Question 170
Let $f(x,y)$ and $g(x,y)$ be real-valued functions defined for all $x, y \in \{1, 2, ..., 2000\}$. If one can find two 1000-element subsets $X, Y$ of $1, 2, ..., 2000$ such that $f(x, y) = g(x, y)$ whenever $x \notin X$ and $y \notin Y$, find the maximal number of ordered pairs $(x, y)$ at which $f$ and $g$ can take different values.