“Oh emperor my wishes are simple. I only wish for this. Give me one grain of rice for the first square of the chessboard, two grains for the next square, four grains for the next square, eight for the next square and so on for all 64 squares, with each square having double the number of grains as the square before.” Question: How much rice did the emperor owe the inventor? Problem statement: 64 𝚺2ⁿ-1 n=1
Process: My process for this was to draw out a chess board and begin by writing how many grains of rice were in each square. As the number got bigger and bigger I decided to write an equation for the problem. My equation is shown above. I found out this equation by using the amount of squares (64) over the sigma sign. I then found the equation by determining how much each square goes up by then subtracting one. I then looked at how many grains of rice was needed to fill the Grand Canyon.
6500 grains of rice in one cup.
The Grand canyon is 4.17 trillion cubic meters.
4446 cups in a cubic meter
So 4170000000000 cubic meters × 4446 cups = 18539820000000000 cups × 6500 grains of rice = 120508830000000000000 grains of rice to fill the Grand Canyon to the rim. The rice that the inventor got was 3.6893488147 × 10¹⁹ That means that the inventor could take his rice and will the Grand Canyon a third of the way full.
Extra Question: What if the man got 4 pieces of rice for the first square then 8 then 16 then 20? How much rice would he have then?