MathDB

C4

Part of 2015 JBMO Shortlist

Problems(1)

number of parallelograms inside a square grid under conditions

Source: JBMO Shortlist 2015 C4

4/24/2019
Let n≥1n\ge 1 be a positive integer. A square of side length nn is divided by lines parallel to each side into n2n^2 squares of side length 11. Find the number of parallelograms which have vertices among the vertices of the n2n^2 squares of side length 11, with both sides smaller or equal to 22, and which have tha area equal to 22.
(Greece)
parallelogramsquare gridgridarea