  We consider the minimum number of lines $h_n$ and $p_n$ needed to intersect
or pierce, respectively, all the cells of the $n \times n$ chessboard.
Determining these values can also be interpreted as a strengthening of the
classical plank problem for integer points. Using the symmetric plank theorem
of K. Ball, we prove that $h_n = \lceil \frac n 2 \rceil$ for each $n \geq 1$.
Studying the piercing problem, we show that $0.7n \leq p_n \leq n-1$ for $n\geq
3$, where the upper bound is conjectured to be sharp. The lower bound is proven
by using the linear programming method, whose limitations are also
demonstrated.
