A quadrilateral can be partitioned into 2 equal-area triangles if and only if one diagonal divides equally the other diagonal.

It can be proved that most quadrilaterals cannot be partitioned into 3 equal-area triangles.

Conjecture: For any natural number $n$, there exists a quadrilateral that cannot be partitioned into $n$ equal-area triangles.

How can one prove this?

[Original question by bo.gu (MO user20491).]