MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
2016 Greece National Olympiad
4
4
Part of
2016 Greece National Olympiad
Problems
(1)
"Nice" Rhombuses In A Grid
Source: Greek MO 2016,Problem 4
3/3/2016
A square
A
B
C
D
ABCD
A
BC
D
is divided into
n
2
n^2
n
2
equal small (fundamental) squares by drawing lines parallel to its sides.The vertices of the fundamental squares are called vertices of the grid.A rhombus is called nice when:
∙
\bullet
∙
It is not a square
∙
\bullet
∙
Its vertices are points of the grid
∙
\bullet
∙
Its diagonals are parallel to the sides of the square
A
B
C
D
ABCD
A
BC
D
Find (as a function of
n
n
n
) the number of the nice rhombuses (
n
n
n
is a positive integer greater than
2
2
2
).
counting
combinatorics