There is a grid of 20 squares by 10 squares. How many different rectangles are possible?
(Note that square is a rectangle).

A 20 x 10 grid is made up of 21 x 11 nodes.
Each node forms a diagonal with (21-1) x (11-1) = 200 out-of-plane nodes.
Total number of diagonals = 21 x 11 x 200 = 46200
The diagonals of each rectangle have now been drawn twice.
The number of rectangles equals half the number of possible diagonals.
Therefore, total number of rectangles = 11550

Posted by retiarius on 2004-01-21 09:45:39