Question 5
Facu and Nico play the following game with a $13 \times 13$ grid square. Facu cuts the square into rectangles having a side equal to $1$, in any way he wishes. Then Nico chooses a number $k$ among $1, 2, \ldots, 13$ and takes all the obtained rectangles $1 \times k$. How many grid cells can he take with certainty?