A president of a bank wants to put some locks on the door to the vault. He has two Directors and five Managers. Each lock has a different key, and multiple copies can be given out to different people. All locks must be opened to open the door. He would like:
1. To be able to open the door by himselfwww.ddhw.com
2. Both Directors can open the door if together (but not one director)
3. Any director with any two Managers can open the door (but not one manager)
4. Any four Managers can open the door (but not three managers)
What is the fewest number of locks needed, and how are the keys distributed?