Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 21036, 21 November 1931, Page 5 (Supplement)

Intellect Sharpeners.

JONIES' SECOND WIFE=

BY T. L. BKITON.

Jones was a widower when he ma'fVfed his present wife, and yesterday was the 18th arniversary of his last wedding His wife reminded lyatt- of this fact at breakfast, and the ensuiiag conversation upon ages and happenings' during the past period of two decades, less two years,: form the basis of this problem. It transpired that the age of Jones' first wife on her wedding day, added to the age of the present one on the day that she commenced her 18 years of married life represented the exact age of Jones on the latter day, he being then three times as old as his wife. As the conversation took place in the year 1931, when the wife's age is only one-half that of her spouse, can the reader say in what year was the latter born, and what were the ages of the first and second wives on their respective wedding clays. 1 SHOPKEEPER'S STOCK. A shopkeeper seeking further capital for his business issued the following statement of his position, and upon it will ho based a question. On January 1, 1930, his stock was worth £BOOO, and on that date he had £350 in cash in the safe or at the bank, his debts at that time amounting to £IB7O. The shopkeeper's personal expenses, £3OO, for the year 1930 were paid out of the proceeds of that year's business, and at January 1, 1931, his stock was of the value of £7950, his cash was £570, and the amount owing to creditors £lslO. If the amount absorbed by the premiums on his own life assurance were included in the expenses of the business and totalled £4l ss, can the reader say what percentage of the profits of the business they represented, five per cent, interest being deducted on the assets with widen he commenced the year ? NOT SO VERY EASY. Hero is an interesting puzzle that will give the reader an opportunity of testing his ingenuity. Make a diagram of H square containing 16 :-ells, and, using three counters only, find in 'what posir tions they should lie placed—not more than ono occupying a cell at the same time —so that at least one of the eell3 will not be in a direct line, horizontally,: perpendicularly or diagonally with a, counier, and at the same time no counter, in a line with another. There is only one arrangement of the counters that, will create this actual position, and if the reader can find it within the space oE half-an-hour, the average time that, it has taken others to accomplish the feat will not have been exceeded. When it is stated that there is only one such arrangement, it is assumed that a reversal or a reflection is virtually the same position. DUTY ON IMPORTED GOODS. It is said that the worries of a Minister of Customs in framing a Customs tariff commence after his well-thought-out plans have been cut and slashed about in Parliament, when the task of readjustment has to be taken in hand, and his estimates remodelled to accord with the dictates of the House. On a certain commodity the Minister's proposed duty was in this way reduced by 40 ,per cent., and when an amendment to that effect was submitted, the mover; stated that the reduction would mean no loss of revenue, because it was almost certain, he said, that the importation world increase by at least 40 per cenU on that particular commodity. As, per-t haps, the reader may desire to dispute the mathematics of the member, he may do so in the form of finding the solu-< tion of the following problem: If a proposed duty is reduced in the manner, stated, namely, by 40 per cent., by how; much per cent, should the consumption of that article be increased, in order that the revenue" based, on the original duts will remain the same ? STROKES OF A CLOCK. Timepieces afford interesting material for formulating useful problems, and those which chime and strike have ior this purpose more attraction. Here is an arithmetical puzzle of the kind, that should interest the reader. The first stroke of the chimes of a public chick at the quarter, half and the three-quarter hour indicate the correct time, but at the full hour it is the first stroke denoting the hour which denotes the precise time shown by the hands, and not the first stroke of the chimes._ A watch that loses one minute a day is employed to check the strokes of the "big clock, and by it the time that elapsed from the instant the clock made the third stroke at six o'clock .to the exact moment of the sixth stroke at twelve o'clock, six hours later, was that number of hours exactly. The question arising from this statement is what is the intervaj of time betw f een the strokes of the clock at, any hour of striking,, these being regular? Just ■'* little thought will enable the question to be readily answered, for the arithmetic is very simple, an even number; of seconds being sufficient. LAST WEEK'S SOLUTIONS. Maori Chief's Age.—Eighty-eight vear«., "A" equals eight, and "B" eleven. A Puzzling Arrangement.—Seven hundred- aiid fifteen multiplied by 46 gives 32.890, which, the author says, is tha only example. A Curious Situation.—Seven dozen forIs, but the price of each of the ones left over was 3s. This is the only solution under the conditions expressed. Saving the Cherry Trees.—Exactly onehalf the area will bo cut out in order to make, the largest rectangular plot* Bisect ihe two smallest sides and drop perpendiculars from each of those points to the longest side, then join the bisected points. Economical Fencing.—The four cornerposts of the old fencing are the - only, parts that remain in their original positions, these being the exact centres of the newlv-erected fence, which runs at "rightangles to the diagonals of the* original square. The new area is double the old. ANSWERS TO CORRESPONDENTS. J.C.W.—One of the -kind mentioned will appear next week. " Curious." —The British equivalents of metric measures to which you refer are based upon approximate relations, but quite near enough for any but technical matters; 1000 yards are equivalent to 915 metres under this scale, 1000 pints to 570 litres, 10001b/ to 455 kilograms and so on.