[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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