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Fun! When I do puzzles, I often wonder how much variation there is in the way people do the puzzle. With standard puzzles, the edge is probably the first thing to come together, and there are often other features that are easier to do in the puzzle, like the planets in this one. I wonder if you took time lapse pictures of a bunch of people doing the same puzzle, how much variation there would be in the order people did them in.

That’s a good question. Maybe even more interesting to a mathematician: how should that variation be measured?

Yes! I’ve thought about that too, but it’s hard to figure out. We could label pieces by xy coordinates in the finished puzzle and just calculate mean squares differences between solvers, but it would probably be better if we could label clusters somehow and see if people did clusters in a certain order. (Doing Mars and then Jupiter wouldn’t be that different than doing Jupiter then Mars, but they would be different in xy coordinate terms.) But that would require the experimenter to declare what the likely puzzle solving strategies would be before the experiment is performed, which seems pretty sketchy. This seems like a problem for topological data analysis, which I know hardly anything about.