INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20426, 30 November 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

.TWO AIR JOURNEYS.

BY T. L. BRITON.

Two aviators, in their respective machines, " The Eagle" and " The Hawk," the former travelling direct north and the other due south, met at an airport "W" en route. Both were flying to the same destination, " X," which was situated more or less east by south from " W," but neither was going direct to the place, " The Eagle " travelling- direct north from " W," having to call at tno airport " Y," while " The Kawk " was to fly to " X," b- way of another airport " Z," due south from the spot.iwhere tho two aviators had met. Befdrb leaving "W" they checked their speedometers and watches, so that upon arrival at "X" the relative distances travelled by the two routes could ho determined. The distance froin " W " to " Z " was known to be exactly 18 miles, " The Hawk " flying direct east fioin that point to " X," a distance of 45 miles. Supposing that " The Eaglu flew direct north to " Y " and thence direct to "X," and 'that the speedometers then showed that both machines had'travelled exactly the same distance after leaving " W," how far is it from " Y " to " X ? "

A QUESTION OF PROFIT. An article in a shop was marked for sale at a figure which represented exactly thirty-three and a third per cent, on its cost price, but during a period called " Sale Week " it -was ticketed at a price indicating that a discount of ten per cent, would be allowed off that price. It--was sold within the prescribed time for £l2. What profit did the shopkeeper make in the transaction ? The reader may elect, to solve this little problem " sans " pea or pencil, but whether he does or no, the point that should be kept in mind is that tho calculation is governed by the mathematical rules of percentages, and not by the practice of those who.ignore those laws iu the interest of expediency."

" TALLY-HO." In a "tally-ho" contest, the fox'had a start of exactly twenty minutes, and ran the whole distance at the rate of nine miles an hour. One of the hounds, which was much faster than the others of the pack, covered the same course as the fox at the rate of ten miles an hour. It is quite a simple matter to calculate the correct distance of the run when we are told how long it was after the fox had completed the course, that the fleetest hound arrived home, but if the full distance travelled by both is given as eighteen miles, the reader can no doubt find without undue mental effort how long the fox arrived before the hound.

RAILWAY TRAVELLING. Although the modern styla of dress •• enables people, particularly -women, to travel with an ample supply of clothing in their trunks, well within the limit of the weight allowed to railway passengers, . occasionally one hears of a zealous official holding up luggage to be checked for " excess " dues. One such case happened recently, in which an over-charge was inadvertently claimed by an official. The luggage of a party of two was being checked on one of the passengers' tickets only, and an excess charge demanded of 19s, instes.d of the proper dues of' 3s 7d and 8s s(i. respectively, payable on the " 5 production of two tickets. Now if all excess luggage dues are at the rate of one halfpenny per pound, can the reader calculate what weight is allowed free to each passe nger ?

SALI3 OF GRAMOPHONES.

There' was a sale, of gramophones the other day in a.city auction mart. They were a heterogenous lot, all of foreign production.-- viz., French, German, Japanese, and Swedish, but there were only three classes of instruments, viz., " Cabinet," " Ordinary," and "Portable," and all of inferior workmanship, hence the low price fetched. There were five different owners, and, strange to say, every vendor hud the same number of instruments, a still further coincidence being that the eight dealers to whom the auctioneer " knocked " the whole lot down all bought the same numbe.r each, The fotal sum realised was £l5O 10s—"Cabinet!?," £8 10s; "Ordinaries," £2 each; anc'l " Portable," £1 each. Assuming that there were more than two of each clas,'! in the collection the total number of instruments being the largest possible untiier the conditions % stated, can the reader say how many of each kind there were and the respective amounts fetched by the three sets ?

LAIiIT WEEK'S SOLUTIONS.

mat Was the Score?

The innings closed with 300 runs, " A " being top scorer with 65.

Five Golf Balls. The five golfers each taking a ball together at random that did not belong to him, could do so in 44 different ways, the box, of course, containing five balls only.

Milkman's " Easy " Money.

The d airyman's " easy" money was £5 16s 13d,*- being the difference between 280 gallons and 330 gallons at 2s 4d per gallon.

Investments In Coconuts. £175, £7OO, and £1575. • Simple Questions. | One and one-fifth miles, the averfge being 2>l m.p.h., not 25, as it mifht appear. , ' \