MathDB

Given a regular hexagon with a side of

100

. Each side is divided into one hundred equal parts. Through the division points and vertices of the hexagon, all sorts of straight lines parallel to its sides are drawn. These lines divided the hexagon into single regular triangles. Consider covering a hexagon with equal rhombuses. Each rhombus is made up of two triangles. (These rhombuses cover the entire hexagon and do not overlap.) Among the lines that form our grid, we select those that intersect exactly to the rhombuses (intersect diagonally). How many such lines will there be if: a)

k = 101

; b)

k = 100

; c)

k = 87

Problem Statement