number of squares on chessboards Archives

Proof of the Sum of Square Numbers

May 27, 2012 GB High School Mathematics, High School Number Theory

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

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Counting the Number of Squares on a Chess Board

May 26, 2012 GB Games and Puzzles, High School Mathematics

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

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