INTELLECT SHARPENERS

Otago Daily Times, Issue 21987, 23 June 1933, Page 3

INTELLECT SHARPENERS

Written for the Otago Dally Times, By T. L. Britok.

A TRINKET BOX. « Zeno ” hag forwarded an interesting arithmetical puzzle concerning the making of a small box for keeping knickknacks out of a sheet of copper, and asks ■for some information before proceeding with the job. His request is therefore put in the form of a little problem which the reader should enjoy while exercising his ingenuity. “Zeno” has simplified the matter by not requiring a lid to the box, and his question is put in the following way: —The copper sheet is eight inches by five inches, and he knows that by cutting a piece from each corner all of the same size he can by folding and soldering make a rectangular box minus a Bd. But “Zeno” imposes two conditions of the making—the first, that each piece from the four corners must be a squaie of equal size, and the second, that the box will have the largest capacity under these conditions that is possible. -the limitation as to the shape and size of the pieces cut off is important, for as^ the reader knows the smaller the portions cut from the corners the shallower must be the vessel. Can the reader assist “Zeno” in this interesting question bysaying what is the exact size of the square corners to be cut off in order that the box may have the largest possible capacity under tlio conditions stated? TRIIN SPEEDS. The reader is of course aware that when two objects are moving in exactly opposite directions (two trains for in stance on parallel lines), the rate of approach before meeting, or , the rate of separation afterwards is obtained by adding together their respective rates of travelling; just as their respective rates of passing or their rates of sepaiation afterwards when travelling in the same direction is always equal to the difference of their respective travelling speeds. Here is a useful little question on the point. A train travelling at 30 miles per hour passes another train 450 feet long, on a parallel line, and exactly and completely passes it in S 4 seconds. If these trains had been travelling in opposite directions at similar speeds, instead of both moving along in the same direction, they would have passed one another in 12 seconds. From these details two interesting questions present themselves. What was the speed in miles per hour of train No. 2, and the length of that train, which obviously was a shorter one than the first-mentioned, being known', what was the exact length of train No. 1? . I SALARY INCREASES. . Calculations of percentages being an essential part of almost every type of business and commercial transaction, questions relating to them are always useful and interesting, particularly interesting when the calculation shows a profitable return. Here is one concerning the incomes of two persons, Atkins and Brown, who were amongst the few. who were able to say that their salaries had been increased during the past two or three years. Their respective incomes in this way in the year 1930 were such that for every £2 10s received by Atkins the other man received £2, the actual difference in salaries in that year being £2OO. Atkins’s salary for the year 1931 showed an increase over the amount received in the previous year of 10 per cent., and though Brown’s salary for 1931 was also increased, the rate of advance was different. The year 1932 gave each of them another increase at the same rates respectively as in 1931, the difference in their salaries for 1932 showing that Brown received for that year a sum only £SB less than the other man. Can the reader find their respective salaries for the year 1931, and by what rate per cent. Brown’s was increased in 1931 and 1932? THREE FOR THE ARMCHAIR. Here are three simple questions for the reader who prefers those that do not necessitate the use of pen or pencil, but merely a, little mental exercise that is not too strenuous. A picture 30 inches long and 27 inches wide was photographed on a reduced scale. The distance between two trees shown in the picture is nine inches, and the distance between the same points:in the photograph is only four inches. What size is the photograph? . A clock is set correctly at midnight on Sunday evening. When it was noon by the clock next day the true time was exactly half an hour in advance of the time that the hands showed. In these circumstances how much would the clock lose in 12 hours, true time? A little extra caution with this question may not be amiss. How much would a person’s annual taxation bo if it were equivalent to 10 per cent, on Ms income from April 19 to the end of June of the same year, both days inclusive? His income was £350 per annum, and the year in question an ordinary one with an average of 30 5-12ths days per month. The reader need not take fright at this - fraction, for the figures have been so fixed that the question is purely one for the armchair. FROM FIVE REGIMENTS. The following puzzle will he found to be one for the exercise of the reader’s ingenuity rather than a test of Ms arithmetical attainments. From each of five regiments —A, B, C, D, E five men are selected, each group of five men comprising soldiers of different ranks, namely a sergeant, a rifleman, a gunner, a lancer, and a private. The 25 men were arranged in the form of a square, with five men in a row, and when inspected by the G. O. Commanding, it was noted that neither regiment nor rank was represented more than once in any direct lino—that is, in' any row, column, or in either of the two long diagonals of the square. This is a capital puzzle that should give the reader half an hour of excellent mental exercise, to take .25 counters representing the different ranks and regiments, and endeavour to arrange them as described above. There need be only five different colours to represent the five regiments, the five of any one colour to be marked to indicate the several ranks, A to represent a sergeant, B a rifleman, C a gunner, and so on. SOLUTIONS OF LAST WEEK’S PROBLEMS. MEN AND BOYS AT WORK. Three more men would be necessary. TWO PUMPS. The respective answers to the questions submitted arc {1 22-J feet, and (2) 3hr 30min. A “RELAY” CONTEST. As the men travelled the full distance at the rate of a mile in sJmin, one and one-eleventh miles were covered, the diameter of the central track being 28 chains. TWO FOR THE ARMCHAIR. (1) The length of the ladder was 13 feet. Method:—The square of the height of the window-sill less two feet, phis the square of the distance from wall to foot of ladder, the square root of the total giving the answer. (2) Ten per emit. A “ RESTORATION ” PUZZLE. Divisor 1111, dividend 2769723 and the quotient 2493. Without the conditions imposed there are several examples

in which a sum in long division could be reconstructed from the divisor xxxx, dividend x7x9x2x and quotient x4x3, the x representing a deleted figure. ANSWERS TO CORRESPONDENTS. q j 5. F.—Your suggestion noted. r’ c.—Yes, one digit only, not two, is not repeated, namely the “ four ” as you mention. By deductive reasoning. . . “ Curious.” —If the errors in the sides are equal, and each error is equal to one quarter of an inch, the error in the area must ho one/juarter of the sum of both sides, mmcly 4. “ Mark.” —Thanks; probably next month.