NUTS TO CRACK.

Otago Witness, Issue 3862, 20 March 1928, Page 10

NUTS TO CRACK.

By

T. L. Briton.

(For thr Otago Witness.)

R«ad«ri with a little ingenuity will find in its column an abundant store of entertainmert and amuse■aant, and the solving of the problems should provide excellent mental exhilaration. While some of the “nuts” may appear harder than it will bo found that none will require a sledge-hammer to crack them. Solutions will appear in our next Issue together with some fresh cuts.*' . R **4«rs ;re requested not to send la their solutions, unless these are specially asked for, but to keep them for comparison with those published in the issue following the publioation of the problems. 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 Uie Saturday following tlie publication of the problems. . SCHOOL ATHLETES. Three school athletes of different ages were engaged in a foot race, and as they did not possess equal speed the task of fairly handicapping the boys, so that they would have equal chances of winning the race, was not an easy one for the sportsmaster. Acland, the senior lad, was the school champion, and it was agreed that he was about 10 per cent, a faster sprinter than Boyd at any distance up to 220yds, and about 15 per cent, speedier than Copeland. Assuming that when Acland gave the other boys 10yds and 15yds respectively in 100yds, the race invariably resulted in a dead heat, what start should ■Boyd give Copeland in a race of 150yds, at the relative speeds indicated, so that the judges would not be able to separate the two athletes when they breasted the tape ? THE SPEED OF TRAINS.

Estimating the speed and length of a train by taking the time as it passes a fixed object, is both an interesting pastime and an easy calculation, but two things are always to be distinguished one from the other. The first is the case in which a train passes a fixed point, and the other that in which it passes an object of given length, such as a bridge, station, or a standing train. In the former instance it should bo noted, in order to arrive at the correct result, that the train must move forward a distance of its own length, whereas in tlie latter case that distance must be added to the length of the object at rest. Here is a useful problem on the point. A person standing on a railway station platform, 396 ft in length, observes that a non-stop train passes him in Bsec, and also that it passed completely through the station, of the length stated, m 20sec. At what rate was the train, travelling and what was its length? ANOTHER TRAIN. Whilst on the subject of trains, can the reader determine the rate of travelling from the following few simple facts? A train 88yds in length overtook a person walking at the rate of 4 m.p.h. in the same direction along the road, and completely passed him in lOsec. Continuing on at the same speed, it overtook another man walking along an avenue running parallel with the railway line, the end of the train passing him exactly 9se c after the foremost part of the locomotive was abreast of .the walker. At what rate wa s the latter pedestrian walking? THE FOUR TRAVELLERS. Io complete the present series of speed problems, here is one that vyill give the reader the mental stimulant that always affords enjoyment, because it is not difficult, and the incident involved is one that may occur to any of us. Four people wished to be conveyed from A to B, a distance of 16 miles. They required to reach there before 3 p.m., it being then 11.45 a.m., but there was no train till 6 o clock, and the only available vehicle was a motor car capable of carrying two persons only besides the chauffeur, as none of the four could drive. All of them, however, were fairly good walkers, so two of the party set out on foot at noon, the car also starting then with the other two. The vehicle travelled a certain distance and set the two passengers down to continue on foot, returning to bring the other two, who were then driven right through to B. arriving there at the same time as the other two. Assuming that the car travelled at 20 miles per hour and the walkers at four miles per hour throughout, with no perceptible stop, at what points did the car set down the first two and pick up the. others, and at what time did thev all arrive at B? DOMINOES IN PROGRESSION. An interesting curiosity in the form of a domino problem was propounded a few years ago by Henry Dudeney, an English mathematician of distinction, and as his solution (the correct one) caused some controversy amongst devotees to this form of. entertainment, chiefly in America, it is published for the consideration of the reader. The first six dominoes played ir? tlie course of an ordinary game were (reading from left to right) blank four, four one, one five, five two, two six, and six three. It will be noted that the total numbers of spots on the dominoes, each taken in the order played, in arithmetical nrogression, that is they increase by the same number, yiz., one. The. problem is to discover in how many different ways six dominoes (taken from an ordinary box of 28) can be played in the ordinary way, and lie in regular progression as indicated ? The difference may be any number provided it is the same throughout, but the dominoes must lie in increasing, not de-

creasing, progression as played from left to right. LAST WEEK’S SOLUTIONS. MONETARY' EXCHANGE. At the rates of exchange quoted there would be no pecuniary advantage to the Buenos Aires merchant by remitting the sum in the form of a draft for £762 purchased in New York, as the cost would be the same as the local quotation, viz.. 27,432 pesestas. CLOCK PROBLEMS. The explanation of the presence of fractions with “ 11 ” as denomination was given last week when referring to the solution , five and five-elevenths minutes past 4 o’clock, and this covers the point raised. A GREASY POLE. Hie pole was Bft high from the ground to the top, but only 6ft between the two platforms. AVERAGES. The average is not obtained by adding the amourxe together and dividing by three. The. daiiv expenditure is arrived a.t by dividing the total sum spent by the aggregate number of days. The solution is 2s 9d. THE BRIDGE TOURNAMENT. There is no better arrangement than the one published last week. ANSWERS TO CORRESPONDENTS. C. T. B.—lf the compass had a fixed radius, the area described by it should be the same whether the figure be a circle drawn on a plane or an irregular-shaped figure that might be possible on a- curved surface. It is not clear, however, that any figure but a circle is possible. «• G.—A geometrical curiosity but your diagram of the ellipse and circle of equal areas hardly conforms to the conditions. P. C.—Sent