"NUTS!"

Evening Post, Volume CVII, Issue 22, 26 January 1929, Page 6

"NUTS!"

I nI INTELLECT SHARPENERS I All rights reserved. I (By T. L. Briton.) Boadora with a llttls ingenuity will find In this column an abundant store of entertainment Mid amusement, and tha solving of ihm problems should provide excellent mental exhilaration. While bourn of the "nuts" may appear harder than others, It will be round tba* none will require a slodg«-tuiiani«r to crack them. A SPIDSR AND A FLY. In a shed thirty feet long, twelve feet wide, and twelve feet high, lived a spider and a fly, and on tho occasion, which concerns this problem the former, on tho alert for food, took up a position on one of the end walls at a spot equidistant from the sides and exactly; one foot from the ceiling. On tho opposite end wall a fly reposed at a spot one foot from the floor, and as in tba case of the enemy, just midway between the two side walls. If, as no doubt wa3 the ease, the spider desired to reach the fly in its then position, by the shortest possible way, can the reader say what route it should take, assuming, of course, that it either walks or crawls on the ceiling, walls, or floor? When tackling this interesting little poser the reader will no doubt keep in mind "that things are not always what they seem," and he will find that a very useful calculation is involved, one that should provide him with material for a few moments of hard thinking. AN AUCKLAND-WELLINGTON EXPRESS. Although there is no non-stop train, running between Auckland and Wellington in regular service, a problem assuming that there is, will be quite in order. Let it be granted that the ordinary express, as scheduled, takes sixteen, hours to travel between the two cities, a distance in round figures of four hundred miles, the number of stops being cloven. It has been correctly estimated that at this travelling rate the same train on a non-stop run would cover the full distance at a uniform rate of speed of twenty-eight and foursevenths miles an hour. On this basis a nice little problem for the reader presents itself, viz., how long does tha ordinary express train (which as indicated travels at the rate, including stops, of twenty-five miles per hour) stop at Frankton' Junction,' if. the stay at that place is twice as long as at each of the other stops, which are all of the same duration as one another? TWO OTHER TRAINS. Whilst on this theme, here is a little problem that should interest others besides those numerous "railway" readers who are known to be "rather keen on this column," to quote one correspondent. Two trains on parallel lines run past each other in opposite directions, one at forty miles an hour, the other at thirty. One has twelve carriages, each thirty-two feet in length, the other seventeen carriage's of similar size, each train having an engine and tender forty feet in length. If tho coupling spaces are each five feet, can the reader dis- ■ cover; by a very brief calculation how much time will elapse from the moment that the engines meet till the last carriages have completely passed one another? The solution may be given in an even number of seconds, ignoring fractions if mot, and this should render the calculation quite simplo and at the same time more practical. .:.■; . - A DUTIFUL ELECTOR. ' The reported incident of' a West Coast elector walking a long distance in order to record his vote at the last election, only to arrive just as the polling booth closed, has prompted this little problem. Let us suppose that the distance to be walked was ten miles, and that he started off at exactly 4 o 'clock, which would thus give him three hours, as all polling booths closed at 7 o'clock. He covered the first four miles at a uniform rate of three and three-quarter miles an hour, the next two miles at an even rate of three and one-third miles per hour, and the next mile at three miles an hour. At what rate did he travel the last three miles if, as reported, ha arrived at the polling booth just as the doors closed, walking at a uniform rate over this last lap? And what time would this dutiful elector have arrived if the last three miles had been walked at the same rate as the sevenfli mile was travelled? ... , A DOMINO QUERY. Here is a little poser which, though' it concerns the game of dominoes, should be as interesting to the non-player (provided he knows how each of tho twenty-eight dominoes arc numbered) as to the devotee to tho game, because it involves a very useful calculation. In how many different ways can six: dominoes be played, as in the ordinary, game, so that, reading from left to right, the total number of spots on each successive domino will*be one more than the preceding one? Hero is an example: Blank-four, four-one, one-five, five-two, two-six, six-three. How many other instances aro there, each different from the other? Apart from the amusement ' to be derived from this little problem, the reader will find an instructive calculation in it. LAST WEEK'S SOLUTIONS. Two Four-Sided Figures.—The easiest way that this can be done is to make one figure in the form of an oblong two matches by one, which will absorb six matches, the area enclosed being two squaro inches on the basis of one-inch matches. In the other figure twelve matches will bo used in forming a. rhombus, four matches by two, the distance between the two longer sides being one and , a half matches. By making all tho matches one inch in! length it will be obvious without calculation that the rhombus encloses exactly three times the space of thai; j within the oblong. A Horse Deal.—The full amount made in tho buying and selling of the horse was £2, not £3 as might be supposed. A Curious Situation.—Peter claimed 3s 9d on the ground that if another game had been played and lost by him tho score would bo three all, and so entitle him to half the pool, whereas if he won it, the entire games would be finished and he would be entitled to "'the whole pool of ss. So Pan agreed to accept Is I'd on this curious reasoning. Imported Timber.—An increase of 2o per cent, in the quantity imported would leave the revenue unaffected, whereas a 50 per cent, increase of imports would raise the Customs receipts under that head 20 per cent. only. A Greasy-Pole Climb.—The boy must have taken one minuto • and fit'ty-five seconds to reach the top of the pole under tho conditions stated. ANSWERS TO CORRESPONDENTS. "Cricket".—He scored 27 if your statement of the incident is correct, but it was the other batsman who must have been "not out," otherwise your "average" figures are at fault. "Postage Stamp."—Yes, it is quite possible, and a problem on the point will be propounded later.

[n the accounts for the City of London for the year elided 31st March, J92S, are the items: Holies for Lord Mayor, £194 15s Cd; fuel for the "Mansion House, £354 4s lOd; and £11,551 for entertaining the city's important guests, including £2133 10s lid for the visit of the Duke and Duchess of. York, and £2400 19s lOd fo> the King of Afghanistan.