In a small city there are $n$ bus routes, with $n > 1$, and each route has exactly $4$ stops. If any two routes have exactly one common stop, and each pair of stops belongs to exactly one route, find all possible values of $n$.
Source: 2015 Peru Cono Sur TST P4
Tags: combinatorics, graph
In a small city there are $n$ bus routes, with $n > 1$, and each route has exactly $4$ stops. If any two routes have exactly one common stop, and each pair of stops belongs to exactly one route, find all possible values of $n$.