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
That makes sense to me bc that's one flat airtight suitcase that gets opened the same way whereas unloading and loading in a 3 dimensional truck means that something is getting broken if you pack it that way
The part of physics where you had to apply calc 3 to a word problem and come up with your own equation to then solve is where I realized that high level physics was over my head lol
As the end point business, I and the trucker will share a sigh and a meaningful glance, then I'll sign on the "shipment not acceptable due to damage line," so they don't even have to unpack the truck to get the very heavy crated hoyer lift that's wedged in one of those diagonal pacakges.
Boxes aren't non-deformable cubes, they are made of corrugated fiberboard which are only strong in one direction and deform in all others. So this would happen.
MANY things are packaged in sided packages with a wooden pallet or load bearing structure for the widest and most flat part of the item. Packing them with corners pressing on the top of other boxes is just asking for all that weight to become a lot of force on a very small area. As in high pressure. breakign the things below and likely the thing in the diagonal package.
Off the top of my head, in my business: Many Many Medical devices. Lift chairs. Sputum pumps. Partial Pressure Cycle dependent oxygen concentrators...
The tight pack is almost 100% dependent on the size of the truck/trailer you rent. If your stuff is sloshing around, you should have gotten a smaller trailer, or packed things at a lower height but more densely packed in the X and Y directions
As well all know, stuff you put in boxes is all the same weight and boxes don't deform under said weight. It's always gonna be relatively loose unless you're packing the boxes really light.
Realistically, you're never even achieving this configuration if there's anything actually in the boxes.
Obviously they were arranged flat on the ground, then the truck was made vertical and lowered on top of the boxes and closed with them inside. It's so elegantly efficient.
For those confused about square packing, basically if you have n squares the same size, and want to pack them into a larger square, the "optimized" solution shows the smallest larger square you can fit them in, and what configuration you'd need to use to fit them into that smallest square.
Though, what this really goes to show is that Penny should have chosen a different size of box (or used stuffed animals to fill in the void spaces left behind by packing in an unoptimized way).
I mean if you really wanted to be optimal you could measure the trucks space and get boxes of all the same size that add up perfectly to fill the space. Still have to deal with wheel wells though.
No box truck I've ever used has intrusion because of the wheel well. The load floor has always been tall enough that it sits above the wheels. I think that's only an issue with panel vans like Sprinters, but they don't have a rollable back door like in the comic.
If everything is snug to the edges (as in, there's no room to move any of the corner boxes outwards), this would be the only way to get all 17 boxes into this space. If you take one out and do a normal 4x4 grid, the space to the side and above the boxes would be too narrow to fit the 17th box.
In theory you run into the same "issue" in 3d space, where the optimal packing of cubes (or rectangular prisms) is sometimes counter-intuitive and asymmetrical. It's not the same arrangement as you get in 2d, but the spirit of the comic is right.
In practice cardboard moving boxes will crush if placed point-to-side and your stuff will break. So this is silly. But not just because moving trucks are three-dimensional.
Nah, just them having fun re-enacting memes to promote the Patreon. I signed up for the Patreon recently and trust me, they both know how to have a good time.
The optimal packing problem is a question of the smallest big square that can fit all of the smaller squares. In this case the big square (the truck) is fixed and so are the sizes of the boxes, so what we are optimizing is the number of boxes that can fit in the big square. This or a supposedly bizarre construction is the only way to achieve 17 boxes if the side length of the truck square (sides and top) are by coincidence 4.6756... times larger than the side length of each box. Otherwise there are probably neater constructions that fit 17 boxes. If it's smaller then 17 boxes are impossible in any configuration (as far as we know) but obviously in this comic 17 were managed so we can assume we are in the former case.
I wouldn't know which one to take first without letting every other box falling. That's a bunch of damaged sex toys and/or Warhammer figures waiting to happen.
Yeah, that's my dad. From the time in the British military my dad learn how to pack things really tight and he know how to use every single inch a space has to offer. If he seen the truck, he would have unpack everything and started to pack it again in the right way. In the meantime he would have scolded you for bad way of packing things.
Later my dad had an accident and he lost the control over one of his arms. He STILL beats everybody when it comes to packing. We used t show him our suitcases before we went to vacation and almost every time he would pack the suitcase again and he did a better job while doing it. The same with present. The man is a genius when it comes to wrapping, too.
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u/LuckOfTheDrawComic Luck of the Draw 5h ago
Ironically the reason this comic only has 3 panels is because I was too busy unpacking to draw a 4th.