Sometimes math can be bullshit...

How are the arrangements ranked/ordered? Like what is meant by wasted space here?

I wouldn't say "bullshit;" I'd say sometimes math defeats your expectations of simplicity or symmetry. Sometimes math says your intuition is wrong.

what a mess!

This sort of geometry is actually useful if you do lock picking, especially ib sporting events. You gotta look for manufacturing flaws to exploit in the plug, and know which sort of pick to use, and visualize what pins are moving and which are stuck, what kind of pins they are (lots of types of high security lins exist), etc. And some locks are designed bizarre, where you gotta have a equally perplexing key to get in. This sort of puzzle is the sort of thinking you need to solve such tasks. And the reward is you get to keep whatever you find locked up, so it is a potentially useful skill.

Very interesting post. These are surprisingly complicated problems. Similar to sphere-packing, or even soap bubble geometry.

It's a minima problem. Not a maxima problem.

Most will think Maxima. So you give up!

It's really about changing your point of view! See it from a different perspective. And that's hard for most to do.

Is the image the problem or is it the solution?

4 squares of side length 4
4 squares of side length 3
4 squares of side length 2
5 squares of side length 1

I'm gonna use this knowledge before my shift ends today.

day 16087... still not a circumstance ive ever had to use Algebra... 😡

I suspect there are a few other Answers as well

No mathematics are always b*******

Looks like geometry.

Stack them?