Question 4
Consider a $2007 \times 2007$ board. Some cells of the board are painted. The board is called *charrúa* if no row is completely painted and no column is completely painted.
a) What is the maximum number $k$ of painted cells that a charrúa board can have?
b) For this number $k$, compute the number of distinct charrúa boards that exist.
a) What is the maximum number $k$ of painted cells that a charrúa board can have?
b) For this number $k$, compute the number of distinct charrúa boards that exist.