INTELLECT SHARPENERS

Otago Daily Times, Issue 21621, 16 April 1932, Page 20

INTELLECT SHARPENERS

Written for the Otago Daily Times.’ By T. li. Briton. ! i, AX ALPHABETICAL DIVISION RUM. “Alphabetical sums are very puzzling," writes a correspondent, M. E.V’H., “ especially when no clue whatever ! <jj' given,” and the writer adds that --sha thinks at least one digit might be sub*, stituted for a letter when the sum is stated. Well, here is one in which the letter Z stands appropriately for zero, or, as most readers know it by, the cipher 0. Whether this knowledge will enable M. B. H. and other readers who think similarly in-this regard, to solve this interesting Tittle puzzle within a quarter of an' •hour., mhy be doubtful, for even with; the aid- of this clue.' the would-be • solver will have .to give it some hard thinkings— > WX)UWZR T V ( I X X Q DYQ - " TY 11 * ' '■ TU S V, T Q.T -v. h-v T U.S ■ Y X V . ... v, YX V • .... S'; ih; ; . \ D THE PURCHASE OF GRAIN. The sum of seven pounds, was voted by the committee of an Egg Circle for the purchase of grain to be supplied to several small poultry farmers who had just started business, but were unfortunate, to be the victims-Of serious bush fires in which they lost everything. The.grain was made up in bags of varying' weights, and 1 , consisted of three different grades. The cheapest ot the three .cost, .six. and eight-, pence per bag, the‘second quality, ten shillings per bag, and the best grade twenty, shillings per bag. The farmers comprised both men and women; the same pumber of each, and though some of them had had greater loss than others, the committee made no ;diffefence in the quantities distributed to each applicant, and directed that the whole seven pounds should be divided equally among'them in the form of produce. ’ If we assume that each of the farmers was supplied with more than one grade. of grain, and that everybody received the same, quantity as well as the same monetary value, can the reader find the number of men, and women who benefited by tlie vote"of the committee? As it may be taken for granted that only whole bags were supplied, there is only one solution of this useful problem. TWO FOR THE ARMCHAIR. A man rowed a certain distance with the stream in exacty two hours, but returning against the tide which flowed at the same rate as before, the journey took him four hours longer. On the, assumption that he rowed uniformly at the same stroke on both occasions how long would it take him to row the same distance one way in still water? This little question should not be dismissed as “too elpment- - ary—.because the correct answer may not be what may seem obvious to some solvers. ' The aver age, speed of ; a!,train for a certain ntimber of hours ' was given as 30 miles, per hour; when, ’ a hot box almost caused a complete stoppage, for' only six miles were travelled in the next hour and .this ■ reduced the average speed to 26 miles per hour. Without the aid of pen or pencil, as .in the preceding case,'can the reader say how long the train had’ beep travelling - prior to • the mishap? BY RAIL AND SERVICE CAR.

A -man was- obliged to travel over a certain'distance from>X to Y by service car for parfof the journey and by train for the .remainder of the 60 miles between the two places. The whole journey occupied exactly three hours. He was aware before starting that the train service was the more expeditious method of travelling,, but be was obliged to take the car for part of .the .way owing to the necessity of calling -at a place en route. Had he gone the whole distance by train be could have ended bis journey in one hour sooner than it actually took to travel from X to Y, and at the same time he would, by that method, have' saved exactly two-fifths of the actual time that he was travelling in the service car. The question is. How far did he travel by car and at. what speed did it ■ travel? For the purpose of this problem it may be assumed that the whole three hours were occupied in covering the 60 miles without any time lost by reason of having to make a call on tfie way,- and that train and car each travelled evenly-at its own speed throughout. S- TO CATCH A TRAIN. .Three young men were obliged to travel by some means or another from A to. B, where they desired to catch a train for the city which was timed to leave B at 12.30 p.m., and the 'time would not allow of walking the whole 24 miles; ns it was then half-past 9 in the One of the three had a motor cycle .which, - ', 'however, would only carry two persons. They decided, therefore, to start off- together, two on the machine and one on foot. In this way they left Aat exactly. ,10 o’clock and arranged that Bill, who owned the machine and. was the only one of ,there who understood driving it, should, take Fred first and drop him at a point within walking distance from B, and then return to meet Dick. By this means they were. all able to catch the train, and the ouestion is, If, after starting off, Dick walked continually until picked up by Bill,, and-Fred after being dropped started to walk to B, what margin of ■ time, did they have to spare at B before the train was timed to leave, if the three of them arrived there at precisely the same moment, the walkers travelling at four miles an hour and the machine at '2O miles per hour without any perceptible delay en.route? As there is more than one method of arriving in time to catch the train; the question will assume that they had the maximum time to spare upon arrival.’ ' . SOLUTIONS OF LAST WEEK’S PROBLEMS. “ RESTORATION ” PROBLEM. Divisor 1 2 5 4 7 3, divident 7 3 7 5 4 2 8 4 1 3 and quotient 5 8 7 8 1. EXPLORING A DESERT. Under the conditions the maximum number of days that any one of the party could travel “out” before his return to the starting point 'is eight, the farthest point being thus .160 miles. The simple formula when no depots are formed, is number of men multiplied by number of days that one man can carry provisions for one, divided by the number of men, plus one. This gives the maximum days .out before returning. AN ALPHABETICAL SUM. Two plug 7 multiplied by 6 equals 54, from which 18 ig taken. The remainder ig therefore the equivalent of H multi- , plied by E, namely 36. TEST CRICKET. Vivian 100, Dempster 80, Weir GO and Roberts 40. <■ TWO CRICKET QUESTIONS. Ho had played 12, innings before. (2) His average after the sixth innings was 40 runs per , innings, Ids score of 20 in the seventh reducing it to 38. ANSWERS TO CORRESPONDENTS. C. J. W.—Much obliged; unusual for H. D. C.- C. A.—Thanks. “Centaur.” —If carefully studied the method of treatment will be clearly understood. The preliminary statement made shows that you are on , the right track. “Curious.” —It is the exception to find a technical problem in this column, but it is intended to publish one shortly.