Chessboard

Calculate the total number of squares formed by the grid lines of a standard 8x8 chessboard.

64 204 65 impossible to count 100

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1 solution

Gourab King
Jul 31, 2015

we will start counting from small squares......That is the no. of smallest squares are (8x8)then let us count squares of grid 2x2 .....If you count wisely you will find there are 7 such grids in length and breadth , hence such squares are 7*7 ...... In this way the total no. of squares are (8x8)+(7x7)+(6x6)+5x5+4x4+3x3+2x2+1x1=204

The generalization to your solution is n(n+1)(2n+1)/6.

Raven Herd - 5 years, 10 months ago

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It is n(n+1)(2n+1)/6

gourab king - 5 years, 10 months ago

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