Rice in the world and the Indian chessboard fable

[meggy90]

I'm trying to prove to my friend that the Indian Chessboard fable (1 grain on first square, 2 on second, 4 on third, 8 on fourth etc) is true - that if all squares are filled then there would be more rice than there is in the world. She says you can't possible quantify the amount rice in the world to prove that.

[KenR]

18,446,744,073,709,600,000 grains... that's an awful lot of rice LOL
and isn't Excel a wonderful piece of kit :-)

[nickmo]

forget the amount of rice in the world - you have to get to a planet 6 times the present biomass - let alone rice grains.

Extract here to explain:

".......The total number of grains of rice on the first half of the chessboard is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 ... + 2,147,483,648, for a total of exactly 232 − 1 = 4,294,967,295 grains of rice, or about 100,000 kg of rice, with the mass of one grain of rice being roughly 25 mg[3]. This total amount is about 1/1,000,000th of total rice production in India per annum (in 2005) and was considered economically viable to the emperor of India.

The total number of grains of rice on the second half of the chessboard is 232 + 233 + 234 ... + 263, for a total of 264 − 232 grains of rice. This is about 460 billion tonnes, or 6 times the entire weight of the Earth biomass....."

Hope that wins the prize!

Read info at http://en.wikipedia.org/wiki/Second_Half_of_th e_Chessboard if you get bored later....