Our computer system at work requires users to change their password every few weeks, and you cannot have the same password as you had previously. It remembers something like 20 of your last passwords. I discovered most people simply increment a digit at the end of their password, so "thisismypassword1" becomes "thisismypassword2" then 3, 4, 5 etc.

Since all of these passwords are stored somewhere, I wondered if there was any weakness in the hashes themselves, for standard hashing algorithms used to store passwords like MD5. Could a hacker increase their chances of brute-forcing the password if they have a list of hashes of similar passwords?