing with the deeper cut Rashkey above, and have colored the full puzzle to show the orbits:

The triangular pieces (red and purple above) appear to behave the same as the triangular pieces on a Rashkey, as do the large square pieces (grey above). Interestingly, it does not appear to be possible to actually scramble the square centers (orange and yellow above). It looks to me like they would provide a fixed 'correct' orientation for each circle unless all the centers in each orbit were indistinguishable. I may have to draw some outlines suitable for laser cutting and order pieces for a two color Sun-Moon style version...

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Fri Oct 28, 2011 3:06 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
HeavyTanHat wrote:
Interestingly, it does not appear to be possible to actually scramble the square centers (orange and yellow above).

If they're colored with orientation they're sort of like a Dual Circles.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Fri Oct 28, 2011 5:20 pm

Joined: Mon Mar 30, 2009 5:13 pm
TomZ wrote:
Question: what do these puzzles add over traditional 3D twisty puzzles? It seems most 3D puzzles can be "unfolded" onto a 2D plane and vice versa. Of course there is a problem going from 3D to 2D but you'd end up with a puzzle that behaves similarly. However, it should always be possible to fold a 2D twisty puzzle onto a sphere and end up with a regular twisty puzzles.
This just made me think of a way to make the first ever 4D twistypuzzle, so I've started a separate discussion on that idea here.

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 Post subject: Re: An oversight in puzzles which have been made so farPosted: Mon Dec 05, 2011 1:34 am

Joined: Tue Jan 29, 2002 11:38 pm
Quote:
How would you sticker that such that each piece had a unique position and orientation?

Carl

Easy - with a photograph or other detailed artwork. There are a zillion-or-so variations of this with 15-puzzles using everything from Escher's work to photographs of famous landmarks, animals, etc. Flat puzzles just lend themselves to a more jigsaw-puzzle-like "stickering" method than 3D puzzles do.

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