2023-12-13 16:13 UTC
@TomSwirly@toot.community @mbonsma@mastodon.social I'm no scientist, nor mathematician, but my impression is that this is not being offered as some sort of rigorous, theoretical mathematical proof applicable to all real or imagined puzzles—it's a study of "typical" jigsaw puzzles in the real world, meant to predict “realistic assembly scenarios”. The word "proof" appears nowhere.
Grousing that it doesn't address unrealistic, imaginary puzzles is like complaining that a Klein bottle is a bad vessel for transporting liquids.
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@TomSwirly@toot.community 2023-12-13 16:42
@stillmoms@mastodon.social @mbonsma@mastodon.social Oops, I'm sorry, you're right - "proof" didn't appear in there, I thought it did. Yes, my standards are lower for non-proofs. 😃 I don't see a puzzle with long or thin shapes in it as being "unrealistic" though. One of the simplest non-trivial tiling puzzles are pentominos https://en.wikipedia.org/wiki/Pentomino#Constructing_rectangular_dimensions which have both long and right angle pieces.