A wealthy king wanted to reward the inventor of chess for creating a beautiful game. The king offered the inventor a chest of jewels, a palace, or land to rule.
The inventor declined these rewards and said that all he wished for were some grains of rice.
Shocked, the king demanded an explanation.
The inventor explained, “On the first day, give me 2 grains of rice for the first square on the chessboard. On the second day, give me 4 grains of rice for the second square on the board, and 8 on the third day. Keep doubling the grains of rice each day for each of the 64 squares on the board.”
The king and all the members of his court burst out into laughter. “How foolish! You decline the treasures I offer for a few handfuls of rice?”
Do you think the inventor was foolish?
- Complete this table to show the number of grains on the first 5 days.
day expression with repeated multiplication expression with exponents number of grains of rice 1 2 2 4 3 8 4 5 -
What does
represent in this situation? Find the value of without a calculator.
Pause for discussion. - How many days would it take for the number of grains of rice to exceed 50,000?
- Will the number of grains of rice exceed 1 million before half of the chessboard is reached? Explain or show your reasoning.