Friday, 13 June 2014

Chess Board

Total Number Of Squares in a Chess Board

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total number of 1 X 1 square   = 8x8 = 64

total number of 2 X 2 square   = 7x7 = 49

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total number of 3 X 3 square   = 6x6 = 36

total number of 4 X 4 square   = 5x5 = 25

total number of 5 X 5 square   = 4x4 = 16

total number of 6 X 6 square   = 3x3 = 9

total number of 7 X 7 square   = 2x2 = 4

total number of 8 X 8 square   = 1 = 1


 Total number of squares in chess board = 204


Total Number of squares in n x n board is  

 n*(n+1)(2n+1)/6

 

 

Total Number Of Squares in 9 x 8 board

   
total number of 1 X 1 square   = 9x8 =72

total number of 2 X 2 square   = 8x7 =56

total number of 3 X 3 square   = 7x6 =42

total number of 4 X 4 square   = 6x5 =30

total number of 5 X 5 square   = 5x4 =20

total number of 6 X 6 square   = 4x3 =12

total number of 7 X 7 square   = 3x2 =6

total number of 8 X 8 square   = 2x1 =2


Total number of squares in 9x8 board = 240
Total number of squares in 10x8 board = 276
Total number of squares in 11x8 board = 312

 

Total Number of squares in m x n board is  

note: m>n

 n*(n+1)(2n+1)/6 + (m-n)*n*(n+1)/2

final equation for Total Number of squares in m x n board is
is given bellow:
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