You can find out more about "the chess number" at Wikipedia in the article about Powers of Two and also in the article about the Wheat and Chessboard Problem. Carl Sagan tells the story of "The Persian Chessboard" in Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium. You can also see a version of the story as told by the 9th-century historian al-Yaqubi in Murray's A History of Chess.
The story below is my own paraphrase of the story. I have combined elements from the two versions (mostly the al-Yaqubi version in Murray) to tell my version of the story in my own words... and if you are looking for other types of chain-tales, click here for previous Stories-of-the-Day.
THE INVENTION OF CHESS
(pixnio)
Long ago, there was a queen. In the country of that queen, there was a rebellion, and the rebel leader killed the queen's son; he was the crown prince, the heir to the throne. The queen's councilors did not want to give this news to the queen. How could they tell her that the king-to-be was dead?
In desperation, they went to a philosopher and told him of their trouble. After thinking the matter over for three days and three nights, the philosopher said, "Bring me a carpenter, and supply him with two colors of wood: white and black." The philosopher then instructed the carpenter how to carve pieces from the wood: there was to be a black king and a white king; a black queen and a white queen; black knights, white knights; black pawns, white pawns, and so on. Yes, they were chess pieces! But no one had played the game of chess before.
Next, the philosopher had the carpenter construct a board eight squares by eight squares, alternating black and white. He then requested an audience with the queen and her councilors.
As the philosopher showed the chess pieces and the board to the queen, he said to her, "This is war without bloodshed. It is a game, and I will show you how to play."
He then played the game with the queen, and the game was over when he captured her king. "Shah-mat," he said. Which means in the language of that country "the king is dead" — and that is why, in English, we say "checkmate" at the end of the game.
When the queen heard these words, she gazed at the philosopher in astonishment. "My son is dead," she said.
The philosopher nodded solemnly in reply.
The queen then told the doorkeeper to let the people come in to comfort her. And she wept.
Then, after she was done weeping, she said to the philosopher, "How may I reward you? Ask me for whatever you want."
He replied, "I ask a gift of grain; use the board to measure it out. On the first square, put one grain. On the next square, put two. Then on the next square, put four. And on the next, eight. Continue until you reach the final square."
The queen said, "One grain, two grains, four grains, and so on: that is too small a reward for such a fine invention. Please let me give you something greater. I will give you jewels. I will give you gold. Ask me for anything you desire."
The philosopher insisted that all he wanted was wheat: one grain, two grains, four grains, eight grains, and so on.
The queen began to measure out the grains: one grain, two grains, four grains, eight grains, sixteen, thirty-two, sixty-four, and then one hundred and twenty-eight grains at the end of the first row.
Then the second row: two hundred and fifty-six, then five hundred and twelve, then over a thousand. Then over two thousand, four thousand, eight thousand, sixteen thousand. Thirty-two thousand.
Astonished, the queen summoned the court mathematician. He explained that by the middle of the third row, the queen would need over a million grains for a single square.
Over a billion grains for a square in the fourth row.
Beyond the fourth row, the numbers had no words.
Not all the wheat in all the country could satisfy what the philosopher had asked of her. Not even all the wheat in all the world would be enough.
(If the queen had possessed an electronic calculator, she could figure out the so-called chess number for herself, and the quintillions of grains of wheat would weigh 75 billion tons.)
Then the second row: two hundred and fifty-six, then five hundred and twelve, then over a thousand. Then over two thousand, four thousand, eight thousand, sixteen thousand. Thirty-two thousand.
Astonished, the queen summoned the court mathematician. He explained that by the middle of the third row, the queen would need over a million grains for a single square.
Over a billion grains for a square in the fourth row.
Beyond the fourth row, the numbers had no words.
Not all the wheat in all the country could satisfy what the philosopher had asked of her. Not even all the wheat in all the world would be enough.
(If the queen had possessed an electronic calculator, she could figure out the so-called chess number for herself, and the quintillions of grains of wheat would weigh 75 billion tons.)
When the philosopher saw that the queen understood, he smiled. "Do not fear, my queen," he said; "I have no need of a reward. Your thanks are reward enough."
And so the game of chess was invented.
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