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HOW MANY SQUARES ON A CHESSBOARD (n x n)? n DIAGRAM 1 PROBLEM STATEMENT We were asked to find how many squares were on a chessboard. By observation a chessboard has 8 rows by 8 columns of squares plus one big square, which is the board itself. This will give 65 squares as the answer. However looking at the question in depth, it is seen that many squares can be formed within in the chessboard. The most systematic approach to find exactly how many squares there are in a chessboard, would be to start from the smallest square to the largest square. We know that a square has 4 equal sides, therefore we can move up n row(s) and across n column(s) on the chessboard, which gives us (n x n) and is also equal to n2 (n squared). Since the chessboard is an 8 by 8, we can rewrite (n x n)...

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