To complete this activity, you’ll need some rice and a checkerboard. You can download the checkerboard… I can’t fit the rice through the slot in my computer, though.

There is a famous story about the meeting between a Chinese emperor and the inventor of the game of chess. There is a less famous story about the meeting between the emperor and the inventor of the game of checkers.

However, the emperor was so overjoyed by both games that he offered each inventor anything he wanted in the kingdom. Both inventors said they wanted some grains of rice.

The inventor of chess said, “I would like one grain of rice on the first square of the board, two grains on the second, four on the third, eight on the fourth, and so on. I would like all of the grains of rice that are placed on the board in this way.”

The inventor of checkers, however, was greedy and said, “ I would like one *million* grains of rice for every square on the board. I would like all of the grains of rice that are placed on the checker board in this way.”

The Chinese emperor laughed in the face of the inventor of checkers and said he wouldn’t be able to afford such an amount of rice. Instead, the emperor said he would give the checkers inventor the same amount he gave to the chess inventor.

- What do you think of each inventor’s proposition and the emperor’s response?
- What do you notice about the amount on a square of the chessboard and the amount on the previous square?
- What do you notice about the amount on a square of the chessboard and the amount on all the previous squares put together?
- What do you notice about the amount on a square of the checkerboard and the amount on the previous square?
- How many grains of rice will be on the entire checkerboard? The entire chessboard?