"NUTS I"

Evening Post, Volume CXIV, Issue 50, 27 August 1932, Page 22

"NUTS I"

[INTELLECT SHARPENERS I | All rights reserved. = | (By T. L. Briton.) |

Readers with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent meatal exhilaration. While some of the "nuts" may appear harder than others, it will be found that none will require a sledgo-liammae to crack them. SYBIL'S AGE. Sybil is the only child of Jlr. aud Jlrs. 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 year (1932), 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 as many again as her daughter's, and the question is in what year was Sybil born? Arithmetical puzzles from the correspondent, "F. 5.," the sender of this one, generally require tho would-be solver to don his best "thinking cap," particularly when the problem is one purely for the armchair, as in this instance. EXCHANGING "SCRIP." Three speculators, Smith, Jones, and Brown, had each a number of shares in four ventures, W, X, V, and Z, the original prices being ■ all different; and after the market .had been subjected to "bull" and "bear.";influences, their comparative .market values were also very different from the prices. at which the three speculators 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 concern, 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 "Wfor'3oo in Z, one result of this transfer being that Brown had twice as many shares altogether than Smith then held. Now it so happened that before making any exchanges, one of the speculators held together 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 V to Brown for 400 of the latter's shares in Z, how many did each investor hold, if the bartering left them each wifli the same number as before? HUNTER AND HAKE. A keen mathematician, "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 mental effort," and this one readily fits that description. A game hunter was walking due north along a bush track which ran for more than a mil& 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 long-oared rodent was disturbed by' the hound. The hunter ran forward towards the same point and fired at %ha quarry at a distance of 60 yards. Tha question that the correspondent asks is, if the hare ran at the rate of 18 yarda per second,, and the hunter at exactly one-third of that speed, what interval elapsed from the moment the quarry started troiii cover to the-moment tho man fired his first shot? When reaching: the correct answer the reader may find that the man carried either a doublebarrelled 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 Ist June, Atkins invested in s business in which he put the sum of £7000, 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 Ist November, exactly three mouths after taking in his first partner Banks, lie sold another share of the business to a third person, Coles, for tho-sum" of £800. At the-end of the same year, or exactly seven months after Atkins commenced on, his owi» account, the profits of the concern wera found to bo £.1960, and the question is how should the profits be divided between the three partners in accordanca with the facts related? : A GOOD PRICE FOX WOOL. Here is a little alphabetical .sum, tha 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." Tho unravelling of the puzzle should test the reader's ingenuity, if not his mathematical skill, and the would-be eolver who has "no time" for "unknown quantities ". need not be scared by. tha algebraical look of the statement. Z3T multiplied by V equals WTJ, and when tho latter is subtracted from TS> the result will be SB, which represents the price per pound, in pence, that we all wish, with the optimistic sheep owner, 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 V be equivalent to 2 and Z to 9. The cipher is not employed. LAST WEEK'S SOLUTIONS. ' 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.—(l) The loss-ia the two transactions- was two-thirds of a pound. (2) Twelve guarantors.at first at £11 each, the non-liability, of one making the individual share of each of the others one pound more. A Useful Code.—The text is: "Tha Governor-General convincingly expounded the principles on which the economic prosperity of the Dominion, as*a» integral part of the Empire, can bs soundly developed." At a Cabaret. —Thirty-five couples, five single ladies and fifty gentlemen.. A Mental Posers—A two florinv-B three florins, C one half-crown,' and D;four half-crowns. 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."—rThanks, will be looked into. . ■ "Puketea."—Communication unsigned, H. Pitt.—(l) "Idling I sit." (2) SJU R.M.—Yes, one bag held 1 coin only. "Argyle Street."—Hardly' maths* maties. "Mark."—Thanks. . 4 * Avilie' * and ''.'P.O.' N—Correct version.