Legend About The Chessboard

Chess is an ancient game. It has existed for many centuries, and it is therefore not surprising that legends are linked to it whose honesty is difficult to prove due to its antiquity. I want to tell you about one of them. To understand it, it is not necessary to know how to play chess; it is enough to know that the board where it is played is divided into 64 squares (black and white squares, arranged alternately).

The game of chess was invented in India. When the Hindu king Sheram met him, he was amazed at how ingenious it was and at the variety of positions possible on it. When he learned that the inventor was one of his subjects, the king sent for him to reward him for his successful invention personally.

The inventor, called Seta, presented himself to the sovereign. He was a wise man dressed in modesty, who lived by the means provided by his disciples.

- Seta, I want to reward you with dignity for the original game you have invented - said the king.

The wise man replied with a bow.

- I am rich enough to be able to fulfil your highest wish - continued the king. Say the reward that satisfies you and you will receive it.

Seta continued in silence.

- Do not be shy," the king encouraged him. Express your wish. I will not spare anything to satisfy it.

- Great is your kindness, sovereign. But grant me a short time to meditate on the answer. Tomorrow, after mature reflection, I will communicate to you my request.

When the next day Seta appeared before the throne again, he left the king in awe with his request, unprecedented in his modesty.

- Sovereign," said Seta, "command that a grain of wheat be delivered to me by the first square of the chessboard.

- A single grain of wheat? - replied the king in admiration.

- Yes, sovereign. For the second square, order that they give me two grains; for the third, 4; for the fourth, 8; for the fifth, 16; for the sixth, 32...

- That's enough," the king interrupted irritably. You will receive the wheat corresponding to the 64 squares of the board according to your wish: for each square twice as much as for the previous one. But you must know that your request is unworthy of my generosity. By asking me for such a miserable reward, you are disregarding, irreverently, my benevolence. Indeed, as a wise man, you should have given more significant proof of respect to the goodness of your sovereign. My servants will take a sack of wheat from you, which you ask for.

Seta smiled, left the chamber, and stood to wait at the palace gate.

During the meal, the king remembered the inventor of chess and sent them to find out if they had already given the thoughtless Seta his small reward.

- Sovereign, they are carrying out your order - was the answer. The court mathematicians calculate the number of grains that are due to him.

The king frowned. He was not used to them taking so long to carry out his orders.

In the evening, as he retired to rest, the king asked again how long it had been since Seta had left the palace with his sack of wheat.

- Sovereign," he was answered, "your mathematicians work without rest and hope to finish the calculations at dawn.

- Why does this matter go so slowly? - shouted the king angrily. Tomorrow, before I wake up, they will have delivered to Seta every last grain of wheat. I am not in the habit of giving the same order twice.

In the morning, the king was informed that the senior court mathematician was requesting an audience to present him with a critical report.

The king ordered that he be brought in.

- Before you start your report," said Sherman, "I want to know if the miserable reward he has requested has finally been given to Seta.

- That is precisely why I dared to come so early," replied the old man. We have carefully calculated the total amount of grain that Seta wishes to receive. It is such an enormous figure...

- Whatever its magnitude," the king haughtily interrupted, "my granaries will not be impoverished. I have promised to give him that reward, and therefore, it must be given to him.

- Sovereign, it is not up to your will to fulfill such a wish. In all your barns, there is not the amount of wheat that Seta demands. Neither does it exist in the barns of the whole kingdom. Even the barns of the world is insufficient. If you wish to deliver the promised reward without fail, command that all the nations of the earth be turned into farmlands, the power that the seas and oceans be dried up, the power that the ice and snow that cover the far-off deserts of the North be melted. Let all the space be sown with wheat, and command that all the harvest obtained in these fields be given to Seta. Only then will he receive his reward.

The king listened in amazement to the words of the wise older man.

- Tell me what this monstrous figure is - he said reflecting.

- O sovereign! Eighteen trillion four hundred and forty-six thousand seven hundred and forty-four billion seventy-three thousand seven hundred and nine million five hundred and fifty-one thousand six hundred and fifteen.

18,446,744,073,709,551,615

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