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Can you imagine the size of 100 million It is said that king sherhan wanted to reward the inventor of chess, the prime minister Dayer. Dayer pointed to the chess board and said, "Your Majesty, please give me one grain of wheat in the first small space of the board, two grains of wheat in the second small space, and four grains of wheat in the third small space. Go on like this, The wheat in each small grid is twice as much as that in the previous one. Then give all the 64 grids of wheat on the chessboard to your servant! "The king ordered his servant to put a bag of wheat in front of the chessboard, but the bag was empty before it was put into the 20th grid. So the wheat was carried in bag by bag, and the warehouse was empty, The checkerboard has not put all the grains of wheat on it. King sherhan thought that he had been cheated If you put the wheat in the () grid, it will have more than 100 million grains; if you put the wheat in the 64th grid, it will have about 100 million grains
The increasing number of wheat according to the lattice is: 1,2,4,8... 2 ^ (n-1) is an exponential growth. The number of wheat in the nth lattice is 2 ^ (n-1), and the number of wheat in the first n lattice is s = 1 + 2 + 4 +... + 2 ^ (n-1) 2S = 2 + 4 + 8 +... + 2 ^ (n-1) + 2 ^ n. if s > 10 ^ 8, 2 ^ n > 10 ^ 8-1 ≈ 10 ^ 98
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