Question 134
There are $n$ cities in a country. A monopoly company intends to establish air traffic between some of these cities. The government demands that the air traffic satisfy the following conditions. People should be able to get from each city to any other of these cities by one or several flights. Besides, there must be an equal number of flights from each city. Note that two flights, from $A$ to $B$ and from $B$ to $A$, are considered as one flight between the cities $A$ and $B$. Moreover, there may be at most one flight between two cities. But the company wants to cancel as few flights as possible so that one can no longer get from each city to any other city. What is the minimal number of flights the company has to cancel if:
a) $n = 2008$;
b) $n = 2007$?
a) $n = 2008$;
b) $n = 2007$?