Question 49
Let $k$ and $n$ be positive integers. An international company has connected $k$ cities of Armenia with $k$ cities of Belarus by direct two-way airlines. From each of these Belarusian cities there is a direct flight to exactly $n$ Armenian ones. It turned out that for any two Armenian cities there are exactly two Belarusian cities that are connected by airlines to both of them.
a) Prove that each of the Armenian cities is connected by airlines to exactly $n$ Belarusian cities.
b) Prove that it is possible to travel on planes of a given airline without repeating cities, while visiting at least $\left\lfloor \frac{(n+1)^2}{4} \right\rfloor$ cities in each of the countries.
a) Prove that each of the Armenian cities is connected by airlines to exactly $n$ Belarusian cities.
b) Prove that it is possible to travel on planes of a given airline without repeating cities, while visiting at least $\left\lfloor \frac{(n+1)^2}{4} \right\rfloor$ cities in each of the countries.