PMQ30 is a simplified version of a real maths competition problem. This is from Paper 2 of the IrMO 1988; such papers have only three questions so are closer to the IMO than Paper 1. Having said that, I think most solvers will need to go through the process of solving PMQ30 to understand how to construct more complicated networks.
A city has a system of bus routes laid out in such a way that
(a) there are exactly 11 bus stops on each route;
(b) it is possible to travel between any two bus stops without changing routes;
(c) any two distinct bus routes have exactly one bus stop in common.
What is the number of bus routes in the city?
[IrMO 1988 Paper 2 Question 3]
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