A large roomful of people divides into teams of size 2 or 3 each for a project. Midway through, they go outside for a break. While outside, you survey them (not knowing who was on what team), asking each person for the size of their team. You learn that exactly half of the people are on teams of size 2 and exactly half of the people are on teams of size 3. What is the average size of each team?
