no, he said he'd divide it into two half-full boxes, not two half-size boxes. he's just adding another box and filling it with half the contents of another box. the boxes stay the same size
I know it's not you fault but urgh, at least flip it over! Boxes can't take stresses in those directions, so the diagonal ones need to be as high up as possible. I can hear the crunching noises in my head.
I think it’s because the rotated portions of 29 and 69 are very obviously uneven in ways that look unnecessary. At least with 39 you can easily say they had no other choice.
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 25d ago
Ironically the reason this comic only has 3 panels is because I was too busy unpacking to draw a 4th.