The Emperor's Chess Board

The emperor, impressed by the game of chess, offers its inventor any reward. The inventor asks for rice, doubling the amount for each square on the chessboard. The emperor agrees, not realizing the exponential growth involved. The treasurer later reveals that the amount of rice exceeds all of China's supply. This story illustrates exponential growth, where each term is a power of 2, leading to a massive total by the 64th square.

What did the inventor request as a reward from the emperor?

• A palace in the empire

• A grain of rice that doubles on each chessboard square

• A new chess set

• A chest of gold

Why was the emperor surprised by the inventor's request?

• The request seemed too simple and modest

• The request was for a large sum of money

• The request involved a complex mathematical problem

• The request was for a rare artifact

What did the treasurer discover about the amount of rice needed?

• It was easily available in the empire

• It was more than the empire's annual production

• It was more than all the rice in China

• It was less than expected

What mathematical concept did the inventor use to outsmart the emperor?

• Linear growth

• Arithmetic sequence

• Geometric sequence

• Exponential growth

By the 64th square, how many grains of rice was the inventor owed?

• Over 9 quintillion

• Over 9 million

• Over 9 billion

• Over 9 trillion