INTELLECT SHARPENERS

Otago Daily Times, Issue 21627, 23 April 1932, Page 20

INTELLECT SHARPENERS

Written for the Otago Daily Times. By T. L. Briton. THE PERRY., SERVICE. Under normal conditions the two steamers which run between Wellington and Lyttelton daily in the service, which tourists have so often remarked as the best ferry in the world, leave their respective ports at precisely the same hour, and under those conditions they usually pass one another six hours later. A correspondent, G. J. W., was a passenger on the northern-bound packet recently, and on that occassion. the vessel upon which he travelled departed from Lyttelton one hour later than schedule time, namely, at .9 pan. instead off 8 pan. His vessel is a faster steamer than the other by exactly one mile per hour, and upon this trip those were the relative speeds. (J. J. W. was curious to know what time the packets would pass under these conditions, especially as he correctly assumed that, the steamer bound southwards left her port at the usual time, viz., 8 o'clock, and the fact of the steamers passing the morning afterwards exactly 31 minutes later than usual, viz., 31 minutes past 2 o’clock: prompted the question,—what is the distance between the two places, based upon .the facts now related and without any regard to the actual geographical mileage? Though by no means difficult, this problem should give the reader what he enjoys, viz., a little hard thinking! A CIRCULAR EARTH-TRACK. A circular-shaped earth-track for motor cycling is situated within a fenced enclosure which is perfectly square/ Two sides of the enclosure touch, in the manner to tangents, the other circumference of the track, the other two sides of the square being some distance away from the course to allow space for building and extra seating accommodation as well as for the judge’s box. Immediately opposite this box on the other side of the track and on the outer circumference of the running track stands a post indicating a distance of 10 chains from the one-mile starting gate. This post is exactly three chains in a direct line from one side of the square which touches the outer circumference in the manner desfiribed, and six chains from the side forming the other tangent of the, outer circle as indicated. The interesting question for the reader is, what is the actual distance round the racing track, measured by the outer circumference, given in an even number of chains; ignoring fractions. There is a simple arithmetical rule for arriving at the solution of a problem of this kind, and there is no necessity to bother with quadratics or other algebraical process. THE GABLE END OF A SHED. ; The gable end of a roughly-built shed used for storing ploughs and other agricultural implements consists of a solid round-timber upright slabs or poles built closely together and nailed to cross pieces running the full width of the shed. There are thirty-three (33) of these round slabs with the longest in the centre, and, though from the centre to,the outside posts on each side- each ohe decreases m height in rt regular way, the shortest or outside slab on one side is higher than the similar pole on the other side, the gable end, ,aud, in,fact, the whole shod being built on level ground. This loprsided appearance has prompted a little question which the render will no doubt find as interesting as it is useful to knoiV the calculation and method of arriving at the solution. Let it be assumed that the total length of the ,33 slabs measured from the level ground upon which they stand is 270 ft Klin, From the central slab (seventeenth) each successive one down to the last one one side is five inches shorter than the preceding pole, - and from the outside pole to the central one, on?the other side, each successive pole,.*is seven inches and u-half higher than the one immediately preceding it. the gradations on both sides including the central and longest slab. Can the reader find the height of tiio 'gable measured by its highest plank? ■ STOPPING THE IMG. A correspondent some time ago sent the following question, hut not in the complete form that it appears now, illustrating it by ia diagram which, however, is not necessary. 0. J. W. does not consider that the problem is a difficult one, but lie is one whom mathematical puzzles can never scare, and his view of this problem may not be shared by all the readers of this column. The correct solution should not trouble the reader unduly, however, even though lie may have to clou his best “ thinking cap” before reaching the answer to it. A field of grass is in the form of a square, fenced on all four sides, each of winch is one hundred yards in length. At the top left-hand corner, A, is an open gate; in the opposite corner, B, direct easterly from A, a pig is feeding unhampered by sty or tether; and at the cornet, G, due south from B, the owner of Ifoth field and animal is debating in ins mind how he can reach the gate to shut it without disturbing the young swine. At that moment the pig, seeing the open gate, immediately darted off in a direct line to the opening, racing at full speed. Supposing that the man,stavted off at precisely the same moment, but, instead of running direct to the gate, ran continually in the direction of the moving animal, would he catch the pig, aud if so, at what point, on the assumption that the man travelled at twice the speed of the 'hog?

A PTERODACTYL, , Any difficulty,Hint the reader may have had in deciding the result of the contest between the pig and its owner will perhaps appear less real when the tusk of solving this curious problem which has come to hand from “ C. L. IL,” is being tackled. The sender states that the question was designed by a number of students of House attached to University College, “ to puzzle the lecturer in mathematics.” A vertical pole 12 inches in diameter at its base is 20 feet high and tapers uniformly to the top, which ia six inches in diameter, A rope of uniform cross-section and one inch in diameter has one end of it fixed to the base of the pole and is wound tightly and closely in single rows'round the pole for its entire length. A pterodactyl, or flying lizard, sits on the top of the pole with the other end of the rope attached to, its leg, and the quest is if it flies around the pole so ns to unwind the rope, which is always kept taut at an angle of 110 degrees with the axis of the pole, how far does the winged reptile fly until the rope has been unwound? The fact that so many readers of this column have been anxious for an occasional problem of this character renders an apology for a technical one unnecessary.