I think that conveys what a zero knowledge proof achieves but it doesn't really correspond to any real zero knowledge proof algorithms. You can't do that over the phone, which is kind of the whole point.
no, that's not even close to the whole point. the analogy is to introduce the concept of proving something to a verifier without giving the verifier the solution
the paint-mixing analogy of diffie-hellman also can't be done over the phone, but it helps people understand how a shared secret can be established even if all communication is intercepted
