Question 105
In each cell of a $10 \times 10$ board one arrow is placed. Each arrow is pointing in one of the four directions $\{\uparrow, \to, \downarrow, \leftarrow\}$. Find the smallest number $n$ with the following property: it is always (regardless of the initial placement of the arrows) possible to remove at most $n$ arrows from the board in such a way that among the remaining ones no two are pointing at each other. Note: arrows are pointing at each other also if there are some other arrows or empty cells between them.