# The Center of Math Blog

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## Thursday, September 4, 2014

### Throwback Fact of the Week - Wheat on a Chessboard - 9/4/14

Wheat on a Chessboard

This 800-year-old problem in mathematics is notable because of the fluency at which it illustrates the startling nature of geometric growth.

The legend goes that the Indian King, Shirham, asked his Grand Vizier, Sissa ben Dahir, what reward he would like for inventing the game of chess. The Grand Vizier asked for one grain of wheat for the first square of the chessboard, two grains for the second square, four grains for the third, eight grains for the fourth square, and so on for the sixty-four total squares. This appeared to the king to be a small and foolish request, so he granted the grand vizier's wish.

Little did the king know just how many grains of wheat would accumulate by the 64th square. This number would be the sum 1+2+22+23+…+263 = 264-1. This comes out to be 18,446,744,073,709,551,615 grains of wheat (over 18 quintillion!). Clearly the king would run out of grain long before this total. This is enough wheat to cover the entire earth several inches deep!

Watch the video below to get an illustration of this legend and the absurd amount of wheat!

Video Credit: Jill Britton