In a software project that is behind schedule, the number of developers was increased from 5 to 10. By what factor does the number of communication paths between two people (the number of pairs) increase?

Answer: C. 4.5 times

The number of paths among n people is the number of pairs, n(n − 1)/2. It is 5 × 4 ÷ 2 = 10 for 5 people and 10 × 9 ÷ 2 = 45 for 10 people, so it increases 45 ÷ 10 = 4.5 times. Doubling the team increases the coordination and communication effort roughly with the square of the number of people, and training the newcomers also takes time from the existing developers. Brooks's law, 'adding manpower to a late software project makes it later', comes from these reasons.

• A. This assumes the paths grow in proportion to the number of people. They grow faster than that.
• B. This is the ratio of the squares (25 and 100); counted exactly with n(n − 1)/2, it is 4.5 times.
• C. Correct. It grows from 10 to 45, which is 4.5 times.