INTELLECT SHARPENERS

Otago Daily Times, Issue 21538, 9 January 1932, Page 16

INTELLECT SHARPENERS

By T. L. Briton.

Written for the Otago Daily Times.

AN EXAMINER’S POSER. A correspondent, D. M., has sent one of the questions set by the examiner in the methematics paper at the last entrance examination, and asks for my opinion of it. He states that the candidates regard it as insoluble owing to in sufficient data, and that there is ambiguity in the phraseology of it. D. M. also states that the question has since been referred to several teachers, who also think it insoluble, adding that it is “bound to produce some controversy in the newspapers.” Here is the question: On a piece of work three men and four boys are employed who do one-half of it in six days. One more man and one jnore boy are then put on and onethird more is done in three days. How many men must be put on that the whole may be completed in one day more ? The writer of this column regards the problem as a fair one, well within the capacity of the reader, and must assume that the “ teachers ” mentioned by D. M. are teachers of subjects other than mathematics, for the question has ample data and is interesting enough to invite the consideration of it between this and next week, when the solution will be published. FITTED EXACTLY. The “knock-off” signal sounded when one of the painters on a job was burning off the old paint on one of the doors, and the workman immediately “ downed tools." Unfortunately in his hurry he forgot to extinguish his lamp, and by the time he returned a large hole had been burned in the lower panel of the door. As it had not been noticed by the foreman, the painter quickly squared off the burned edges and found that the hole to be patched was 9in by 16in, and, the matter being one that he considered. should be remedied at once and without the “heads" being made aware of the damage, the painter took the first suitable piece of wood at hand, which was Ift square, and in less than an hour had patched up the hole, which, after a coat of paint, was almost unnoticable. The painter saw at once that the superficial area of the piece of wood was the same as the hole to be patched, and knowing something of the carpentering trade, he cut the board into the fewest number of pieces possible to effect his purpose. The reader is asked what method the painter adopted in order to utilise the foot-square board to fill the hole exactly. A SQUARE WITH CIRCLES. The titlfc of this problem may seem to indicate something involving higher mathematics, .but the non-technical reader may safely proceed, for the question is no more than a puzzle which calls for the exercise of ingenuity only, not even elementary arithmetic being necessary to unravel it. Take four pennies, new ones if at hand for better demonstration, and place them flat upon the table, after which they may be moved (without being lifted) into such positions that a perfect square will be formed. No. instrument is necessary, not even a pencil to form the square, and, that being so, the reader will quickly note that the desired result is not to be achieved by the drawing of tangents of the four circles, for it may be assumed that the pennies are spherical. The statement of the puzzle should bo carefully read before one proceeds to find the correct answer, for it is expressed in terms that will not permit of any reasonable criticism of the method of accomplishing the feat of placing the pennies in their exact positions.

ONE FOR THE ARMCHAIR. Here is a little question which the reader will no doubt readily answer correctly without the trouble of putting any figures on paper, it being merely one of estimating the possibilities, or more correctly the probabilities, of a certain happening under certain fixed conditions. From time to time we read of predictions that the world is coming to an end upou a certain date, and perhaps many of ua are aware that several of these definite “last days" prophesied by well-meaning folk have long since passed. . But the question for the reader .to examine from a mathematical viewpoint only is: Why is a recently-reported prediction by an American pastor of some congregation in the United States incorrect when he states that the world is coming to an end on Wednesday, the first day of January in the year 2000? PAYMENT IN KIND. Here is another little question which may puzzle the reader for a minute or two, especially if lie elects to find the correct answer without pen and pencil. An orchardist gave a number of women the job of gathering his. apple crop, the work comprising the storing of the apples in the shed in addition to the labour ot picking them. It was agreed before starting that the payment would be in kind, and that instead of cash the eight women were to receive between them one-eighth of the total number of cases stored by them in this way. The forewoman received 10 cases more than each ot the other seven, who got equal shares, ann if, after they all .had received their quota, the orchardist had 1750 cases left, can the reader say how many the women received respectively? A somewhat similar question was put by the writer of these notes to three young friends who had passed the sixth standard school test, but, strange to say. not one of them managed to get the correct answer, simple though the reader will find it. SOLUTIONS OF LAST WEEK’S PROBLEMS. STEALING EGGS. There were 260 dozen eggs altogether, one being a "baker’s” dozen, so that out ot the 3121 eggs 2101 were stolen. REDUCING THE SPEED. The distance between the two places is 120 miles. ECONOMICAL PACKING. Forty extra sticks could be packed if the bottom layer contained 50, the next 48, and so on alternately to the top. In this way 11 layers could be placed m a box instead of 10, the gain being possible by alternate layers.fitting into the grooves instead of lying on the surface of the pieces. A CRICKET MATCH. 1400 at Is, 1000 at 9d, 900 at 6d, and 900 complimentary. THE ARABS’ DATES. As the men shared equally, each had two and two-third pounds, so Zed could only have provided one-third of a pound for the traveller’s meal, being thus entitled to one shekel to Abdul’s seven. ANSWERS TO CORRESPONDENTS. “High Finance.” —As the information involves a somewhat complicated calculation, it would be better to have the official figures, which would make the result more interesting. This will be done ns soon as the statistics are available, A.B.C.—Another scries will appear next month. “Curious.” —About the middle of February.