INTELLECT SHARPENERS

New Zealand Herald, Volume LXXII, Issue 22100, 4 May 1935, Page 5 (Supplement)

INTELLECT SHARPENERS

LIBRARY PUZZLE The honorary secretary of a small library had instructions from the committee to spend the amount of a donation, which was a cheque for a certain number of guineas, in purchasing new books. In ordering from a catalogue, he found ho could get exactly 54 books of the same- price for tho money available, but tho bookseller promised him a rebate of threepence on each book. This enabled him to order four more books, and actually left sixpence with which to pay the cost of the money order. At what price were tho books quoted? PROBLEM IN AGES William is tho eldest of a family of three. Ho says, rather vaguely, that ho lias still some time to wait for his twenty-first birthday, but he does not say how long. What he is willing to stato is that tho sum of the ages of his brother and himself is twice as great as the ago of his brother, but his own ago is only three-quarters of tho sum of the ages of his brother and sister. It is to lie understood that ho is not speaking of fractions of years, and the problem is to find what tho tlireo ages are. A FEW DOZEN EGGS There is a well-worn puzzle concerning a woman, who sold eggs to three customers, one after tho other, in each ease parting with half the number she had in stock plus half an egg. She finished her very small transaction with ouo egg left over, and probably every one to-day knows that she started with fifteen eggs. Another business woman, who felt a desire to set a more up-to-date problem, sold her eggs according to the same scheme, and had 31 after she had served her third customer, but the complication in her case is that some of the eggs were stolen from her. Tho person, whom sho employed as her assistant, was absent on his annual vacation, so that she had to carry the eggs to tho purchasers' door herself. While she was thus delivering the first lot, someone entered her car and stole a number of eggs, and she did not take these into account when counting out half tho remainder and half an egg for her second customer. The peculiar thing about it was that she started with a number of eggs, which was a multiple of 31, and the number left unsold was exactly 31. The problem is to discover how many of her eggs were stolen. HIGH STAKES A man started gambling for rathiir high stakes, and the money he had available for this purpose had been entirely in fifty-pound notes, until he changed one of them by spending £l, Tho first night's pla.v resulted in a loss of one-seventeenth of all the money ho had, and he was not keen to play again on the second night, until his frienda persuaded him to try his luck just once. He began by winning £ls, but after that he had no luck, and when play ceased, he had parted with onethirteenth of what he had after his only win. On the third night he was again persuaded to try once, but he stated definitely that, whether ho won or lost,

By C. J. WHEREFORE

ho would not continue to play. As it happened, lie lost iust enough to mako the remainder of his money equal to a sum which could be paid in fiftypound notes. How much money had he at the start, and what did he lose the last night? ARGUMENTATIVE PROBLEM Four candidates, A, B, C and 1), sit for an examination in mathematics, and are placed in that order. Only four problems are set, and a complete solution of any one of them receives 5 marks. Loss successful attempts may receive 4, 3, 2, or 1 mark, and none of the four fails to get at least one for any problem. Forty-six marks are allotted altogether, and each candidate's total exceeds that of the one below him by the same amount. A just missed getting full marks, because he was penalised for a piece of carelessness in one problem. 0 and D had the same marks for the last problem, which was admitted to bo the most difficult. In the other three, C's marks were never exactly twice as many as those of 1). Only one 5 was scored in addition to those oj' A. B was equally successful with the last two problems, but not with the last three. How many did B got for each of the problems in its turn? PROBLEMATICAL CAR A canvasser has been trying to persuade Professor Aftermath to buy a new car, but he admits that he is making very little impression. Ha pointed out that the present car is very old, but the professor replied that it still continues to do good work. Last week the numbers of miles ho had driven it on different days, when multiplied together, make a product of equal to the number of pence in the sum ho gave for it, namely £212, with fourteen shillings and threepence added. The sum of thesti numbers is fourteen times the number of years he has had the car. The salesman, who has failed to get an order, considers these details a waste of time, but if he were interested in problems, he could find pleasure in discovering what were the longtut and shortest daily journeys which were made in the car last week, and how many years have elapsed since the professor purchased it. LAST WEEK'S SOLUTIONS Laying Tiles.—When W has finished removing all his tiles, H has 10 left. Railway Tickets.—Fourteen persons paid halfcrowns for tickets which cost two shillings and fourpence. Substitution. —8561 plus 3748 equals 12309. The title of the book is: " The English Language." Large or Small Book? There were 4820 pages, or at any rate that appears to he the smallest possible number. Purchase of Bicycles.—The prices for cash were £6 and £9, and the instalments were continued for 44 and for 45 weeks, respectively. Salvage.—There are two solutions, which come equally close to perfect equality in the number of journeys made, namely, 27, 31, 32 and 28, 29, 33, in both cases by A, B and C, respectively.