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A woman labels the squares of a very large chessboard 1 through 64. On each square k, the woman puts 2^k grains of rice. How many more grains of rice are placed on the \(10^{th}\) square than on the first 8 squares combined?

 Oct 15, 2019
 #1
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On the first 8 squares we have

 

2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8  =

  2    +  4   +   8  +   16   + 32 + 64  +  128  + 256  =

510 grains     (1) 

 

On the 10th square we have 2^10   =  1024 grains   (2)

 

Subtract  (2)  - (1)   for your answer

 

cool cool cool

 Oct 15, 2019

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