Ask Dr. Math Squares in a Checkerboard

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 How Many Squares in a Checkerboard?, a selection of answers from the Dr. Math archives. Squares on a Checkerboard How many squares are there on a checkerboard? Squares in a Square If you have a 50x50 square with small squares inside it, how many squares will there be altogether? Squares, Rectangles on a Chessboard How many squares are there on a chessboard? How many rectangles? Counting Squares in Bigger Squares How many edge 2 squares (2x2 squares) can be found in an edge 4 square (a 4x4 square)? Chessboard Squares We discovered that there are 204 squares on a chessboard and found that you would add the different squares - 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64. Our teacher wants to know why it works and if there is a quick way to get the answer. Checkerboard Squares Suppose you have a square checkerboard not 8x8 - what is the easiest way to find how many squares there are in it? Number of Squares in an NxN Square How many squares are there in an 8 x 8 square? How many rectangles are there? Formula for Squares inside Rectangles Is there an equation for how many squares there are in a rectangle divided up into 1cm blocks? Checkerboard Problem Is there an exponential pattern for how many squares there are on a checkerboard? Squares in Rectangle Formula What is the equation for the number of squares in a rectangle (like the chessboard puzzle)? Rectangles on a Chessboard How many rectangles are there on a chessboard? Checkerboard Rectangles A checkerboard has 8 horizontal boxes and 8 vertical boxes. How many rectangles are possible inside that board?