MathDB

Let

n\ge 1

be a positive integer. A square of side length

n

is divided by lines parallel to each side into

n^2

squares of side length

1

. Find the number of parallelograms which have vertices among the vertices of the

n^2

squares of side length

1

, with both sides smaller or equal to

2

, and which have tha area equal to

2

.
(Greece)

Problem Statement