Question 11
A city is a point in the plane. There are $n\ge2$ cities. For each city $X$, there is another city $N(X)$ whose distance from $X$ is strictly smaller than the distance from $X$ to any other city. The government builds a road between each city $X$ and $N(X)$, and no other roads. Assume that every city can be reached from any other city by a sequence of roads.
A city $Y$ is called suburban if $Y=N(X)$ for some city $X$. Prove that there are at least $(n-2)/4$ suburban cities.
A city $Y$ is called suburban if $Y=N(X)$ for some city $X$. Prove that there are at least $(n-2)/4$ suburban cities.