THE CHESS-BOARD PROBLEM 



N Arabian author, Al Sephadi, relates the follow- 

 ing curious anecdote : 



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 liberal- 

 ity. 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 mathe- 

 matician, 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 



163 



