【Example 7】A newly built city, to solve the city's traffic problems, has purchased a large number of buses. They plan to set up bus stops at 1985 different locations, connecting them with several routes, with the following wishes:
(1) To open as many routes as possible;
(2) Each pair of routes should have at least one common bus stop;
(3) Each bus stop can be shared by at most two routes.
According to these wishes, what is the maximum number of routes they can open? How many stops should each route have at least?
Let the city have $n$ bus routes, then the stations shared by these routes should be at least $C_{n}^{2}$. Obviously, there should be $C_{n}^{2} \leqslant 1985$, that is,
$$
n^{2}-n-3970 \leqslant 0
$$

The largest integer satisfying this inequality is $n=63$, so the city can have at most 63 bus routes. Since every two routes must have at least one common station, each route should pass through at least 62 stations.

Combinatorial theory is extensively used in urban planning to solve urban layout problems. The example we just saw is a simple one. Readers who are interested in this topic can