Resolves YES if Erich's packing center (https://erich-friedman.github.io/packing/squinsqu )
lists that the packing of 11, 12, 13, or 17 squares in a square is "proved" (contrast with "found") at any time before 2024.
Currently proven smaller packings are 1-10 and 14-16.
@tom For a larger sample size, you can check out other shape combinations here: https://erich-friedman.github.io/packing/
Even there the most recent update is from 2019
It’s possible there will be renewed interest in these packings in particular, because they have been trending on Twitter lately. I agree it seems unlikely though.
Maybe someone here will see this as a bounty if it gets bid down far enough?
13 might be the easiest.
@JimHays 13 has, purportedly, already been proven and published in the Electronic Journal of Combinatorics (the same place which published Erich Friedman's survey.)
@Nadja_L Since it’s already proved, that points out a bit of disagreement between the question and description. I will side with the more concrete market description here, so if before 2024 the website is updated to show 13 is proved, I will resolve YES, even though it’s not “currently unproved”.