Proof of the Sum of Square Numbers

In the first part of this series, we have counted  the number of squares on a chessboard, and we have discovered that it is equal to the sum of the squares of the first 8 positive integers. The numbers 1^2, 2^2, 3^2 and so on are called  square numbers.


This method can be generalized to compute for the number of squares on larger square boards. If the measure of a board is n \times n, then the number of squares on it is » Read more

Counting the Number of Squares on a Chess Board

Chess is one good source of mathematical problems and puzzles.  In this post, we discuss one of the most basic problems in chess:  Counting the number of squares on the chessboard.

How many squares are there in a standard chessboard measuring 8 by 8 units? » Read more