Fun fact most puzzle makers use the same jigsaw patterns to make the actual pieces. You can mix and match puzzles to make some beautiful art. https://mymodernmet.com/montage-puzzle-art-tim-klein/
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Are you asking to get answers about the philosophical question, or did you argue with her about it and you want to find out what the lemmynet thinks?
As others have mentioned, "complete" does not have to refer to the puzzle itself. It could refer to the effort.
On the other hand, her puzzle, her frame, her wall: she gets to decide.
Personally, I'd want to craft replacement pieces and draw in the missing parts of the picture. Or maybe paint them gold like Kintsugi. That way the puzzle can be "complete" while still acknowledging the history of the puzzle.
Who cares? If it matters to her, she's right. If it matters to you... Why? And what are you gonna do about it?
This.
Both sides technically have a point to argue but if they like the puzzle so much to hang it on the wall you win nothing with arguing. Just enjoy the win.
She completed a harder puzzle than the original. If she says it's complete, it's complete. And it's now a much more interesting art piece than if it had all the pieces.
I liken it to a human being missing the little finger on their left hand. They are still a complete human being, just missing a little pinky.
If she's used all the pieces and solved enough to reverse engineer the shape of all the missing pieces, then it is fully solved. If the missing pieces cannot be individually identified due to shared edges, then it is still solved, but is no longer a 1000 piece puzzle and she should only claim to have solved the 999 or 998 piece subpuzzle.
I like to build puzzles except for the last piece, just to prove to myself that finishing most tasks is a societal pressure, not an existential one.
Your very existence makes me sweat behind the knees
I can think of two arguments for why some might think it's incomplete.
- It is physically missing pieces.
If you painted something and were really proud of it but there was an accident that ripped 3/1000ths 0.03% of the painting off, would that stop you from hanging it up? Maybe some people would, but I think most people would still hang it up if they really liked it.
- She didn't perform the action of putting all 1000 pieces into the puzzle.
This is more of a "does she deserve the right to say she completed a puzzle without every piece?". There's definitely a line here: if someone just put the edge pieces together and said they had completed it, I would disagree, but honestly, is there any possible way that if you gave her those last three pieces she wouldn't immediately know what to do with them?
It's complete and she earned it.
I tend to think in « how much time did she invest in it » so yeah it’s complete
Like the Puzzle Project is complete, even if the puzzle lacks 3 of the pieces?
I come from art and a project is never really complete. Sometimes you have to let go and affirm that it is complete even if it lacks 3 pieces

No.
You're done with it. It's finished.
But it's not complete.
She finished an incomplete puzzle. If that makes any sense.
It's a near miss.
Make the missing pieces. Various ways to do that, from hand drawing it in if you're good or the picture there is simple. Do a reverse search to find the puzzle box photo or the original image it came from and use that. AI, if you're not against that, could probably fill in that pretty well. Or just leave it, chances are depending where the pieces are most people may not even notice.