Wheat and Chessboard Problem

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


a Mersenne number. Plugging in n=8×8=64 then gives 2^(64)-1=18446744073709551615.

See also

Mersenne Number

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Pappas, T. "The Wheat & Chessboard." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 17, 1989.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 23-24, 1999.

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Wheat and Chessboard Problem

Cite this as:

Weisstein, Eric W. "Wheat and Chessboard Problem." From MathWorld--A Wolfram Web Resource.

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