Rice Grain and Chessboard Problem

The chessboard and grain of rice problem is actually in the history of mathematical thinking It is known as a classical problem that has a very important place.

The power of mathematics once again unshakably proving This problem shows us the importance of mathematics and science, accompanied by an interesting story.

According to legend, a wise king of India wanted to give a reward to the inventor of the game of chess.

Invented by the inventor game of chess The king liked it very much and called the inventor to him. “Ask me whatever you wish.” he says and is surprised by the answer he gets.

Because the inventor asked the king to put a grain of rice on the first square of the chessboard and say, twice as many grains of rice in each next square He asked him to go ahead and do this across the 64 squares on the chessboard.

The reward claimed by the inventor will accumulate over 64 frames was the sum of rice grains.

Although the king thought this was a small amount at first, he would soon realize the truth.

The king was very angry when he heard this request. Because the inventor He didn’t take advantage of the opportunity he had. he was thinking.

But the situation was exactly the opposite. The inventor was quite clever and perhaps smarter than he should have been. much, much more He demanded a reward.

The reward requested by the inventor was exactly 18,446,744,073,709,551,615 pieces of brass! Well, how did this happen?!

This number, which you probably say “onsekfdfds” while reading, is exactly 18 quintillion 446 quadrillion 744 trillion 73 billion 709 million 551 thousand 615 It is read as.

Assuming that the weight of a grain of rice is 0.029 grams on average, the exact amount of rice that the king should give to the inventor is 534,955,578,138 tons.

This is such a large amount that in 2020 total amount of rice produced in the world even 500,000,000,000 tons. In other words, the amount the inventor wants one thirty-sixth much.

So how exactly did we arrive at this amount?

The grain of rice problem is actually a geometric sequence expresses. Once a grain of rice is placed in the first square, the amount of rice grains placed in each subsequent square is twice the amount in the previous square.

So, one for each frame number exponential increase has. As a result, the total amount of rice increases rapidly and a rather large number is obtained.

The exponential increase function we mentioned 2^x-1 is. In this direction, x is the number of the square on the chessboard.

in function 64 instead of x As we mentioned before, the result you will get when you write this will be 18 quintillion 446 quadrillion 744 trillion 73 billion 709 million 551 thousand 615.

Let’s get back to our story. What happened to our inventor’s rice?

According to legend, the king realized that he could not fulfill his promise, so he built a temple and made sure that everyone who came to the temple to worship was offered a rice dessert. In this way, even if not at that moment In time he would be able to keep his promise.

krishna temple It is said that a kind of dessert made of rice is still offered to people who come to worship in this temple.

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