What about encrypting your 'secret' password with normal password? So you get assigned this 30 characters password, which you learn. Then you use normal password (like 'password123' :) ) to encrypt that string. Then when you need to log on, you first type in you normal password to decrypt your 'secret' password, which is then used to authenticate you further. I know, sounds ridiculous, just thinking out loud.
edit: yes, i know, encrypting the key with another string makes it just that tiny little bit secure, technically it's still plain text...
And it's not unbreakable. For starters, this system absolutely requires that the passwords be stored in the clear.