INTELLECT SHARPENERS

Otago Daily Times, Issue 21733, 26 August 1932, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By T. L. Briton.

SYBIL’S AGE. Sybil is the' only child of Mr and Mrs Jones, and, like* some of her sex, seldom wittingly divulges her age, 'and even gets a little vexed if her mother happens to tell visitors the date that she was born. But if the reader is curious to find out for himself the age of the fair maid at the present time he may quite easily do so with the few details that follow. At the present time, which may be regarded for problem purposes the present yean Mr Jones is as much older than his wife as he is younger than his wife’s'mother, the difference being equal to the age of Sybil. Twenty years ago the girl’s mother was exactly half the age of her own mother, but in eight years time the latter’s years will total only half ae many again as her daughter’s, and the question is in what year Sybil was born? Arithmetical puzzles from the correspondent “ F: 5.,” the sender of this one, generally require the would-be solver to don his best “thinking cap,” particularly when the problem is one purely for the armchair, as in this instance.

Three speculators, Smith, Jones, and Brown, had each a number of shares in four ventures —W, X, Y, and Z—the original prices being all different. After the market had been subjected to “bull” and “bear” influences their comparative market values were also very different from the prices at which they had invested. It was then that the following exchanges of scrip were made between them:—Smith gave Jones 200 shares in X for- 100 in Z, which made the total number of shares in all ventures held by the latter investor exactly double the number then owned by Smith. The ‘next exchange was between Brown and Smith, the former giving Smith 400 shares in W for 300 in Z, one result of this transfer being that Brown had twice as many shares altogether as Smith then held. Now, it so happened that, before making any exchanges, one of the speculators held altogether 300 shares more than one of his colleagues, and 400 fewer than the third. The very interesting question is: If in the third exchange Jones gave 500 shares in Y to Brown for 400 of the latter’s shares in Z, how many did each investor hold, if the bartering left each with the same number as before? HUNTER AND HARE. A keen mathemetician, C. J. W., the sender of this little puzzle, says -that he enjoys this column because “ the problems found in it recreate the brain without demanding strenuous ipental effort,” and this one readily fits that description.. A game-hunter was walking due north along a bush track-which ra'nfor more than a mile in that direction. His dog was at a point north and easterly of him, when a hare jumped from cover at that spot and started , to run due west towards a point on the track mentioned exactly three chains ahead of the hunter and 138 yards distant from the point where the hare was disturbed by the hound. The hunter ran forward towards the same point and fired at the quarry at a distance of 60 yards. The question that the correspondent asks is, If the hare ran at the rate of 1% yards per second, and the hunter at Exactly onethird of that speed, what interval elapsed from the moment the quarry started from cover to the moment the man fired -his first shot? When reaching the correct answer the reader may find that the man carried either a double-barrelled gun or a repeating rifle, for if we take it for granted that he “ bagged ” the hare, it was not with the first shot. TWO MORE-PARTNERS. • On June 1, Atkins invested in a business in which he put the sum of £7OOO, but two months afterwards he set free part of this capital by selling a share in the concern to banks for the sum of £2200. Later on in the year—namely, on the first day of November exactly three months after taking in his first partner Banks, he sold another share of the business to the third person Coles for the sum of £BOO. At the end of the same year, or exactly seven months after Atkins com; menced on his own account, the profits of the concern were found to be £1960, and .the question is how should the profits be divided between the three partners in accordance with the facts related? A GOOD PRICE FOR WOOL. Here is a little alphabetical sum the answer to which is a sum in pence which a large sheep owner was heard to say the - other day should be realised next season if everything at Ottawa “went according to schedule.” The unravelling of the puzzle should test the reader’s ingenuity if not his mathematical skill, and the would-be solver who has “no time ” for unknown quantities need not be seared by the algebraical look of the statement. ZY multiplied by V equals WU, and when the latter is subtracted from TS the result will be XR. which represents the price per pound, in pence, which we all, with the optimistic sheep owner, wish wool will soon fetch. Each letter stands for a different digit, 1 to 9, and when two letters are side by side as, for, example YZ, the numerical value of it is 29 if Y be equivalent to 2 and Zto 9. The cipher is not employed.

SOLUTIONS OF LAST WEEK’S PROBLEMS. A “ RESTORATION ” PROBLEM. Dividend 16992 and divisor 472. The answer to the second part of the question is 8384714/ 2561 equal 3274. FOR THE ARMCHAIR. (1) The loss in the two transactions was two-thirds of a pound. (2) Twelve guarantors at first at £ll each, the nonliability of one making the individual share of each of the others £1 more. A USEFUL CODE. The text is: “ The Governor-General convincingly expounded the principles on which the economic prosperity of the Dominion, as an integral part of the Empire, can be soundly developed.” AT A CABARET. Thirty-five* couples, five single ladies, and fifty gentlemen. A MENTAL POSER. “A” two florins, “B ” three florins, “ C ” one half-crown, and “ D ” four halfcrowns. ANSWERS TO CORRESPONDENTS, “ Code.” —Any system of shorthand, if specially invented for communication by code, is a true cipher. A great number of these systems are copyright. "Magic Squares.” Alternative methods are always being expounded, and there seems to be no end of new combinations. "Curious.” —Thanks; will be looked into. “ Puketua.” —Communication unsigned. H. Pitt —(1) "Idling I sit.”' (2) 31. R. M. —Yes; one bag held only one coin. “Argyle Street.” —Hardly mathematics. “ Mark.”—Thanks. “Airlic” and F. C. —Correct version.