Question 3
There are $n \ge 5$ cities in some country. Some of the cities are connected with each other by roads, and the next three conditions are satisfied:
1) there is at most one road between any two cities;
2) not all cities are connected with each other;
3) there are exactly $k \ge 1$ roads between any four cities.
Find all $n$ and $k$ at which this situation is possible.
1) there is at most one road between any two cities;
2) not all cities are connected with each other;
3) there are exactly $k \ge 1$ roads between any four cities.
Find all $n$ and $k$ at which this situation is possible.