This is fabulous.

It's clear from just watching video clips of them that it's not just about being able to squeeze through gaps. They evidently experience puzzles with an enthusiasm that is unusual even in puzzle-solving birds, can seemingly understand quite complex things like how to non-destructively unscrew bottle tops, and from what I can gather they are kind of obsessed with jars and containers?

As an untrained nerd I have often wondered if they have, due to the maximally prehensile nature of their bodies, a genuinely superhuman, volumetric cognition of 3D shape -- a way to "glance" with their touch senses at an object they hold and recall every detail of its shape later, a way to look at a semi-enclosed space and assess how their bodies will precisely fill it, to then look at an object and know what would feel like to cover it, etc.

The lack of trial and error when you see some of these puzzles being solved suggests they might have a much better grasp of 3D shape interaction than adult humans.

They love playing with containers and jars, absolutely. The male I have been describing especially enjoyed opening tightly sealed jars - although he displayed an aversion to all jars for a bit of time after one of the few times we put him with the octopus I'd call the "alpha female". He had handed her a large jar to play with, in what I would describe as an act of kindness. She proceeded to open it and take it back to him. He squeezed inside the jar - and then with intense rapidity, she immediately began screwing the lid back on, trapping him inside. We had to let the poor guy out after she waltzed away and seemingly had zero interest in letting him out. We never let the two of them play together unsupervised after that, worried for his safety.

Oof! A jarring misunderstanding about personal space.

>a way to "glance" with their touch senses at an object they hold and recall every detail of its shape later, a way to look at a semi-enclosed space and assess how their bodies will precisely fill it, to then look at an object and know what would feel like to cover it, etc.

Watching an Octopus effortlessly change colour, size and texture to camouflage themselves might lend to this.

> Watching an Octopus effortlessly change colour, size and texture to camouflage themselves might lend to this.

Yes -- I was thinking about this bit myself.

I don't know whether it has been demonstrated that they have any kind of conscious control over this texture control, or whether it happens as a sort of evolved feedback loop, but I did wonder.

That's fascinating. Would love to hear about what kinds of contraptions you made that were breakable, given I'm struggling to imagine how you couldn't conceive of a way to keep said octopus trapped. How difficult can it be?

As noted above - you leave the tiniest hole and they'll escape. Or we might be trying to confine him to a portion of the habitat for a certain purpose and he would break his way out of his "sub-domain".