Why not just fix the computer?Discrete Mathematics Level 4
Techno is a large island country with exactly 101 cities. The country is extremely advanced when it comes to technology, and, as a result, they have assigned a quantum supercomputer in order to manage all of the construction and management in the country.
The supercomputer, though, encountered a glitch. One day, when it was asked to connect all of the cities in the country using roads, it encountered an error which caused it to build a road between a random pair of cities, only stopping when all of the cities have been connected. In the worst case scenario, how many roads will the country have to build such that any two cities are connected?
Note: If you can find a path from city A to city B (possibly passing through other cities) then city A and city B are connected.