JBMO Shortlist 2019 C2
Source:
September 12, 2020
combinatorics
Problem Statement
In a certain city there are straight streets, such that every two streets intersect, and
no three streets pass through the same intersection. The City Council wants to organize
the city by designating the main and the side street on every intersection. Prove that
this can be done in such way that if one goes along one of the streets, from its beginning
to its end, the intersections where this street is the main street, and the ones where it is
not, will apear in alternating order.Proposed by Serbia