Question 2
A country has $2018 n+1$ cities, where $n$ is a nonzero natural number. Some pairs of cities are joined by direct railway lines, in such a way that there is at most one line between two cities; each line runs in both directions. The distance between two cities $A$ and $B$ is then the minimal number of lines one must take to go from $A$ to $B$.
Find the set of integers $n$ for which it is possible to build a railway network satisfying the following criterion:
For every city $C$ and every $i \in \{1,2, \ldots, 2018\}$, there are exactly $n$ cities at distance $i$ from $C$.
Find the set of integers $n$ for which it is possible to build a railway network satisfying the following criterion:
For every city $C$ and every $i \in \{1,2, \ldots, 2018\}$, there are exactly $n$ cities at distance $i$ from $C$.