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Solve a bunch of math problems really fast? They don't have to be complex, as long as they're completed far quicker than a person typing could manage.

you'd also have to check if it's a human using an AI to impersonate another AI

We try to do the same for a human using another human by making the time limits shorter.

Seems fundamentally impossible. From the other end of the connection, a machine acting on its own is indistinguishable from a machine acting on behalf of a person who can take over after it passes the challenge.

Maybe asking how it reacts to a turtle on it's back in the desert? Then asking about it's mother?

Cells. Interlinked.

Blade Runner 2049 | "Cells Interlinked" and Pale Fire

https://youtu.be/OtLvtMqWNz8

The best video essay on the movie

its*

hahahaa

I'm sure most people are looking for serious takes on this, but here are two SMBC comics on this specific theme ("prove you are a robot"):

https://www.smbc-comics.com/comic/2013-06-05

https://www.smbc-comics.com/comic/captcha

which may be either funner or scarier in light of the actual existence of Moltbook.