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.)
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.
