Are you ready for an extremely challenging, yet extremely unsatisfying puzzle?
https://youtube.com/shorts/A1xIHoCRcwQ?feature=share
What configuration enables n equal squares to fit within the smallest possible bounding square? The current answers for n=11, and n=17 are very counterintuitive, and make a great puzzle! N=11 is the lowest number where the blocks are at an angle besides 0 or 45 degrees, and n=17 is the lowest number for which the blocks are placed at 3 different angles.
For more information, check out this website: https://erich-friedman.github.io/papers/squares/squares.html
I have included STL files for both DUPLO and LEGO sizes. In both cases, I used the following numbers to get the frame size: Square Width= OPTIMUM_EDGE* BLOCK_WIDTH For 11 squares, OPTIMUM_EDGE=3.8771 For 17 squares, OPTIMUM_EDGE=4.6756 For DUPLO, BLOCK_WIDTH=31.7 mm, and for Lego, BLOCK_WIDTH= 16 mm.
Depending on the tolerances of your printer, you may need to slightly scale the frame up or down to get a snug fit.