Question 9
A very secret company develops a hi-tech machine. There are 20 different blueprints needed to construct it. Every employee has access to exactly 5 different blueprints and every combination of 5 different blueprints is accessible by at least one employee. The CEO wants to distribute employees into departments so that no department could make the machine by itself. That is, there should not be any department where every blueprint is accessible by at least one of its members. What is the smallest number of departments the CEO needs to create?