How to use logic gates?

[Eric119]

I think this does what you're looking for. Assuming at most one of the buttons is ever held down at a time, only the output of the later one's latch will be on. If you want to control whether a button opens a door, you can (for instance) feed the latch output into an AND gate and have the button connected to the other input of the AND gate. All this is easily extended to any number of latches.