# Group work, Brooks’ Law and Triangular Numbers

When I set group assignments, I’m quite specific in how big the groups can be.

No less than three, no more than five.

Students often prefer bigger groups. Maybe they think that more people on a project of the same size means less individual effort.

I short-circuit the drive to bigger groups with something I learned from Fred Brooks’ Mythical Man Month: the group intercommunication formula. It’s also the formula for calculating triangular numbers.

If two people work together on a project, they have one connection to manage, in addition to getting the project done.

If three people work together, they have three connections to manage. This means that person A has to be aware of how they’re working with person B and with person C and what has to be produced to complete the assignment. Person A also has to be aware of how B and C are working together, in case that has an impact on their own work.

If four people work together, they have six connections to manage.

And if five people work together, they have ten connections to mange.

Six people have fifteen connections to mange, in addition to trying to get the project done.

The formula for this is (n(n-1))/2. Try it for seven people.

Brooks used this concept to formulate Brooks’ Law, which states that “adding more people to a project makes it later”. This is because there is a point at which the n-th person added to a project causes everyone to spend more time on interpersonal management than on project work.

And that’s why I limit group size when I teach.