Generate two random 32 length strings. For the sake of this example, let them be 2quvs7jriTXQK8sFv4LzBZRtSN9hqp9q and qFTNX4f5sduaLYShWx96EyZw9ZRNLmqY.

Designate the first to "heads" and the second to "tails". Every time you're prompted to login with a password, flip a coin and enter that designated password. If it fails, then enter the second password.

For those interested in basic cryptography, feel free to point out the major and obvious flaw in this approach.