INTELLECT SHARPENERS.

Otago Daily Times, Issue 20318, 28 January 1928, Page 19

INTELLECT SHARPENERS.

By T. L. Briton. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. THE COUNT AND HIS RIVAL. The result of an important race last Boxing Day has since been the subject of discussion in sporting circles, the merits of the first and second horses being the point at issue. According to the expert reporters, the winner ran close to the rails during the whole distance, whereas The Count, which ran second, had to take an outside position throughout. The question is: 'Which horse made the fastest time? A little problem is suggested by this discussion. Let it be granted that the com • (for easier calculation) is circular, cud completely railed on the inner cir. umference, which is exactly two miles in length. Assuming that the first horse ran only the rail distance throughout the race, and that The Count ran uniforraly syds out from the rails, which of the two horses travelled the faster if the winners’ time was 3min 25sec, and was three lengths (Byds) ahead at the finish, ■ the starting and finishing marks being at the same point. Of course, it is taken for granted that both horses started together. A STOP-WATCH, Someone has calculated that an ordinary stop-watch when going ticks at the rate of 5,342,170,869 per annum. Whether this information is of any practical value is doubtful, but it is noted that the figures comprise every digit and the cipher once only, and the whole number may therefore be used for a little counter-moving problem concerning the dial of a timepiece. Take 10 counters each numbered with one of the figures given, and make a diagram of a clock dial, leaving out the 12. The 10 counters should be placed on the dial in the following order, commencing at 7 and going in a clock-movement direction, viz., 2,7, 8, 9,4, 0,6, 5,3, 1, the one being on the 5 and the six being without a counter. The problem is to get the counters into proper order indicating the yearly number of ticks stated and leaving the blank as at present. There are two groups of figures—o, 6,5, 3, 1 move clockwise, 4,9, 8,7, 2 move into the opposite direction. A counter may jump over another of a different group if the vacant space is next beyond, but not over one of its own group. 'This problem will require some thought if the feat is to be achieved in 26 moves. “ ENQUIRE WITHIN.” A copy of an early edition of the wellknown book " Enquire Within ” has a question in its mathematical section. Upon one looking into it and being unable to find a logical answer, the solutions ” were sought, and they showed clearly that the question was certainly not in its right place in the mathematical pages. For the problem demands some stratagem, though the solution given is strictly in accordance with the expressed terms. It is now reproduced, but only Oil the grounds that some ingenuity will be required to discover the little artifice. Here is the question:—A farmer had a small flock of 18 wethers and one ewe in his paddock, and said that he could place them, and did so, in five pens, so that there would be an equal number in each pen. How could he do it? Although there is a catch in the question it is not that the ewe gave birth to a lamb upon being placed in a pen. A PREROGATIVE OF THE LADIES. A lady has written to the press pointing out the unfairness of the present custom of limiting women’s right to “ propose ’ to one year in every four (or sometimes eight). To make the practice one of fiftyfifty seems desirable, if onlv to moderate the overwhelming number of proposals in leap year. Some statistics in this connection recently came under notice which show thgt during last bissextile, one-eighth of the total proposals made by women were by widows, and one-eleventh of the number of men to be married in consequence were widowers. These heroes declined one-fifth of the total proposals, though no widows’ offers were rejected bv anyone. Thirtyfive forty-fourths of the widows married bachelors, and altogether 1021 spinsters’ proposals were declined hv these men without previous matrimonial experience, jut all the same they accepted seven times as many maidens as widows. From these records can the reader find how many women proposed ? PACKING SILVER INGOTS. A quantity of unwrought silver in the form of ingots was to be packed in a case, each slab measuring 12iin long, llin wide, and lin thick. From these figures it would be an easy matter to determine the size of a case of equal length and breadth that would hold exactly any particular number of ingots without any space to spare, but if other conditions are attached a much more interesting problem may be created without making the calculation very difficult. For instance, if it be agreed that not more than 12 slabs shall be laid on edee, and that the case shall be of equal length and breadth and of necessary height, what should be the inside measurements if the case had to hold exactly 800 ingots of the stated size, leaving no unoccupied space? LAST WEEK’S SOLUTIONS. CALENDARS. As it is not possible for the first day of a century to fall on a Friday, the probabilities are of course nil. A DEAL IN BROAD ACRES. The area of the new section was exactly 50 acres, and therefore it cost the farmer £IOSO to purchase it. A CIRCLE AND AN OVAL. If the drawings be made by a compass with fixed radius and the paper placed around a cylinder (a bottle, for instance") a perfect oval can be mads with one sweep of the compass. The circle should, of course, be made on a flat surface with the same fixed compass. A COMBINATION OF LINKS. The nine links may be joined together under the prescribed conditions in 282,240 different ways. PLAYING BRIDGE. There are, as stated, 33 arrangements in which no player has the same partner more than once, nor the same opponent more than twice. As space will not permit of the 33 sets being published, they will be sent to any reader desiring them. ANSWERS TO CORRESPONDENTS. L. O. B.—Thanks for particulars of the historic tree at Rotorua, and later on a problem will be propounded based on the official returns. “ Melrose.”—ln the “ queer form of legacy” sum all denominations of £ s. d. should be represented. The shunting problem has been sent you. P. H. M.—Thanks for reference to Merriman’s “ Hydraulics.” It will be of interest to amateur engineers to know that by doubling the diameter of the pipes the discharge is increased 5.6 times. “ Waikino.”—See answer to “ Melrose. ’