Piercing the chessboard
Gergely Ambrus, Imre Bárány, Frankl Péter, Varga Dániel · SZTE Publicatio Repozitórium (University of Szeged) · 2023
We consider the minimum number of lines and needed to intersect or pierce, respectively, all the cells of the 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 for each . Studying the piercing problem, we show that for , 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.