Replying to @vgr
I've always found these ZKP analogies to be too simple. Gives no intuition of how you go from here to (eg) an anonymity preserving cryptocurrency. So I wrote a more involved analogy (more boring, more useful?)
https://docs.google.com/document/u/1/d/1aOZBVj-AmzpprZgWmIT_sNmGVWcAa2SbTE8I_lFTAAs/mobilebasic…