MathDB

Let

n

be a positive integer. Consider a figure of a equilateral triangle of side

n

and splitted in

n^2

small equilateral triangles of side

1

. One will mark some of the

1+2+\dots+(n+1)

vertices of the small triangles, such that for every integer

k\geq 1

, there is not any trapezoid(trapezium), whose the sides are

(1,k,1,k+1)

, with all the vertices marked. Furthermore, there are no small triangle(side

1

) have your three vertices marked. Determine the greatest quantity of marked vertices.

Problem Statement