31 Dec 2013

Squares on a Chess Board

Puzzle :
      How many squares are there on a Chess board. ?

64 as answer is wrong !!

The Answer is ofcourse not 64. Since Chess boards of size 1x1 , 2x2 , 3x3 ..... 7x7 , 8x8 can be made.
For 1x1
8*8 = 64
For 2x2
7 horizontal and 7 vertical positions are available to place 2x2 chess board.
So we have 7*7= 49 , 2x2 Chess boards
For 3x3
6 horizontal and 6 vertical positions are available to place 2x2 chess board.
So we have 6*6= 36 , 3x3 Chess boards
and so on
1×1 8 x 8 = 64 squares
2×2 7 x 7 = 49 squares
3×3 6 x 6 = 36 squares
4×4 5 x 5 = 25 squares
5×5 4 x 4 = 16 squares
6×6 3 x 3 = 9 squares
7×7 2 x 2 = 4 squares
8×8 1×1 = 1 square
Therefore , total squares are 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 = 204 squares


  1. Ans is 204, not 214.

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