AP EAMCET Engineering 17 Sep 2020 Shift 2 Paper

Number of rectangles in a chess board (including squares) =Σn3
=‌

n2(n+1)2

4

Number of squares in a chess board
=Σn2=‌

n(n+1)(2n+1)

6

So, Number of rectangles which are not squares
=Σn3−Σn2
By comparison we get
∴‌‌n=6
Hence, total number of black and white squares
=n×n=6×6=36
Half of there are white
=‌

36

2

=18 squares.