MathDB

Let

n

be a positive integer. A regular hexagon

ABCDEF

with side length

n

is partitioned into

6n^2

equilateral triangles with side length

1

. The hexagon is covered by

3n^2

rhombuses with internal angles

60^{\circ}

and

120^{\circ}

such that each rhombus covers exactly two triangles and every triangle is covered by exactly one rhombus. Show that the diagonal

AD

divides in half exactly

n

rhombuses.

4