Earlier quoted context omitted.
It's a nice idea, but you have to consider the complexity of the word puzzles compared to the average human's brain power. Most people are quite dumb. If there aren't a sufficient number of problems/answers, or they're simple enough for computers to solve, or they're too complex for a minority of humans to solve, you're boned. The whole thing is a technology arm's race. The best solution would be one where you simply…
Except you lose the benefit of anonymity, which is a big draw for many of the places using Captchas. Unless I don't understand your idea, which is possible.
You can still come up with new ways to verify someone is a human for specific uses where you want anonymity, but they will always be part of the tech arms race if you want them frictionless. To avoid them getting more annoying you need a way to authenticate an individual identity, as that allows you to rate-limit access.
You could, of course, do TOTP and totally preserve anonymity. Unless the TOTP service provider is compromised, in which case all bets are off (but perfect-forward secrecy might solve that?)
