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this post was submitted on 14 Jun 2025
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https://kingbird.myphotos.cc/packing/squares_in_squares.html
The rub with this design is that the length of the sides of the little squares is not an even integer division of the length of the sides of the big square, though.
Doing it the naive way, i.e. keeping all the edges parallel, you can only fit 16. However it's trivial to fit 17 in there without it looking like a warehouse accident, like so:
Or, a slightly easier to follow rendering:
This may correlate with #17 on your linked list, but I was not rigorous with the math. (I.e. I just traced this off of the screenshot.)
I'm positive I've seen this as a 3D printed puzzle somewhere at some point...
The posted arrangement is the tightest known packing of 17 squares. The outer square has a side length of 4.6756 times a small sqare's. So unless you've just found one no mathematician has thought of since 1998 yours is slightly larger.
Edit:
I found this tool to play around and your packing is 4.7 https://markorastas.github.io/PackingProblem/
Edit edit:
I'm a dummy you just need pythagoras, yours is 4+√0.5≈4.7071
Yep, if I'm not mistaken, your version has s = 4 + sqrt(2) which is approximately 4.70710678119. Very close to the ideal 4.67553009360455 !
There's a link for alternate packings on that page, where you can see older versions, some with more aesthetically pleasing patterns of minimal tilted squares or symmetry. All of them use a larger value for
sthough and it's hard to tell where your version would fit in.Yeah, I just winged it based on a hazy recollection of a block puzzle I'm pretty sure I saw once. I'm sure the puzzle in question was not mathematically rigorous both so it could look nicer (with the same or similar solution to what I doodled, there) and also so it could be like, you know, actually manufactured.
Blender calculates this as the optimal packing. It's smaller than the ideal, but I've seen Blender be wrong before.
WITCHCRAFT!
(... which makes it very cool!)