Lousy ManagementLogic Level 3
You have just been hired for a new job. You are told that you will work with two other employees, Adam and Eve.
In your new office, there are three locked configuration boxes: one for electricity, one for plumbing, and one for gas.
Because your employer is cheap and unwilling to pay for repairs, you and your coworkers have to do routine maintenance on these boxes.
Originally, your employer bought three keys for each safe so each of you could access it. However, he has lost all of the keys and is only willing to pay for the absolute minimum number of keys to the boxes. Additionally, he doesn't trust you or your coworkers, so he will refuse to buy as many of any type of a key as there are of you.
What is the minimum number of keys that must be bought such that at any time, you or your coworkers are able to access all three configuration boxes, regardless of how many of you are at the office?
Note: Keys cannot be left out as your employer refuses to pay for minimal security and the janitors may throw them away by accident.