cities and streets in kingdom of Pinguinia
Source: 9th QEDMO p10 Seniors (21-22. 9. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507
May 15, 2021
combinatorics
Problem Statement
The kingdom of Pinguinia has various cities and streets, the latter being all one-way streets always run between exactly two cities, so there are no intermediate stops. Every city has exactly two streets that lead out of it and exactly two that lead into it. Prove that the streets can be divided into black and white streets so that exactly one exit of each city is black and one is white and exactly one white and one black entrance in each city.