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### Caliph's Bride Chessboard Calculation

In the calculations below the symbol ^ represents "to the power of" so the 64th square requires 2 to the power of 63 (2 x 2 x 2... with sixty-three 2's in the calculation) grains of rice to cover it.

A very rough and ready calculation using a pair of dodgy kitchen scales gave approx 100 grains of long grain rice as being 1 gram. (It was about 108 but let's try and keep it simple!)

1000 grams in a kilo, so 100,000 grains is a kilo.
1000 kilos in a tonne so 100,000,000 grains in a tonne.

The first row of the chessboard looks like this:
Square 1 = 1 grain of rice
Square 2 = 2^1 = 2 grains of rice
Square 3 = 2^2 = 4 grains of rice
Square 4 = 2^3 = 8 grains of rice
Square 5 = 2^4 = 16 grains of rice
Square 6 = 2^5 = 32 grains of rice
Square 7 = 2^6 = 64 grains of rice
Square 8 = 2^7 = 128 (just over a gram in weight) The Caliph still has a smile on his face

Skip a few rows and look at the last row of the chessboard

Square 57 = 2^56 = 72,057,594,037,927,936 grains of rice (this is more than the amount of rice produced in the entire world in 1994*)
Square 58 = 2^57 = 144,115,188,075,855,872 grains of rice
Square 59 = 2^58 = 288,230,376,151,711,744 grains of rice
Square 60 = 2^59 = 576,460,752,303,423,488 grains of rice
Square 61 = 2^60 = 1,152,921,504,606,846,976 grains of rice
Square 62 = 2^61 = 2,305,843,009,213,693,952 grains of rice
Square 63 = 2^62 = 4,611,686,018,427,387,904 grains of rice
Square 64 = 2^63 = 9,223,372,036,854,775,808 grains of rice

So on square 64 the amount of rice is in excess of 92,233,720,368 tonnes.

* World rice production in 1994 was about 535,000,000 tons.
(Source http://www.riceweb.org/geo_intro.htm

Like in astrophysics numbers become so big you talk about "light years" to describe huge distances. Let's invent the term "rice year". This is the total amount of rice produced in the world in a single year (based on my available 1994 figure).

By the beginning of the last row of the chessboard the Caliph is having to provide more than a rice year to cover the 57th square and by the last square he is up to 172 rice years. And these squares are all covered separately, so to cover the last 8 squares he would need over 341 rice years worth of rice!