this post was submitted on 04 Mar 2026
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The optimisation objective is to fit n smaller squares (in this case, n=17) into the larger square, whilst minimising the size of the outer square. So that means that in this problem, the dimensions of the outer square isn't a thing that we're choosing the dimensions of, but rather discovering its dimensions (given the objective of "minimise the dimensions of the outer square whilst fitting 17 smaller squares inside it)
Specifically, the optimal side length of the larger square for any natural number of smaller squares 'n' is the square root of n (assuming the smaller squares are unit squares). The closer your larger side length gets to sqrt(n), the more efficient your packing.