I've always wondered why websites don't offer a "variable password" option, in which a user's password is constantly changing based on the day of the week or time of the day. e.g. "my password is 'foo' followed by the current hour of the day, always expressed as two digits".
I understand basic security 101, the need for trapdoor functions, and the prudence of never storing the user's actual password.
That said, is there some inherent security reason why variable passwords won't work? I imagine you could simply trapdoor the non-variable parts of the user's given password, then prepend/append the variable parts. (Yes, I really haven't given this more than 2 minutes of thought).