4.64 The city's public bus network is laid out according to the following principles:
(1) From any station, it is possible to reach any other station without transferring;
(2) Any two lines have exactly one station in common, which can be used for transferring;
(3) Each line has exactly 3 stations.
How many bus lines does the city have?
[Solution] Let there be $n$ lines passing through station $A$, then the other $2n$ stations on these $n$ lines are all different from each other. Take two stations $B$ and $C$ different from $A$ such that $A, B, C$ are not on the same line. Then, by (1) and (3), $B, C$ are on some line, and there is another station $D \neq A$ on this line. By (2), each of the first $n$ lines intersects with the next line at exactly one station, and these $n$ common stations are all different, hence we get $n=3$. Therefore, the total number of different stations in the city is $m=n(n-1)+1=7$.

Each station is on exactly 3 lines, and with 7 stations, there are a total of 21 lines. However, in this counting process, each line is counted exactly 3 times, so there are 7 different lines in the city. The diagram on the right has 7 stations and exactly 7 lines: 3 sides, 3 medians, and the incircle. It is easy to see that this network of 7 lines meets the requirements of the problem.