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MathNet 2020 — Math Olympiad Vault — Part 06 Question 93

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 06

Question 93

There are four countries, each consists of several cities. The cities of any two countries are connected by at least $\frac{5}{6}$ of a number of all possible roads between these two countries. Prove that it is possible to choose one city from each country so that any two of them are connected. Any pair of cities can be connected by no more than one road.
(Nazar Serdyuk)