NUTS TO CRACK.

Otago Witness, Issue 3823, 21 June 1927, Page 23

NUTS TO CRACK.

By

T. L. Briton.

(For the Otago Witness.) Reader, with a little ingenuity will find in its column an abundant store of entertainmer* and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the “nuts" may appear harder than others, it will be found that none will require a sledge-hammer to crack them. Solutions will appear in our next Issue together with some fresh “nuts.”

Readers • re requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. GATE RECEIPTS. The gate receipts at a football match were £ll7, after a deduction of 10 per cent, for charity in accordance with the expressed desire of the contesting teams. There were exactly 4200 people present. There were 400 more men than women and 100 more women than boys, all of whom paid for admission. Included in the 4200, however, were ■nils, children, and visitors who were on the free list, these comprising three-elevenths of those who paid. If every three men were charged as much as four women who in turn paid as much at the gate as every six boys, what was the respective tariff, and the number of men, women, and boys who paid for admission? PASSENGERS BY TRAIN. A railway official remarked, the other day, in conversation, that there were indications that the railways were certainly coming into their own again, as an admittedly safe means of travelling, for the increasing number of motor cars now on the roads were causing people to adopt the safer means of transit afforded by the trains, and 1 e quoted some recent figures in support. His remarks suggest a little problem. Supposing that a train starts from A for its destination C, with 300 pasengers, not necessarily all or any for C as the train stops at B en route. The fare from A to B is 6s, from B to C 7s, and from A to C 12s. If the train were a full one, what would be the greatest number of nasengers that could be carried when the booking offic.es showed the total receipts for the trip to be £190? It is assumed that all fares "were prepaid. The same number of passengers travelled on each of two sections only on the trip. THE AGE OF A COB. It is generally agreed that a horse’s age cannot be determined witli any degree of accuracy after he has turned seven except by documentary evidence. Two men were discussing the age of a cob in a sale ring, and both agreed that it was an aged horse. Beyond that neither could express a definite opinion. A farmer, hearing the discussion. said he knew the cob well, as it was foaled on rn adjoining farm in January of the year in which he returned from the war. He added that a year ago the cob was exactly three tim.es as old as the horse he was then riding, and that in two years’ time his own horse would be half as old a the other. The farmer said that he did not care to tell them straight out the precise age of the horse, as the owner was present and no doubt would tell them if asked. As the incident occurred less than a month ago, can the reader determine the calendar year the cob was foaled? MARKETING. Some of the regular fruit and vegetable dealers plying their trade in the city, though not of the educated class, are particularly quick in calculating possible profits in relation to prices and overhead charges. A sale of cucumbers was just being concluded as the writer dropped in the other morning, and the list lot was knocked down to a dealer who, judged by his conversation, had spent part of his life in the East End of London. “1 beat ’m for tenpence a hundred,” he said to his mate. “ Bli me, Bill, that ain’t much, but any 'ow it gives us twenty more ‘kukes ’ (cucumbers) in every five bob’s worth than we’d a got if yer 'adnt beat ’im.’ As the deal worked out at less than Old per dozen, how much per hundred did Bill give for his cumbers? CANADIAN FOOTBALLERS. Two of the Canadian football team touring New Zealand do very little training afoot. They get into and retain their form chiefly by cycling. Most of the others do their work on the roads, walking long distances. Though they generally start off together, there are gaps between them at the finish, if the route covers a long distance. If one of them (F.) takes 14 hours longer than G. to walk 52J miles, and if B. (a cyclist), riding at exactly double F.’s rate of walking, covers the 52} miles in four hours less than G., how far would F. be behind G. at the end of two hours’ walking, on the assumption that they started together and maintained their uniform pace as indicated? .LAST WEEK’S SOLUTIONS. TOWARDS THE CARDINAL POINTS. The cyclist riding west must have had eight miles to travel from the cross roads to the circumference of the circle, the walker two miles east, -and the two horsemen travelling north and south respectively four miles each. The rates of travel were therefore 16, 4, and the horsemen eight miles an hour respectively. GATHERING COCONUTS. There must have been 3121 coconuts in the original heap, this being the largest number less than 5000 possible under the conditions. A MAP WITHOUT A SCALE. The scale of the map must have been one-fifth of an inch per mile. The travellers assumed it to be one-quarter inch. PACKING LEAD PENCILS. If 25 parcels be placed in the bottom row they will, as exactly fill the width of the box. The next row should

be 24 only, each fitting into the hollow formed by tllo contiguity of the pencils in the botton row. The other rows should then be packed alternately 25 and 24, and in tfvis way 11 rows can be packed, occupying in depth dicimal 68 of the diameter cf a pencil less than when packed in 10 rows of 25 each. The number of extra pencils therefore that can be put into the box is 20.

ANSWERS TO CORRESPONDENTS. “C. B.”—The idea is as you state, and there are many examples. “W. C. S. G.”—See to-day’s issue for second instalment. “L. S. R.’ —Sixteen years, not 14. “F. J. B.”—Published June 11. “F.W.A.”—Replied by letter. Will welcome your communications. Miss D. C.—Acknowledged with thanks.