Question 3
An $n\times n$ city has building heights from one to $n$, with no repeated height in a row or column. A building is visible from a side exactly when all preceding buildings in that row or column are shorter. The left diagram illustrates a $4\times4$ city with individual visibility counts. In the right $5\times5$ city, five heights are given. Total visible counts are north ten, east eleven, south thirteen, west twelve. Determine the remaining heights.
