is Client Puzzle a challenge-response variant of Proof-of-work? I am kind of new to crypto, sorry if the question is kind of dumb. If it's not can you give examples of algorithms that implement the idea of a challenge-response variant of proof of work? And can you explain why the Client Puzzle is not challenge-response, please?
Yes, client puzzles as outlined by Joel’s and Brainard are an example of a challenge-and-response proof-of-work protocol. A difference from proof-of-work usage in distributed ledger updates is that client puzzles are not competitive: a separate challenge is set to each user. Another difference is that the challenge has a known solution, which puts an absolute bound on the required work rather than having the work follow an exponential distribution. Otherwise, the idea is very similar to modern cryptocurrency usage.