A note on the minimum number of red lines needed to pierce the intersections of blue lines

• We study the number of red lines required to pierce the intersections of a finite family of blue lines. • If B is the family of blue lines and R is the family of red lines as above, the best previous lower bound of |R| is improved. • An application of this result is given. Let L be a set of n non-concurrent blue lines and let R be a set of m red lines in the real projective plane. In this note, using elementary geometric arguments, we show that if L ∩ R = ∅ and there is a line from R through every intersection point of lines in L, then m ≥ 4 11 ( n − 13 11 ). This lower bound improves the previous ones whenever n ≥ 4. Also we give an application of this result.