"Nice" Rhombuses In A Grid
Source: Greek MO 2016,Problem 4
March 3, 2016
countingcombinatorics
Problem Statement
A square is divided into 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:
It is not a square
Its vertices are points of the grid
Its diagonals are parallel to the sides of the square Find (as a function of ) the number of the nice rhombuses ( is a positive integer greater than ).