MathDB

Squares

ABCD

and

EFGH

have a common center and

\overline{AB}\parallel \overline{EF}

. The area of

ABCD

2016

, and the area of

EFGH

is a smaller positive integer. Square

IJKL

is constructed so that each of its vertices lies on a side of

ABCD

and each vertex of

EFGH

lies on a side of

IJKL

. Find the difference between the largest and smallest possible integer values of the area of

IJKL

Problem Statement