Question 83
Let $A$ be a finite collection of squares in the coordinate plane such that the vertices of all squares that belong to $A$ are $(m, n)$, $(m+1, n)$, $(m, n+1)$, and $(m+1, n+1)$ for some integers $m$ and $n$. Show that there exists a subcollection $B$ of $A$ such that $B$ contains at least $25\%$ of the squares in $A$, but no two of the squares in $B$ have a common vertex.