Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 20868, 9 May 1931, Page 5 (Supplement)

Intellect Sharpeners.

TWO WINDOW CASEMENTS*

BY T. L. BRITON. There are two square, windows in- a room, the inside measurements of which aro the same, and the panes of glass are so glazed that in each sash their edges join one another without any overlapping, except, of course, the outer edges, which abutt on the surface of the sashes and not "let in" the wood to any appreciable extent. There are 192 panes in the eastern window, rectangular in shape and all of the same size, the length of each being one inch longer than its width. The window at the western end of the room contains 256 panes and these are also rectangular of one size. These, however, differ from the others in as much that the length of each pane is two inches more than the length of each of the others, and one and a-half inches in width less than the width of those in window No. 1. By making a. very simple calculation can the reader find what the respective measurements of these two windows are, taking the inside lengths and breadth of the sashes as indicated above ? SCHOOL STATISTICS. , The publication in . the School Journal/ of sonic enrolment figures in one of the primary schools has suggested a useful little problem concerning the comparative increase of the boys and girls in attendance. The question asked will be found to be quite a simple one, yet it mav give the reader material for a little hard thinking if no pen or pencil is used. During last year the number ill all standards, including the infants* department, increased by 10 per cent., but in the girls? section the increase during tlio same period was only half that percentage. Now, if the enrolment figures for the whole of that year of the full school showed an advance of 7 per cent, upon the figures at the end of the previous year, can the reader say, without the aid of pencil, what was the proportion of the numbers of boys to girls at the commencement of the school year .n question ?

IN OPPOSITE DIRECTIONS. Two towns, *X" and "Y " are situated on the main highway, but a considerable distance apart. A car left X bound for "Y" at eight o'clock cm a certain morning, which was exactly hours before another car left "Y, its destination being "X." They met on the road at 24 minutes past, one o clock that afternoon, but did not stop, and, curiously enough, both ears arrived at their destinations at identically the same time, vhich was 10 minutes before sunset according to the x calendar. What time was that and what is the distance between the two places? Easy as this question may seem, the reader is not asked to make an armchair problem of it, because it is quite possible that to solve it in this manner will involve an unfair amount of mental strain, which is not the intention of this column. but with pencil and paper the solution should be readily found.

A TRIANGULAR PLOT. In a small triangular plot of a garden a bulb of a rare exotic plant was placed and a stake erected to locate the position, which is the centre of the plot, tn so far that the three corners of this small area are equidistant from the stake. The base of the plot is exactly 14ft. in length, and,the other two sides are 13ft. and 15ft. long respectively. With these measurements it is obvious that the area of the triangular piece of garden is 84 square feet, but can the reader find how far the bulb was planted from each of the three corners T There is a simple little formula for calculations of this kind which will be published with the solution next Saturday. IF IT WERE FOUR-SIDED. But let us take a plot of the garden that is a quadrilateral instead of a triangle in shape and assume that the bulb, as in the other case, was also situated in its centre equidistant from,all tMe four corners of the small section. As the reader is aware, the arfca of a four-sided figure with merely the measurements of its sides given may vary according to the form of the figure, because there are a:i infinite number of different shapes a quadrilateral could take a condition. But as in this the position of the bulb in relation to the four sides is definitely known, there can be only one area of the plot, and from the lengih of each of the four sides given, the quadrilateral is one that may be inscribed in a circle. Can tho reader find the area of this plot, the sides of which are 80, 45, 100, and 63 inches respectively ? There is also a simple formula for questions like these and this will be published next week.

LAST WEEK'S SOLUTIONS. Paying in Cash. —The sum of £37 2s 6<i must have been in tho cash-box originally, and this amount was made up of 18 one-pound notes and 153 half-crowns. Covering a Square.—l 7is the largest number that can bo left uncut, and if the remaining 12 bo each cut into two pieces, the square can bo covered exactly without overlapping. v A "Petrol" Test.—lso miles is the maximum distance that can bo travelled outward under the conditions, one car only sjoing that length. The method is for one car to drop out at every 30 miles, and, retaining just sufficient for return, the balance of the petrol is divided equally between those going on. By omitting to state in the problem that each car ran on a consumption of 30 miles a gallon, this solution was unattainable. Mother's Deal.—Ten dozen altogether.

ANSWERS TO CORRESPONDENTS, » C.M.P." —A " seven " square will appear on May 23. " Billie." —Tho same colour or digit must not, appear twice in the same row* or column. " Diagonal ' was inadvertently omitted. . "H.E.W." —Thanks for interest, but if you look into the matter again you will no doubt see that the solution published is the correct one. Though quite a simple matter it has " floored " others before you. You went off tho track by not realising that the cash given in change was not the dealer's, but the ono who cashed the note.