How many squares are there in a chessboard?

How many squares are there in a chessboard?




How many squares are there in a chessboard?


  If I ask you that how many squares are there in a chessboard, you might say that a chessboard is 8x8 and thus the number of squares in a chessboard are 64. But you are wrong, see how...

  Its true that a chessboard has 64 squares. But those 64 squares are only the 1x1 squares. There are many more squares of different sizes on the same chessboard. If you look closely at the left top, there is a big square consisting of 4 1x1 squares. So this means that the total square count of a chessboard doesn't stop at 64. But then how much are they in total?

Total number of 1x1 squares are 64 i.e (8-0)^2

Total number of 2x2 squares are 49 i.e (8–1)^2

Total number of 3x3 squares are 36 i.e (8–2)^2

Total number of 4x4 squares are 25 i.e (8–3)^2

Total number of 5x5 squares are 16 i.e (8–4)^2

Total number of 6x6 squares are 9 i.e (8–5)^2

Total number of 7x7 squares are 4 i.e (8–6)^2

Total number of 8x8 squares is 1 i.e (8–7)^2

Now if you sum up all the squares 64+49+36+25+16+9+4+1 you will get 204. So finally there are 204 squares in a chessboard. So now don't be confused if someone asks you the total number of squares on a chess board...
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