MathDB

Consider a grid board of

n \times n

, with

n \ge 5

. Two unit squares are said to be far apart if they are neither on the same row nor on consecutive rows and neither in the same column nor in consecutive columns. Take

3

rectangles with vertices and sides on the points and lines of board so that if two unit squares belong to different rectangles, then they are apart . In how many ways is it possible to do this?

Problem Statement