Lateral Thinking, Analytical Mathematics and Computing: Find the total number of squares and rectangles in an NxN chessboard.

Lateral Thinking, Analytical Mathematics and Computing: Find the total number of squares and rectangles in an NxN chessboard.

Asked here http://geeksforgeeks.org/forum/topic/interview-question-for-software-engineerdeveloper-about-puzzle-4#post-7819

Solution:

For example, consider 8 X 8 chess board.

Note that we need 9 integers to represent one side (say x-axis) of the chess board. Similarly we need 9 integers on other side (say y-axis).

Rectangles:

Every square is a rectangle. A rectangle requires two co-ordinates (horizontal line) on x-axis and two co-ordinates (vertical line) on y-axis. The horizontal line needs two integers out of these 9 integers on x-axis. Similarly the vertical line needs two integers out of 9 on the y-axis. Hence we can draw the horizontal line in 9C2 different ways, and same with vertical line. Overall we can have (9C2)*(9C2) = (36)*(36) = 1296 rectangles on the chess board.

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