The Legend about a Checkered Board

The Indian King Sheram was so delighted with the game of chess that he told its inventor, Sessa, that he would reward him for his marvellous invention. 

"Sire," Sessa said, "I would like to have 1 grain of wheat for the first square of the chessboard, 2 for the second, 4 for the third, 8 for the fourth, 16 for the fifth, 32 for the sixth" ...

"Enough," the king was irritated. "You shall get the grains for each of the 64 squares of the chessboard as you wish: for each square double the amount of the preceding square. But your request is not worthy of my generosity. By asking for such a trite reward you have shown disrespect for me. Go! My servants shall bring you the sack of grain."

Sessa smiled and went out, and then waited at the gate for his reward.

At dinner, the king remembered Sessa and inquired whether the "foolhardy" inventor had been given his miserable reward. He was told that the sages were calculating the number of grains Sessa was to receive. He frowned. He was not accustomed to seeing his commands fulfilled so slowly. In the evening, before going to bed, he asked whether Sessa had been given his bag of grain. 

"Sire," was the reply, "the mathematicians are working incessantly and hope to compute the sum before dawn breaks."

"Why are they so slow?" the king demanded angrily. "Before I awake Sessa must be paid in full!"

In the morning, the chief court mathematician reported to the king that the number of grains was indeed tremendous.

"The granaries do not hold the amount of grain Sessa has asked for. There is not that much grain in the whole of the kingdom; in fact, in the whole world."

The king listened awe-struck to the wise man. "Name this giant number," the king said thoughtfully. "It is 18 446 744 073 709 551 615." The sage replied.

Adapted from: Ya. Perelman, Mathematics Can Be Fun. Mir.Publishers Moscow 1985. p98-101

If you want to have a clear picture of what this giant number is really like, just imagine the size of the granary that will be required to store all this grain. It is well known that a cubic metre of wheat contains 15 000 000 grains. Hence, the reward asked by the inventor of chess would require a granary of approximately 12 000 000 000 000 cubic metres or 12 000 cubic kilometres. If we take a granary 4 metres in height and 10 metres in width, its length must be 300 000 000 kilometres, i.e. twice the distance from the earth to the sun.