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 A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chessboard. On the second square, the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on square31​? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pounds.)

 

How many grains of wheat should be placed on square

31​?

 Mar 30, 2021
 #1
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Number  on  any particular  square =  2^(n - 1)

On the  31st  square  we  have   2^(31 - 1) = 2^30  =  1073741824 grains

 

 

Total  cumulative  number  through  square  n  =  2^n  - 1 =  2^31 - 1  =  2147483647 grains

 

Total weight  =  2147483647 /  7000   ≈  306783 lbs

 

 

cool cool cool

 Mar 30, 2021

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