INTELLECT SHARPENERS.

Otago Daily Times, Issue 21242, 24 January 1931, Page 20

INTELLECT SHARPENERS.

Written for the Otago Daily I'imes. By T. L. Briton. A FUGITIVE. A constable on night duty espied a man tampering with the front door of a city shop and gave chase. The affrighted one immediately ran off, the officer following in hot pursuit. The latter was not only a more hefty man than his quarry, but was more fleet, and though the strides he took were not so many over a given distance they were longer, enabling him to overtake the law breaker. Let us have a little problem on the incident, and assume that the constable's strides were exactly two and a-half times as long at the other’s, and that for every eight stops of the fugitive the officer took only five. If they both started to run at precisely the same time, and the fugitive was then a distance of exactly 27 of his own steps ahead of the constable, can the reader find, without bothering with pen or pencil, how many strides the policeman took before catching the tunaway, as obviously he must have done since both he and the hunted one maintained their own length of stops uniformly throughout the race? WDO WON THE RAGE? The last problem suggests another of the same kind concerning a foot race between two athletes, Brown and Jones, the distance of the contest being one mile. Throughout the event each stride of the former was five feet in length, and he took three and three-tenths strides per second uniformly. Jones, however, varied both the length of his stride and the rate, making in the first three-quarters of the distance Strides of six feet in length at the rate of three per second, whilst in the latter quarter of the mile these were reduced to five and a-ha)f feet and two and a-half to the second. The reader in this case is not asked to make an armchair problem of the question who won the race, and in what time, though it is extremely easy to calculate this with pen or pencil, for it may be taken for granted that the two men started simultaneously. This little question was referred to the writer of these notes by two young ladies who indulge in this healthy sport at times, but cannot agree as to the answers. Their reference, however, is in simpler form, and the figures have been altered in order to make a more suitable question for this column, the relative merits of the runners being the same as submitted by the inquirers.

AMOS AND BINNS. Amos and Binns went together into a business, in which the former invested only two-thirds as much as his partner, At the end of seven months Amos withdrew one-quarter of his capital, and two months later Binns, eyeing that the amount of business likely to be done did not warrant eo much capital as he had invested, withdrew from it exactly the same proportion as Amos had done. The S"ts at the end of the year were only 12s, and the question is how should these be divided between the two partners? TWELVE SENTRIES. Here is a little route problem that requires practically no mathematics, but should nevertheless give the reader a few moments of serious thinking. Twelve sentries are to be visited by an officer, and the question is to discover. the shortest route that is possible, starting from any one of them. To simplify it we will assume that their positions are such that they can be reached only via single straight paths, all of which form six complete rectangles. There are three sentry posts on each of four lines running east and west, and four similar posts on each of the three lines running north and south, 12 positions altogether, which are all equi-distant. If a diagram be drawn from this description, it will be seen that there are 17 paths, each of which leads from one sentry to another in direct line, none being in a diagonal direction, and the question is, what is the shortest route that can be taken by an inspecting officer who visits every sentry, starting and finishing at any of the 12 points, following, of course, the paths described? The answer may be given in distance, one sentry being ten chaind from his neighbour north, south, east or west? SOMEWHAT DIFFICULT. Here is a little puzzle which the reader may find difficult to solve. It was sent by a correspondent who admits he is not able to unravel it. It. is similar to one that appeared in this column some considerable time back, and concerns a five-roomed house with 16 doors, the problem being to enter each room without using any door more than once. Draw an oblong with its long sides running east and west. First divide it into two equal parts by a line running parallel to the long sides, divide the top half into two rooms of equal size, and the bottom portion into three equal parts. There are two doors leading outside from each room on the north, east, and west, and also one from each of the three rooms on the south. In addition, there are inside doors leading from each room to the one adjoining, making a total of 16 doors in the house. As stated above, the problem is to enter every room at least once and as often afterwards as desired, but no door must be used more than once. Can the reader succeed in this? SOLUTION OF LAST WEEK’S PROBLEMS. ' WAYS AND MEANS. The holiday was extended by 12 days, 36 being the duration of it as previously planned. LIMITED TO ONE METHOD. Twelve at ss, seven at 4a 6d, and one at the lowest price. A BY-ELECTION. “W.,” 3106; “X.,” 8070; “Y.,” 2814; and “ Z.,” 1956. LEFT THE LIGHTS ON. Four and one-fifth miles an hour. AN EXTENSION OF TIME. * £IO3O (Ten hundred and thirty). ANSWERS TO CORRESPONDENTS. P. W. D. —The 18 should be arranged in the form of a square. “ Wairarnpa.”—Grafton bridge runs east and west approximately. “ Conumdrum.”—A lengthy search to find the etymology of this word was not successful. “ Colenso,”—Why not use logarithms, which are allowed in cases not specifically “ barred ”7