"NUTS!"

Evening Post, Volume CV, Issue 23, 28 January 1928, Page 28

"NUTS!"

I (By T. L. Briton.) |

I INTELLECT SHARPENERSj All rights reserved. = .

Beadan with a little Ingenuity will find -In this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the "nuts" may appear harder than others, U will be found that none win require a sledge-hammer to crack.them. The result of an important race last Jtoxing 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 issue being which equine made the fastest time. A little problem is suggested by this discussion. Let it be granted that the course (for easier calculation) is circular, and completely railed on the inner circumference, which is exactly two mijes in length. Assuming that the first horse ran only the rail distance throughout the race, and that "The Count" ran uniformly five yards out from the rails, which of the two horses travelled the faster if the pinner's time was 3 minutes 25 seconds and was three lengths (8 yards) 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 STOPWATCH. Someone has calculated that an ordinary stopwatch 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 tho 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 ten counters each numbered with one of the figures given, and make a diagram of a clock dial, leaving out the twelve. The ten counters should be< placed on the dial in the following order, commencing at seven and going in a clock movement direction—viz., 2, 7, 8, 9, 4, 0, 6, 5, 3, 1, the latter being given on the five, the six being without a counter. The problem is to get the counters into proper order, indicating the yearly number of ticks stated, leaving the blank as at present. There are two groups of figures—viz., 0, 6, 5, 3, 1, which move clockwise; 4, 9, 8, 7, 2, moving in 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 be achieved in 26 moves. "INQUIRE WITHIN." A copy of an early edition of this well-known book has the following question in its mathematical section, but upon looking into it and being unable to find a logical answer, the "Solutions" were sought, which showed clearly that the question was certainly not in its Tight place in the mathematical pages. For the problem demands some strategom, though the solution given is strictly in accordance with the expressed terms. It is now reproduced, but only on the grounds that some ingenuity will be required to discover the little artifice. Here it is: A farmer had a

small flock ,of eighteen 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 their right to "propose" to one year in every four (or sometimes eight). To make the practice one of fifty-fifty seenss desirable, if only to moderate the overwhelming number of proposals in leap years. .Some statistics in this connection recently came under notice which show that during last bissextile onq-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 by anyone. Thirty-five forty-fourths of the widows married bachelors, and altogether one thousand two hundred and twenty-one spinsters' proposals were declined by these men without previous matrimonial experience, but 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 were to be packed in a case, each slab measuring 124 in 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 be attached it would be • a much more interesting problem without making the calculation very difficult. For instance, if it bo agreed that not more than twelve slabs should be laid on edge,and that the case 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 ,£ 1050 to purchase it. A Circle and an Oval. —lf 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 made 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 prescribe'! conditions in 282,240 different ways. Playing Bridge. —There are, as stated, thirty-three 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 thirty-three 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 Eotorua, and later on a problem will be propounded based on the official figures. "Melrose." —In the "queer form of legacy" sum all denominations of L 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 tho discharge is increased 5.6 times.