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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 $8\times 8$ Chessboard? Since this is a Geometric Series, the answer for $n$ squares is

\sum_{i=0}^{n-1} 2^i=2^n-1.

Plugging in $n=8\times 8=64$ then gives $2^{64}-1=18446744073709551615$.


Pappas, T. ``The Wheat & Chessboard.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 17, 1989.

© 1996-9 Eric W. Weisstein