A mathematician named Sessa, the son of Dahar, the subject of an Indian Prince, having invented the game of chess, his sovereign was highly pleased with the invention, and wishing to confer on him some reward worthy of his magnificence, desired him to ask whatever he thought proper, assuring him that it should be granted. The mathematician, however, only asked for a grain of wheat for the first square of the chess-board, two for the second, four for the third, and so on to the last, or sixty-fourth. The prince at first was almost incensed at this demand, conceiving that it was ill-suited to his liberality. By the advice of his courtiers, however, he ordered his vizier to comply with Sessa's request, but the minister was much astonished when, having caused the quantity of wheat necessary to fulfil the prince's order to be calculated, he found that all the grain in the royal granaries, and even all that in those of his subjects and in all Asia, would not be sufficient. He therefore informed the prince, who sent for the mathematician, and candidly acknowledged that he was not rich enough to be able to comply with his demand, the ingenuity of which astonished him still more than the game he had invented. It will be found by calculation that the sixty-fourth term of the double progression, beginning with unity, is 9,223,372,036,854,775,808, and the sum of all the terms of this double progression, beginning with unity, may be obtained by doubling the last term and subtracting the first from the sum. The number, therefore, of the grains of wheat required to satisfy Sessa's demand will be 18,446,744,073,709,551,615. Now, if a pint contains 9,216 grains of wheat, a gallon will contain 73,728, and a bushel (8 gallons) will contain 589,784. Dividing the number of grains by this quantity, we get 31,274,997,412,295 for the number of bushels necessary to discharge the promise of the Indian prince. And if we suppose that one acre of land is capable of producing in one year, thirty bushels of wheat, it would require 1,042,499,913,743 acres, which is more than eight times the entire surface of the globe; for the diameter of the earth being taken at 7,930 miles, its whole surface, including land and water, will amount to very little more than 126,437,889,177 square acres. If the price of a bushel of wheat be estimated at one dollar, the value of the above quantity probably exceeds that of all the riches on the earth. THE NAIL PROBLEM A gentleman took a fancy to a horse, and the dealer, to induce him to buy, offered the animal for the value of the twenty-fourth nail in his shoe, reckoning one cent for the first nail, two for the second, four for the third, and so on. The gentleman, thinking the price very low, accepted the offer. What was the price of the horse?