Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an 8×8 chessboard? Since this is a geometric series, the answer for n squares is sum_(i = 0)^(n - 1) 2^i = 2^n - 1, a Mersenne number. Plugging in n = 8×8 = 64 then gives 2^64 - 1 = 18446744073709551615.
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