Question 49
Let $n \gt 2$ be a natural number. In the country there are $n$ cities and every two of them are connected by a direct road. We enumerate roads with numbers $1, 2, \ldots, m$ (we can assign the same number to several roads, even if they are going from the same city), where $m$ is a natural number. The *ID* of a city is a sum of numbers assigned to roads which are going from it. Find the smallest $m$ such that it is possible to enumerate the roads in such way that ID's of the cities are all distinct.