INTELLECT SHARPENERS

Otago Daily Times, Issue 22065, 22 September 1933, Page 3

INTELLECT SHARPENERS

By T. L. Briton. TWO FOR THE ARMCHAIR. There is an excise duty on locally grown and manufactured tobacco which yields to the Government a fair revenue. Supposing that, on the recommendation of the Tariff Commission, this duty was reduced by 25 per cent., can the reader say, without using either pen or pencil, by how much per cent, the consumption of this class of tobacco must increase in order that the revenue under that head may be the same? Proportion being an equality of ratios, a " mean proportional,” as the reader knows, exists when the second and third proportionals are equal to one another, for example, in the expression 24 : 12 equals 12 ; 6, 12 is a mean proportional between 24 and 6. Here is a simple little question in this connection to be answered, of course, straight off, namely: What is a mean proportional between 8 and 32? A MONETARY GIFT. At a certain "old peoples’” home the inmates comprise both men and women, and amongst the privileges they have is pocket money given by the Government, the men getting 5s monthly in this way and the women 2s 9d each. A lady who had died recently provided in her will for the distribution to each inmate every month of a certain sum, the total amount of the monthly allocation beinf£ such that every inmate could receive os. The Supervising Committee which had charge of the distribution decided that the sum that every man and woman should receive under the terms of the will would be 9cl per head more than the sum that each 'received monthly from the Government, so that the monetary gift of the deceased lady resulted in each man getting an extra 5s 9d and each woman an additional 3a 6d. As the sum to be distributed monthly under the will was sufficient for every inmate to receive ss, it is obvious that the sexes were not evenly divided in the institution, and the question is: How many per cent, of the inmates were men and women respectively? A BASKET OF DAFFODILS. A group of boys and girls with the headmistress met on a recent morning in the quadrangle at a city college awaiting the arrival of the motor cars that were to convey them to the trysting-place for a day’s outing. While waiting the youngsters amused themselves by handing around a quantity of daffodils that formed part of the equipment for the holiday, and the incident affords material for a useful little arithmetical puzzle. Every boy present gave a flower to every girl, to every other boy, and also to the headmistress, and every girl followed the same procedure in every detail. In this way the whole of the flowers were absorbed, though it should be noted that, although the teacher was the recipient of a daffodil from every girl and boy, she herself gave none away. The number of flowers distributed was exactly one less than fiftytwo dozen, and there could be several ways that the number of people in the quadrangle that morning could be made up, but if it is stated that the number of boys was half as many again as the number of girls, how many were in the group, differentiating between girls and boys? It is quite possible that, simple as this calculation is, it may be that the careless reader will be a long way out in his reckoning. A NOVEL CALCULATION. The sides of a square room are together four times the height of each of the four walls, r the superficial area of the room being of'no concern to this problem. A lizard starting on the floor at the bottom of one of the walls crawls up the wall in a straight line to the point where that wall joins the ceiling, travelling uniformly at the rate of one foot per second. Without any perceptible delay the reptile continues to crawl in the same line across the ceiling, and stops at the junction of the ceiling and the wall opposite the one climbed. The latter part of the crawl being evidently more difficult, the rate of travelling that section on the ceiling was slower, namely, six inches per second, and if the entire journey over wall and. ceiling took three-quarters of a minute, there being no stops en route, can the reader say what the dimensions of the room are. This question or one on “ all fours ” to it, was given to a couple of fairly-advanced girl students the other day, _and both agreed .that there was not sufficient information in the data, and the matter was left at that. But perhaps the reader may find the correct solution of the puzzle as it stands. THS SOLITARY “FOUR” The reader is no doubt familiar with the fascinating "restoration” problem called “ The Solitary Seven,” by the Rev. “E. P. 0.,” in which all the figures of a sum in long division are missing except one . “ seven.” A reader who is something of a genius at these interesting puzzles, "R. C.,” has composed one of the same kind which perhaps is not any less fascinating than- the puzzle mentioned, the name given by “ R. C.” to the problem being that stated above. This puzzle has every figure missing from the sum itself, and only one figure (a four) in the whole of the working, as will be seen, excepting a cipher which comes automatically into the calculation by reason of the decimal in the quotient. This decimal to one place is repeating, and it may be added that this circumstance makes the reconstruction of the sum logically possible, though the solution could no doubt be arrived at by the laborious trialmethods without that help, x x x)x x x x x x x(x x x xdecimal x x x x x repeating. X XX X XXX XX X X XXX XX X X XXX xx x 0 XX X X XX X SOLUTIONS OF LAST WEEK’S PROBLEMS. TWO CLOCKS AT VARIANCE. The clock at “ B ” was five minutes fast. TWO FOR THE ARMCHAIR. (1) The youngest of the three was 11 years and eight months, (2) Eighteen miles. A “WAGES” BILL. With equal numbers of the two classes of men, the total wages bill would be £6OOO. A ROAD PUZZLE. As both speedometers showed the same mileage, the distance from “ A ” to “ E ” is 20 miles, thus one travelled 20 and 106 miles, and the other 36 and 90 miles. RESTORING MISSING FIGURES. Divisor 222222, dividend 740065926, quotient 3333. The solver of this reconstruction problem, no doubt, quickly discovered the clue after the first line multiplied. ANSWERS TO CORRESPONDENTS. “ Anxious.”—Your friend is correct, as there are 27 different ways in which the figures can be placed. “Traveller." “Wagon-lit” means a sleeping-car of a train. J. T. M. —The solution was as given, the arithmetical progression of three of the numbers limiting it to one answer. See issue of August 18.