In a certain country, there are \(n\) cities. Some of them are connected by
roads, all of which go in both directions. It is possible to get from
any city to any other city using only roads. However, for any pair of
cities, there is always only one way to get from one of them to the
other and there are no alternative routes.
Show that there are exactly \(n-1\)
roads in this country.