[HN Gopher] How can a jigsaw have two distinct solutions? [video]
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How can a jigsaw have two distinct solutions? [video]
Author : patrakov
Score : 70 points
Date : 2024-09-29 03:56 UTC (19 hours ago)
(HTM) web link (www.youtube.com)
(TXT) w3m dump (www.youtube.com)
| hinkley wrote:
| It's kind of a shame they had to use AI to get the images to
| tessellate properly. Seems like there should be some math there.
|
| Escher would do something more with this if he were alive.
| gilleain wrote:
| I'm not sure how jigsaws are usually modelled in maths. I feel
| like there should be a graph model? Perhaps each piece could be
| labelled and have 'dangling' half-edges that are coloured such
| that they can only be connected to the appropriate partner.
|
| Then a two solution jigsaw would be a set of these pieces that
| reconstruct into two different labelled graphs.
|
| Hmm ok I realise this is all very dumb, as it's the labelling
| (the image!) that is the tricky part here ...
| timonoko wrote:
| As Steve Mould describes it, solution is very mechanical. You
| start from chaos and gradually improve it so that it matches
| two different image classes. Pattern-matching is not considered
| AI nowadays.
| GolDDranks wrote:
| Uh, that's literally how Stable Diffusion works, and I think
| it's considered GenAI?
| nkrisc wrote:
| It's not like they just wrote a prompt and got a result. It
| sounded like a very hands-on process.
|
| While they used the same process generative AI uses, it doesn't
| sound like they really used AI.
| lupire wrote:
| They literally explained how they used GenAI and to generate
| the image.
| Jaxan wrote:
| Yes they explain it very clearly and it's not just a single
| prompt in an off the shelf genAI.
| donatj wrote:
| It seems like there's a simpler, lazier solution to having a
| puzzle with just two solutions.
|
| Just make two corners diagonal from each other interchangeable,
| then simply print "this side up" on one of the corner pieces and
| have the image be a rotational illusion that look like different
| items when rotated 180deg
| bawolff wrote:
| Trivial solutions aren't interesting solutions.
| HKH2 wrote:
| Or just flip over a normal jigsaw and give yourself a
| challenge.
| pavel_lishin wrote:
| The most recent one I did had a grid of letters on the back,
| to make sure things align. I wonder if that would make it
| easier or harder to solve than if it were a single color
| extraduder_ire wrote:
| There's a jigsaw brand (impossipuzzle, I think) that does
| something like that to make them as difficult as possible.
| They're printed on both sides, and the rows/columns are cut
| from different sides.
|
| I have aunts that took almost a year solving one that was an
| 5*7 foot picture of baked beans and chips. Most of the
| patterns are repetitive and non-distinct on purpose.
| klyrs wrote:
| What do you do with such a monstrosity when it's finished?
| filipezf wrote:
| Long before this Matt video, I've done just that. A generator
| of devilish no-image jigsaw puzzles :-) which I indeed wanted
| to do a little Show HN someday. I made a small python script
| call a SAT solver to create a MxN puzzle with only 1 solution
| but only a few jig shapes, so maaany 'almost solutions'. Then
| I laser cut a plastic board and made it real, and gave one
| copy to a friend. At least a nice use of SAT solvers that is
| more efficient than Matts brute force approach.
| nkrisc wrote:
| And in the video Matt talks about the effort he went to in
| order to avoid trivial solutions like that. He wanted to find
| the least trivial one he could.
| pavel_lishin wrote:
| Or don't print an image at all, leave it a solid color, and
| then you have _four_ solutions - two landscape, two portrait -
| if you leave yourself restricted to 90deg angles.
|
| (Technically eight, if you also flip the puzzle upside down.)
| bawolff wrote:
| I feel like using AI to make optical illusions have been some of
| the more interesting things to come out of the generative image
| AI thing.
|
| I suppose when it comes down to it, image AI could be viewed as a
| fancy way to interopolate between human meaningful images where
| the inbetween values are still human meaningful. I wish that the
| AI discussions had more of a focus on that, as it seems unique
| and novel, and much more interesting than the tired moral panic
| around "what is art?"
|
| There was a post a while back about making QR codes that look
| like other things that was also super cool.
| karmakaze wrote:
| This could probably be extended to more than two images. Don't
| know how far you can push it before the images look too contrived
| to be interesting.
|
| In thinking how I would start, I imagined starting with only one
| kind of shape, except filling/flattening out the edges/corners.
| Then come up with a dual picture that depends on 2 arrangements
| of the pieces. Finally adjust the edges of the piece shapes
| without breaking the 2 selected arrangements but allowing all the
| other possible arrangements to collapse down.
|
| It's like making a repeating/tiling shape where you start with a
| blank tiled plane then start drawing anywhere, all the repeated
| places also get drawn in, and you keep drawing/undoing until you
| like what you see. i.e. 'maintain the constraint from the
| beginning'. The tricky bit is in the drawing/painting. I imagine
| the same could be done with this jigsaw, blank the pieces, show
| both arranged blanks, and let someone paint on the pieces
| updating both as you go. When you like what you see, you're done.
| WorldWideWebb wrote:
| Check out Stave Puzzles if you want to get into insanely
| difficult jigsaw puzzles with multiple solutions. Some have
| multiple solutions (3+) and some go 3 dimensional. I have one
| that is either a 3 or 4 leaf clover.
| Tyr42 wrote:
| That appears to be $1k for a single puzzle. Yikes.
| Tempat wrote:
| Similar theme: https://dangeng.github.io/visual_anagrams/
| Zanni wrote:
| Not remotely the same idea, but the Magic Puzzle Company [1]
| makes fantastic puzzles with "two solutions." They're traditional
| puzzles with hand-drawn art, but the first solution is in four
| distinct pieces that can be reassembled to make a slightly larger
| rectangle with a hole in the middle. (Similar to Sam Loyd's
| Missing Square puzzle. [2])
|
| Then, a second set of pieces (in a separate envelope) allow you
| to fill in the hole with an image that (typically) wildly alters
| the interpretation of the original image.
|
| [1] https://magicpuzzlecompany.com/ [2]
| https://proofwiki.org/wiki/Sam_Loyd%27s_Missing_Square
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