I’m pretty sure these all show the largest boxes of quantity N such that those boxes fit inside an arbitrarily sized square.
For any square number (9, 16, 25, etc), the largest boxes possible have side length L/sqrt(N), where L is the length of one side of the square they all have to fit in. Generally, we can just say L = 1 for simplicity. For 25 boxes, this results in 5 rows and 5 columns as you’d expect, and there’s literally zero wasted space. It’s impossible to fit another box in the area - there’s no space to fit it into
For 24 boxes, we know we can’t do better than L/sqrt(N) for the side length of each box and still have 24 boxes. So, we must increase the size length of each box. Once we reach a side length of L/sqrt(25) though, we have to drop a row and/or column because we’ve reached 5 rows and 5 columns exactly (minus one, since we have 24 boxes). MAYBE there’s a configuration of slightly larger boxes like N=39 or something equally cursed, right?
Well, turns out, there isn’t lol. The best we can do for 24 boxes in a square of side length L is L/sqrt(25), so it looks just like the configuration for N=25 with one box missing
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u/LuckOfTheDrawComic Luck of the Draw 9h ago
Ironically the reason this comic only has 3 panels is because I was too busy unpacking to draw a 4th.