What is the answer to the Rice on a Chess Board question?

Answer 1

This is based on the myth of a Chinese philosopher that did a great act of service for an emperor; he subsequently asked that his reward be as follows: * "Put one grain of rice on the first square of a chessboard. Then put two on the next, and four on the one after that. For each square, put double the number of grains on the square before it." The emperor agreed without thinking this through; the reward bankrupted the kingdom/empire before getting halfway and the philosopher was executed. We can calculate the number of grains on any square by the formula R = 2(n-1), where n is the square in numerical order and R is the number of grains on the nth square. If we were to work out each individual value for R from n = 1 to n = 64, it would take a while BUT since this is a geometrical sequence, we can calculate the sum of values for R, from a given range of values for n, by use of a formula developed for the purpose. This is as follows: RT = Σ64n=1(2n-1)* RT = Σ-- (20 + 21 + 22 + ... + 264) RT = 1(1 - 264)(1 - 2) RT = 1 x 1 x (264 - 1)** RT = 264 - 1 RT = 1.84467 x 1019 grains of rice, or thereabouts. In other words, reaching the total would mean almost 20 billion billion grains of rice; such an amount does not, and cannot, exist on Earth. *These values should be directly above and below the sigma sign, but WA doesn't work that way. **Note that the minus sign on the 1 has been negated by moving it into the brackets and simplifying.

Answer 2

2 to the power of 63 +2 to the power of 62 + 2 to the power of 61........+2 to the power of 0.