There is such a math story. In ancient India, there was a minister named Siddhartha. He was clever enough to invent a chess piece. The king enjoyed it, so he decided to reward Sita Qin. Siddhartha said, "Your Majesty, I just want some wheat. Please find someone to put the wheat in the sixty-four squares of the chessboard I invented. Put one grain in the first grid, two grains in the second grid, four grains in the third grid, eight grains in the fourth grid and sixteen grains in the fifth grid, and put twice the number of grains in the previous grid until sixty-four grids are full. "
The king smiled. He thinks Sito is really interesting. He doesn't want the treasure. Instead, he made such a "stupid" request. There is a lot of wheat in the barn. Filling in 64 squares is a piece of cake. So he ordered the minister of grain: "agree to Sito's request and pull the wheat out of the grain depot now." Everyone present thought that a small bag of wheat could fill more than a dozen squares on the chessboard, and some people even couldn't help laughing.
After the wheat was pulled out, the grain minister filled it grain by grain. At first, one grain, two grains, four grains, eight grains, the squares in front were filled up quickly, and a small bowl of wheat was not used up. But slowly, the wheat used began to increase obviously, 32,64,128,256,512, 1024 grains.
With more and more squares for placing wheat grains, the tools for transporting wheat grains have changed from bowls to pots and from pots to baskets. Even at this time, ministers are still laughing, and some even suggest that you don't have to bother, just fill a carriage of wheat and give it to Sito!
I don't know from which moment, the noisy crowd suddenly quieted down. Because when you put rice grains on the square of 16, you need to take out 1 kg of rice, and by the 20th square, you need a car full of rice. In this way, the king can't provide enough rice to put on the 64th square of the chessboard. The ministers and the king opened their mouths in surprise: even if all the money were poured into the country, it would not fit into the next box.
Although we don't know how the king ended up, one thing is certain: Siddhartha's demands could not be met by the king. This requirement of intelligent tin tower is actually the principle of geometric multiplication in mathematics. The terrible thing about this mathematical model is that if a number is greater than or equal to 2 and grows in geometric series, the rate of multiplication is amazing.
Assuming that a grain of rice in the first cell is written as the 0 th power of 2, the second cell is written as the 1 power of 2, and the third cell is written as the 2 nd power, then the nth cell can be written as the N- 1 power of 2. There are 64 squares in chess. By the 64th square, the number of rice grains to be put is 2 to the 63rd power, that is, 9,223,372,036,854,780,000, which is just the capacity of this square. If all are added up, it is 18446740. If 1000 grains of rice weigh one gram, then if converted, 9223372036 tons of rice need to be put in the 64th box. With such a large number of people, it seems that the king will hand over the country.