Intellect Sharpeners

New Zealand Herald, Volume LXIX, Issue 21344, 19 November 1932, Page 5 (Supplement)

Intellect Sharpeners

CUTTING STEEL RODS

BX T- L- BRITON

A contractor took a hundred-weight of steel rods to an engineering shop to be cut into one-foot lengths, the rods being each 3ft. long, tlio charge for the cutting being £l. On # a later occasion the contractor had another hundred-weight of rods of the same quality and the same thickness as in the first order, but in this case the rods were 6ft. in length and these had to be cut in one-foot lengths also. As there were obviously double the number of rods in the first order as in the other, the weight and the quality oi steel being similar in both instances, the contractor argued, when objecting to the second price quoted by the cutter, that the fact that one lot contained rods only half the length of those in the other should make the cost of cutting the longer rods precisely tho same a3 charged in the first job, particularly, he contended, as the total length of steel was the same in both lots. But the metal-worker could not see the logic of the contractor's argument, and the reader is asked to decido the point, and find how much should be charged for the second lot based upon the same rates as in the first order. MOTHER AND THE GIRLS A problem sent by a reader, "F.S.,"' and published last month, concerning the ages of four persons has prompted another correspondent, " Zeno," to forward the following puzzle:—Fifteen years ago Mrs. Jones had three children, Alma, Betty and Clair, whose combined ages then totalled exactly half that of the mother. Six years later, namely, in 1925, her age was equal to tho combined ages of her children, which, however, included a fourth child, Daisy, who was born'during that six-year period. In the present year, 1932, there are five children, the youngest, Emma, arriving after 1923, and when she was born the mother's age was nine years less than the united ages of the other four, Alma's age then being one year less than the, ages of Clair and Daisy together, while Betty's and Daisy's combined ages at that time totalled half as much again as Clair's years. This year (1932) the mother's age is a year less than twice Alma's, and two years more than Alma's and Betty's together. If Emma's age this year is exactly onethird of Clair's, and the total of the six people 119 years, what are the respective ages? "Zeno" evidently intends the would-be solver to be supplied with plenty of data, but the reader will no doubt sift it well and ase only the essential details. DIVIDED INTO ZONES Here is '■ an arithmetical calculation which some readers may consider suitable for the armchair, though it is not a condition. It concerns a recent authorised street collection in the city, there being 75 collectors, though only £265 was the net result. The city was divided into four zones, "A," " B," " C " and " D," 12 workers being allotted to "A," hall as many again to " B," two-thirds as many again to " C,". the latter's quota being four-fifths of the number of collectors allotted to the largest zone, " D." The results showed that "B" topped the score both in the matter of the total amount collected as well as the average for each worker, while "A" had the lowest total, though-its average was high. Six collectors in "B" zone received as much as eight in "A>" 12 in " C," as much as nine in " B," while five in " D " got as much money in their boxes as four in "C" zone. How much did each section collect ? TWO FOR THE ARMCHAIR During training exercise a party of footballers who had gone leisurely along the road from "A" to "B" at the rate of one mile and a-half an hour, returned by the same route at a " jog-trot," keeping an even rate of travelling of six miles an hour. There was no perceptible delay on the road and the question is if the journey from "A" to "B" and back took exactly five hours, how far is it between the two places ? If Jack's age be added to twice James* the total would be 44, but if the age of James be added t n twice! Jack's the total would be only' 4U years. How old are they respectively ? And can tho reader say offhand and before making a calculation who is the older ? AN ALPHABETICAL SUM

A correspondent, " Rex," states that a recent alphabetical sum took him some hours to solve, which he did empirically, and asks whether there is any other method by which it can be done. Most certainly there is, namely, by deductive reasoning, and the object of this class \ of problem is that this method alone should be adopted. Here is an example that permits of the sum being constructed very simply in that way, which will be fully explained with the solution next week, and in the meantime the reader may try to reason it out logically. It is a long division sum, G.F. being the divisor, E.D.C.C.F. the dividend, and F.B.F. the quotient, with no remainder. The three mutiplied lines are respectively E.C.F., K.E.H. and E.C.F., while the results of the two in -which there are remainders are: K.K. with C brought down, and E.C. with the final dividend letter F brought down. LAST WEEK'S SOLUTIONS A Bank's Gilt to Charity.—The mayor had £IBOO, which was divided equally by nine. Hidden Word No. 3. —The hidden word is "Unimproved" and the three clues " Ripe," " Dump " and " Oven." The Clowns' Argument.—The length of the red-painted part of the pole from "D" to "C" is 10ft., and the bar, " CD," 53ft. Value ol City Block. —The frontage is exactly one-fourth the length of the depth,' namely, 33ft., the block being sold on that measurement at £l4O a foot. Church Hymn-board.—The smallest number of plates that would be necessary is 81, but if an inverted " six" be not allowed to be used as a " nine," 86 plates would be the minimum number. ANSWERS TO CORRESPONDENTS " Amateur."—Will be kept in view. C.H.L. —Am afraid it will have to stand over for the present. " Curious."—lt is exactly the same thing in a different form for th© calcuuition is based on precisely the same principle. "Almanac." —The difference bctwc-ii . four ordinary vears and four solar years • is barely one day. By adding a whole dav to every fourth year as is,done, l i too much, so the extra day is 01 m three times every four hundred yeai». "Ranolf Street."—(l) First in Germany in 1770 but there is no matical formula for it, ( ) - lies in the fact that 9s a foot for one p. nml lis a foot for the other cannot aver age 10s for the whole unless the dIB J*Jg s in both sets are the same. Io apt to trip the unwary. v -,y