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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 chess board. 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 square

18​?

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 pound.)

 Apr 20, 2022
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He placed the following amount on square #18

 

2^(18 - 1) ==2^17 ==131,072 - grains of wheat

 

[2^64] - 1 ==18,446,744,073,709,551,615 - total number of grains of wheat on the chess board.

 

18,446,744,073,709,551,615 x 1 / 7000 ==2,635,249,153,387,078.80 - pounds of grain, or their total weight.

 Apr 20, 2022

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