INTELLECT SHARPENERS.

Otago Daily Times, Issue 20312, 21 January 1928, Page 19

INTELLECT SHARPENERS.

By T. L. Briton. Headers civo vcQuostod not to sona in their solutions, unless these arc specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. CALENDERS. Calenders arc usually a topic of discussion at the beginning of another year, and the subject offers abundant material for the purposes of propounding interesting and practical problems. Quite a little debate took place upon this theme not many evenings ago, when a lady put to the company an apparently simple f|UCSfion, which, it is stated, is still without a proper solution This was it:—Supposing at some future date that all the nations signed a compact abolishing war and guaranteeing a perpetual world peace to be inaugurated on and commencing from the first day of January in the year 2000 A.D., what are the probabilities that that day would be a Friday? This little poser will give the reader plenty to think about between this and next Saturday. A DEAL IN BROAD ACRES. A dairy farmer had a paddock, oblong in shape, which was the only block on the whole farm suitable for agriculture Th e north boundary, 40 chains in length, ran direct cast and west the eastern end terminating at a river which flowed from that point in a direct south-easterly course. The south boundary of the area was 2S chains from the northern line of fencing, and all the land from the eastern boundary to the river belonged to a neighbour who offered to sell it. The fanner, although requiring more cropping land for his growing herds, hesitated to buy, saying that the size of it was too small, and that nothing less than 40 acres in that locality was of any use to him unless he got it at a much lower price than was asked by the owner. This section was bounded by the river, by the : east boundary of the fanner’s block and also by a line continued easterly from the south-east comer to the river. The land was not surveyed, and the two men agreed that if. upon measurement, it was found to be 40 acres or more, the farmer should pay £2l an acre for it, but if it was less than that area, £ls an acre only was to be charged. How much did the farmer pay for th e section ? A CIRCLE AND AN OVAL. A simple but very interesting question was set at a recent examination in practical geometry. It floored nearly 90 per cent of the candidates, most of whom complained that only the time limit of ten minutes prevented them from submitting the correct answer. Yet had the candidates kuowm of the simple method of demonstration, less than half that time would have sufficed. Hero is the question:—Draw a perfect oval and a circle on a sheet of paper, using any instruments desired, so that the area of the latter shall be exactly equal to the superficial measurement of the elliptical figure. No technical knowledge whatever is necessary to make these drawings accurately. It can be done in each case by one sweep of the compass, and it is very useful to know how it can be done. A COMBINATION OP LINKS. A man possessed a curious chain of nine links, all of different shapes and sizes, excepting two of them, which were circular, and these two were not linked together. Each of the nine links was similar on both sides and ends. The owner, a keen devotee to problems, asked his friend, the local pedagogue, whether it would be possible to calculate the number of chances against _ the chain being made up precisely as it was then if the links were taken apart and handed to a jeweller separately to make into a chain, one condition being that the two circular links should be separate from one another. The schoolmaster said he had no time then to make the calculation, and promised it later on, but up to date he has not found the necessary leisure to give his friend the_ answer. Can the reader determine this? Of course, it is obvious that each successive link can be attached to another in one of two ways.

PLAYING BRIDGE. If six ladies and six gentlemen arrange to play bridge together on 11 separate occasion's, so that no player shall have the same partner more than once nor the same opponent more than twice during the whole series of games, in what manner should the players be arranged, and how should the 33 groups be determined? The six ladies may be called LI, L2, L 3, L 4, L 5, L 6, and the gentlemen Gl, G2, G 3, G 4, G 5, G 6, and any of the 12 may be partners. It frequently happens that tournaments are required to be arranged somewhat on these lines, and the reader may therefore find the problem very useful apart from the fact that to work it out will sharpen the intellect considerably.

LAST WEEK’S SOLUTIONS. AN ASPHALT TRACK. The inner circumference of the track was approximately 138yds, or practically 29yds less than the outer. “ BREAKING UP.” Class I contained 17 boys while 19 were in class 11, the number of walnuts distributed between them being 811. FIVE CARS AND THEIR PETROL. As stated last Saturday the view put forward by the two readers mentioned was ingenious and technically good, the only objection being its impracticability of achievement. SIX PEDIGREED YEARLINGS. There are 63 different ways of submitting for sale any one, any two, any three, and so on. THREE HOUSES AND THREE DRAINS Several readers have written since Miss L. raised the question, and all thought that there w 7 as no method by which the feat could be accomplished. The explanation published last week shows the only way. ANSWERS TO CORRESPONDENTS. S.M.—You have by now no doubt seen the point. J.B.—Thanks for continued interest—it only applies to the one instance wher© the two figures are the same. J.W.G.G. —Thanks. Glad to know it was not so serious as thought.