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Take a box in the shape of a cube and cut $7$ of its edges so that all the faces stay connected and flatten it out onto a table. It turns out, there are $11$ distinct meshes that emerge: https://math.stackexchange.com/questions/4446200/how-many-distinct-ways-to-flatten-a-cube.

This is a problem that doesn't have a nice closed form and yet isn't so computationally challenging that a single human can't solve it without a computer.

Which makes me wonder, what is the first recorded evidence of someone knowing there are $11$ ways to open up a cube?

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    $\begingroup$ Probably all the kids who did this did not document their activity! :) $\endgroup$ Jul 17, 2022 at 0:09
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    $\begingroup$ Someone documented it at some point. Who was the first kid to do so? $\endgroup$ Jul 17, 2022 at 0:15
  • $\begingroup$ Durer drew one in Painter's Manual (1625), but judging by Friedman's History of Folding in Mathematics, recreational enthusiasts were not concerned with enumerating all possibilities. Current authors who refer to the 11 cite Turney 1984, but he already enumerates 4-cube nets answering Gardner's 1966 question (p.171). Presumably, Gardner knew back then, although he does not say so explicitly. $\endgroup$
    – Conifold
    Jul 17, 2022 at 6:22
  • $\begingroup$ In Gardner's book, at the end of the chapter you referenced, there is a section on "answers" where he does list out the $11$ unfoldings. But it is unclear if this was added in 1966 or later since he also references the 1984 paper. $\endgroup$ Jul 17, 2022 at 16:44
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    $\begingroup$ I remember reading the Mathematical Games column in Scientific American where he shows these nets. I believe it was one or two months after the original column when he discusses them. So indeed, it would have been around 1966 again for these. So that will correspond to the addendum in the book in which it is published (which I would need to hunt through my library to find). $\endgroup$ Jul 18, 2022 at 14:39

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