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There are many different sized squares on a chessboard. The smallest squares are in an 8x8 grid, so we have 64 small squares.

There are 7x7 2x2 squares, so we have 49 2x2 squares

There are 6x6 3x3 squares, so we have 36 3x3 squares

There are 5x5 4x4 squares, so we have 25 4x4 squares

There are 4x4 5x5 squares, so we have 16 5x5 squares

There are 3x3 6x6 squares, so we have 9 6x6 squares

There are 2x2 7x7 squares, so we have 4 7x7 squares

And there's the one big square that's the chessboard.

All this adds up to 204 squares.

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