Question 11
We have a rectangular $9 \times 2007$ board divided into $1 \times 1$ unit squares. Initially all the unit squares are white. In each step, 4 white unit squares lying at the intersection of two rows and two columns of the board are coloured black. When there are no longer 4 white unit squares at the intersection of two rows and two columns of the board, the process stops. What is the minimum number of unit squares that will remain uncoloured? And if the board were $99 \times 2007$?