INTELLECT SHARPENERS

Otago Daily Times, Issue 21196, 29 November 1930, Page 21

INTELLECT SHARPENERS

By T. L. Briton.

BY SHADOW MEASUREMENT.' The shadow of an object is a useful factor for ascertaining an inaccessible height in certain cases, by comparing the. length one’s own shadow under the same conditions. Of course a height can only be approximate when obtained in this way, but generally the result is pear enough for practical purposes. Here is a little problem on the point. The length of the ground shadow of a flagstaff at a certain time in the morning is exactly 100 feet, and when the sun is at the same altitude in the afternoon the shadow of the pole is east partly on a wall reaching a point 12 feet from the bottom, which represents two-thirds of the height of the wall. The ground between the flagstaff and the wall is perfectly level, and as the two objects mentioned are perpendicular the reader should have no difficulty in findiiig what the length of the shadow is when first caught by the wall, remembering Longfellow’s or some other wise man’s saying that things are seldom, or. anyhow not always, what they seem. Perhaps the reader would prefer to ignore the height of the wall if told that the height of the flagstaff i s 80 feet.' ‘ THAT WHEEL CURIOSITY. The perennial question as to whether a point on the circumference of a wheel moves at a faster rate through space when at the top" than when the fixed point is nearest to the ground, cropped up recently at a meeting of motorists after the business of the evening had concluded, Though all were not agreed that it was so, there was unanimity on the question that the hub of a wheel only makes one revolution while the outer circumference, the tyre also, completes one round, t A wheel, for example, one foot in diameter, travels three feet two, inches approximately in one revoiurion, yet at the same time the hub of the wheel travels the same distance in one revolution though its diameter is only one inch, and its circumference three and a seventh inches. Can the reader explain this apparent anomaly? COMPARING THEIR SPEEDS. Three school athletes of different ages were engaged in a foot race, and, as they did not - possess equal speed, they of course were handicapped accordingly. The senior Jad •* A” was the college sprint champion, being 10 per cent, a faster runner than “ B ” over any distance up to 220 yards, and 15 per cent, more than “C ” under exactly similar conditions. In view of the general breaking of records happening in the athletic world of late, let us have a little problem on the subject. Upon the figures given above let us state that when A gives B ten yards, and C IS yards in a race of a distance of 100 yards, the three starting together, the result is a dead heat.” What start, therefore, should B give C under similar circumstances, in a race ovqr a distance of 150 .yards, so that both starting simultaneously, they would breast the tape together, or in other words make a “dead heat” of it? Another speed question. Here is another speed problem, one concerning the running of a train, and besides its speed, we have an opportunity, if curious enough, of finding its length. The reader will note that in ,order to arrive at the correct solutions,' in one case the fact that the train must move,forward a distance of its own length,, and in the' other that that length should be added to the length of the platform, must he taken into consideration. A person , standing on the platform of a railway station, watches a train dashing through, and observes that it passed him in exactly eight seconds. At the same time it was noted that the train completely passed the platform, which is 132 feet long, m 20 seconds. The question to be decided- by the* reader is,‘ At what speed was the train travelling when it passed the observer, and also how many vehicles, each 33 feet long, in addition to the .brake-van, locomotive "and tender of the combined length of one chain (all measurements to include the distances between vehicles), made iip the train? / WAGES PATH IN KIND. A farmer was in the habit of paying the wages of his employees in kind, and for doing so was fined substantially, according to a recent newspaper report from Australia. Let us take a case in which the legal maxim “ volenti non fit injuria ’’ applies. By consent of the employee a farmer paid him in eggs, first, however, fixing the cash snm to be paid weekly, hut paying in the commodity mentioned at the current price, the quantity to be 10 cent, of the total production, irrespective of whether the proceeds from the employee’s quota were more or less than the weekly cash, sum fixed by the farmer. When eggs were at a low price this arrangement operated in favour of the employer, but, of course, it wqa against him at Easter time when the product was fetching high prices. Supposing then, that in one of the weeks when eggs were of high value the wage-earner received 10s more for his 10 per cent, of the week’s production than he would have received if he were being paid at the fixed sum in cash as mentioned above. If that week’s output realised 2a Gd per dozen, and the fanner’s quantity was 126 dozen after the employee’s ten per cent, had been deducted, can he reader find what snm per week, the latter would have received had he been paid at the rate first fixed in cash? This is one for the armchair. . LAST WEEK’S SOLUTIONS. THE THREE PIPE LINES. It is not possible geometrically, but it can be done by running one pipe through the house or enclosure belonging to a neighbour. That method, however, would not comply with the conditions. MAKING TWENTY-FIVE POUNDS. The last sale of 250 shares were sold for 34s each, which with those quitted at 24s would give him the profit stated. A HAZARDOUS SWIM. Four miles 1270 yards. ALMOND ROCK. Each of three boys and the same number of girls received two at 4d and one at 6d. THE TALLOW MARKET. £1 16s and £2 4s. ANSWERS TO CORRESPONDENTS. “Logic.”—(l) Certain things are antecedently assumed, and the answer depends entirely on the truth of those assumptions. (2) There are only 44 different ways in the example you quote. Your method is correct, but you do not cover the whole ground in the calculation. “ Marine.”—Seychelles . Islands are in the Indian Ocean, and about 1000 miles north-west of Mauritius. “Puzzles.”—Some problem-games will he included in issue of the Saturday before Christmas. .