Draughts Board Calculations

Otago Witness, Issue 1994, 12 May 1892, Page 37

Draughts Board Calculations

It is related of an ingenious artizan who, as tradition records the matter, was the subject of a kindly monarch who reigned in an Eastern empire many centuries ago. The king was wont to know the happenings in his territory and was solicitous for the welfare of his loyal people. Being apprised of the mechanic's efforts in arranging 64 squares on a board and perfecting a number of pieces, his primary object being the invention of a game that would interest his children, the goodly king invited the peasant to visit the regal palace and teach himself and the members of the royal family the intr jcacies of tbe new pastime.- Having finished his task, the monarch promised his subject that he should have any reward he might ask for. He meekly replied that he would be content if the king would give him one kernel of wheat on the first square, two on the second, four on the third, eight on the fourth, and so on, doubling up to the sixty-fourth square. The king gladly acceded to this seemingly modest request, and ordered his attendants to bring in the wheat, which they began to do; but, to the astonishment of tho monarch, it was found that there was not wheat enough in the whole dominion to pay off the crafty inventor ! A mathematician who claims to have been figuring on this checker board curiosity says that to fulfill the king's promise it would take 30,027,097,184,485, bushels of wheat — allowing 600.000 kernels to each bushel. This prodigious amount would cover the states of New York, Pennsylvania, New Jersey, and Delaware, an area of 110,000 square miles, all over with wheat to the depth of a mile and a-quarter. In a few words here is the exact number of wheat kernels asked for — 9,627, 268,786,934,775,168. JFigure it up and prove or disprove it.