The Rice And Chessboard Story

If you were to take a chess regular chessboard, and place one grain of rice on the first square, two on the second, four on the third and so on, you would end up with 18,446,744,073,709,551,615 grains of rice – that’s a huge amount of rice! If you were to take each grain and line them up next to each other, you could travel approximately 15 light years.

A modern version, if you like, of the rice and chessboard legend. It goes like this.

You are offered a job, which lasts for 7 weeks. You get to choose your salary.

Either, you get $100 for the first day, $200 for the second day, $300 for the third day. Each day you are paid $100 more than the day before.
Or, you get 1 cent for the first day, 2 cents for the second day, 4 cents for the third day. Each day you are paid double what you were paid the day before.

Which do you choose?

Most people unfamiliar with this kind of dilemma will choose the first option.

For the first choice, the person earns $2800 in week 1, then $7700, $12600, $17500, $22400, $27300 then $32200, for a grand total of $122,500

For the doubling scheme, the person earns $1.27 in week 1, then $162.56, $20807.68, $2,663,383.04, $340,913,029.12, $43,636,867,727.36 then $5,585,519,069,102.08 for a total of $5,629,499,534,213.11.