The legend of the rice and chessboard illustrates the magnitude of exponential functions. In scientific research, numbers in mathematical models can increase so exponentially that they require massive amounts of computing power to solve them. The following examples illustrate the "power of doubling."

**Inventor of Chess and Emperor of India**

It is believed that chess was invented some 1,500 years ago in India, and the game's inventor so impressed the emperor that he was asked to name his reward. A chessboard has 64 squares, and the inventor asked for one grain of rice on the first square and double that number for the next square and so on for all 64 squares.

The emperor thought it was such insignificant compensation for so marvelous a game that he agreed only to find out that by the time the 64th square was reached, there was not enough rice in the kingdom to fulfill the request. One version of the legend claims the inventor was then beheaded.

There are stories that use wheat instead of rice, but in either case, 1 doubled 64 times yields the number 18 followed by 18 zeros.

**Water Lilies on a Lake**

Another example of doubling is water lilies on a lake. There is one water lily on day one, and they double every day. At the end of 30 days, if half the lake is filled with lilies, how many days until the entire lake is covered? Do you know the answer? If not, see water lilies answer. See quantum computing.

It is believed that chess was invented some 1,500 years ago in India, and the game's inventor so impressed the emperor that he was asked to name his reward. A chessboard has 64 squares, and the inventor asked for one grain of rice on the first square and double that number for the next square and so on for all 64 squares.

Another example of doubling is water lilies on a lake. There is one water lily on day one, and they double every day. At the end of 30 days, if half the lake is filled with lilies, how many days until the entire lake is covered? Do you know the answer? If not, see water lilies answer. See quantum computing.

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