# Chessboard puzzles

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How many squares are on a chess board?

If you think the answer is 64, think again!

SherlockHolmes Expert Asked on 23rd December 2017 in

There are 8 by 8 Square, 7 by 7, 6 by 6 and so on …
The complete list of squares with count is shown below:

 1, 8×8 square 4, 7×7 squares 9, 6×6 squares 16, 5×5 squares 25, 4×4 squares 36, 3×3 squares 49, 2×2 squares 64, 1×1 squares

Therefore, there are actually 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 squares on a chessboard! (in total 204).

Can also be calculated-
The number of squares present in  square matrix of size N*N =N*N+(N-1)*(N-1)+(N-2)*(N-2)+…..+1*1.

For a Chess Board , the size is of 8*8=8*8+7*7+6*6+5*5+4*4+3*3+2*2+1*1

=64+49+36+25+16+9+4+1=204.

SherlockHolmes Expert Answered on 29th December 2017.

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