I am studying at NUS in Singapore, and they have a mac-equipped computer lab here at school. All users (students) have our own personal accounts that we use to log in to the computers with. Sometimes when you approach a computer to log in only the alternative "thinkmac", which is the school's administrator account, I presume. Some other computers have the alternative "thinkmac" as well as "Others..." where you can input your own login credentials.

One day as I sat down by a computer and there was only the "thinkmac" alternative. I was about to get up and find another one when the guy sitting next to me says -

Just click 'thinkmac' - the computer will ask for your password - then hit escape to get back to the login screen. Repeat until "Others..." appear.

So: If you click any user account, hit ESC to get taken back to the login screen, repeat for 5-10x, eventually the alternative "Others..." will appear.

Why is this? Is there an internal counter that keeps track on how many times you have clicked a/any given user account, and after a certain threshold it displays the "Others"? What is the logical reasoning behind this?