MathDB

Lines parallel to the sides of an equilateral triangle are drawn so that they cut each of the sides into n equal segments and the triangle into n congruent triangles. Each of these n triangles is called a “cell”. Also lines parallel to each of the sides of the original triangle are drawn through each of the vertices of the original triangle. The cells between any two adjacent parallel lines form a “stripe”.
(a) If

n =10

, what is the maximum number of cells that can be chosen so that no two chosen cells belong to one stripe?
(b)The same question for

n = 9

.
(R Zhenodarov)

Problem Statement