Packing, when limited to a plane is called Tiling. Roger Penrose found a way to tile an infinite plane with identical tiles with an arrangement that has no regularity. Now that is mind-bending!
I'm like: yeah, so? because I can't even grasp it well enough to realize that it's mind-bending. Beyond "big potatoes rise to the top of the barrel during transport", things get murky for me really quickly.
SOMETIMES HEAVIER OBJECTS GO TO THE TOP: HERE'S WHY
On a completely wild tangent, the limitations of a vacuum pump are pretty interesting. My Dad could never understand how any of his children could doubt that it is impossible to lift water more than about 33 feet with an Earthly vacuum pump. (Hmmm... what about where atmospheric pressure is vastly different?)
One of my favorite puzzles is the Monty Hall puzzle:
3 curtains with a prize behind each curtain. Only one of the prizes is worth having. You select a curtain. Monty then reveals a booby prize behind one of the two curtains that you did not select, and offers you the chance to trade your chosen curtain for the remaining unrevealed curtain. What are your odds of winning if you keep your original pick? What are your odds of winning if you trade curtains with Monty? The answer surprises most people.
I'm vaping, I'm vaping! See?
