Question 101
Positive integers $n$ and $k$ satisfy $n \gt 2023k^3$. Kingdom Kitty has $n$ cities, with at most one road between each pair of cities. It is known that the total number of roads in the kingdom is at least $2n^{3/2}$. Prove that we can choose $3k+1$ cities such that the number of roads with both endpoints among the chosen cities is at least $4k$.